Finite Group Databasebeta

← #34019320

Subgroups — #34019320

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#22626811C211yesmaximal, characteristic, complemented
2#22626787C211yesmaximal, characteristic, complemented
3#22625579C211yesmaximal, characteristic, complemented
4#22625564C211yesmaximal, characteristic, complemented
5#22625553C211yesmaximal, characteristic, complemented
6#22625552C211yesmaximal, characteristic, complemented
7#22625532C211yesmaximal, characteristic, complemented
8#22625530C211yesmaximal, characteristic, complemented
9#22625527C211yesmaximal, characteristic, complemented
10#22625511C211yesmaximal, characteristic, complemented
11#22625502C211yesmaximal, characteristic, complemented
12#22625290C211yesmaximal, characteristic, complemented
13#22625230C211yesmaximal, characteristic, complemented
14#22625152C211yesmaximal, characteristic, complemented
15#22619926C211yesmaximal, characteristic
16#17989622C2211yescharacteristic
17#17989622C2211yescharacteristic
18#17989622C2211yescharacteristic, complemented
19#17989621C2211yescharacteristic, complemented
20#17989620—21no—
21#17989618—21no—
22#17989618—21no—
23#17989615C2211yescharacteristic, complemented
24#17989614—21no—
25D4×#10596833C2211yescharacteristic
26D4×#10596833C2211yescharacteristic
27D4×#10596833C2211yescharacteristic, complemented
28#17989608C2211yescharacteristic
29#17989604C2211yescharacteristic
30#17989603C2211yescharacteristic
31#17989603C2211yescharacteristic
32#17989561—21no—
33#17989560—21no—
34#17989557—21no—
35C2×C22⋊#10596833—21no—
36#17989451C2211yescharacteristic, complemented
37#17989450C2211yescharacteristic, complemented
38#17989449C2211yescharacteristic, complemented
39#17989448C2211yescharacteristic, complemented
40#17989435C2211yescharacteristic, complemented
41#17989435C2211yescharacteristic, complemented
42D4⋊#10596833C2211yescharacteristic
43D4⋊#10596833C2211yescharacteristic
44D4⋊#10596833C2211yescharacteristic
45D4⋊#10596833C2211yescharacteristic
46D4⋊#10596833C2211yescharacteristic, complemented
47D4⋊#10596833C2211yescharacteristic, complemented
48#17989429C2211yescharacteristic, complemented
49#17989429C2211yescharacteristic, complemented
50#17989428C2211yescharacteristic, complemented
51C8×#10596833C2211yescharacteristic, complemented
52#17989132C2211yescharacteristic
53C2×D4×Dic73C2211yescharacteristic
54#17988901C411yescharacteristic
55#17988898C411yescharacteristic
56#17988865C411yescharacteristic
57#17988865C411yescharacteristic
58#17988780C411yescharacteristic
59#17988780C411yescharacteristic
60#17988721C411yescharacteristic
61D8×Dic73C2211yescharacteristic
62D8×Dic73C2211yescharacteristic
63#17988667C2211yescharacteristic
64#17988667C2211yescharacteristic
65#17988637C2211yescharacteristic
66#447×C73C411yescharacteristic
67C2×#11924038—21no—
68C2×#11924037—21no—
69C2×#11924037—21no—
70C2×#11924037—21no—
71C2×#11924036—21no—
72C22×#10596833—21no—
73C22×#10596833—21no—
74C22×#10596833—21no—
75#14556658D411yescharacteristic
76#14556658D411yescharacteristic
77C4⋊#10596833—21no—
78C4⋊#10596833C2311yescharacteristic
79C4⋊#10596833C2311yescharacteristic
80C4⋊#10596833C2311yescharacteristic
81C4⋊#10596833C2311yescharacteristic
82#14556648—21no—
83#14556648—21no—
84C22⋊#10596833—21no—
85C22⋊#10596833—21no—
86C22⋊#10596833—21no—
87C22⋊#10596833—21no—
88C22⋊#10596833—21no—
89C22⋊#10596833—21no—
90C22⋊#10596833—21no—
91C22⋊#10596833—21no—
92C22⋊#10596833—21no—
93C22⋊#10596833D411yescharacteristic
94C22⋊#10596833D411yescharacteristic
95#14556646—21no—
96C4×#10596833—21no—
97C4×#10596833C2311yescharacteristic
98C4×#10596833C2311yescharacteristic
99C4×#10596833C2311yescharacteristic
100C4×#10596833C2311yescharacteristic
101C2×#11924027—21no—
102C23×Dic73—21no—
103C2×#11924013C2×C411yescharacteristic
104C2×#11924013C2×C411yescharacteristic
105#14556590C2×C411yescharacteristic
106#14556587C2×C411yescharacteristic
107#14556577—21no—
108#14556565C2×C411yescharacteristic
109#14556563—21no—
110D4×Dic73—21no—
111D4×Dic73—21no—
112D4×Dic73C2×C411yescharacteristic
113D4×Dic73C2×C411yescharacteristic
114D4×Dic73C2311yescharacteristic
115D4×Dic73C2311yescharacteristic
116D4×Dic73C2311yescharacteristic
117#14556553C2311yescharacteristic
118#14556551—21no—
119C2×C4⋊Dic73C2×C411yescharacteristic
120C2×C22⋊Dic73—21no—
121C2×C4×Dic73C2311yescharacteristic
122#14556525C2×C411yescharacteristic
123#14556525C2×C411yescharacteristic
124#14556524C2×C411yescharacteristic
125#14556524C2×C411yescharacteristic
126#14556520C2×C411yescharacteristic
127#14556520C2×C411yescharacteristic
128#14556513C2×C411yescharacteristic
129#14556513C2×C411yescharacteristic
130#14556512C2×C411yescharacteristic
131#14556512C2×C411yescharacteristic
132#14556512C2×C411yescharacteristic
133#14556512C2×C411yescharacteristic
134C22⋊#10596831C2×C411yescharacteristic
135C8×Dic73C2311yescharacteristic
136C8×Dic73C2311yescharacteristic
137C22×D4×C73C2×C411yescharacteristic
138C2×D8×C73C2×C411yescharacteristic
139C2×D8×C73C2×C411yescharacteristic
140#121×C73C2×C411yescharacteristic
141#102×C73C2×C411yescharacteristic
142#102×C73C2×C411yescharacteristic
143C22⋊C8×C73C2×C411yescharacteristic
144#11924038—81no—
145#11924037—81no—
146#11924037—81no—
147#11924037—81no—
148#11924036—81no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—21no—
154C2×#10596833—21no—
155C2×#10596833—81no—
156C2×#10596833—81no—
157C2×#10596833—81no—
158C2×#10596833C2×D411yescharacteristic
159C2×#10596833C2×D411yescharacteristic
160C2×#10596833C2×D411yescharacteristic
161C2×#10596833C2×D411yescharacteristic
162#11924027—81no—
163#11924027—81no—
164C2×Dic146—21no—
165C2×D292C22×C411yescharacteristic
166C2×C22⋊D73—21no—
167C2×C22⋊D73—21no—
168C2×C22⋊D73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—81no—
176C22×Dic73—81no—
177C22×Dic73C2×D411yescharacteristic
178C22×Dic73#4111yescharacteristic
179C2×C4×D73—21no—
180#11924013—22no—
181#11924013—41no—
182C2×#10596831C22×C411yescharacteristic
183C2×#10596831C22×C411yescharacteristic
184C4⋊Dic73—21no—
185C4⋊Dic73C22×C411yescharacteristic
186C4⋊Dic73C22×C411yescharacteristic
187C4⋊Dic73C22×C411yescharacteristic
188#11924007—21no—
189C22⋊Dic73—21no—
190C22⋊Dic73—21no—
191C22⋊Dic73—21no—
192C22⋊Dic73—21no—
193C22⋊Dic73—21no—
194#11924005—21no—
195#11924005—21no—
196C4×Dic73C22×C411yescharacteristic
197C4×Dic73C2×D411yescharacteristic
198C4×Dic73#4111yescharacteristic
199C4×Dic73C2411yescharacteristic
200C24×C73—21no—
201C2×D4×C73—22no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—41no—
205C2×D4×C73C22×C411yescharacteristic
206C2×D4×C73C22×C411yescharacteristic
207C2×D4×C73C22×C411yescharacteristic
208C22×C4×C73C22×C411yescharacteristic
209D8×C73—22no—
210D8×C73—41no—
211C2×C8×C73C22×C411yescharacteristic
212C2×C8×C73C22×C411yescharacteristic
213C4⋊C4×C73C22×C411yescharacteristic
214C22⋊C4×C73—21no—
215C23×C73—21no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—42no—
219C23×C73—42no—
220C23×C73—81no—
221C23×C73C4×D411yescharacteristic
222C22×D73—21no—
223D4×C73—21no—
224D4×C73—21no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—21no—
228D4×C73—42no—
229D4×C73—81no—
230D4×C73#13112yes—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73C4×D411yescharacteristic
235C2×C4×C73C23×C411yescharacteristic
236C22⋊D73—42no—
237C22⋊D73—81no—
238C22⋊D73—81no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—81no—
252C2×Dic73—81no—
253C2×Dic73—81no—
254C2×Dic73C4×D411yescharacteristic
255C2×Dic73C4×D411yescharacteristic
256C2×Dic73C22×D411yescharacteristic
257C2×Dic73C2×#4111yescharacteristic
258D292—21no—
259D292—21no—
260C4×D73—41no—
261C4×D73—41no—
262Dic146—81no—
263#10596833—21no—
264#10596833—21no—
265#10596833—21no—
266#10596833—21no—
267#10596833—41no—
268#10596833—41no—
269#10596833—41no—
270#10596833—41no—
271#10596833—41no—
272#10596833—41no—
273C8×C73—21no—
274C8×C73—21no—
275#10596831—21no—
276#10596831—21no—
277C22×C73—21no—
278C22×C73—22no—
279C22×C73—21no—
280C22×C73—21no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73—41no—
286C22×C73—41no—
287C22×C73—41no—
288C22×C73—41no—
289C22×C73—84no—
290C22×C73C2×C4×D411yescharacteristic
291C2×D73—41no—
292C2×D73—41no—
293C2×D73—41no—
294C4×C73—21no—
295C4×C73—41no—
296C4×C73C2×#13111yescharacteristic
297C4×C73#56811yescharacteristic
298Dic73—21no—
299Dic73—21no—
300Dic73—21no—
301Dic73—41no—
302Dic73—41no—
303Dic73—41no—
304Dic73#57611yescharacteristic
305Dic73#57611yescharacteristic
306#18026—731nomaximal, Sylow
307C2×C73—41no—
308C2×C73—42no—
309C2×C73—81no—
310C2×C73—81no—
311C2×C73#293311yescharacteristic
312C2×C73#294811yescharacteristic
313C2×C73#295511yescharacteristic
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#1454—731no—
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#6440811yescharacteristic
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#431—731no—
360#431—731no—
361#431—731no—
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#322—731no—
379#322—731no—
380#322—731no—
381C82—731no—
382C2×#41—1461no—
383C22×D4C2×#6440811yescharacteristic
384C23×C4—1461no—
385C2×D8—731no—
386C2×D8—731no—
387C2×D8C2×#6440811yescharacteristic
388C2×D8C2×#6440811yescharacteristic
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—1461no—
402#121C2×#6440811yescharacteristic
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×C42—731no—
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—731no—
424C4⋊C8—731no—
425C4⋊C8—731no—
426C4⋊C8—731no—
427C4⋊C8—1461no—
428#102—731no—
429#102—731no—
430#102—731no—
431#102—731no—
432#102—731no—
433#102—731no—
434#102C2×#6440811yescharacteristic
435#102C2×#6440811yescharacteristic
436C22⋊C8—731no—
437C22⋊C8—731no—
438C22⋊C8—731no—
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⋊C8—1461no—
448C22⋊C8—1461no—
449C22⋊C8—1461no—
450C22⋊C8C2×#6440811yescharacteristic
451#97—1461no—
452C4×C8—731no—
453C4×C8—731no—
454C4×C8—731no—
455C4×C8—731no—
456C4×C8—731no—
457C4×C8—731no—
458C4×C8—1461no—
459C24—21no—
460#41—5841no—
461#41—5841no—
462C2×Q8—1461no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—731no—
468C2×D4—1461no—
469C2×D4—1461no—
470C2×D4—1461no—
471C2×D4C22×#6440811yescharacteristic
472C2×D4C22×#6440811yescharacteristic
473C2×D4C22×#6440811yescharacteristic
474C22×C4—5841no—
475C22×C4—5841no—
476C22×C4—731no—
477C22×C4—731no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4C22×#6440811yescharacteristic
486D8—22no—
487D8—41no—
488D8—2921no—
489D8—1462no—
490M16—5841no—
491M16—5841no—
492M16—5841no—
493M16—5841no—
494C2×C8—5841no—
495C2×C8—5841no—
496C2×C8—5841no—
497C2×C8—5841no—
498C2×C8—731no—
499C2×C8—731no—
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×C8—1461no—
509C2×C8—1461no—
510C2×C8C22×#6440811yescharacteristic
511C2×C8C22×#6440811yescharacteristic
512C4⋊C4—731no—
513C4⋊C4—731no—
514C4⋊C4—731no—
515C4⋊C4—1461no—
516C4⋊C4—1461no—
517C4⋊C4C22×#6440811yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—1461no—
520C22⋊C4—1461no—
521C22⋊C4—1461no—
522C22⋊C4—1461no—
523C22⋊C4—1461no—
524C22⋊C4—1461no—
525C22⋊C4—1461no—
526C42—731no—
527C42—731no—
528C42—731no—
529C42—731no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—42no—
534C23—42no—
535C23—81no—
536C23—1461no—
537C23D4×#6440811yescharacteristic
538Q8—5841no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—42no—
545D4—81no—
546D4—2922no—
547D4—5841no—
548D4—5841no—
549D4—1461no—
550D4—1461no—
551D4#1455667812yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—2921no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—5841no—
565C2×C4—5841no—
566C2×C4—5841no—
567C2×C4—731no—
568C2×C4—731no—
569C2×C4—731no—
570C2×C4—731no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4—1461no—
576C2×C4D4×#6440811yescharacteristic
577C2×C4C23×#6440811yescharacteristic
578C8—21no—
579C8—21no—
580C8—2921no—
581C8—2921no—
582C8—2921no—
583C8—2921no—
584C8—2921no—
585C8—2921no—
586C8—1461no—
587C8—1461no—
588C8—1461no—
589C8—1461no—
590C8—1461no—
591C8—1461no—
592C22—21no—
593C22—22no—
594C22—21no—
595C22—21no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—84no—
605C22—2921no—
606C22—2921no—
607C22—2921no—
608C22C2×D4×#6440811yescharacteristic
609C4—21no—
610C4—41no—
611C4—2921no—
612C4—2921no—
613C4—2921no—
614C4—731no—
615C4—731no—
616C4—1461no—
617C4—1461no—
618C4—1461no—
619C4C2×#1455667811yescharacteristic
620C4#1798966511yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—81no—
625C2—5841no—
626C2#2262666311yescharacteristic
627C2#2262669011yescharacteristic
628C2#2262670311yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#447×C73C4
socleC22×C73C2×C4×D4
prime radical#22619926C2
cosocleC4×Dic73C24
hypercenter#447#64408
hypocenterC73#18026
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #22626811C2semidirect
2. #22626787C2semidirect
3. #22625579C2semidirect
4. #22625564C2semidirect
5. #22625553C2semidirect
6. #22625552C2semidirect
7. #22625532C2semidirect
8. #22625530C2semidirect
9. #22625527C2semidirect
10. #22625511C2semidirect
11. #22625502C2semidirect
12. #22625290C2semidirect
13. #22625230C2semidirect
14. #22625152C2semidirect
18. #17989622C22semidirect
19. #17989621C22semidirect
23. #17989615C22semidirect
27. D4×#10596833C22semidirect
36. #17989451C22semidirect
37. #17989450C22semidirect
38. #17989449C22semidirect
39. #17989448C22semidirect
40. #17989435C22semidirect
41. #17989435C22semidirect
46. D4⋊#10596833C22semidirect
47. D4⋊#10596833C22semidirect
48. #17989429C22semidirect
49. #17989429C22semidirect
50. #17989428C22semidirect
51. C8×#10596833C22semidirect
330. C73#18026semidirect

Maximal subgroups

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

subgroupindex
#226268112
#226267872
#226255792
#226255642
#226255532
#226255522
#226255322
#226255302
#226255272
#226255112
#226255022
#226252902
#226252302
#226251522
#226199262
#1802673