Finite Group Databasebeta

← C151×#14534 #50319459

Subgroups — C151×#14534 #50319459

Order 38656.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C151C211yesmaximal, characteristic
2C2×#390×C151C211yesmaximal, characteristic, complemented
3C2×#390×C151C211yesmaximal, characteristic, complemented
4C2×#388×C151C211yesmaximal, characteristic, complemented
5C2×#386×C151C211yesmaximal, characteristic, complemented
6C2×#386×C151C211yesmaximal, characteristic, complemented
7C2×#385×C151C211yesmaximal, characteristic, complemented
8#1440×C151C211yesmaximal, characteristic, complemented
9#1439×C151C211yesmaximal, characteristic, complemented
10#1439×C151C211yesmaximal, characteristic, complemented
11#1438×C151C211yesmaximal, characteristic, complemented
12#1438×C151C211yesmaximal, characteristic, complemented
13#1437×C151C211yesmaximal, characteristic, complemented
14#1436×C151C211yesmaximal, characteristic, complemented
15#1436×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C24×C4×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23C22×C22⋊C4×C151C2211yescharacteristic
24C22×C22⋊C4×C151C2211yescharacteristic
25C22×C22⋊C4×C151C2211yescharacteristic
26C22×C22⋊C4×C151C2211yescharacteristic
27C22×C22⋊C4×C151C2211yescharacteristic
28C22×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2211yescharacteristic
30C22×C22⋊C4×C151C2211yescharacteristic
31C22×C22⋊C4×C151C2211yescharacteristic
32C22×C22⋊C4×C151C2211yescharacteristic
33C22×C22⋊C4×C151C2211yescharacteristic
34C22×C22⋊C4×C151C2211yescharacteristic
35C22×C22⋊C4×C151C2211yescharacteristic
36C22×C22⋊C4×C151C2211yescharacteristic
37C22×C42×C151C2211yescharacteristic
38C22×C42×C151C2211yescharacteristic
39#392×C151C418yescomplemented
40#390×C151—24no—
41#390×C151—24no—
42#388×C151—24no—
43#386×C151—24no—
44#386×C151—24no—
45#385×C151—24no—
46C2×#95×C151C2211yescharacteristic
47C2×#95×C151C2211yescharacteristic
48C2×#95×C151C2211yescharacteristic
49C2×#95×C151C2211yescharacteristic
50C2×#95×C151C2211yescharacteristic
51C2×#95×C151C2211yescharacteristic
52C2×#95×C151C2211yescharacteristic
53C2×#95×C151C2211yescharacteristic
54C2×#95×C151C2211yescharacteristic
55C2×#95×C151C2211yescharacteristic
56C2×#95×C151C2211yescharacteristic
57C2×#95×C151C2211yescharacteristic
58C25×C151C2311yescharacteristic
59C25×C151C2311yescharacteristic
60C25×C151C2311yescharacteristic
61C22×D4×C151—22no—
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—22no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—41no—
70C22×D4×C151—41no—
71C22×D4×C151—41no—
72C22×D4×C151—41no—
73C22×D4×C151—41no—
74C22×D4×C151—41no—
75C22×D4×C151—41no—
76C22×D4×C151—41no—
77C22×D4×C151—41no—
78C22×D4×C151—41no—
79C22×D4×C151C2×C414yes—
80C22×D4×C151C2×C414yes—
81C22×D4×C151C2×C414yescomplemented
82C23×C4×C151—22no—
83C23×C4×C151—22no—
84C23×C4×C151—22no—
85C23×C4×C151—41no—
86C23×C4×C151—41no—
87C23×C4×C151—41no—
88C23×C4×C151—41no—
89C23×C4×C151C2311yescharacteristic
90C23×C4×C151C2311yescharacteristic
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C23×C4×C151C2311yescharacteristic
94C23×C4×C151C2311yescharacteristic
95C23×C4×C151C2311yescharacteristic
96C23×C4×C151C2311yescharacteristic
97C23×C4×C151C2311yescharacteristic
98C23×C4×C151C2311yescharacteristic
99C23×C4×C151C2311yescharacteristic
100C23×C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151—22no—
102C2×C4⋊C4×C151—22no—
103C2×C4⋊C4×C151—22no—
104C2×C4⋊C4×C151—22no—
105C2×C4⋊C4×C151—41no—
106C2×C4⋊C4×C151—41no—
107C2×C4⋊C4×C151—41no—
108C2×C4⋊C4×C151—41no—
109C2×C4⋊C4×C151D414yescomplemented
110C2×C22⋊C4×C151—22no—
111C2×C22⋊C4×C151—22no—
112C2×C22⋊C4×C151—22no—
113C2×C22⋊C4×C151—22no—
114C2×C22⋊C4×C151—22no—
115C2×C22⋊C4×C151—22no—
116C2×C22⋊C4×C151—22no—
117C2×C22⋊C4×C151—22no—
118C2×C22⋊C4×C151—22no—
119C2×C22⋊C4×C151—22no—
120C2×C22⋊C4×C151—22no—
121C2×C22⋊C4×C151—22no—
122C2×C22⋊C4×C151—22no—
123C2×C22⋊C4×C151—22no—
124C2×C22⋊C4×C151—22no—
125C2×C22⋊C4×C151—22no—
126C2×C22⋊C4×C151—22no—
127C2×C22⋊C4×C151—22no—
128C2×C22⋊C4×C151—22no—
129C2×C22⋊C4×C151—22no—
130C2×C22⋊C4×C151—41no—
131C2×C22⋊C4×C151—41no—
132C2×C22⋊C4×C151—41no—
133C2×C22⋊C4×C151—41no—
134C2×C22⋊C4×C151—41no—
135C2×C22⋊C4×C151—41no—
136C2×C22⋊C4×C151—41no—
137C2×C22⋊C4×C151—41no—
138C2×C22⋊C4×C151—41no—
139C2×C22⋊C4×C151—41no—
140C2×C22⋊C4×C151—41no—
141C2×C22⋊C4×C151—41no—
142C2×C22⋊C4×C151—41no—
143C2×C22⋊C4×C151—41no—
144C2×C22⋊C4×C151—41no—
145C2×C22⋊C4×C151—41no—
146C2×C22⋊C4×C151—41no—
147C2×C22⋊C4×C151—41no—
148C2×C22⋊C4×C151C2×C414yes—
149C2×C22⋊C4×C151C2×C414yescomplemented
150C2×C22⋊C4×C151C2×C414yescomplemented
151C2×C22⋊C4×C151D414yescomplemented
152C2×C42×C151—22no—
153C2×C42×C151—22no—
154C2×C42×C151—22no—
155C2×C42×C151—41no—
156C2×C42×C151—41no—
157C2×C42×C151—41no—
158#95×C151—22no—
159#95×C151—22no—
160#95×C151—22no—
161#95×C151—22no—
162#95×C151—22no—
163#95×C151—22no—
164#95×C151—22no—
165#95×C151—41no—
166#95×C151—41no—
167#95×C151—41no—
168#95×C151C2×C414yescomplemented
169#95×C151D414yescomplemented
170C24×C151—21no—
171C24×C151—21no—
172C24×C151—21no—
173C24×C151—21no—
174C24×C151—21no—
175C24×C151—21no—
176C24×C151—21no—
177C24×C151—21no—
178C24×C151—21no—
179C24×C151—21no—
180C24×C151—21no—
181C24×C151—21no—
182C24×C151—21no—
183C24×C151—21no—
184C24×C151—21no—
185C24×C151—21no—
186C24×C151—21no—
187C24×C151—21no—
188C24×C151—21no—
189C24×C151—21no—
190C24×C151—21no—
191C24×C151—21no—
192C24×C151—21no—
193C24×C151—21no—
194C24×C151—21no—
195C24×C151—21no—
196C24×C151—21no—
197C24×C151—21no—
198C24×C151—21no—
199C24×C151—21no—
200C24×C151—21no—
201C24×C151—21no—
202C24×C151—21no—
203C24×C151—21no—
204C24×C151—21no—
205C24×C151—21no—
206C24×C151—21no—
207C24×C151—21no—
208C24×C151—21no—
209C24×C151—21no—
210C24×C151C22×C412yes—
211C24×C151C22×C412yes—
212C24×C151C22×C412yes—
213C24×C151C2×D412yes—
214C24×C151#4112yes—
215C24×C151C2411yescharacteristic
216C2×D4×C151—28no—
217C2×D4×C151—28no—
218C2×D4×C151—28no—
219C2×D4×C151—28no—
220C2×D4×C151—44no—
221C2×D4×C151—44no—
222C2×D4×C151—44no—
223C2×D4×C151—44no—
224C2×D4×C151—44no—
225C2×D4×C151—44no—
226C2×D4×C151—44no—
227C2×D4×C151—44no—
228C2×D4×C151—44no—
229C2×D4×C151—44no—
230C2×D4×C151—44no—
231C2×D4×C151—44no—
232C2×D4×C151—44no—
233C2×D4×C151—44no—
234C2×D4×C151—44no—
235C2×D4×C151—44no—
236C2×D4×C151—44no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—21no—
264C22×C4×C151—21no—
265C22×C4×C151—21no—
266C22×C4×C151—21no—
267C22×C4×C151—21no—
268C22×C4×C151—21no—
269C22×C4×C151—21no—
270C22×C4×C151—21no—
271C22×C4×C151—21no—
272C22×C4×C151—21no—
273C22×C4×C151—21no—
274C22×C4×C151—21no—
275C22×C4×C151—21no—
276C22×C4×C151—21no—
277C22×C4×C151—21no—
278C22×C4×C151—21no—
279C22×C4×C151—21no—
280C22×C4×C151—21no—
281C22×C4×C151—21no—
282C22×C4×C151—21no—
283C22×C4×C151—21no—
284C22×C4×C151—21no—
285C22×C4×C151—21no—
286C22×C4×C151—21no—
287C22×C4×C151—21no—
288C22×C4×C151—21no—
289C22×C4×C151—21no—
290C22×C4×C151—21no—
291C22×C4×C151—21no—
292C22×C4×C151—21no—
293C22×C4×C151—21no—
294C22×C4×C151—21no—
295C22×C4×C151—21no—
296C22×C4×C151—21no—
297C22×C4×C151—21no—
298C22×C4×C151—21no—
299C22×C4×C151—21no—
300C22×C4×C151—21no—
301C22×C4×C151—21no—
302C22×C4×C151—21no—
303C22×C4×C151—21no—
304C22×C4×C151—21no—
305C22×C4×C151—21no—
306C22×C4×C151—21no—
307C22×C4×C151—44no—
308C22×C4×C151—44no—
309C22×C4×C151—44no—
310C22×C4×C151—44no—
311C22×C4×C151—44no—
312C22×C4×C151—44no—
313C22×C4×C151—44no—
314C22×C4×C151C22×C412yes—
315C22×C4×C151C22×C412yes—
316C22×C4×C151C22×C412yes—
317C22×C4×C151C22×C412yes—
318C22×C4×C151C2×D412yes—
319C22×C4×C151C2×D412yes—
320C22×C4×C151C2×D412yes—
321C22×C4×C151C2×D412yes—
322C22×C4×C151C2×D412yes—
323C22×C4×C151C2×D412yes—
324C22×C4×C151C2×D412yes—
325C22×C4×C151C2×D412yes—
326C22×C4×C151#4112yes—
327C22×C4×C151#4112yes—
328C4⋊C4×C151—44no—
329C4⋊C4×C151—44no—
330C4⋊C4×C151—44no—
331C22⋊C4×C151—28no—
332C22⋊C4×C151—28no—
333C22⋊C4×C151—44no—
334C22⋊C4×C151—44no—
335C22⋊C4×C151—44no—
336C22⋊C4×C151—44no—
337C22⋊C4×C151—44no—
338C22⋊C4×C151—44no—
339C22⋊C4×C151—44no—
340C22⋊C4×C151—44no—
341C22⋊C4×C151—44no—
342C22⋊C4×C151—44no—
343C22⋊C4×C151—44no—
344C22⋊C4×C151—44no—
345C42×C151—44no—
346C42×C151—44no—
347C23×C151—22no—
348C23×C151—22no—
349C23×C151—22no—
350C23×C151—22no—
351C23×C151—22no—
352C23×C151—22no—
353C23×C151—22no—
354C23×C151—22no—
355C23×C151—22no—
356C23×C151—22no—
357C23×C151—22no—
358C23×C151—22no—
359C23×C151—22no—
360C23×C151—22no—
361C23×C151—22no—
362C23×C151—22no—
363C23×C151—22no—
364C23×C151—22no—
365C23×C151—22no—
366C23×C151—22no—
367C23×C151—22no—
368C23×C151—22no—
369C23×C151—22no—
370C23×C151—22no—
371C23×C151—22no—
372C23×C151—22no—
373C23×C151—22no—
374C23×C151—22no—
375C23×C151—22no—
376C23×C151—22no—
377C23×C151—22no—
378C23×C151—22no—
379C23×C151—41no—
380C23×C151—41no—
381C23×C151—41no—
382C23×C151—41no—
383C23×C151—41no—
384C23×C151—41no—
385C23×C151—41no—
386C23×C151—41no—
387C23×C151—41no—
388C23×C151—41no—
389C23×C151—41no—
390C23×C151—41no—
391C23×C151—41no—
392C23×C151—41no—
393C23×C151—41no—
394C23×C151—41no—
395C23×C151—41no—
396C23×C151—41no—
397C23×C151—41no—
398C23×C151—41no—
399C23×C151—41no—
400C23×C151—41no—
401C23×C151—41no—
402C23×C151—41no—
403C23×C151—41no—
404C23×C151—41no—
405C23×C151—41no—
406C23×C151—41no—
407C23×C151—41no—
408C23×C151—41no—
409C23×C151—41no—
410C23×C151—41no—
411C23×C151—41no—
412C23×C151—41no—
413C23×C151—41no—
414C23×C151—41no—
415C23×C151—41no—
416C23×C151—41no—
417C23×C151—41no—
418C23×C151—41no—
419C23×C151—41no—
420C23×C151—41no—
421C23×C151—41no—
422C23×C151—41no—
423C23×C151—41no—
424C23×C151—41no—
425C23×C151—41no—
426C23×C151—41no—
427C23×C151—41no—
428C23×C151—41no—
429C23×C151—41no—
430C23×C151—41no—
431C23×C151—41no—
432C23×C151—41no—
433C23×C151—41no—
434C23×C151—41no—
435C23×C151—41no—
436C23×C151—41no—
437C23×C151—41no—
438C23×C151—41no—
439C23×C151—41no—
440C23×C151—41no—
441C23×C151—41no—
442C23×C151—41no—
443C23×C151—41no—
444C23×C151—41no—
445C23×C151—41no—
446C23×C151—41no—
447C23×C151—41no—
448C23×C151—41no—
449C23×C151—41no—
450C23×C151—41no—
451C23×C151C4×D414yes—
452C23×C151C23×C411yescharacteristic
453C23×C151C22×D411yescharacteristic
454C23×C151C22×D411yescharacteristic
455C23×C151C22×D411yescharacteristic
456C23×C151C2×#4111yescharacteristic
457C23×C151C2×#4111yescharacteristic
458C23×C151C2×#4111yescharacteristic
459C23×C151H(5,𝔽2)11yescharacteristic
460C23×C151H(5,𝔽2)11yescharacteristic
461C23×C151H(5,𝔽2)11yescharacteristic
462C23×C151H(5,𝔽2)11yescharacteristic
463C23×C151H(5,𝔽2)11yescharacteristic
464C23×C151H(5,𝔽2)11yescharacteristic
465C23×C151H(5,𝔽2)11yescharacteristic
466C23×C1512−1+411yescharacteristic
467D4×C151—416no—
468D4×C151—416no—
469D4×C151—416no—
470C2×C4×C151—22no—
471C2×C4×C151—22no—
472C2×C4×C151—22no—
473C2×C4×C151—22no—
474C2×C4×C151—22no—
475C2×C4×C151—22no—
476C2×C4×C151—22no—
477C2×C4×C151—22no—
478C2×C4×C151—22no—
479C2×C4×C151—22no—
480C2×C4×C151—22no—
481C2×C4×C151—22no—
482C2×C4×C151—22no—
483C2×C4×C151—22no—
484C2×C4×C151—22no—
485C2×C4×C151—22no—
486C2×C4×C151—22no—
487C2×C4×C151—22no—
488C2×C4×C151—22no—
489C2×C4×C151—22no—
490C2×C4×C151—22no—
491C2×C4×C151—22no—
492C2×C4×C151—22no—
493C2×C4×C151—22no—
494C2×C4×C151—22no—
495C2×C4×C151—22no—
496C2×C4×C151—22no—
497C2×C4×C151—22no—
498C2×C4×C151—22no—
499C2×C4×C151—22no—
500C2×C4×C151—22no—
501C2×C4×C151—22no—
502C2×C4×C151—22no—
503C2×C4×C151—22no—
504C2×C4×C151—22no—
505C2×C4×C151—22no—
506C2×C4×C151—416no—
507C2×C4×C151—41no—
508C2×C4×C151—41no—
509C2×C4×C151—41no—
510C2×C4×C151—41no—
511C2×C4×C151—41no—
512C2×C4×C151—41no—
513C2×C4×C151—41no—
514C2×C4×C151—41no—
515C2×C4×C151—41no—
516C2×C4×C151—41no—
517C2×C4×C151—41no—
518C2×C4×C151—41no—
519C2×C4×C151—41no—
520C2×C4×C151—41no—
521C2×C4×C151—41no—
522C2×C4×C151—41no—
523C2×C4×C151—41no—
524C2×C4×C151—41no—
525C2×C4×C151—41no—
526C2×C4×C151—41no—
527C2×C4×C151—41no—
528C2×C4×C151—41no—
529C2×C4×C151—41no—
530C2×C4×C151—41no—
531C2×C4×C151—41no—
532C2×C4×C151—41no—
533C2×C4×C151—41no—
534C2×C4×C151—41no—
535C2×C4×C151—41no—
536C2×C4×C151—41no—
537C2×C4×C151—41no—
538C2×C4×C151—41no—
539C2×C4×C151—41no—
540C2×C4×C151—41no—
541C2×C4×C151—41no—
542C2×C4×C151—41no—
543C2×C4×C151—41no—
544C2×C4×C151—41no—
545C2×C4×C151—41no—
546C2×C4×C151—41no—
547C2×C4×C151—41no—
548C2×C4×C151—41no—
549C2×C4×C151—41no—
550C2×C4×C151—41no—
551C2×C4×C151—41no—
552C2×C4×C151—41no—
553C2×C4×C151C4×D414yes—
554C2×C4×C151C4×D414yes—
555C22×C151—24no—
556C22×C151—24no—
557C22×C151—24no—
558C22×C151—42no—
559C22×C151—42no—
560C22×C151—42no—
561C22×C151—42no—
562C22×C151—42no—
563C22×C151—42no—
564C22×C151—42no—
565C22×C151—42no—
566C22×C151—42no—
567C22×C151—42no—
568C22×C151—42no—
569C22×C151—42no—
570C22×C151—42no—
571C22×C151—42no—
572C22×C151—42no—
573C22×C151—42no—
574C22×C151—42no—
575C22×C151—42no—
576C22×C151—42no—
577C22×C151—42no—
578C22×C151—42no—
579C22×C151—42no—
580C22×C151—42no—
581C22×C151—42no—
582C22×C151—42no—
583C22×C151—42no—
584C22×C151—81no—
585C22×C151—81no—
586C22×C151—81no—
587C22×C151—81no—
588C22×C151—81no—
589C22×C151—81no—
590C22×C151—81no—
591C22×C151—81no—
592C22×C151—81no—
593C22×C151—81no—
594C22×C151—81no—
595C22×C151—81no—
596C22×C151—81no—
597C22×C151—81no—
598C22×C151—81no—
599C22×C151—81no—
600C22×C151C2×C4×D411yescharacteristic
601C22×C151C2×C4×D411yescharacteristic
602C22×C151C2×C4×D411yescharacteristic
603C22×C151#51811yescharacteristic
604C22×C151#51811yescharacteristic
605C22×C151#51811yescharacteristic
606C22×C151#52011yescharacteristic
607C22×C151#53411yescharacteristic
608C22×C151#53411yescharacteristic
609C22×C151#53511yescharacteristic
610C22×C151#53511yescharacteristic
611C22×C151#53511yescharacteristic
612C22×C151#53711yescharacteristic
613C22×C151#53811yescharacteristic
614C22×C151#53811yescharacteristic
615C22×C151#53811yescharacteristic
616C22×C151#53811yescharacteristic
617C22×C151#54011yescharacteristic
618C22×C151#54211yescharacteristic
619C22×C151D4211yescharacteristic
620C22×C151D4211yescharacteristic
621C22×C151D4211yescharacteristic
622C22×C151#54611yescharacteristic
623C22×C151#54611yescharacteristic
624C22×C151#54711yescharacteristic
625C22×C151#54811yescharacteristic
626C22×C151#55011yescharacteristic
627C22×C151#55011yescharacteristic
628C22×C151#55111yescharacteristic
629C22×C151#55311yescharacteristic
630C22×C151#55911yescharacteristic
631C22×C151#56011yescharacteristic
632C22×C151#56011yescharacteristic
633C22×C151#56211yescharacteristic
634C22×C151#56211yescharacteristic
635C4×C151—24no—
636C4×C151—24no—
637C4×C151—42no—
638C4×C151—42no—
639C4×C151—42no—
640C4×C151—42no—
641C4×C151—42no—
642C4×C151—42no—
643C4×C151—42no—
644C4×C151—42no—
645C4×C151—81no—
646C4×C151—81no—
647C2×C151—44no—
648C2×C151—82no—
649C2×C151—82no—
650C2×C151#232111yescharacteristic
651C2×C151#232111yescharacteristic
652C2×C151#232411yescharacteristic
653C2×C151#235811yescharacteristic
654C2×C151#236111yescharacteristic
655C2×C151#236611yescharacteristic
656C2×C151#237711yescharacteristic
657C2×C151#266911yescharacteristic
658C2×C151#267311yescharacteristic
659C2×C151#267611yescharacteristic
660C2×C151#268211yescharacteristic
661C2×C151#271011yescharacteristic
662C2×C151#271411yescharacteristic
663C2×C151#273011yescharacteristic
664C2×C151#279711yescharacteristic
665#14534C15111yesmaximal, characteristic, direct product factor, Sylow
666C151#1453411yescharacteristic, direct product factor, Sylow
667C2×#392C2×C15111yescharacteristic
668C2×#390C2×C15111yescharacteristic, complemented
669C2×#390C2×C15111yescharacteristic, complemented
670C2×#388C2×C15111yescharacteristic, complemented
671C2×#386C2×C15111yescharacteristic, complemented
672C2×#386C2×C15111yescharacteristic, complemented
673C2×#385C2×C15111yescharacteristic, complemented
674#1440C2×C15111yescharacteristic, complemented
675#1439C2×C15111yescharacteristic, complemented
676#1439C2×C15111yescharacteristic, complemented
677#1438C2×C15111yescharacteristic, complemented
678#1438C2×C15111yescharacteristic, complemented
679#1437C2×C15111yescharacteristic, complemented
680#1436C2×C15111yescharacteristic, complemented
681#1436C2×C15111yescharacteristic, complemented
682C23×D4C22×C15111yescharacteristic
683C23×D4C22×C15111yescharacteristic
684C23×D4C22×C15111yescharacteristic
685C24×C4C22×C15111yescharacteristic
686C22×C4⋊C4C22×C15111yescharacteristic
687C22×C4⋊C4C22×C15111yescharacteristic
688C22×C4⋊C4C22×C15111yescharacteristic
689C22×C22⋊C4C22×C15111yescharacteristic
690C22×C22⋊C4C22×C15111yescharacteristic
691C22×C22⋊C4C22×C15111yescharacteristic
692C22×C22⋊C4C22×C15111yescharacteristic
693C22×C22⋊C4C22×C15111yescharacteristic
694C22×C22⋊C4C22×C15111yescharacteristic
695C22×C22⋊C4C22×C15111yescharacteristic
696C22×C22⋊C4C22×C15111yescharacteristic
697C22×C22⋊C4C22×C15111yescharacteristic
698C22×C22⋊C4C22×C15111yescharacteristic
699C22×C22⋊C4C22×C15111yescharacteristic
700C22×C22⋊C4C22×C15111yescharacteristic
701C22×C22⋊C4C22×C15111yescharacteristic
702C22×C22⋊C4C22×C15111yescharacteristic
703C22×C42C22×C15111yescharacteristic
704C22×C42C22×C15111yescharacteristic
705#392C4×C15118yescomplemented
706#390—24no—
707#390—24no—
708#388—24no—
709#386—24no—
710#386—24no—
711#385—24no—
712C2×#95C22×C15111yescharacteristic
713C2×#95C22×C15111yescharacteristic
714C2×#95C22×C15111yescharacteristic
715C2×#95C22×C15111yescharacteristic
716C2×#95C22×C15111yescharacteristic
717C2×#95C22×C15111yescharacteristic
718C2×#95C22×C15111yescharacteristic
719C2×#95C22×C15111yescharacteristic
720C2×#95C22×C15111yescharacteristic
721C2×#95C22×C15111yescharacteristic
722C2×#95C22×C15111yescharacteristic
723C2×#95C22×C15111yescharacteristic
724C25C23×C15111yescharacteristic
725C25C23×C15111yescharacteristic
726C25C23×C15111yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4C2×C4×C15114yes—
746C22×D4C2×C4×C15114yes—
747C22×D4C2×C4×C15114yescomplemented
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—41no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4C23×C15111yescharacteristic
756C23×C4C23×C15111yescharacteristic
757C23×C4C23×C15111yescharacteristic
758C23×C4C23×C15111yescharacteristic
759C23×C4C23×C15111yescharacteristic
760C23×C4C23×C15111yescharacteristic
761C23×C4C23×C15111yescharacteristic
762C23×C4C23×C15111yescharacteristic
763C23×C4C23×C15111yescharacteristic
764C23×C4C23×C15111yescharacteristic
765C23×C4C23×C15111yescharacteristic
766C23×C4C23×C15111yescharacteristic
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4D4×C15114yescomplemented
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4C2×C4×C15114yes—
815C2×C22⋊C4C2×C4×C15114yescomplemented
816C2×C22⋊C4C2×C4×C15114yescomplemented
817C2×C22⋊C4D4×C15114yescomplemented
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—41no—
822C2×C42—41no—
823C2×C42—41no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—41no—
832#95—41no—
833#95—41no—
834#95C2×C4×C15114yescomplemented
835#95D4×C15114yescomplemented
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24C22×C4×C15112yes—
877C24C22×C4×C15112yes—
878C24C22×C4×C15112yes—
879C24C2×D4×C15112yes—
880C24#41×C15112yes—
881C24C24×C15111yescharacteristic
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4C22×C4×C15112yes—
981C22×C4C22×C4×C15112yes—
982C22×C4C22×C4×C15112yes—
983C22×C4C22×C4×C15112yes—
984C22×C4C2×D4×C15112yes—
985C22×C4C2×D4×C15112yes—
986C22×C4C2×D4×C15112yes—
987C22×C4C2×D4×C15112yes—
988C22×C4C2×D4×C15112yes—
989C22×C4C2×D4×C15112yes—
990C22×C4C2×D4×C15112yes—
991C22×C4C2×D4×C15112yes—
992C22×C4#41×C15112yes—
993C22×C4#41×C15112yes—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C42—44no—
1012C42—44no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23C4×D4×C15114yes—
1118C23C23×C4×C15111yescharacteristic
1119C23C22×D4×C15111yescharacteristic
1120C23C22×D4×C15111yescharacteristic
1121C23C22×D4×C15111yescharacteristic
1122C23C2×#41×C15111yescharacteristic
1123C23C2×#41×C15111yescharacteristic
1124C23C2×#41×C15111yescharacteristic
1125C23H(5,𝔽2)×C15111yescharacteristic
1126C23H(5,𝔽2)×C15111yescharacteristic
1127C23H(5,𝔽2)×C15111yescharacteristic
1128C23H(5,𝔽2)×C15111yescharacteristic
1129C23H(5,𝔽2)×C15111yescharacteristic
1130C23H(5,𝔽2)×C15111yescharacteristic
1131C23H(5,𝔽2)×C15111yescharacteristic
1132C232−1+4×C15111yescharacteristic
1133D4—416no—
1134D4—416no—
1135D4—416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—416no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4C4×D4×C15114yes—
1220C2×C4C4×D4×C15114yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22C2×C4×D4×C15111yescharacteristic
1267C22C2×C4×D4×C15111yescharacteristic
1268C22C2×C4×D4×C15111yescharacteristic
1269C22#518×C15111yescharacteristic
1270C22#518×C15111yescharacteristic
1271C22#518×C15111yescharacteristic
1272C22#520×C15111yescharacteristic
1273C22#534×C15111yescharacteristic
1274C22#534×C15111yescharacteristic
1275C22#535×C15111yescharacteristic
1276C22#535×C15111yescharacteristic
1277C22#535×C15111yescharacteristic
1278C22#537×C15111yescharacteristic
1279C22#538×C15111yescharacteristic
1280C22#538×C15111yescharacteristic
1281C22#538×C15111yescharacteristic
1282C22#538×C15111yescharacteristic
1283C22#540×C15111yescharacteristic
1284C22#542×C15111yescharacteristic
1285C22D42×C15111yescharacteristic
1286C22D42×C15111yescharacteristic
1287C22D42×C15111yescharacteristic
1288C22#546×C15111yescharacteristic
1289C22#546×C15111yescharacteristic
1290C22#547×C15111yescharacteristic
1291C22#548×C15111yescharacteristic
1292C22#550×C15111yescharacteristic
1293C22#550×C15111yescharacteristic
1294C22#551×C15111yescharacteristic
1295C22#553×C15111yescharacteristic
1296C22#559×C15111yescharacteristic
1297C22#560×C15111yescharacteristic
1298C22#560×C15111yescharacteristic
1299C22#562×C15111yescharacteristic
1300C22#562×C15111yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C2—44no—
1314C2—82no—
1315C2—82no—
1316C2#2321×C15111yescharacteristic
1317C2#2321×C15111yescharacteristic
1318C2#2324×C15111yescharacteristic
1319C2#2358×C15111yescharacteristic
1320C2#2361×C15111yescharacteristic
1321C2#2366×C15111yescharacteristic
1322C2#2377×C15111yescharacteristic
1323C2#2669×C15111yescharacteristic
1324C2#2673×C15111yescharacteristic
1325C2#2676×C15111yescharacteristic
1326C2#2682×C15111yescharacteristic
1327C2#2710×C15111yescharacteristic
1328C2#2714×C15111yescharacteristic
1329C2#2730×C15111yescharacteristic
1330C2#2797×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC2×#392×C151C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#390×C151C2semidirect
3. C2×#390×C151C2semidirect
4. C2×#388×C151C2semidirect
5. C2×#386×C151C2semidirect
6. C2×#386×C151C2semidirect
7. C2×#385×C151C2semidirect
8. #1440×C151C2semidirect
9. #1439×C151C2semidirect
10. #1439×C151C2semidirect
11. #1438×C151C2semidirect
12. #1438×C151C2semidirect
13. #1437×C151C2semidirect
14. #1436×C151C2semidirect
15. #1436×C151C2semidirect
39. #392×C151C4semidirect
81. C22×D4×C151C2×C4semidirect
109. C2×C4⋊C4×C151D4semidirect
149. C2×C22⋊C4×C151C2×C4semidirect
150. C2×C22⋊C4×C151C2×C4semidirect
151. C2×C22⋊C4×C151D4semidirect
168. #95×C151C2×C4semidirect
169. #95×C151D4semidirect
665. #14534C151direct (N × H)
666. C151#14534direct (N × H)
668. C2×#390C2×C151semidirect
669. C2×#390C2×C151semidirect
670. C2×#388C2×C151semidirect
671. C2×#386C2×C151semidirect
672. C2×#386C2×C151semidirect
673. C2×#385C2×C151semidirect
674. #1440C2×C151semidirect
675. #1439C2×C151semidirect
676. #1439C2×C151semidirect
677. #1438C2×C151semidirect
678. #1438C2×C151semidirect
679. #1437C2×C151semidirect
680. #1436C2×C151semidirect
681. #1436C2×C151semidirect
705. #392C4×C151semidirect
747. C22×D4C2×C4×C151semidirect
775. C2×C4⋊C4D4×C151semidirect
815. C2×C22⋊C4C2×C4×C151semidirect
816. C2×C22⋊C4C2×C4×C151semidirect
817. C2×C22⋊C4D4×C151semidirect
834. #95C2×C4×C151semidirect
835. #95D4×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#392×C1512
C2×#390×C1512
C2×#388×C1512
C2×#386×C1512
C2×#385×C1512
#1440×C1512
#1439×C1512
#1438×C1512
#1437×C1512
#1436×C1512
#14534151