Finite Group Databasebeta

← #33057218

Subgroups — #33057218

Order 18688.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619980C211yesmaximal, characteristic
2#22619093C211yesmaximal, characteristic, complemented
3#22618965C211yesmaximal, characteristic, complemented
4#22608846C211yesmaximal, characteristic, complemented
5#22608835C211yesmaximal, characteristic, complemented
6#22608776C211yesmaximal, characteristic, complemented
7#22608769C211yesmaximal, characteristic, complemented
8#22608762C211yesmaximal, characteristic, complemented
9#22608762C211yesmaximal, characteristic, complemented
10#22608756C211yesmaximal, characteristic, complemented
11#22608745C211yesmaximal, characteristic, complemented
12#22608716C211yesmaximal, characteristic, complemented
13#22608392C211yesmaximal, characteristic, complemented
14C2×#17988316C211yesmaximal, characteristic, complemented
15C73×#1452C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18#17988923C411yescharacteristic
19#17988906C411yescharacteristic
20#17988888C411yescharacteristic
21#17988888C411yescharacteristic
22#17988803C411yescharacteristic
23#17988803C411yescharacteristic
24#17988740C411yescharacteristic
25#17988723C411yescharacteristic
26#17988717C2211yescharacteristic, complemented
27C8×Dic146C2211yescharacteristic, complemented
28C4×#11924017C2211yescharacteristic
29C4×#11924017C2211yescharacteristic
30C4×D584C2211yescharacteristic
31C4×D584C2211yescharacteristic
32#17988666C2211yescharacteristic
33#17988666C2211yescharacteristic
34#17988666C2211yescharacteristic, complemented
35#17988657—21no—
36#17988657—21no—
37#17988655—21no—
38C8×D292C2211yescharacteristic
39C8×D292C2211yescharacteristic
40C8×D292C2211yescharacteristic, complemented
41#17988650—21no—
42#17988647—21no—
43#17988644C2211yescharacteristic
44#17988612—21no—
45C2×C4⋊#10596831C2211yescharacteristic
46#17988549—21no—
47C22⋊C8×D73—21no—
48#17988340C2211yescharacteristic, complemented
49#17988340C2211yescharacteristic, complemented
50#17988338C2211yescharacteristic, complemented
51#17988338C2211yescharacteristic, complemented
52#17988319C2211yescharacteristic, complemented
53#17988319C2211yescharacteristic, complemented
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988316C2211yescharacteristic
57#17988316C2211yescharacteristic
58#17988316C2211yescharacteristic, complemented
59#17988316C2211yescharacteristic, complemented
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic, complemented
64#322×C73C2211yescharacteristic, complemented
65#322×C73C2211yescharacteristic, complemented
66#322×C73C2211yescharacteristic, complemented
67C22×D292C2×C411yescharacteristic
68C22×C4×D73—21no—
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×D584C2×C411yescharacteristic
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×#11924011—21no—
76C22×#10596831—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80#14556585—21no—
81#14556583C2×C411yescharacteristic
82#14556579C2×C411yescharacteristic
83#14556574—21no—
84#14556570C2×C411yescharacteristic
85#14556565C2×C411yescharacteristic
86C4×Dic146C2311yescharacteristic
87C4×D292—21no—
88C4×D292—21no—
89C4×D292C2×C411yescharacteristic
90C4×D292C2×C411yescharacteristic
91C4×D292C2311yescharacteristic
92C4×D292C2311yescharacteristic
93C4×D292C2311yescharacteristic
94C4×C22⋊D73—21no—
95#14556548—21no—
96C2×C4⋊Dic73C2×C411yescharacteristic
97C2×#11924005—21no—
98#14556525C2×C411yescharacteristic
99#14556525C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101#14556523C2×C411yescharacteristic
102C4⋊#10596831—21no—
103C4⋊#10596831C2311yescharacteristic
104C4⋊#10596831C2311yescharacteristic
105C4⋊#10596831C2311yescharacteristic
106C4⋊#10596831C2311yescharacteristic
107#14556520—21no—
108#14556520—21no—
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556513C2×C411yescharacteristic
115#14556513C2×C411yescharacteristic
116#14556513C2×C411yescharacteristic
117C22⋊#10596831—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556503—21no—
122#14556503—21no—
123#14556503—21no—
124#14556502—21no—
125#14556501—21no—
126C8×Dic73—21no—
127C22×C8×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C22⋊C8×C73C2×C411yescharacteristic
134C22⋊C8×C73C2×C411yescharacteristic
135C22⋊C8×C73D411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137C4×C8×C73—21no—
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C23×D73—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×D292—22no—
147C2×D292—21no—
148C2×D292—41no—
149C2×D292C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×D292C22×C411yescharacteristic
152C2×C22⋊D73—21no—
153C22×Dic73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—81no—
160C2×C4×D73—81no—
161#11924017—22no—
162#11924017—41no—
163D584—22no—
164D584—41no—
165#11924011—81no—
166#11924011—81no—
167#11924011—81no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—81no—
173C8×D73—81no—
174C8×D73—81no—
175C8×D73—81no—
176C4⋊Dic73—21no—
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179C4⋊Dic73C22×C411yescharacteristic
180C4⋊Dic73C22×C411yescharacteristic
181#11924007—21no—
182#11924007—21no—
183#11924007—21no—
184#11924007—21no—
185C22⋊Dic73—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190#11924005—21no—
191#11924005—21no—
192#11924005—21no—
193#11924005—21no—
194C4×Dic73—21no—
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73#4111yescharacteristic
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—42no—
201C2×C8×C73C22×C411yescharacteristic
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C2×C8×C73C2×D411yescharacteristic
208C2×C8×C73C2×D411yescharacteristic
209C42×C73C22×C411yescharacteristic
210C42×C73C2×D411yescharacteristic
211C42×C73#4111yescharacteristic
212C42×C73C2411yescharacteristic
213C23×C73C4×D411yescharacteristic
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C22×D73—42no—
218C22×D73—42no—
219C22×D73—81no—
220C2×C4×C73—22no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C4×D411yescharacteristic
228C2×C4×C73C23×C411yescharacteristic
229C2×C4×C73C22×D411yescharacteristic
230C2×C4×C73C2×#4111yescharacteristic
231C22⋊D73—42no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—81no—
238D292—21no—
239D292—21no—
240D292—21no—
241D292—21no—
242D292—21no—
243D292—42no—
244D292#13112yes—
245C4×D73—41no—
246C4×D73—41no—
247C4×D73—41no—
248C4×D73—41no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—81no—
252C4×D73—81no—
253Dic146—21no—
254Dic146—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—21no—
260C8×C73—21no—
261C8×C73—21no—
262C8×C73—21no—
263C8×C73—41no—
264C8×C73—41no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268#10596831—41no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73#44412yes—
272C22×C73C2×C4×D411yescharacteristic
273C2×D73—22no—
274C2×D73—41no—
275C2×D73—41no—
276C2×D73—41no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—41no—
282C2×D73—84no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—21no—
287C4×C73C2×#13111yescharacteristic
288C4×C73#56811yescharacteristic
289C4×C73#57611yescharacteristic
290C4×C73#57711yescharacteristic
291Dic73—41no—
292Dic73—41no—
293Dic73—41no—
294Dic73—41no—
295Dic73—41no—
296#18020—731nomaximal, Sylow
297C2×C73—22no—
298C2×C73#293311yescharacteristic
299C2×C73#294611yescharacteristic
300C2×C73C2×#44411yescharacteristic
301D73—42no—
302D73—81no—
303D73—81no—
304#3105—731no—
305#2994—731no—
306#2974—731no—
307#1594—731no—
308#1592—731no—
309#1583—731no—
310#1582—731no—
311#1581—731no—
312#1581—731no—
313#1580—731no—
314SD16⋊C8—731no—
315#1573—731no—
316#1494—731no—
317C2×D4⋊C8—731no—
318#1452D7311yescharacteristic, complemented
319C73#1802011yescharacteristic, complemented, Sylow
320#529—731no—
321C2×C4×D4—731no—
322#484—731no—
323#481—731no—
324#478—731no—
325#478—731no—
326#463—731no—
327#463—731no—
328#450—731no—
329#447—731no—
330#446—731no—
331C8×Q8—731no—
332C4×SD16—731no—
333C4×SD16—731no—
334C4×D8—731no—
335C4×D8—731no—
336#436—731no—
337#436—731no—
338#436—731no—
339#435—1461no—
340#435—1461no—
341#435—1461no—
342C8×D4—731no—
343C8×D4—731no—
344C8×D4—731no—
345C8×D4—1461no—
346#433—1461no—
347#432—731no—
348#431C2×D7311yescharacteristic
349#431C2×D7311yescharacteristic
350#424—1461no—
351C2×C4⋊C8—731no—
352#407—1461no—
353C2×C22⋊C8—1461no—
354C2×C4×C8C2×D7311yescharacteristic
355#335—731no—
356#335—731no—
357#334—731no—
358#334—731no—
359Q8⋊C8—731no—
360Q8⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
366D4⋊C8—731no—
367#322C2×D7311yescharacteristic, complemented
368#322C2×D7311yescharacteristic, complemented
369#322C2×D7311yescharacteristic, complemented
370#322C2×D7311yescharacteristic, complemented
371C22×D4—731no—
372C23×C4—1461no—
373C2×SD16—731no—
374C2×SD16—731no—
375C2×D8—731no—
376C2×D8—731no—
377C2×M16—1461no—
378C2×M16—1461no—
379C2×M16—1461no—
380C22×C8—21no—
381C22×C8—1461no—
382C22×C8—1461no—
383C22×C8—1461no—
384C22×C8—1461no—
385#126—1461no—
386#125—731no—
387#124—731no—
388#123—1461no—
389C22⋊Q8—731no—
390#121—731no—
391C4×Q8—731no—
392C4×D4—731no—
393C4×D4—731no—
394C4×D4—731no—
395C4×D4—731no—
396C4×D4—731no—
397C4×D4—1461no—
398C4×D4—1461no—
399C4×D4—1461no—
400#117—1461no—
401C2×C4⋊C4—731no—
402C2×C22⋊C4—1461no—
403C2×C42C22×D7311yescharacteristic
404#107—731no—
405#107—731no—
406#106—731no—
407#106—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8—1461no—
415C4⋊C8C4×D7311yescharacteristic
416C4⋊C8C4×D7311yescharacteristic
417C4⋊C8D29211yescharacteristic
418C4⋊C8D29211yescharacteristic
419#103—731no—
420#103—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102—731no—
426#102—731no—
427C22⋊C8—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8C4×D7311yescharacteristic
435C22⋊C8C4×D7311yescharacteristic
436C22⋊C8D29211yescharacteristic
437C22⋊C8D29211yescharacteristic
438#97—1461no—
439#97—1461no—
440C4×C8—21no—
441C4×C8—1461no—
442C4×C8C22×D7311yescharacteristic
443C4×C8C22×D7311yescharacteristic
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446C4×C8C22×D7311yescharacteristic
447C4×C8C22×D7311yescharacteristic
448C24—1461no—
449C2×Q8—731no—
450C2×D4—2921no—
451C2×D4—731no—
452C2×D4—731no—
453C2×D4—731no—
454C2×D4—1462no—
455C2×D4—1461no—
456C2×D4—1461no—
457C22×C4—5841no—
458C22×C4—5841no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4—1461no—
465C22×C4C2×C4×D7311yescharacteristic
466C22×C4C2×D29211yescharacteristic
467C22×C4#1192402811yescharacteristic
468SD16—2921no—
469SD16—1462no—
470D8—2921no—
471D8—1462no—
472M16—5841no—
473M16—5841no—
474M16—5841no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—5841no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8C2×C4×D7311yescharacteristic
487C2×C8C2×C4×D7311yescharacteristic
488C2×C8C2×C4×D7311yescharacteristic
489C2×C8C2×C4×D7311yescharacteristic
490C2×C8C2×D29211yescharacteristic
491C2×C8C2×D29211yescharacteristic
492C2×C8C2×D29211yescharacteristic
493C2×C8C2×D29211yescharacteristic
494C4⋊C4—731no—
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—731no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4—1461no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C22⋊C4—1461no—
511C22⋊C4—1461no—
512C42—1461no—
513C42C2×C4×D7311yescharacteristic
514C42C2×D29211yescharacteristic
515C42#1192402811yescharacteristic
516C42C23×D7311yescharacteristic
517C23—2922no—
518C23—2922no—
519C23—5841no—
520C23—1461no—
521C23—1461no—
522C23—1461no—
523C23C4×D29211yescharacteristic
524Q8—1461no—
525Q8—1461no—
526D4—2922no—
527D4—2922no—
528D4—732no—
529D4—1461no—
530D4—1461no—
531D4—1461no—
532D4—1461no—
533D4—1461no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—5841no—
546C2×C4—5841no—
547C2×C4—5841no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4C4×D29211yescharacteristic
554C2×C4C4×D29211yescharacteristic
555C2×C4C4×D29211yescharacteristic
556C2×C4C22×C4×D7311yescharacteristic
557C2×C4C22×D29211yescharacteristic
558C2×C4C2×#1192402811yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—2921no—
570C8—2921no—
571C8—2921no—
572C8—2921no—
573C22—21no—
574C22—21no—
575C22—2921no—
576C22—2921no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22—2921no—
581C22—2921no—
582C22—2921no—
583C22—5844no—
584C22—1462no—
585C22#1798871012yes—
586C22C2×C4×D29211yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—2921no—
592C4—2921no—
593C4—2921no—
594C4—2921no—
595C4—2921no—
596C4#131×D7311yescharacteristic
597C4#1798935211yescharacteristic
598C4#1798939211yescharacteristic
599C4#1798939911yescharacteristic
600C2—22no—
601C2—2922no—
602C2—5841no—
603C2—5841no—
604C2#2261865911yescharacteristic
605C2#2261876511yescharacteristic
606C2C2×#1798871011yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1452C2
socleC22×C73C2×C4×D4
prime radical#17988723C4
cosocleC42×C73C24
hypercenter#1452D73
hypocenterC73#18020
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1452

Complements

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

NH ≅ G/Ntype
2. #22619093C2semidirect
3. #22618965C2semidirect
4. #22608846C2semidirect
5. #22608835C2semidirect
6. #22608776C2semidirect
7. #22608769C2semidirect
8. #22608762C2semidirect
9. #22608762C2semidirect
10. #22608756C2semidirect
11. #22608745C2semidirect
12. #22608716C2semidirect
13. #22608392C2semidirect
14. C2×#17988316C2semidirect
15. C73×#1452C2semidirect
26. #17988717C22semidirect
27. C8×Dic146C22semidirect
34. #17988666C22semidirect
40. C8×D292C22semidirect
48. #17988340C22semidirect
49. #17988340C22semidirect
50. #17988338C22semidirect
51. #17988338C22semidirect
52. #17988319C22semidirect
53. #17988319C22semidirect
58. #17988316C22semidirect
59. #17988316C22semidirect
63. #322×C73C22semidirect
64. #322×C73C22semidirect
65. #322×C73C22semidirect
66. #322×C73C22semidirect
318. #1452D73semidirect
319. C73#18020semidirect
367. #322C2×D73semidirect
368. #322C2×D73semidirect
369. #322C2×D73semidirect
370. #322C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199802
#226190932
#226189652
#226088462
#226088352
#226087762
#226087692
#226087622
#226087562
#226087452
#226087162
#226083922
C2×#179883162
C73×#14522
#1802073