Finite Group Databasebeta

← C151×#15316 #50320241

Subgroups — C151×#15316 #50320241

Order 38656.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C151C211yesmaximal, characteristic
2C2×#396×C151C211yesmaximal, characteristic, complemented
3C2×#394×C151C211yesmaximal, characteristic, complemented
4C2×#394×C151C211yesmaximal, characteristic, complemented
5C2×#394×C151C211yesmaximal, characteristic, complemented
6C2×#390×C151C211yesmaximal, characteristic, complemented
7C2×#389×C151C211yesmaximal, characteristic, complemented
8C2×#385×C151C211yesmaximal, characteristic, complemented
9#1441×C151C211yesmaximal, characteristic, complemented
10#1439×C151C211yesmaximal, characteristic, complemented
11#1439×C151C211yesmaximal, characteristic, complemented
12#1438×C151C211yesmaximal, characteristic, complemented
13#1438×C151C211yesmaximal, characteristic, complemented
14#1437×C151C211yesmaximal, characteristic, complemented
15C22⋊#95×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C24×C4×C151C2211yescharacteristic
20C2×#121×C151—24no—
21C2×#121×C151—24no—
22C2×#121×C151—24no—
23C22×C4⋊C4×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2211yescharacteristic
25C22×C4⋊C4×C151C2211yescharacteristic
26C22×C4⋊C4×C151C2211yescharacteristic
27C22×C4⋊C4×C151C2211yescharacteristic
28C22×C4⋊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×C22⋊C4×C151C2211yescharacteristic
38C22×C22⋊C4×C151C2211yescharacteristic
39C22×C22⋊C4×C151C2211yescharacteristic
40C22×C22⋊C4×C151C2211yescharacteristic
41C22×C22⋊C4×C151C2211yescharacteristic
42C22×C22⋊C4×C151C2211yescharacteristic
43C22×C42×C151C2211yescharacteristic
44#396×C151—24no—
45#394×C151—24no—
46#394×C151—24no—
47#394×C151—24no—
48#390×C151—24no—
49#389×C151—24no—
50#385×C151—24no—
51C2×#95×C151C2211yescharacteristic
52C2×#95×C151C2211yescharacteristic
53C2×#95×C151C2211yescharacteristic
54C2×#95×C151C2211yescharacteristic
55C2×#95×C151C2211yescharacteristic
56C2×#95×C151C2211yescharacteristic
57C2×#95×C151C2211yescharacteristic
58C2×#95×C151C2211yescharacteristic
59C2×#95×C151C2211yescharacteristic
60C2×#95×C151C2211yescharacteristic
61C25×C151C2311yescharacteristic
62C25×C151C2311yescharacteristic
63C25×C151C2311yescharacteristic
64C22×D4×C151—22no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—22no—
72C22×D4×C151—22no—
73C22×D4×C151—22no—
74C22×D4×C151—22no—
75C22×D4×C151—22no—
76C22×D4×C151—22no—
77C22×D4×C151—22no—
78C22×D4×C151—41no—
79C22×D4×C151—41no—
80C22×D4×C151—41no—
81C22×D4×C151—41no—
82C22×D4×C151—41no—
83C22×D4×C151—41no—
84C22×D4×C151D414yes—
85C23×C4×C151—22no—
86C23×C4×C151—22no—
87C23×C4×C151—22no—
88C23×C4×C151—22no—
89C23×C4×C151—22no—
90C23×C4×C151—41no—
91C23×C4×C151—41no—
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
101C23×C4×C151C2311yescharacteristic
102C23×C4×C151C2311yescharacteristic
103C23×C4×C151C2311yescharacteristic
104#121×C151—232no—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151—22no—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—22no—
110C2×C4⋊C4×C151—22no—
111C2×C4⋊C4×C151—22no—
112C2×C4⋊C4×C151—22no—
113C2×C4⋊C4×C151—22no—
114C2×C4⋊C4×C151—22no—
115C2×C4⋊C4×C151—22no—
116C2×C4⋊C4×C151—22no—
117C2×C4⋊C4×C151—22no—
118C2×C4⋊C4×C151—41no—
119C2×C4⋊C4×C151—41no—
120C2×C4⋊C4×C151—41no—
121C2×C4⋊C4×C151D414yes—
122C2×C4⋊C4×C151D414yescomplemented
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—22no—
131C2×C22⋊C4×C151—22no—
132C2×C22⋊C4×C151—22no—
133C2×C22⋊C4×C151—22no—
134C2×C22⋊C4×C151—22no—
135C2×C22⋊C4×C151—22no—
136C2×C22⋊C4×C151—22no—
137C2×C22⋊C4×C151—22no—
138C2×C22⋊C4×C151—22no—
139C2×C22⋊C4×C151—22no—
140C2×C22⋊C4×C151—22no—
141C2×C22⋊C4×C151—22no—
142C2×C22⋊C4×C151—22no—
143C2×C22⋊C4×C151—22no—
144C2×C22⋊C4×C151—22no—
145C2×C22⋊C4×C151—22no—
146C2×C22⋊C4×C151—22no—
147C2×C22⋊C4×C151—22no—
148C2×C22⋊C4×C151—22no—
149C2×C22⋊C4×C151—22no—
150C2×C22⋊C4×C151—22no—
151C2×C22⋊C4×C151—22no—
152C2×C22⋊C4×C151—22no—
153C2×C22⋊C4×C151—41no—
154C2×C22⋊C4×C151—41no—
155C2×C22⋊C4×C151—41no—
156C2×C22⋊C4×C151—41no—
157C2×C22⋊C4×C151—41no—
158C2×C22⋊C4×C151—41no—
159C2×C22⋊C4×C151—41no—
160C2×C22⋊C4×C151—41no—
161C2×C22⋊C4×C151—41no—
162C2×C22⋊C4×C151—41no—
163C2×C22⋊C4×C151D414yes—
164C2×C22⋊C4×C151D414yescomplemented
165C2×C42×C151—22no—
166C2×C42×C151—22no—
167C2×C42×C151—41no—
168#95×C151—22no—
169#95×C151—22no—
170#95×C151—22no—
171#95×C151—22no—
172#95×C151—22no—
173#95×C151—22no—
174#95×C151—22no—
175#95×C151—22no—
176#95×C151—41no—
177#95×C151—41no—
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×C151—21no—
211C24×C151—21no—
212C24×C151—21no—
213C24×C151—21no—
214C24×C151—21no—
215C24×C151—21no—
216C24×C151—21no—
217C24×C151—21no—
218C24×C151C2×D412yes—
219C24×C151C2×D412yes—
220C24×C151C2×D412yes—
221C24×C151C2×D412yes—
222C24×C151#4112yes—
223C24×C151C2411yescharacteristic
224C2×D4×C151—28no—
225C2×D4×C151—28no—
226C2×D4×C151—28no—
227C2×D4×C151—28no—
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—
237C2×D4×C151—44no—
238C2×D4×C151—44no—
239C2×D4×C151—44no—
240C2×D4×C151—44no—
241C2×D4×C151—44no—
242C2×D4×C151—44no—
243C2×D4×C151—44no—
244C2×D4×C151—44no—
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—28no—
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—21no—
308C22×C4×C151—21no—
309C22×C4×C151—21no—
310C22×C4×C151—21no—
311C22×C4×C151—21no—
312C22×C4×C151—21no—
313C22×C4×C151—21no—
314C22×C4×C151—21no—
315C22×C4×C151—21no—
316C22×C4×C151—44no—
317C22×C4×C151—44no—
318C22×C4×C151—44no—
319C22×C4×C151—44no—
320C22×C4×C151—44no—
321C22×C4×C151—44no—
322C22×C4×C151C2×D412yes—
323C22×C4×C151C2×D412yes—
324C22×C4×C151C2×D412yes—
325C22×C4×C151C2×D412yes—
326C22×C4×C151C2×D412yes—
327C22×C4×C151C2×D412yes—
328C22×C4×C151C2×D412yes—
329C22×C4×C151C2×D412yes—
330C22×C4×C151C2×D412yes—
331C22×C4×C151C2×D412yes—
332C22×C4×C151C2×D412yes—
333C22×C4×C151#4112yes—
334C22×C4×C151#4112yes—
335C22×C4×C151#4112yes—
336C4⋊C4×C151—28no—
337C4⋊C4×C151—28no—
338C4⋊C4×C151—44no—
339C4⋊C4×C151—44no—
340C4⋊C4×C151—44no—
341C4⋊C4×C151—44no—
342C22⋊C4×C151—28no—
343C22⋊C4×C151—28no—
344C22⋊C4×C151—28no—
345C22⋊C4×C151—44no—
346C22⋊C4×C151—44no—
347C22⋊C4×C151—44no—
348C22⋊C4×C151—44no—
349C22⋊C4×C151—44no—
350C22⋊C4×C151—44no—
351C22⋊C4×C151—44no—
352C22⋊C4×C151—44no—
353C22⋊C4×C151—44no—
354C22⋊C4×C151—44no—
355C22⋊C4×C151—44no—
356C42×C151—44no—
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—22no—
380C23×C151—22no—
381C23×C151—22no—
382C23×C151—22no—
383C23×C151—22no—
384C23×C151—22no—
385C23×C151—22no—
386C23×C151—22no—
387C23×C151—22no—
388C23×C151—22no—
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×C151—41no—
452C23×C151—41no—
453C23×C151—41no—
454C23×C151—41no—
455C23×C151—41no—
456C23×C151—41no—
457C23×C151—41no—
458C23×C151—41no—
459C23×C151—41no—
460C23×C151—41no—
461C23×C151#12114yes—
462C23×C151C22×D411yescharacteristic
463C23×C151C22×D411yescharacteristic
464C23×C151C22×D411yescharacteristic
465C23×C151C22×D411yescharacteristic
466C23×C151C22×D411yescharacteristic
467C23×C151C2×#4111yescharacteristic
468C23×C151C2×#4111yescharacteristic
469C23×C151C2×#4111yescharacteristic
470C23×C151C2×#4111yescharacteristic
471C23×C151H(5,𝔽2)11yescharacteristic
472C23×C151H(5,𝔽2)11yescharacteristic
473C23×C151H(5,𝔽2)11yescharacteristic
474C23×C151H(5,𝔽2)11yescharacteristic
475C23×C1512−1+411yescharacteristic
476C23×C1512−1+411yescharacteristic
477D4×C151—416no—
478D4×C151—416no—
479D4×C151—416no—
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—22no—
507C2×C4×C151—22no—
508C2×C4×C151—22no—
509C2×C4×C151—22no—
510C2×C4×C151—22no—
511C2×C4×C151—22no—
512C2×C4×C151—22no—
513C2×C4×C151—416no—
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×C151—41no—
554C2×C4×C151—41no—
555C2×C4×C151—41no—
556C2×C4×C151—41no—
557C2×C4×C151—41no—
558C2×C4×C151—41no—
559C2×C4×C151—41no—
560C2×C4×C151—41no—
561C2×C4×C151—41no—
562C2×C4×C151#12014yes—
563C2×C4×C151#12114yes—
564C2×C4×C151#12114yescomplemented
565C22×C151—24no—
566C22×C151—24no—
567C22×C151—24no—
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—42no—
585C22×C151—42no—
586C22×C151—42no—
587C22×C151—42no—
588C22×C151—42no—
589C22×C151—42no—
590C22×C151—42no—
591C22×C151—42no—
592C22×C151—42no—
593C22×C151—42no—
594C22×C151—81no—
595C22×C151—81no—
596C22×C151—81no—
597C22×C151—81no—
598C22×C151—81no—
599C22×C151—81no—
600C22×C151—81no—
601C22×C151—81no—
602C22×C151—81no—
603C22×C151—81no—
604C22×C151—81no—
605C22×C151—81no—
606C22×C151—81no—
607C22×C151—81no—
608C22×C151—81no—
609C22×C151—81no—
610C22×C151C2×#12011yescharacteristic
611C22×C151C2×#12111yescharacteristic
612C22×C151C2×#12111yescharacteristic
613C22×C151C2×#12111yescharacteristic
614C22×C151#52911yescharacteristic
615C22×C151#53211yescharacteristic
616C22×C151#53411yescharacteristic
617C22×C151#53511yescharacteristic
618C22×C151#53611yescharacteristic
619C22×C151#53711yescharacteristic
620C22×C151#53711yescharacteristic
621C22×C151#53811yescharacteristic
622C22×C151#53911yescharacteristic
623C22×C151#54011yescharacteristic
624C22×C151#54211yescharacteristic
625C22×C151D4211yescharacteristic
626C22×C151D4211yescharacteristic
627C22×C151D4211yescharacteristic
628C22×C151D4211yescharacteristic
629C22×C151#54611yescharacteristic
630C22×C151#54611yescharacteristic
631C22×C151#54611yescharacteristic
632C22×C151#54611yescharacteristic
633C22×C151#54611yescharacteristic
634C22×C151#54711yescharacteristic
635C22×C151#54711yescharacteristic
636C22×C151#54711yescharacteristic
637C22×C151#54811yescharacteristic
638C22×C151#54811yescharacteristic
639C22×C151#54811yescharacteristic
640C22×C151#55011yescharacteristic
641C22×C151#55311yescharacteristic
642C22×C151#55311yescharacteristic
643C22×C151#56211yescharacteristic
644C22×C151#56211yescharacteristic
645C4×C151—24no—
646C4×C151—24no—
647C4×C151—24no—
648C4×C151—42no—
649C4×C151—42no—
650C4×C151—42no—
651C4×C151—42no—
652C4×C151—42no—
653C4×C151—81no—
654C4×C151—81no—
655C4×C151—81no—
656C4×C151—81no—
657C2×C151—44no—
658C2×C151—82no—
659C2×C151—82no—
660C2×C151#240811yescharacteristic
661C2×C151#241011yescharacteristic
662C2×C151#241611yescharacteristic
663C2×C151#241611yescharacteristic
664C2×C151#242511yescharacteristic
665C2×C151#242611yescharacteristic
666C2×C151#242811yescharacteristic
667C2×C151#243211yescharacteristic
668C2×C151#255911yescharacteristic
669C2×C151#267211yescharacteristic
670C2×C151#267611yescharacteristic
671C2×C151#268111yescharacteristic
672C2×C151#268211yescharacteristic
673C2×C151#270111yescharacteristic
674C2×C151#271111yescharacteristic
675#15316C15111yesmaximal, characteristic, direct product factor, Sylow
676C151#1531611yescharacteristic, direct product factor, Sylow
677C22×#121C2×C15111yescharacteristic
678C2×#396C2×C15111yescharacteristic, complemented
679C2×#394C2×C15111yescharacteristic, complemented
680C2×#394C2×C15111yescharacteristic, complemented
681C2×#394C2×C15111yescharacteristic, complemented
682C2×#390C2×C15111yescharacteristic, complemented
683C2×#389C2×C15111yescharacteristic, complemented
684C2×#385C2×C15111yescharacteristic, complemented
685#1441C2×C15111yescharacteristic, complemented
686#1439C2×C15111yescharacteristic, complemented
687#1439C2×C15111yescharacteristic, complemented
688#1438C2×C15111yescharacteristic, complemented
689#1438C2×C15111yescharacteristic, complemented
690#1437C2×C15111yescharacteristic, complemented
691C22⋊#95C2×C15111yescharacteristic, complemented
692C23×D4C22×C15111yescharacteristic
693C23×D4C22×C15111yescharacteristic
694C23×D4C22×C15111yescharacteristic
695C24×C4C22×C15111yescharacteristic
696C2×#121—24no—
697C2×#121—24no—
698C2×#121—24no—
699C22×C4⋊C4C22×C15111yescharacteristic
700C22×C4⋊C4C22×C15111yescharacteristic
701C22×C4⋊C4C22×C15111yescharacteristic
702C22×C4⋊C4C22×C15111yescharacteristic
703C22×C4⋊C4C22×C15111yescharacteristic
704C22×C4⋊C4C22×C15111yescharacteristic
705C22×C22⋊C4C22×C15111yescharacteristic
706C22×C22⋊C4C22×C15111yescharacteristic
707C22×C22⋊C4C22×C15111yescharacteristic
708C22×C22⋊C4C22×C15111yescharacteristic
709C22×C22⋊C4C22×C15111yescharacteristic
710C22×C22⋊C4C22×C15111yescharacteristic
711C22×C22⋊C4C22×C15111yescharacteristic
712C22×C22⋊C4C22×C15111yescharacteristic
713C22×C22⋊C4C22×C15111yescharacteristic
714C22×C22⋊C4C22×C15111yescharacteristic
715C22×C22⋊C4C22×C15111yescharacteristic
716C22×C22⋊C4C22×C15111yescharacteristic
717C22×C22⋊C4C22×C15111yescharacteristic
718C22×C22⋊C4C22×C15111yescharacteristic
719C22×C42C22×C15111yescharacteristic
720#396—24no—
721#394—24no—
722#394—24no—
723#394—24no—
724#390—24no—
725#389—24no—
726#385—24no—
727C2×#95C22×C15111yescharacteristic
728C2×#95C22×C15111yescharacteristic
729C2×#95C22×C15111yescharacteristic
730C2×#95C22×C15111yescharacteristic
731C2×#95C22×C15111yescharacteristic
732C2×#95C22×C15111yescharacteristic
733C2×#95C22×C15111yescharacteristic
734C2×#95C22×C15111yescharacteristic
735C2×#95C22×C15111yescharacteristic
736C2×#95C22×C15111yescharacteristic
737C25C23×C15111yescharacteristic
738C25C23×C15111yescharacteristic
739C25C23×C15111yescharacteristic
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4D4×C15114yes—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4C23×C15111yescharacteristic
769C23×C4C23×C15111yescharacteristic
770C23×C4C23×C15111yescharacteristic
771C23×C4C23×C15111yescharacteristic
772C23×C4C23×C15111yescharacteristic
773C23×C4C23×C15111yescharacteristic
774C23×C4C23×C15111yescharacteristic
775C23×C4C23×C15111yescharacteristic
776C23×C4C23×C15111yescharacteristic
777C23×C4C23×C15111yescharacteristic
778C23×C4C23×C15111yescharacteristic
779C23×C4C23×C15111yescharacteristic
780#121—232no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—22no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—41no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4—41no—
797C2×C4⋊C4D4×C15114yes—
798C2×C4⋊C4D4×C15114yescomplemented
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—41no—
833C2×C22⋊C4—41no—
834C2×C22⋊C4—41no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4—41no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—41no—
839C2×C22⋊C4D4×C15114yes—
840C2×C22⋊C4D4×C15114yescomplemented
841C2×C42—22no—
842C2×C42—22no—
843C2×C42—41no—
844#95—22no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—41no—
853#95—41no—
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—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24C2×D4×C15112yes—
895C24C2×D4×C15112yes—
896C24C2×D4×C15112yes—
897C24C2×D4×C15112yes—
898C24#41×C15112yes—
899C24C24×C15111yescharacteristic
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
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—28no—
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—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C15112yes—
999C22×C4C2×D4×C15112yes—
1000C22×C4C2×D4×C15112yes—
1001C22×C4C2×D4×C15112yes—
1002C22×C4C2×D4×C15112yes—
1003C22×C4C2×D4×C15112yes—
1004C22×C4C2×D4×C15112yes—
1005C22×C4C2×D4×C15112yes—
1006C22×C4C2×D4×C15112yes—
1007C22×C4C2×D4×C15112yes—
1008C22×C4C2×D4×C15112yes—
1009C22×C4#41×C15112yes—
1010C22×C4#41×C15112yes—
1011C22×C4#41×C15112yes—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C42—44no—
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—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
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—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23#121×C15114yes—
1138C23C22×D4×C15111yescharacteristic
1139C23C22×D4×C15111yescharacteristic
1140C23C22×D4×C15111yescharacteristic
1141C23C22×D4×C15111yescharacteristic
1142C23C22×D4×C15111yescharacteristic
1143C23C2×#41×C15111yescharacteristic
1144C23C2×#41×C15111yescharacteristic
1145C23C2×#41×C15111yescharacteristic
1146C23C2×#41×C15111yescharacteristic
1147C23H(5,𝔽2)×C15111yescharacteristic
1148C23H(5,𝔽2)×C15111yescharacteristic
1149C23H(5,𝔽2)×C15111yescharacteristic
1150C23H(5,𝔽2)×C15111yescharacteristic
1151C232−1+4×C15111yescharacteristic
1152C232−1+4×C15111yescharacteristic
1153D4—416no—
1154D4—416no—
1155D4—416no—
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—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—416no—
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×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4#120×C15114yes—
1239C2×C4#121×C15114yes—
1240C2×C4#121×C15114yescomplemented
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22C2×#120×C15111yescharacteristic
1287C22C2×#121×C15111yescharacteristic
1288C22C2×#121×C15111yescharacteristic
1289C22C2×#121×C15111yescharacteristic
1290C22#529×C15111yescharacteristic
1291C22#532×C15111yescharacteristic
1292C22#534×C15111yescharacteristic
1293C22#535×C15111yescharacteristic
1294C22#536×C15111yescharacteristic
1295C22#537×C15111yescharacteristic
1296C22#537×C15111yescharacteristic
1297C22#538×C15111yescharacteristic
1298C22#539×C15111yescharacteristic
1299C22#540×C15111yescharacteristic
1300C22#542×C15111yescharacteristic
1301C22D42×C15111yescharacteristic
1302C22D42×C15111yescharacteristic
1303C22D42×C15111yescharacteristic
1304C22D42×C15111yescharacteristic
1305C22#546×C15111yescharacteristic
1306C22#546×C15111yescharacteristic
1307C22#546×C15111yescharacteristic
1308C22#546×C15111yescharacteristic
1309C22#546×C15111yescharacteristic
1310C22#547×C15111yescharacteristic
1311C22#547×C15111yescharacteristic
1312C22#547×C15111yescharacteristic
1313C22#548×C15111yescharacteristic
1314C22#548×C15111yescharacteristic
1315C22#548×C15111yescharacteristic
1316C22#550×C15111yescharacteristic
1317C22#553×C15111yescharacteristic
1318C22#553×C15111yescharacteristic
1319C22#562×C15111yescharacteristic
1320C22#562×C15111yescharacteristic
1321C4—24no—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C2—44no—
1334C2—82no—
1335C2—82no—
1336C2#2408×C15111yescharacteristic
1337C2#2410×C15111yescharacteristic
1338C2#2416×C15111yescharacteristic
1339C2#2416×C15111yescharacteristic
1340C2#2425×C15111yescharacteristic
1341C2#2426×C15111yescharacteristic
1342C2#2428×C15111yescharacteristic
1343C2#2432×C15111yescharacteristic
1344C2#2559×C15111yescharacteristic
1345C2#2672×C15111yescharacteristic
1346C2#2676×C15111yescharacteristic
1347C2#2681×C15111yescharacteristic
1348C2#2682×C15111yescharacteristic
1349C2#2701×C15111yescharacteristic
1350C2#2711×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC22×#121×C151C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#396×C151C2semidirect
3. C2×#394×C151C2semidirect
4. C2×#394×C151C2semidirect
5. C2×#394×C151C2semidirect
6. C2×#390×C151C2semidirect
7. C2×#389×C151C2semidirect
8. C2×#385×C151C2semidirect
9. #1441×C151C2semidirect
10. #1439×C151C2semidirect
11. #1439×C151C2semidirect
12. #1438×C151C2semidirect
13. #1438×C151C2semidirect
14. #1437×C151C2semidirect
15. C22⋊#95×C151C2semidirect
122. C2×C4⋊C4×C151D4semidirect
164. C2×C22⋊C4×C151D4semidirect
564. C2×C4×C151#121semidirect
675. #15316C151direct (N × H)
676. C151#15316direct (N × H)
678. C2×#396C2×C151semidirect
679. C2×#394C2×C151semidirect
680. C2×#394C2×C151semidirect
681. C2×#394C2×C151semidirect
682. C2×#390C2×C151semidirect
683. C2×#389C2×C151semidirect
684. C2×#385C2×C151semidirect
685. #1441C2×C151semidirect
686. #1439C2×C151semidirect
687. #1439C2×C151semidirect
688. #1438C2×C151semidirect
689. #1438C2×C151semidirect
690. #1437C2×C151semidirect
691. C22⋊#95C2×C151semidirect
798. C2×C4⋊C4D4×C151semidirect
840. C2×C22⋊C4D4×C151semidirect
1240. C2×C4#121×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1512
C2×#396×C1512
C2×#394×C1512
C2×#390×C1512
C2×#389×C1512
C2×#385×C1512
#1441×C1512
#1439×C1512
#1438×C1512
#1437×C1512
C22⋊#95×C1512
#15316151