Finite Group Databasebeta

← #33057284

Subgroups — #33057284

Order 18688.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619927C211yesmaximal, characteristic
2#22618965C211yesmaximal, characteristic, complemented
3#22608843C211yesmaximal, characteristic, complemented
4#22608814C211yesmaximal, characteristic, complemented
5#22608795C211yesmaximal, characteristic, complemented
6#22608793C211yesmaximal, characteristic, complemented
7#22608760C211yesmaximal, characteristic, complemented
8#22608758C211yesmaximal, characteristic, complemented
9#22608753C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608709C211yesmaximal, characteristic, complemented
12#22608400C211yesmaximal, characteristic, complemented
13#22608321C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#2979C211yesmaximal, characteristic, complemented
16C2×C4×D292C2211yescharacteristic
17#17988898C411yescharacteristic
18#17988898C411yescharacteristic
19#17988864C411yescharacteristic
20#17988864C411yescharacteristic
21#17988779C411yescharacteristic
22#17988779C411yescharacteristic
23#17988720C411yescharacteristic
24#17988720C411yescharacteristic
25C4×#11924013C2211yescharacteristic
26C4×#11924013C2211yescharacteristic
27C4×#11924013C2211yescharacteristic
28C4×#11924013C2211yescharacteristic
29#17988666C2211yescharacteristic
30#17988666C2211yescharacteristic
31#17988657—21no—
32#17988657—21no—
33C8×D292C2211yescharacteristic
34C8×D292C2211yescharacteristic
35#17988644C2211yescharacteristic
36#17988640C2211yescharacteristic
37#17988640C2211yescharacteristic
38#17988549—21no—
39C22⋊C8×D73—21no—
40#17988339C2211yescharacteristic, complemented
41#17988339C2211yescharacteristic, complemented
42#17988337C2211yescharacteristic, complemented
43#17988337C2211yescharacteristic, complemented
44D4⋊#10596831C2211yescharacteristic, complemented
45D4⋊#10596831C2211yescharacteristic, complemented
46D4⋊#10596831C2211yescharacteristic, complemented
47D4⋊#10596831C2211yescharacteristic, complemented
48#17988314C2211yescharacteristic
49#17988314C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic, complemented
53#17988309C2211yescharacteristic, complemented
54#17988308C2211yescharacteristic, complemented
55C8×#10596831C2211yescharacteristic, complemented
56#532×C73C2211yescharacteristic
57#436×C73—21no—
58#436×C73C2211yescharacteristic, complemented
59#436×C73C2211yescharacteristic, complemented
60C8×D4×C73—21no—
61C8×D4×C73C2211yescharacteristic, complemented
62C8×D4×C73C2211yescharacteristic, complemented
63#431×C73C2211yescharacteristic
64#431×C73C2211yescharacteristic
65#408×C73—21no—
66#408×C73—21no—
67C22×D292C2×C411yescharacteristic
68C22×C4×D73—21no—
69C2×#11924013C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924013C2×C411yescharacteristic
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C4×D292—21no—
78C4×D292—21no—
79C4×D292C2×C411yescharacteristic
80C4×D292C2×C411yescharacteristic
81C4×D292C2311yescharacteristic
82C4×D292C2311yescharacteristic
83C2×C4⋊Dic73C2×C411yescharacteristic
84C2×#11924005—21no—
85#14556524C2×C411yescharacteristic
86#14556524C2×C411yescharacteristic
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89C4⋊#10596831—21no—
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556512C2×C411yescharacteristic
95#14556512C2×C411yescharacteristic
96#14556512C2×C411yescharacteristic
97#14556512C2×C411yescharacteristic
98#14556511C2×C411yescharacteristic
99#14556511C2×C411yescharacteristic
100#14556511C2×C411yescharacteristic
101#14556511C2×C411yescharacteristic
102C22⋊#10596831—21no—
103C22⋊#10596831—21no—
104C22⋊#10596831C2×C411yescharacteristic
105C22⋊#10596831C2×C411yescharacteristic
106#14556503—21no—
107#14556503—21no—
108#14556503—21no—
109#14556503—21no—
110#14556502—21no—
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C4×#10596831C2311yescharacteristic
115C2×#41×C73—21no—
116C2×M16×C73—21no—
117C2×M16×C73—21no—
118C22×C8×C73—21no—
119C22×C8×C73—21no—
120C4⋊Q8×C73C2×C411yescharacteristic
121#127×C73C2×C411yescharacteristic
122#124×C73—21no—
123#121×C73—21no—
124#121×C73C2×C411yescharacteristic
125#121×C73C2×C411yescharacteristic
126C4×D4×C73—21no—
127C4×D4×C73C2311yescharacteristic
128C4×D4×C73C2311yescharacteristic
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73D411yescharacteristic
140C22⋊C8×C73D411yescharacteristic
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C23×D73—21no—
145C2×D292—22no—
146C2×D292—21no—
147C2×D292—41no—
148C2×D292C22×C411yescharacteristic
149C2×D292C22×C411yescharacteristic
150C22×Dic73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—81no—
156C2×C4×D73—81no—
157#11924013—22no—
158#11924013—22no—
159#11924013—41no—
160#11924013—41no—
161#11924011—81no—
162#11924011—81no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C22×C411yescharacteristic
171C8×D73—81no—
172C8×D73—81no—
173C4⋊Dic73—21no—
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176#11924005—21no—
177#11924005—21no—
178#11924005—21no—
179#11924005—21no—
180#41×C73—81no—
181#41×C73—81no—
182C2×Q8×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73C22×C411yescharacteristic
188C2×D4×C73C22×C411yescharacteristic
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73#4111yescharacteristic
194M16×C73—81no—
195M16×C73—81no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—81no—
199C2×C8×C73—81no—
200C2×C8×C73C2×D411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C2×C8×C73C2×D411yescharacteristic
204C4⋊C4×C73—21no—
205C4⋊C4×C73C22×C411yescharacteristic
206C4⋊C4×C73C22×C411yescharacteristic
207C22⋊C4×C73—21no—
208C22⋊C4×C73—21no—
209C22⋊C4×C73—21no—
210C22⋊C4×C73—21no—
211C42×C73C22×C411yescharacteristic
212C42×C73C2×D411yescharacteristic
213C42×C73#4111yescharacteristic
214C42×C73C2411yescharacteristic
215C23×C73—21no—
216C23×C73—21no—
217C23×C73C4×D411yescharacteristic
218C22×D73—21no—
219C22×D73—21no—
220C22×D73—42no—
221C22×D73—42no—
222C22×D73—81no—
223Q8×C73—81no—
224D4×C73—21no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—21no—
228D4×C73—42no—
229D4×C73—81no—
230D4×C73—81no—
231D4×C73—81no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73C4×D411yescharacteristic
244C2×C4×C73C4×D411yescharacteristic
245C2×C4×C73C4×D411yescharacteristic
246C2×C4×C73C23×C411yescharacteristic
247C2×C4×C73C22×D411yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—81no—
252D292—21no—
253D292—21no—
254D292—21no—
255D292—42no—
256D292#13112yes—
257C4×D73—41no—
258C4×D73—41no—
259C4×D73—41no—
260C4×D73—41no—
261C4×D73—81no—
262C4×D73—81no—
263C8×C73—21no—
264C8×C73—21no—
265C8×C73—21no—
266C8×C73—21no—
267C8×C73—41no—
268C8×C73—41no—
269#10596831—21no—
270#10596831—21no—
271#10596831—21no—
272#10596831—21no—
273#10596831—41no—
274#10596831—41no—
275#10596831—41no—
276#10596831—41no—
277C22×C73—21no—
278C22×C73—21no—
279C22×C73—21no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73—41no—
286C22×C73C2×C4×D411yescharacteristic
287C2×D73—22no—
288C2×D73—41no—
289C2×D73—41no—
290C2×D73—41no—
291C2×D73—41no—
292C2×D73—41no—
293C2×D73—84no—
294C4×C73—21no—
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—41no—
299C4×C73—41no—
300C4×C73C2×#13111yescharacteristic
301C4×C73#56811yescharacteristic
302C4×C73#57611yescharacteristic
303C4×C73#57611yescharacteristic
304Dic73—41no—
305Dic73—41no—
306#18026—731nomaximal, Sylow
307C2×C73—41no—
308C2×C73—81no—
309C2×C73—81no—
310C2×C73#293311yescharacteristic
311C2×C73#294811yescharacteristic
312C2×C73#295511yescharacteristic
313D73—42no—
314D73—81no—
315#3100—731no—
316#2979D7311yescharacteristic, complemented
317#2974—731no—
318#1594—731no—
319#1589—731no—
320#1586—731no—
321#1586—731no—
322#1581—731no—
323#1581—731no—
324#1580—731no—
325C8×D8—731no—
326#1572—731no—
327#1496—731no—
328#1478—731no—
329#1454—731no—
330C73#1802611yescharacteristic, complemented, Sylow
331#532C2×D7311yescharacteristic
332C2×C4×D4—731no—
333#480—731no—
334#480—731no—
335#474—731no—
336#474—731no—
337#459—731no—
338#459—731no—
339#447—731no—
340#447—731no—
341C4×D8—731no—
342C4×D8—731no—
343C4×D8—731no—
344C4×D8—731no—
345#436—21no—
346#436—731no—
347#436—731no—
348#436C2×D7311yescharacteristic, complemented
349#436C2×D7311yescharacteristic, complemented
350#435—1461no—
351#435—1461no—
352C8×D4—21no—
353C8×D4—731no—
354C8×D4—731no—
355C8×D4C2×D7311yescharacteristic, complemented
356C8×D4C2×D7311yescharacteristic, complemented
357#432—731no—
358#431—731no—
359#431—731no—
360#431C2×D7311yescharacteristic
361#431C2×D7311yescharacteristic
362#408—21no—
363#408—21no—
364#407—1461no—
365C2×C22⋊C8—1461no—
366#335—731no—
367#335—731no—
368#334—731no—
369#334—731no—
370D4⋊C8—731no—
371D4⋊C8—731no—
372D4⋊C8—731no—
373D4⋊C8—731no—
374D4⋊C8—731no—
375D4⋊C8—731no—
376D4⋊C8—731no—
377D4⋊C8—731no—
378#322—731no—
379#322—731no—
380#322—731no—
381C82—731no—
382C2×#41—21no—
383C22×D4—731no—
384C23×C4—1461no—
385C2×D8—731no—
386C2×D8—731no—
387C2×D8—731no—
388C2×D8—731no—
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—1461no—
392C2×M16—1461no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—1461no—
396C22×C8—1461no—
397C4⋊Q8C4×D7311yescharacteristic
398#127C4×D7311yescharacteristic
399#124—21no—
400#121—21no—
401#121C4×D7311yescharacteristic
402#121C4×D7311yescharacteristic
403C4×D4—21no—
404C4×D4—731no—
405C4×D4—731no—
406C4×D4—731no—
407C4×D4—731no—
408C4×D4—1461no—
409C4×D4—1461no—
410C4×D4C22×D7311yescharacteristic
411C4×D4C22×D7311yescharacteristic
412C2×C4⋊C4—731no—
413C2×C22⋊C4—1461no—
414C2×C42C22×D7311yescharacteristic
415#107—731no—
416#107—731no—
417#107—731no—
418#107—731no—
419C4⋊C8—731no—
420C4⋊C8—731no—
421C4⋊C8—731no—
422C4⋊C8—731no—
423C4⋊C8—1461no—
424C4⋊C8C22⋊D7311yescharacteristic
425C4⋊C8C22⋊D7311yescharacteristic
426C4⋊C8C22×D7311yescharacteristic
427C4⋊C8C22×D7311yescharacteristic
428#102—731no—
429#102—731no—
430#102—731no—
431#102—731no—
432#102—731no—
433#102—731no—
434#102—731no—
435#102—731no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—731no—
442C22⋊C8—731no—
443C22⋊C8—1461no—
444C22⋊C8—1461no—
445C22⋊C8—1461no—
446C22⋊C8—1461no—
447C22⋊C8—1461no—
448C22⋊C8—1461no—
449C22⋊C8C22⋊D7311yescharacteristic
450C22⋊C8C22⋊D7311yescharacteristic
451#97—1461no—
452C4×C8—21no—
453C4×C8—731no—
454C4×C8—731no—
455C4×C8—731no—
456C4×C8—731no—
457C4×C8C22×D7311yescharacteristic
458C4×C8C22×D7311yescharacteristic
459C24—1461no—
460#41—81no—
461#41—81no—
462C2×Q8—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—2921no—
468C2×D4—731no—
469C2×D4—731no—
470C2×D4—1462no—
471C2×D4—1461no—
472C2×D4C2×C4×D7311yescharacteristic
473C2×D4C2×C4×D7311yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—5841no—
477C22×C4—5841no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4C2×C4×D7311yescharacteristic
484C22×C4C2×C22⋊D7311yescharacteristic
485C22×C4#1192402811yescharacteristic
486D8—2921no—
487D8—2921no—
488D8—1462no—
489D8—1462no—
490M16—81no—
491M16—81no—
492M16—5841no—
493M16—5841no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—81no—
497C2×C8—81no—
498C2×C8—5841no—
499C2×C8—5841no—
500C2×C8—731no—
501C2×C8—731no—
502C2×C8—731no—
503C2×C8—731no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8C2×C22⋊D7311yescharacteristic
509C2×C8C2×C22⋊D7311yescharacteristic
510C2×C8C2×C22⋊D7311yescharacteristic
511C2×C8C2×C22⋊D7311yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—731no—
514C4⋊C4—731no—
515C4⋊C4—1461no—
516C4⋊C4C2×C4×D7311yescharacteristic
517C4⋊C4C2×C4×D7311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—1461no—
523C22⋊C4—1461no—
524C22⋊C4—1461no—
525C22⋊C4—1461no—
526C42C2×C4×D7311yescharacteristic
527C42C2×C22⋊D7311yescharacteristic
528C42#1192402811yescharacteristic
529C42C23×D7311yescharacteristic
530C23—21no—
531C23—21no—
532C23—2922no—
533C23—2922no—
534C23—5841no—
535C23—1461no—
536C23—1461no—
537C23C4×C22⋊D7311yescharacteristic
538Q8—81no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—42no—
544D4—81no—
545D4—81no—
546D4—81no—
547D4—2922no—
548D4—732no—
549D4—1461no—
550D4—1461no—
551D4—1461no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—5841no—
568C2×C4—5841no—
569C2×C4—5841no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4C4×C22⋊D7311yescharacteristic
573C2×C4C4×C22⋊D7311yescharacteristic
574C2×C4C4×C22⋊D7311yescharacteristic
575C2×C4C22×C4×D7311yescharacteristic
576C2×C4C22×C22⋊D7311yescharacteristic
577C2×C4C2×#1192402811yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—2921no—
585C8—2921no—
586C8—2921no—
587C8—2921no—
588C8—1461no—
589C8—1461no—
590C8—1461no—
591C8—1461no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—2921no—
602C22—2921no—
603C22—2921no—
604C22—2921no—
605C22—2921no—
606C22—5844no—
607C22—1462no—
608C22C2×C4×C22⋊D7311yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—2921no—
616C4—2921no—
617C4#131×D7311yescharacteristic
618C4#1798935211yescharacteristic
619C4#1798939011yescharacteristic
620C4#1798939011yescharacteristic
621C2—41no—
622C2—81no—
623C2—81no—
624C2—2922no—
625C2—5841no—
626C2#2261865311yescharacteristic
627C2#2261878111yescharacteristic
628C2#2261883211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2979C2
socleC22×C73C2×C4×D4
prime radical#22619927C2
cosocleC42×C73C24
hypercenter#2979D73
hypocenterC73#18026
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #22618965C2semidirect
3. #22608843C2semidirect
4. #22608814C2semidirect
5. #22608795C2semidirect
6. #22608793C2semidirect
7. #22608760C2semidirect
8. #22608758C2semidirect
9. #22608753C2semidirect
10. C8×#11924013C2semidirect
11. #22608709C2semidirect
12. #22608400C2semidirect
13. #22608321C2semidirect
14. #22608231C2semidirect
15. C73×#2979C2semidirect
40. #17988339C22semidirect
41. #17988339C22semidirect
42. #17988337C22semidirect
43. #17988337C22semidirect
44. D4⋊#10596831C22semidirect
45. D4⋊#10596831C22semidirect
46. D4⋊#10596831C22semidirect
47. D4⋊#10596831C22semidirect
52. #17988309C22semidirect
53. #17988309C22semidirect
54. #17988308C22semidirect
55. C8×#10596831C22semidirect
58. #436×C73C22semidirect
59. #436×C73C22semidirect
61. C8×D4×C73C22semidirect
62. C8×D4×C73C22semidirect
316. #2979D73semidirect
330. C73#18026semidirect
348. #436C2×D73semidirect
349. #436C2×D73semidirect
355. C8×D4C2×D73semidirect
356. C8×D4C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199272
#226189652
#226088432
#226088142
#226087952
#226087932
#226087602
#226087582
#226087532
C8×#119240132
#226087092
#226084002
#226083212
#226082312
C73×#29792
#1802673