Finite Group Databasebeta

← #33057292

Subgroups — #33057292

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#22619932C211yesmaximal, characteristic
2#22618997C211yesmaximal, characteristic, complemented
3#22618965C211yesmaximal, characteristic, complemented
4#22608846C211yesmaximal, characteristic, complemented
5#22608817C211yesmaximal, characteristic, complemented
6#22608797C211yesmaximal, characteristic, complemented
7#22608797C211yesmaximal, characteristic, complemented
8#22608762C211yesmaximal, characteristic, complemented
9#22608762C211yesmaximal, characteristic, complemented
10#22608756C211yesmaximal, characteristic, complemented
11C8×D584C211yesmaximal, characteristic, complemented
12#22608711C211yesmaximal, characteristic, complemented
13#22608401C211yesmaximal, characteristic, complemented
14#22608323C211yesmaximal, characteristic, complemented
15C73×#1454C211yesmaximal, characteristic, complemented
16#17989137C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18#17988901C411yescharacteristic
19#17988901C411yescharacteristic
20#17988868C411yescharacteristic
21#17988868C411yescharacteristic
22#17988783C411yescharacteristic
23#17988783C411yescharacteristic
24#17988723C411yescharacteristic
25#17988723C411yescharacteristic
26C4×D584C2211yescharacteristic
27C4×D584C2211yescharacteristic
28C4×D584C2211yescharacteristic
29C4×D584C2211yescharacteristic
30#17988666C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988666C2211yescharacteristic, complemented
33#17988666C2211yescharacteristic, complemented
34#17988664—21no—
35#17988657—21no—
36#17988657—21no—
37C8×D292C2211yescharacteristic
38C8×D292C2211yescharacteristic
39C8×D292C2211yescharacteristic, complemented
40C8×D292C2211yescharacteristic, complemented
41#17988652—21no—
42#17988644C2211yescharacteristic
43#17988640C2211yescharacteristic
44#17988552—21no—
45#17988552—21no—
46#17988549—21no—
47C22⋊C8×D73—21no—
48#17988340C2211yescharacteristic, complemented
49#17988340C2211yescharacteristic, complemented
50#17988338C2211yescharacteristic, complemented
51#17988338C2211yescharacteristic, complemented
52#17988316C2211yescharacteristic
53#17988316C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988316C2211yescharacteristic, complemented
57#17988316C2211yescharacteristic, complemented
58#17988316C2211yescharacteristic, complemented
59#17988316C2211yescharacteristic, complemented
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic, complemented
64#322×C73C2211yescharacteristic, complemented
65#322×C73C2211yescharacteristic, complemented
66C82×C73C2211yescharacteristic, complemented
67C2×#11924028—21no—
68C22×D292C2×C411yescharacteristic
69C22×C4×D73—21no—
70C2×D584C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×D584C2×C411yescharacteristic
73C2×D584C2×C411yescharacteristic
74C2×#11924011—21no—
75C2×#11924011—21no—
76C2×#11924011—21no—
77C2×#11924011—21no—
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80C2×C8×D73—21no—
81C2×C8×D73—21no—
82#14556591C2×C411yescharacteristic
83#14556588C2×C411yescharacteristic
84#14556579—21no—
85#14556565—21no—
86#14556565C2×C411yescharacteristic
87#14556565C2×C411yescharacteristic
88C4×D292—21no—
89C4×D292—21no—
90C4×D292—21no—
91C4×D292C2×C411yescharacteristic
92C4×D292C2×C411yescharacteristic
93C4×D292C2311yescharacteristic
94C4×D292C2311yescharacteristic
95C4×D292C2311yescharacteristic
96C4×D292C2311yescharacteristic
97C2×C4⋊Dic73C2×C411yescharacteristic
98C2×#11924005—21no—
99#14556525C2×C411yescharacteristic
100#14556525C2×C411yescharacteristic
101#14556525C2×C411yescharacteristic
102#14556525C2×C411yescharacteristic
103C4⋊#10596831C2311yescharacteristic
104C4⋊#10596831C2311yescharacteristic
105C4⋊#10596831C2311yescharacteristic
106C4⋊#10596831C2311yescharacteristic
107#14556513C2×C411yescharacteristic
108#14556513C2×C411yescharacteristic
109#14556513C2×C411yescharacteristic
110#14556513C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556513C2×C411yescharacteristic
115C22⋊#10596831—21no—
116C22⋊#10596831—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556503—21no—
122#14556503—21no—
123#14556503—21no—
124#14556503—21no—
125#14556502—21no—
126C4×#10596831—21no—
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73—21no—
129C4⋊C8×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C22⋊C8×C73—21no—
134C22⋊C8×C73C2×C411yescharacteristic
135C22⋊C8×C73C2×C411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137C22⋊C8×C73D411yescharacteristic
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C23×D73—21no—
145#11924028—81no—
146#11924028—81no—
147C2×Dic146—21no—
148C2×D292—22no—
149C2×D292—21no—
150C2×D292—21no—
151C2×D292—21no—
152C2×D292—41no—
153C2×D292C22×C411yescharacteristic
154C2×D292C22×C411yescharacteristic
155C2×D292C22×C411yescharacteristic
156C2×D292C22×C411yescharacteristic
157C2×C22⋊D73—21no—
158C2×C22⋊D73—21no—
159C22×Dic73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—81no—
167C2×C4×D73—81no—
168D584—22no—
169D584—22no—
170D584—41no—
171D584—41no—
172#11924011—81no—
173#11924011—81no—
174#11924011—81no—
175#11924011—81no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C8×D73—81no—
181C8×D73—81no—
182C8×D73—81no—
183C8×D73—81no—
184C4⋊Dic73—21no—
185C4⋊Dic73—21no—
186C4⋊Dic73C22×C411yescharacteristic
187C4⋊Dic73C22×C411yescharacteristic
188C4⋊Dic73C22×C411yescharacteristic
189C4⋊Dic73C22×C411yescharacteristic
190#11924005—21no—
191#11924005—21no—
192#11924005—21no—
193#11924005—21no—
194#11924005—21no—
195#11924005—21no—
196#11924005—21no—
197#11924005—21no—
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73#4111yescharacteristic
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C2×C8×C73C22×C411yescharacteristic
207C2×C8×C73C2×D411yescharacteristic
208C2×C8×C73C2×D411yescharacteristic
209C2×C8×C73C2×D411yescharacteristic
210C2×C8×C73C2×D411yescharacteristic
211C42×C73C22×C411yescharacteristic
212C42×C73C2×D411yescharacteristic
213C42×C73#4111yescharacteristic
214C42×C73C2411yescharacteristic
215C23×C73C4×D411yescharacteristic
216C22×D73—21no—
217C22×D73—21no—
218C22×D73—21no—
219C22×D73—21no—
220C22×D73—42no—
221C22×D73—42no—
222C22×D73—81no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—41no—
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C23×C411yescharacteristic
232C2×C4×C73C22×D411yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C22⋊D73—81no—
235C22⋊D73—81no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—81no—
241D292—21no—
242D292—21no—
243D292—21no—
244D292—21no—
245D292—21no—
246D292—21no—
247D292—21no—
248D292—42no—
249D292—42no—
250D292—81no—
251D292#13112yes—
252C4×D73—41no—
253C4×D73—41no—
254C4×D73—41no—
255C4×D73—41no—
256C4×D73—41no—
257C4×D73—41no—
258C4×D73—41no—
259C4×D73—41no—
260C4×D73—81no—
261C4×D73—81no—
262Dic146—81no—
263C8×C73—21no—
264C8×C73—21no—
265C8×C73—21no—
266C8×C73—21no—
267C8×C73—21no—
268C8×C73—21no—
269C8×C73—21no—
270C8×C73—21no—
271C8×C73—41no—
272C8×C73—41no—
273#10596831—41no—
274#10596831—41no—
275#10596831—41no—
276#10596831—41no—
277C22×C73—21no—
278C22×C73—21no—
279C22×C73—21no—
280C22×C73C2×C4×D411yescharacteristic
281C2×D73—22no—
282C2×D73—41no—
283C2×D73—41no—
284C2×D73—41no—
285C2×D73—41no—
286C2×D73—41no—
287C2×D73—41no—
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×C73C2×#13111yescharacteristic
299C4×C73#56811yescharacteristic
300C4×C73#57611yescharacteristic
301C4×C73#57611yescharacteristic
302Dic73—41no—
303Dic73—41no—
304Dic73—41no—
305Dic73—41no—
306#18026—731nomaximal, Sylow
307C2×C73—41no—
308C2×C73#293311yescharacteristic
309C2×C73#294811yescharacteristic
310C2×C73#295511yescharacteristic
311D73—42no—
312D73—81no—
313D73—81no—
314D73—81no—
315#3100—731no—
316#2979—731no—
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#1454D7311yescharacteristic, complemented
330C73#1802611yescharacteristic, complemented, Sylow
331#532—731no—
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—731no—
346#436—731no—
347#436—731no—
348#436—731no—
349#436—1461no—
350#435—1461no—
351#435—1461no—
352C8×D4—731no—
353C8×D4—731no—
354C8×D4—731no—
355C8×D4—731no—
356C8×D4—1461no—
357#432—731no—
358#431—731no—
359#431C2×D7311yescharacteristic
360#431C2×D7311yescharacteristic
361#431C2×D7311yescharacteristic
362#408—1461no—
363#408—1461no—
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#322C2×D7311yescharacteristic, complemented
379#322C2×D7311yescharacteristic, complemented
380#322C2×D7311yescharacteristic, complemented
381C82C2×D7311yescharacteristic, complemented
382C2×#41—1461no—
383C22×D4—731no—
384C23×C4—1461no—
385C2×D8—731no—
386C2×D8—731no—
387C2×D8—731no—
388C2×D8—731no—
389C2×M16—1461no—
390C2×M16—1461no—
391C2×M16—1461no—
392C2×M16—1461no—
393C22×C8—1461no—
394C22×C8—1461no—
395C22×C8—1461no—
396C22×C8—1461no—
397C4⋊Q8—731no—
398#127—731no—
399#124—1461no—
400#121—731no—
401#121—731no—
402#121—1461no—
403C4×D4—731no—
404C4×D4—731no—
405C4×D4—731no—
406C4×D4—731no—
407C4×D4—731no—
408C4×D4—731no—
409C4×D4—1461no—
410C4×D4—1461no—
411C4×D4—1461no—
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—21no—
420C4⋊C8—731no—
421C4⋊C8—731no—
422C4⋊C8—731no—
423C4⋊C8—731no—
424C4⋊C8C4×D7311yescharacteristic
425C4⋊C8C4×D7311yescharacteristic
426C4⋊C8D29211yescharacteristic
427C4⋊C8D29211yescharacteristic
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—1461no—
438C22⋊C8—1461no—
439C22⋊C8—1461no—
440C22⋊C8—1461no—
441C22⋊C8—1461no—
442C22⋊C8—1461no—
443C22⋊C8—1461no—
444C22⋊C8—1461no—
445C22⋊C8—1461no—
446C22⋊C8—1461no—
447C22⋊C8C4×D7311yescharacteristic
448C22⋊C8C4×D7311yescharacteristic
449C22⋊C8D29211yescharacteristic
450C22⋊C8D29211yescharacteristic
451#97—1461no—
452C4×C8—1461no—
453C4×C8C22×D7311yescharacteristic
454C4×C8C22×D7311yescharacteristic
455C4×C8C22×D7311yescharacteristic
456C4×C8C22×D7311yescharacteristic
457C4×C8C22×D7311yescharacteristic
458C4×C8C22×D7311yescharacteristic
459C24—1461no—
460#41—5841no—
461#41—5841no—
462C2×Q8—1461no—
463C2×D4—2921no—
464C2×D4—731no—
465C2×D4—731no—
466C2×D4—731no—
467C2×D4—731no—
468C2×D4—1462no—
469C2×D4—1461no—
470C2×D4—1461no—
471C2×D4—1461no—
472C2×D4—1461no—
473C2×D4—1461no—
474C22×C4—5841no—
475C22×C4—5841no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4C2×C4×D7311yescharacteristic
484C22×C4C2×D29211yescharacteristic
485C22×C4#1192402811yescharacteristic
486D8—2921no—
487D8—2921no—
488D8—1462no—
489D8—1462no—
490M16—5841no—
491M16—5841no—
492M16—5841no—
493M16—5841no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—5841no—
497C2×C8—5841no—
498C2×C8—5841no—
499C2×C8—5841no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8—1461no—
503C2×C8—1461no—
504C2×C8C2×C4×D7311yescharacteristic
505C2×C8C2×C4×D7311yescharacteristic
506C2×C8C2×C4×D7311yescharacteristic
507C2×C8C2×C4×D7311yescharacteristic
508C2×C8C2×D29211yescharacteristic
509C2×C8C2×D29211yescharacteristic
510C2×C8C2×D29211yescharacteristic
511C2×C8C2×D29211yescharacteristic
512C4⋊C4—731no—
513C4⋊C4—731no—
514C4⋊C4—731no—
515C4⋊C4—731no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C22⋊C4—1461no—
519C22⋊C4—1461no—
520C22⋊C4—1461no—
521C22⋊C4—1461no—
522C22⋊C4—1461no—
523C22⋊C4—1461no—
524C22⋊C4—1461no—
525C22⋊C4—1461no—
526C42C2×C4×D7311yescharacteristic
527C42C2×D29211yescharacteristic
528C42#1192402811yescharacteristic
529C42C23×D7311yescharacteristic
530C23—2922no—
531C23—2922no—
532C23—5841no—
533C23—1461no—
534C23—1461no—
535C23—1461no—
536C23—1461no—
537C23C4×D29211yescharacteristic
538Q8—5841no—
539D4—2922no—
540D4—2922no—
541D4—5841no—
542D4—5841no—
543D4—5841no—
544D4—732no—
545D4—1461no—
546D4—1461no—
547D4—1461no—
548D4—1461no—
549D4—1461no—
550D4—1461no—
551D4—1461no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—5841no—
566C2×C4—5841no—
567C2×C4—5841no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4C4×D29211yescharacteristic
573C2×C4C4×D29211yescharacteristic
574C2×C4C4×D29211yescharacteristic
575C2×C4C22×C4×D7311yescharacteristic
576C2×C4C22×D29211yescharacteristic
577C2×C4C2×#1192402811yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—2921no—
589C8—2921no—
590C8—2921no—
591C8—2921no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—2921no—
596C22—2921no—
597C22—2921no—
598C22—2921no—
599C22—2921no—
600C22—2921no—
601C22—2921no—
602C22—2921no—
603C22—2921no—
604C22—2921no—
605C22—2921no—
606C22—5844no—
607C22—1462no—
608C22C2×C4×D29211yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—2921no—
614C4—2921no—
615C4—2921no—
616C4—2921no—
617C4#131×D7311yescharacteristic
618C4#1798935211yescharacteristic
619C4#1798939211yescharacteristic
620C4#1798939211yescharacteristic
621C2—41no—
622C2—2922no—
623C2—5841no—
624C2—5841no—
625C2—5841no—
626C2#2261865911yescharacteristic
627C2#2261878411yescharacteristic
628C2#2261883511yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1454C2
socleC22×C73C2×C4×D4
prime radical#22619932C2
cosocleC42×C73C24
hypercenter#1454D73
hypocenterC73#18026
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #22618997C2semidirect
3. #22618965C2semidirect
4. #22608846C2semidirect
5. #22608817C2semidirect
6. #22608797C2semidirect
7. #22608797C2semidirect
8. #22608762C2semidirect
9. #22608762C2semidirect
10. #22608756C2semidirect
11. C8×D584C2semidirect
12. #22608711C2semidirect
13. #22608401C2semidirect
14. #22608323C2semidirect
15. C73×#1454C2semidirect
32. #17988666C22semidirect
33. #17988666C22semidirect
39. C8×D292C22semidirect
40. C8×D292C22semidirect
48. #17988340C22semidirect
49. #17988340C22semidirect
50. #17988338C22semidirect
51. #17988338C22semidirect
56. #17988316C22semidirect
57. #17988316C22semidirect
58. #17988316C22semidirect
59. #17988316C22semidirect
63. #322×C73C22semidirect
64. #322×C73C22semidirect
65. #322×C73C22semidirect
66. C82×C73C22semidirect
329. #1454D73semidirect
330. C73#18026semidirect
378. #322C2×D73semidirect
379. #322C2×D73semidirect
380. #322C2×D73semidirect
381. C82C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199322
#226189972
#226189652
#226088462
#226088172
#226087972
#226087622
#226087562
C8×D5842
#226087112
#226084012
#226083232
C73×#14542
#1802673