Finite Group Databasebeta

← C149×#16274 #49195223

Subgroups — C149×#16274 #49195223

Order 38144.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C149C211yesmaximal, characteristic, complemented
2C2×#394×C149C211yesmaximal, characteristic, complemented
3C2×#394×C149C211yesmaximal, characteristic, complemented
4C2×#392×C149C211yesmaximal, characteristic
5C2×#390×C149C211yesmaximal, characteristic, complemented
6C2×#388×C149C211yesmaximal, characteristic, complemented
7#1441×C149C211yesmaximal, characteristic, complemented
8#1439×C149C211yesmaximal, characteristic, complemented
9#1439×C149C211yesmaximal, characteristic, complemented
10#1439×C149C211yesmaximal, characteristic, complemented
11#1439×C149C211yesmaximal, characteristic, complemented
12#1438×C149C211yesmaximal, characteristic, complemented
13#1438×C149C211yesmaximal, characteristic, complemented
14#1438×C149C211yesmaximal, characteristic, complemented
15#1436×C149C211yesmaximal, characteristic, complemented
16C23×D4×C149C2211yescharacteristic
17C23×D4×C149C2211yescharacteristic
18C23×D4×C149C2211yescharacteristic
19C22×C4⋊C4×C149C2211yescharacteristic
20C22×C4⋊C4×C149C2211yescharacteristic
21C22×C4⋊C4×C149C2211yescharacteristic
22C22×C4⋊C4×C149C2211yescharacteristic
23C22×C22⋊C4×C149C2211yescharacteristic
24C22×C22⋊C4×C149C2211yescharacteristic
25C22×C22⋊C4×C149C2211yescharacteristic
26C22×C22⋊C4×C149C2211yescharacteristic
27C22×C22⋊C4×C149C2211yescharacteristic
28C22×C22⋊C4×C149C2211yescharacteristic
29C22×C22⋊C4×C149C2211yescharacteristic
30C22×C22⋊C4×C149C2211yescharacteristic
31C22×C22⋊C4×C149C2211yescharacteristic
32C22×C22⋊C4×C149C2211yescharacteristic
33C22×C22⋊C4×C149C2211yescharacteristic
34C22×C22⋊C4×C149C2211yescharacteristic
35C22×C22⋊C4×C149C2211yescharacteristic
36C22×C22⋊C4×C149C2211yescharacteristic
37C22×C22⋊C4×C149C2211yescharacteristic
38C22×C42×C149C2211yescharacteristic
39#397×C149—24no—
40#394×C149—24no—
41#394×C149—24no—
42#392×C149—24no—
43#390×C149—24no—
44#388×C149—24no—
45C2×#95×C149C2211yescharacteristic
46C2×#95×C149C2211yescharacteristic
47C2×#95×C149C2211yescharacteristic
48C2×#95×C149C2211yescharacteristic
49C2×#95×C149C2211yescharacteristic
50C2×#95×C149C2211yescharacteristic
51C2×#95×C149C2211yescharacteristic
52C2×#95×C149C2211yescharacteristic
53C2×#95×C149C2211yescharacteristic
54C2×#95×C149C2211yescharacteristic
55C2×#95×C149C2211yescharacteristic
56C2×#95×C149C2211yescharacteristic
57C25×C149C2311yescharacteristic
58C25×C149C2311yescharacteristic
59C25×C149C2311yescharacteristic
60C22×D4×C149—22no—
61C22×D4×C149—22no—
62C22×D4×C149—22no—
63C22×D4×C149—22no—
64C22×D4×C149—22no—
65C22×D4×C149—22no—
66C22×D4×C149—22no—
67C22×D4×C149—22no—
68C22×D4×C149—22no—
69C22×D4×C149—22no—
70C22×D4×C149—22no—
71C22×D4×C149—41no—
72C22×D4×C149—41no—
73C22×D4×C149—41no—
74C22×D4×C149—41no—
75C22×D4×C149—41no—
76C22×D4×C149—41no—
77C22×D4×C149—41no—
78C22×D4×C149—41no—
79C22×D4×C149—41no—
80C22×D4×C149—41no—
81C23×C4×C149C2311yescharacteristic
82C23×C4×C149C2311yescharacteristic
83C23×C4×C149C2311yescharacteristic
84C23×C4×C149C2311yescharacteristic
85C23×C4×C149C2311yescharacteristic
86C23×C4×C149C2311yescharacteristic
87C23×C4×C149C2311yescharacteristic
88C23×C4×C149C2311yescharacteristic
89C23×C4×C149C2311yescharacteristic
90C23×C4×C149C2311yescharacteristic
91C23×C4×C149C2311yescharacteristic
92C23×C4×C149C2311yescharacteristic
93C2×C4⋊C4×C149—22no—
94C2×C4⋊C4×C149—22no—
95C2×C4⋊C4×C149—22no—
96C2×C4⋊C4×C149—22no—
97C2×C4⋊C4×C149—22no—
98C2×C4⋊C4×C149—22no—
99C2×C4⋊C4×C149—22no—
100C2×C4⋊C4×C149—41no—
101C2×C4⋊C4×C149—41no—
102C2×C4⋊C4×C149—41no—
103C2×C4⋊C4×C149—41no—
104C2×C4⋊C4×C149—41no—
105C2×C22⋊C4×C149—22no—
106C2×C22⋊C4×C149—22no—
107C2×C22⋊C4×C149—22no—
108C2×C22⋊C4×C149—22no—
109C2×C22⋊C4×C149—22no—
110C2×C22⋊C4×C149—22no—
111C2×C22⋊C4×C149—22no—
112C2×C22⋊C4×C149—22no—
113C2×C22⋊C4×C149—22no—
114C2×C22⋊C4×C149—22no—
115C2×C22⋊C4×C149—22no—
116C2×C22⋊C4×C149—22no—
117C2×C22⋊C4×C149—22no—
118C2×C22⋊C4×C149—22no—
119C2×C22⋊C4×C149—22no—
120C2×C22⋊C4×C149—22no—
121C2×C22⋊C4×C149—22no—
122C2×C22⋊C4×C149—22no—
123C2×C22⋊C4×C149—22no—
124C2×C22⋊C4×C149—22no—
125C2×C22⋊C4×C149—22no—
126C2×C22⋊C4×C149—41no—
127C2×C22⋊C4×C149—41no—
128C2×C22⋊C4×C149—41no—
129C2×C22⋊C4×C149—41no—
130C2×C22⋊C4×C149—41no—
131C2×C22⋊C4×C149—41no—
132C2×C22⋊C4×C149—41no—
133C2×C22⋊C4×C149—41no—
134C2×C22⋊C4×C149—41no—
135C2×C22⋊C4×C149—41no—
136C2×C22⋊C4×C149—41no—
137C2×C22⋊C4×C149—41no—
138C2×C22⋊C4×C149—41no—
139C2×C22⋊C4×C149—41no—
140C2×C22⋊C4×C149—41no—
141C2×C22⋊C4×C149—41no—
142C2×C22⋊C4×C149—41no—
143C2×C22⋊C4×C149—41no—
144C2×C22⋊C4×C149—41no—
145C2×C22⋊C4×C149—41no—
146C2×C22⋊C4×C149—41no—
147C2×C22⋊C4×C149—41no—
148C2×C22⋊C4×C149D414yes—
149C2×C22⋊C4×C149D414yescomplemented
150C2×C42×C149—22no—
151C2×C42×C149—22no—
152C2×C42×C149—41no—
153#95×C149—22no—
154#95×C149—22no—
155#95×C149—22no—
156#95×C149—22no—
157#95×C149—22no—
158#95×C149—22no—
159#95×C149—22no—
160#95×C149—41no—
161#95×C149—41no—
162#95×C149—41no—
163#95×C149—41no—
164#95×C149D414yescomplemented
165C24×C149—21no—
166C24×C149—21no—
167C24×C149—21no—
168C24×C149—21no—
169C24×C149—21no—
170C24×C149—21no—
171C24×C149—21no—
172C24×C149—21no—
173C24×C149—21no—
174C24×C149—21no—
175C24×C149—21no—
176C24×C149—21no—
177C24×C149—21no—
178C24×C149—21no—
179C24×C149—21no—
180C24×C149—21no—
181C24×C149—21no—
182C24×C149—21no—
183C24×C149—21no—
184C24×C149—21no—
185C24×C149—21no—
186C24×C149—21no—
187C24×C149—21no—
188C24×C149—21no—
189C24×C149—21no—
190C24×C149—21no—
191C24×C149—21no—
192C24×C149—21no—
193C24×C149—21no—
194C24×C149—21no—
195C24×C149—21no—
196C24×C149—21no—
197C24×C149—21no—
198C24×C149—21no—
199C24×C149—21no—
200C24×C149—21no—
201C24×C149—21no—
202C24×C149—21no—
203C24×C149—21no—
204C24×C149—21no—
205C24×C149—21no—
206C24×C149—21no—
207C24×C149C2×D412yes—
208C24×C149C2×D412yes—
209C24×C149#4112yes—
210C24×C149C2411yescharacteristic
211C2×D4×C149—28no—
212C2×D4×C149—44no—
213C2×D4×C149—44no—
214C2×D4×C149—44no—
215C2×D4×C149—44no—
216C2×D4×C149—44no—
217C2×D4×C149—44no—
218C2×D4×C149—44no—
219C2×D4×C149—44no—
220C2×D4×C149—44no—
221C2×D4×C149—44no—
222C2×D4×C149—44no—
223C2×D4×C149—44no—
224C2×D4×C149—44no—
225C2×D4×C149—44no—
226C2×D4×C149—44no—
227C2×D4×C149—44no—
228C2×D4×C149—44no—
229C2×D4×C149—44no—
230C2×D4×C149—44no—
231C2×D4×C149—44no—
232C22×C4×C149—21no—
233C22×C4×C149—21no—
234C22×C4×C149—21no—
235C22×C4×C149—21no—
236C22×C4×C149—21no—
237C22×C4×C149—21no—
238C22×C4×C149—21no—
239C22×C4×C149—21no—
240C22×C4×C149—21no—
241C22×C4×C149—21no—
242C22×C4×C149—21no—
243C22×C4×C149—21no—
244C22×C4×C149—21no—
245C22×C4×C149—21no—
246C22×C4×C149—21no—
247C22×C4×C149—21no—
248C22×C4×C149—21no—
249C22×C4×C149—21no—
250C22×C4×C149—21no—
251C22×C4×C149—21no—
252C22×C4×C149—21no—
253C22×C4×C149—21no—
254C22×C4×C149—21no—
255C22×C4×C149—21no—
256C22×C4×C149—21no—
257C22×C4×C149—21no—
258C22×C4×C149—21no—
259C22×C4×C149—21no—
260C22×C4×C149—21no—
261C22×C4×C149—21no—
262C22×C4×C149—21no—
263C22×C4×C149—21no—
264C22×C4×C149—21no—
265C22×C4×C149—21no—
266C22×C4×C149—21no—
267C22×C4×C149—21no—
268C22×C4×C149—21no—
269C22×C4×C149—21no—
270C22×C4×C149—21no—
271C22×C4×C149—21no—
272C22×C4×C149—21no—
273C22×C4×C149—21no—
274C22×C4×C149—21no—
275C22×C4×C149—21no—
276C22×C4×C149—21no—
277C22×C4×C149—21no—
278C22×C4×C149—21no—
279C22×C4×C149—21no—
280C22×C4×C149—21no—
281C22×C4×C149—21no—
282C22×C4×C149—21no—
283C22×C4×C149—21no—
284C22×C4×C149—21no—
285C22×C4×C149—21no—
286C22×C4×C149—21no—
287C22×C4×C149—21no—
288C22×C4×C149—21no—
289C22×C4×C149—21no—
290C22×C4×C149—21no—
291C22×C4×C149—21no—
292C22×C4×C149—21no—
293C22×C4×C149—21no—
294C22×C4×C149—21no—
295C22×C4×C149—21no—
296C22×C4×C149—21no—
297C22×C4×C149—21no—
298C22×C4×C149—21no—
299C22×C4×C149—21no—
300C22×C4×C149—21no—
301C22×C4×C149—21no—
302C22×C4×C149—21no—
303C22×C4×C149—21no—
304C22×C4×C149—21no—
305C22×C4×C149—21no—
306C22×C4×C149C2×D412yes—
307C22×C4×C149C2×D412yes—
308C22×C4×C149C2×D412yes—
309C22×C4×C149C2×D412yes—
310C22×C4×C149C2×D412yes—
311C22×C4×C149C2×D412yes—
312C22×C4×C149C2×D412yes—
313C22×C4×C149#4112yes—
314C22×C4×C149#4112yes—
315C22×C4×C149#4112yes—
316C4⋊C4×C149—44no—
317C4⋊C4×C149—44no—
318C4⋊C4×C149—44no—
319C4⋊C4×C149—44no—
320C22⋊C4×C149—28no—
321C22⋊C4×C149—44no—
322C22⋊C4×C149—44no—
323C22⋊C4×C149—44no—
324C22⋊C4×C149—44no—
325C22⋊C4×C149—44no—
326C22⋊C4×C149—44no—
327C22⋊C4×C149—44no—
328C22⋊C4×C149—44no—
329C22⋊C4×C149—44no—
330C22⋊C4×C149—44no—
331C22⋊C4×C149—44no—
332C22⋊C4×C149—44no—
333C22⋊C4×C149—44no—
334C22⋊C4×C149—44no—
335C42×C149—44no—
336C23×C149—22no—
337C23×C149—22no—
338C23×C149—22no—
339C23×C149—22no—
340C23×C149—22no—
341C23×C149—22no—
342C23×C149—22no—
343C23×C149—22no—
344C23×C149—22no—
345C23×C149—22no—
346C23×C149—22no—
347C23×C149—22no—
348C23×C149—22no—
349C23×C149—22no—
350C23×C149—22no—
351C23×C149—22no—
352C23×C149—22no—
353C23×C149—22no—
354C23×C149—22no—
355C23×C149—22no—
356C23×C149—22no—
357C23×C149—41no—
358C23×C149—41no—
359C23×C149—41no—
360C23×C149—41no—
361C23×C149—41no—
362C23×C149—41no—
363C23×C149—41no—
364C23×C149—41no—
365C23×C149—41no—
366C23×C149—41no—
367C23×C149—41no—
368C23×C149—41no—
369C23×C149—41no—
370C23×C149—41no—
371C23×C149—41no—
372C23×C149—41no—
373C23×C149—41no—
374C23×C149—41no—
375C23×C149—41no—
376C23×C149—41no—
377C23×C149—41no—
378C23×C149—41no—
379C23×C149—41no—
380C23×C149—41no—
381C23×C149—41no—
382C23×C149—41no—
383C23×C149—41no—
384C23×C149—41no—
385C23×C149—41no—
386C23×C149—41no—
387C23×C149—41no—
388C23×C149—41no—
389C23×C149—41no—
390C23×C149—41no—
391C23×C149—41no—
392C23×C149—41no—
393C23×C149—41no—
394C23×C149—41no—
395C23×C149—41no—
396C23×C149—41no—
397C23×C149—41no—
398C23×C149—41no—
399C23×C149—41no—
400C23×C149—41no—
401C23×C149—41no—
402C23×C149—41no—
403C23×C149—41no—
404C23×C149—41no—
405C23×C149—41no—
406C23×C149—41no—
407C23×C149—41no—
408C23×C149—41no—
409C23×C149—41no—
410C23×C149—41no—
411C23×C149—41no—
412C23×C149—41no—
413C23×C149—41no—
414C23×C149—41no—
415C23×C149—41no—
416C23×C149—41no—
417C23×C149—41no—
418C23×C149—41no—
419C23×C149—41no—
420C23×C149—41no—
421C23×C149—41no—
422C23×C149—41no—
423C23×C149—41no—
424C23×C149—41no—
425C23×C149—41no—
426C23×C149—41no—
427C23×C149—41no—
428C23×C149—41no—
429C23×C149—41no—
430C23×C149—41no—
431C23×C149—41no—
432C23×C149—41no—
433C23×C149—41no—
434C23×C149—41no—
435C23×C149—41no—
436C23×C149—41no—
437C23×C149—41no—
438C23×C149—41no—
439C23×C149—41no—
440C23×C149—41no—
441C23×C149C22×D411yescharacteristic
442C23×C149C22×D411yescharacteristic
443C23×C149C22×D411yescharacteristic
444C23×C149C2×#4111yescharacteristic
445C23×C149C2×#4111yescharacteristic
446C23×C149C2×#4111yescharacteristic
447C23×C149C2×#4111yescharacteristic
448C23×C149H(5,𝔽2)11yescharacteristic
449C23×C149H(5,𝔽2)11yescharacteristic
450C23×C149H(5,𝔽2)11yescharacteristic
451C23×C149H(5,𝔽2)11yescharacteristic
452C23×C149H(5,𝔽2)11yescharacteristic
453C23×C149H(5,𝔽2)11yescharacteristic
454C23×C149H(5,𝔽2)11yescharacteristic
455C23×C1492−1+411yescharacteristic
456D4×C149—416no—
457D4×C149—416no—
458D4×C149—416no—
459C2×C4×C149—22no—
460C2×C4×C149—22no—
461C2×C4×C149—22no—
462C2×C4×C149—22no—
463C2×C4×C149—22no—
464C2×C4×C149—22no—
465C2×C4×C149—22no—
466C2×C4×C149—22no—
467C2×C4×C149—22no—
468C2×C4×C149—22no—
469C2×C4×C149—22no—
470C2×C4×C149—22no—
471C2×C4×C149—22no—
472C2×C4×C149—22no—
473C2×C4×C149—22no—
474C2×C4×C149—22no—
475C2×C4×C149—22no—
476C2×C4×C149—22no—
477C2×C4×C149—22no—
478C2×C4×C149—22no—
479C2×C4×C149—22no—
480C2×C4×C149—22no—
481C2×C4×C149—22no—
482C2×C4×C149—22no—
483C2×C4×C149—22no—
484C2×C4×C149—22no—
485C2×C4×C149—22no—
486C2×C4×C149—41no—
487C2×C4×C149—41no—
488C2×C4×C149—41no—
489C2×C4×C149—41no—
490C2×C4×C149—41no—
491C2×C4×C149—41no—
492C2×C4×C149—41no—
493C2×C4×C149—41no—
494C2×C4×C149—41no—
495C2×C4×C149—41no—
496C2×C4×C149—41no—
497C2×C4×C149—41no—
498C2×C4×C149—41no—
499C2×C4×C149—41no—
500C2×C4×C149—41no—
501C2×C4×C149—41no—
502C2×C4×C149—41no—
503C2×C4×C149—41no—
504C2×C4×C149—41no—
505C2×C4×C149—41no—
506C2×C4×C149—41no—
507C2×C4×C149—41no—
508C2×C4×C149—41no—
509C2×C4×C149—41no—
510C2×C4×C149—41no—
511C2×C4×C149—41no—
512C2×C4×C149—41no—
513C2×C4×C149—41no—
514C2×C4×C149—41no—
515C2×C4×C149—41no—
516C2×C4×C149—41no—
517C2×C4×C149—41no—
518C2×C4×C149—41no—
519C2×C4×C149—41no—
520C2×C4×C149—41no—
521C2×C4×C149—41no—
522C2×C4×C149—41no—
523C2×C4×C149—41no—
524C2×C4×C149—41no—
525C2×C4×C149—41no—
526C2×C4×C149—41no—
527C2×C4×C149—41no—
528C2×C4×C149—41no—
529C2×C4×C149—41no—
530C2×C4×C149—41no—
531C2×C4×C149—41no—
532C2×C4×C149—41no—
533C2×C4×C149—41no—
534C2×C4×C149—41no—
535C2×C4×C149—41no—
536C2×C4×C149—41no—
537C2×C4×C149—41no—
538C2×C4×C149—41no—
539C2×C4×C149—41no—
540C2×C4×C149—41no—
541C2×C4×C149—41no—
542C2×C4×C149#12314yes—
543C22×C149—42no—
544C22×C149—42no—
545C22×C149—42no—
546C22×C149—42no—
547C22×C149—42no—
548C22×C149—42no—
549C22×C149—42no—
550C22×C149—42no—
551C22×C149—42no—
552C22×C149—42no—
553C22×C149—42no—
554C22×C149—42no—
555C22×C149—42no—
556C22×C149—42no—
557C22×C149—42no—
558C22×C149—42no—
559C22×C149—42no—
560C22×C149—42no—
561C22×C149—42no—
562C22×C149—42no—
563C22×C149—42no—
564C22×C149—81no—
565C22×C149—81no—
566C22×C149—81no—
567C22×C149—81no—
568C22×C149—81no—
569C22×C149—81no—
570C22×C149—81no—
571C22×C149—81no—
572C22×C149—81no—
573C22×C149—81no—
574C22×C149—81no—
575C22×C149—81no—
576C22×C149—81no—
577C22×C149—81no—
578C22×C149—81no—
579C22×C149—81no—
580C22×C149—81no—
581C22×C149—81no—
582C22×C149—81no—
583C22×C149—81no—
584C22×C149—81no—
585C22×C149—81no—
586C22×C149—81no—
587C22×C149—81no—
588C22×C149C2×#12311yescharacteristic
589C22×C149#52511yescharacteristic
590C22×C149#53211yescharacteristic
591C22×C149#53411yescharacteristic
592C22×C149#53511yescharacteristic
593C22×C149#53511yescharacteristic
594C22×C149#53711yescharacteristic
595C22×C149#53711yescharacteristic
596C22×C149#53711yescharacteristic
597C22×C149#53811yescharacteristic
598C22×C149#53811yescharacteristic
599C22×C149#53811yescharacteristic
600C22×C149#53911yescharacteristic
601C22×C149#54011yescharacteristic
602C22×C149#54011yescharacteristic
603C22×C149#54011yescharacteristic
604C22×C149#54211yescharacteristic
605C22×C149#54211yescharacteristic
606C22×C149#54211yescharacteristic
607C22×C149D4211yescharacteristic
608C22×C149D4211yescharacteristic
609C22×C149D4211yescharacteristic
610C22×C149#54611yescharacteristic
611C22×C149#54611yescharacteristic
612C22×C149#54611yescharacteristic
613C22×C149#54611yescharacteristic
614C22×C149#54611yescharacteristic
615C22×C149#55011yescharacteristic
616C22×C149#55111yescharacteristic
617C22×C149#55311yescharacteristic
618C22×C149#55911yescharacteristic
619C22×C149#56011yescharacteristic
620C22×C149#56011yescharacteristic
621C22×C149#56011yescharacteristic
622C22×C149H(3,𝔽4)11yescharacteristic
623C4×C149—24no—
624C4×C149—42no—
625C4×C149—42no—
626C4×C149—42no—
627C4×C149—42no—
628C4×C149—42no—
629C4×C149—42no—
630C4×C149—42no—
631C4×C149—81no—
632C4×C149—81no—
633C4×C149—81no—
634C4×C149—81no—
635C2×C149—82no—
636C2×C149—82no—
637C2×C149—82no—
638C2×C149#241811yescharacteristic
639C2×C149#244511yescharacteristic
640C2×C149#246411yescharacteristic
641C2×C149#262411yescharacteristic
642C2×C149#263011yescharacteristic
643C2×C149#266211yescharacteristic
644C2×C149#267011yescharacteristic
645C2×C149#267311yescharacteristic
646C2×C149#267511yescharacteristic
647C2×C149#267811yescharacteristic
648C2×C149#269111yescharacteristic
649C2×C149#270511yescharacteristic
650C2×C149#271211yescharacteristic
651C2×C149#279711yescharacteristic
652C2×C149#282811yescharacteristic
653#16274C14911yesmaximal, characteristic, direct product factor, Sylow
654C149#1627411yescharacteristic, direct product factor, Sylow
655C2×#397C2×C14911yescharacteristic, complemented
656C2×#394C2×C14911yescharacteristic, complemented
657C2×#394C2×C14911yescharacteristic, complemented
658C2×#392C2×C14911yescharacteristic
659C2×#390C2×C14911yescharacteristic, complemented
660C2×#388C2×C14911yescharacteristic, complemented
661#1441C2×C14911yescharacteristic, complemented
662#1439C2×C14911yescharacteristic, complemented
663#1439C2×C14911yescharacteristic, complemented
664#1439C2×C14911yescharacteristic, complemented
665#1439C2×C14911yescharacteristic, complemented
666#1438C2×C14911yescharacteristic, complemented
667#1438C2×C14911yescharacteristic, complemented
668#1438C2×C14911yescharacteristic, complemented
669#1436C2×C14911yescharacteristic, complemented
670C23×D4C22×C14911yescharacteristic
671C23×D4C22×C14911yescharacteristic
672C23×D4C22×C14911yescharacteristic
673C22×C4⋊C4C22×C14911yescharacteristic
674C22×C4⋊C4C22×C14911yescharacteristic
675C22×C4⋊C4C22×C14911yescharacteristic
676C22×C4⋊C4C22×C14911yescharacteristic
677C22×C22⋊C4C22×C14911yescharacteristic
678C22×C22⋊C4C22×C14911yescharacteristic
679C22×C22⋊C4C22×C14911yescharacteristic
680C22×C22⋊C4C22×C14911yescharacteristic
681C22×C22⋊C4C22×C14911yescharacteristic
682C22×C22⋊C4C22×C14911yescharacteristic
683C22×C22⋊C4C22×C14911yescharacteristic
684C22×C22⋊C4C22×C14911yescharacteristic
685C22×C22⋊C4C22×C14911yescharacteristic
686C22×C22⋊C4C22×C14911yescharacteristic
687C22×C22⋊C4C22×C14911yescharacteristic
688C22×C22⋊C4C22×C14911yescharacteristic
689C22×C22⋊C4C22×C14911yescharacteristic
690C22×C22⋊C4C22×C14911yescharacteristic
691C22×C22⋊C4C22×C14911yescharacteristic
692C22×C42C22×C14911yescharacteristic
693#397—24no—
694#394—24no—
695#394—24no—
696#392—24no—
697#390—24no—
698#388—24no—
699C2×#95C22×C14911yescharacteristic
700C2×#95C22×C14911yescharacteristic
701C2×#95C22×C14911yescharacteristic
702C2×#95C22×C14911yescharacteristic
703C2×#95C22×C14911yescharacteristic
704C2×#95C22×C14911yescharacteristic
705C2×#95C22×C14911yescharacteristic
706C2×#95C22×C14911yescharacteristic
707C2×#95C22×C14911yescharacteristic
708C2×#95C22×C14911yescharacteristic
709C2×#95C22×C14911yescharacteristic
710C2×#95C22×C14911yescharacteristic
711C25C23×C14911yescharacteristic
712C25C23×C14911yescharacteristic
713C25C23×C14911yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C23×C4C23×C14911yescharacteristic
736C23×C4C23×C14911yescharacteristic
737C23×C4C23×C14911yescharacteristic
738C23×C4C23×C14911yescharacteristic
739C23×C4C23×C14911yescharacteristic
740C23×C4C23×C14911yescharacteristic
741C23×C4C23×C14911yescharacteristic
742C23×C4C23×C14911yescharacteristic
743C23×C4C23×C14911yescharacteristic
744C23×C4C23×C14911yescharacteristic
745C23×C4C23×C14911yescharacteristic
746C23×C4C23×C14911yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—22no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
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⋊C4D4×C14914yes—
803C2×C22⋊C4D4×C14914yescomplemented
804C2×C42—22no—
805C2×C42—22no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C14914yescomplemented
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
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—
861C24C2×D4×C14912yes—
862C24C2×D4×C14912yes—
863C24#41×C14912yes—
864C24C24×C14911yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
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×C4C2×D4×C14912yes—
961C22×C4C2×D4×C14912yes—
962C22×C4C2×D4×C14912yes—
963C22×C4C2×D4×C14912yes—
964C22×C4C2×D4×C14912yes—
965C22×C4C2×D4×C14912yes—
966C22×C4C2×D4×C14912yes—
967C22×C4#41×C14912yes—
968C22×C4#41×C14912yes—
969C22×C4#41×C14912yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—28no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
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—
1095C23C22×D4×C14911yescharacteristic
1096C23C22×D4×C14911yescharacteristic
1097C23C22×D4×C14911yescharacteristic
1098C23C2×#41×C14911yescharacteristic
1099C23C2×#41×C14911yescharacteristic
1100C23C2×#41×C14911yescharacteristic
1101C23C2×#41×C14911yescharacteristic
1102C23H(5,𝔽2)×C14911yescharacteristic
1103C23H(5,𝔽2)×C14911yescharacteristic
1104C23H(5,𝔽2)×C14911yescharacteristic
1105C23H(5,𝔽2)×C14911yescharacteristic
1106C23H(5,𝔽2)×C14911yescharacteristic
1107C23H(5,𝔽2)×C14911yescharacteristic
1108C23H(5,𝔽2)×C14911yescharacteristic
1109C232−1+4×C14911yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
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#123×C14914yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#123×C14911yescharacteristic
1243C22#525×C14911yescharacteristic
1244C22#532×C14911yescharacteristic
1245C22#534×C14911yescharacteristic
1246C22#535×C14911yescharacteristic
1247C22#535×C14911yescharacteristic
1248C22#537×C14911yescharacteristic
1249C22#537×C14911yescharacteristic
1250C22#537×C14911yescharacteristic
1251C22#538×C14911yescharacteristic
1252C22#538×C14911yescharacteristic
1253C22#538×C14911yescharacteristic
1254C22#539×C14911yescharacteristic
1255C22#540×C14911yescharacteristic
1256C22#540×C14911yescharacteristic
1257C22#540×C14911yescharacteristic
1258C22#542×C14911yescharacteristic
1259C22#542×C14911yescharacteristic
1260C22#542×C14911yescharacteristic
1261C22D42×C14911yescharacteristic
1262C22D42×C14911yescharacteristic
1263C22D42×C14911yescharacteristic
1264C22#546×C14911yescharacteristic
1265C22#546×C14911yescharacteristic
1266C22#546×C14911yescharacteristic
1267C22#546×C14911yescharacteristic
1268C22#546×C14911yescharacteristic
1269C22#550×C14911yescharacteristic
1270C22#551×C14911yescharacteristic
1271C22#553×C14911yescharacteristic
1272C22#559×C14911yescharacteristic
1273C22#560×C14911yescharacteristic
1274C22#560×C14911yescharacteristic
1275C22#560×C14911yescharacteristic
1276C22H(3,𝔽4)×C14911yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2#2418×C14911yescharacteristic
1293C2#2445×C14911yescharacteristic
1294C2#2464×C14911yescharacteristic
1295C2#2624×C14911yescharacteristic
1296C2#2630×C14911yescharacteristic
1297C2#2662×C14911yescharacteristic
1298C2#2670×C14911yescharacteristic
1299C2#2673×C14911yescharacteristic
1300C2#2675×C14911yescharacteristic
1301C2#2678×C14911yescharacteristic
1302C2#2691×C14911yescharacteristic
1303C2#2705×C14911yescharacteristic
1304C2#2712×C14911yescharacteristic
1305C2#2797×C14911yescharacteristic
1306C2#2828×C14911yescharacteristic
subgroupG/H
center, socleC24×C149C24
commutator, Frattini, cosocleC24C24×C149
prime radicalC2×#392×C149C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C149C2semidirect
2. C2×#394×C149C2semidirect
3. C2×#394×C149C2semidirect
5. C2×#390×C149C2semidirect
6. C2×#388×C149C2semidirect
7. #1441×C149C2semidirect
8. #1439×C149C2semidirect
9. #1439×C149C2semidirect
10. #1439×C149C2semidirect
11. #1439×C149C2semidirect
12. #1438×C149C2semidirect
13. #1438×C149C2semidirect
14. #1438×C149C2semidirect
15. #1436×C149C2semidirect
149. C2×C22⋊C4×C149D4semidirect
164. #95×C149D4semidirect
653. #16274C149direct (N × H)
654. C149#16274direct (N × H)
655. C2×#397C2×C149semidirect
656. C2×#394C2×C149semidirect
657. C2×#394C2×C149semidirect
659. C2×#390C2×C149semidirect
660. C2×#388C2×C149semidirect
661. #1441C2×C149semidirect
662. #1439C2×C149semidirect
663. #1439C2×C149semidirect
664. #1439C2×C149semidirect
665. #1439C2×C149semidirect
666. #1438C2×C149semidirect
667. #1438C2×C149semidirect
668. #1438C2×C149semidirect
669. #1436C2×C149semidirect
803. C2×C22⋊C4D4×C149semidirect
818. #95D4×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1492
C2×#394×C1492
C2×#392×C1492
C2×#390×C1492
C2×#388×C1492
#1441×C1492
#1439×C1492
#1438×C1492
#1436×C1492
#16274149