Finite Group Databasebeta

← #33144273

Subgroups — #33144273

Order 18688.

744 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22614957C211yesmaximal, characteristic, complemented
2#22612902C211yesmaximal, characteristic
3#22611318C211yesmaximal, characteristic
4#22611304C211yesmaximal, characteristic
5#22611068C211yesmaximal, characteristic
6#22611068C211yesmaximal, characteristic
7#22610882C211yesmaximal, characteristic, complemented
8#22610878C211yesmaximal, characteristic, complemented
9#22610701C211yesmaximal, characteristic, complemented
10#22610524C211yesmaximal, characteristic, complemented
11#22610510C211yesmaximal, characteristic, complemented
12#22610065C211yesmaximal, characteristic, complemented
13#22609932C211yesmaximal, characteristic
14#22609757C211yesmaximal, characteristic
15C73×#1940C211yesmaximal, characteristic, complemented
16C2×#14556591C2211yescharacteristic
17C2×#14556591C2211yescharacteristic
18C2×#14556590—21no—
19C2×C4×D292C2211yescharacteristic
20C2×#14556525C2211yescharacteristic
21C2×#14556523C2211yescharacteristic
22C2×#14556513C2211yescharacteristic
23C2×#14556513C2211yescharacteristic
24C2×#14556513C2211yescharacteristic
25C2×#14556513C2211yescharacteristic
26#17988508—21no—
27#17988508—21no—
28#17988489C2211yescharacteristic
29#17988489C2211yescharacteristic
30#17988486—21no—
31#17988485C2211yescharacteristic
32#17988485C2211yescharacteristic
33#17988477—21no—
34#17988477—21no—
35#17988457C2211yescharacteristic
36#17988453C2211yescharacteristic
37#17988449—21no—
38C4×C4⋊Dic73C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41#17988434—21no—
42#17988350C2211yescharacteristic
43#17988350C2211yescharacteristic
44#17988350C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×#97×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Dic146—21no—
60C22×Dic146—21no—
61C22×D292C2311yescharacteristic
62C22×C4×D73—21no—
63#14556591—22no—
64#14556591—22no—
65#14556591—41no—
66#14556591—41no—
67#14556590—44no—
68C4×D292—22no—
69C4×D292Q814yescomplemented
70C2×C4⋊Dic73—21no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×#11924007—21no—
82C2×#11924007—21no—
83C2×#11924005—21no—
84C2×#11924005—21no—
85C2×#11924005—21no—
86C2×#11924005—21no—
87C2×#11924005—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73—21no—
90C2×C4×Dic73—21no—
91#14556525—22no—
92#14556523—22no—
93#14556513—22no—
94#14556513—22no—
95#14556513—41no—
96#14556513—41no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104C22×C8×C73C2311yescharacteristic
105C22×C8×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C2×C4⋊C4×C73D411yescharacteristic
109C2×C4⋊C4×C73D411yescharacteristic
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C4⋊C8×C73—22no—
114C4⋊C8×C73—41no—
115C4⋊C8×C73—41no—
116#97×C73—22no—
117#95×C73D411yescharacteristic
118#95×C73D411yescharacteristic
119C23×D73—21no—
120C2×Dic146—42no—
121C2×Dic146—42no—
122C2×Dic146—42no—
123C2×Dic146—42no—
124C2×Dic146—81no—
125C2×Dic146—81no—
126C2×D292—21no—
127C2×D292—21no—
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292C2×Q812yes—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C2×C4×D73—24no—
140C2×C4×D73—81no—
141C2×C4×D73—81no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—42no—
154C4⋊Dic73—42no—
155C4⋊Dic73—42no—
156C4⋊Dic73—81no—
157C4⋊Dic73C2×Q812yes—
158C4⋊Dic73#4112yes—
159C4⋊Dic73#4112yes—
160#11924007—42no—
161#11924007—42no—
162#11924005—24no—
163#11924005—42no—
164#11924005—42no—
165#11924005—81no—
166#11924005—81no—
167C4×Dic73—42no—
168C4×Dic73—81no—
169C4×Dic73—81no—
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2411yescharacteristic
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C4⋊C4×C73—22no—
190C4⋊C4×C73—22no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73C2×Q812yes—
196C42×C73#4112yes—
197C23×C73C22×D411yescharacteristic
198C22×D73—22no—
199C22×D73—41no—
200C22×D73—41no—
201C22×D73—41no—
202C22×D73—41no—
203C22×D73—41no—
204C22×D73—41no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73C22⋊Q812yes—
220C2×C4×C73C22⋊Q812yes—
221C2×C4×C73AGL(1,ℤ/8)12yes—
222C2×C4×C73#13712yes—
223C2×C4×C73C22×Q811yescharacteristic
224C2×C4×C73C2×#4111yescharacteristic
225C2×C4×C73C2×#4111yescharacteristic
226C2×C4×C73C2×#4111yescharacteristic
227C2×C4×C73H(5,𝔽2)11yescharacteristic
228C2×C4×C732−1+411yescharacteristic
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—41no—
233C2×Dic73—41no—
234C2×Dic73—41no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250D292—22no—
251D292—22no—
252D292—41no—
253D292—41no—
254C4×D73—84no—
255Dic146—84no—
256Dic146—84no—
257C8×C73—41no—
258C8×C73—41no—
259C8×C73—41no—
260C8×C73—41no—
261C22×C73C2×C22⋊Q811yescharacteristic
262C22×C73#54611yescharacteristic
263C22×C73#54811yescharacteristic
264C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C73C2×#13711yescharacteristic
266C22×C73#57611yescharacteristic
267C22×C73#57711yescharacteristic
268C2×D73—42no—
269C2×D73—42no—
270C2×D73—42no—
271C2×D73—81no—
272C2×D73—81no—
273C2×D73—81no—
274C2×D73—81no—
275C4×C73—22no—
276C4×C73—22no—
277C4×C73—22no—
278C4×C73—22no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73#53311yescharacteristic
282C4×C73#54411yescharacteristic
283C4×C73#55511yescharacteristic
284C4×C73#55611yescharacteristic
285Dic73—42no—
286Dic73—42no—
287Dic73—42no—
288Dic73—81no—
289Dic73—81no—
290Dic73—81no—
291Dic73—81no—
292#26036—731nomaximal, Sylow
293C2×C73#243911yescharacteristic
294C2×C73#307911yescharacteristic
295C2×C73#308111yescharacteristic
296C2×C73#331811yescharacteristic
297C2×C73#332011yescharacteristic
298C2×C73#337311yescharacteristic
299C2×C73#337511yescharacteristic
300D73—82no—
301#2551—731no—
302#2357—731no—
303#2067—731no—
304#2065—731no—
305#2023—731no—
306#2023—731no—
307#1988—731no—
308#1987—731no—
309#1949—731no—
310#1940D7311yescharacteristic, complemented
311#1921—731no—
312#1919—731no—
313#1836—731no—
314#1802—731no—
315#1762—731no—
316C73#2603611yescharacteristic, complemented, Sylow
317C2×C4⋊Q8—731no—
318C2×C4⋊Q8—731no—
319C2×C4⋊Q8—1461no—
320C2×C4×D4—731no—
321C2×#107—731no—
322C2×#106—731no—
323C2×C4⋊C8C2×D7311yescharacteristic
324C2×C4⋊C8C2×D7311yescharacteristic
325C2×C4⋊C8C2×D7311yescharacteristic
326C2×#102—731no—
327C2×#102—731no—
328C2×#102—731no—
329C2×#102—731no—
330C2×#97C2×D7311yescharacteristic
331#395—1461no—
332#395—1461no—
333#390—731no—
334#390—731no—
335#389—731no—
336#389—731no—
337#389—1461no—
338#388—1461no—
339#388—1461no—
340#384—731no—
341#382—731no—
342#381—1461no—
343C4×C4⋊C4—731no—
344C4×C4⋊C4—731no—
345C4×C4⋊C4—731no—
346C4×C4⋊C4C2×D7311yescharacteristic
347C4×C22⋊C4—1461no—
348#340—731no—
349#340—731no—
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358#336C2×D7311yescharacteristic
359#336C2×D7311yescharacteristic
360C22×Q8—1461no—
361C22×Q8—1461no—
362C22×D4—731no—
363C23×C4—1461no—
364C22×C8C22×D7311yescharacteristic
365C22×C8C22×D7311yescharacteristic
366C22×C8C22×D7311yescharacteristic
367C22×C8C22×D7311yescharacteristic
368C4⋊Q8—2921no—
369C4⋊Q8—2921no—
370C4⋊Q8—2924no—
371C4⋊Q8—1462no—
372C4⋊Q8—1462no—
373C4×D4—734no—
374C4×D4—1462no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4—1461no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4—1461no—
387C2×C4⋊C4—1461no—
388C2×C4⋊C4D29211yescharacteristic
389C2×C4⋊C4D29211yescharacteristic
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C22⋊C4—1461no—
393C2×C22⋊C4—1461no—
394C2×C22⋊C4—1461no—
395C2×C42—1461no—
396C2×C42—1461no—
397C2×C42—1461no—
398C2×C42C22×D7311yescharacteristic
399C2×C42C22×D7311yescharacteristic
400C2×C42C22×D7311yescharacteristic
401#107—1462no—
402#106—1462no—
403C4⋊C8—22no—
404C4⋊C8—41no—
405C4⋊C8—41no—
406#102—2921no—
407#102—2921no—
408#102—1462no—
409#102—1462no—
410#97—22no—
411#95—1461no—
412#95—1461no—
413#95—1461no—
414#95—1461no—
415#95—1461no—
416#95—1461no—
417#95—1461no—
418#95D29211yescharacteristic
419#95D29211yescharacteristic
420C24—1461no—
421C2×Q8—2922no—
422C2×Q8—2922no—
423C2×Q8—2922no—
424C2×Q8—2922no—
425C2×Q8—5841no—
426C2×Q8—5841no—
427C2×D4—732no—
428C2×D4—1461no—
429C2×D4—1461no—
430C2×D4—1461no—
431C2×D4—1461no—
432C2×D4—1461no—
433C22×C4—5841no—
434C22×C4—5841no—
435C22×C4—1461no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4—1464no—
443C22×C4C2×D29211yescharacteristic
444C22×C4C2×D29211yescharacteristic
445C22×C4C2×D29211yescharacteristic
446C22×C4C2×D29211yescharacteristic
447C22×C4C2×D29211yescharacteristic
448C22×C4C2×D29211yescharacteristic
449C22×C4C23×D7311yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—2922no—
465C4⋊C4—2922no—
466C4⋊C4—2922no—
467C4⋊C4—2922no—
468C4⋊C4—2922no—
469C4⋊C4—5841no—
470C4⋊C4—732no—
471C4⋊C4—732no—
472C4⋊C4—732no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C22⋊C4—2922no—
485C22⋊C4—2922no—
486C22⋊C4—5841no—
487C22⋊C4—5841no—
488C22⋊C4—1464no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—2922no—
494C42—5841no—
495C42—5841no—
496C42Q8×D7312yes—
497C42#1192402712yes—
498C23—2921no—
499C23—2921no—
500C23—2921no—
501C23—2921no—
502C23—2921no—
503C23—2921no—
504C23—1462no—
505C23C22×D29211yescharacteristic
506Q8—5844no—
507Q8—5844no—
508D4—2921no—
509D4—2921no—
510D4—1462no—
511D4—1462no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—2921no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—2921no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—2921no—
535C2×C4—2921no—
536C2×C4—2921no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—5844no—
545C2×C4—1462no—
546C2×C4—1462no—
547C2×C4—1462no—
548C2×C4#1455657112yes—
549C2×C4#1455657112yes—
550C2×C4#1455661912yes—
551C2×C4#1455662412yes—
552C2×C4C2×Q8×D7311yescharacteristic
553C2×C4#41×D7311yescharacteristic
554C2×C4#41×D7311yescharacteristic
555C2×C4C2×#1192402711yescharacteristic
556C2×C4#1455663611yescharacteristic
557C2×C4#1455663911yescharacteristic
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—2922no—
563C22—2922no—
564C22—2922no—
565C22—5841no—
566C22—5841no—
567C22—5841no—
568C22—5841no—
569C22C2×#1455657111yescharacteristic
570C22#1798923211yescharacteristic
571C22#1798924911yescharacteristic
572C22C2×#1455661911yescharacteristic
573C22C2×#1455662411yescharacteristic
574C22#1798939211yescharacteristic
575C22#1798939911yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—2922no—
583C4—2922no—
584C4—2922no—
585C4—5841no—
586C4—5841no—
587C4—5841no—
588C4—5841no—
589C4#1798914311yescharacteristic
590C4#1798921411yescharacteristic
591C4#1798930111yescharacteristic
592C4#1798930811yescharacteristic
593C2—5842no—
594C2#2261362011yescharacteristic
595C2#2261974711yescharacteristic
596C2#2261976311yescharacteristic
597C2#2262207411yescharacteristic
598C2#2262210411yescharacteristic
599C2#2262272511yescharacteristic
600C2#2262274711yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#1940C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#1940D73
hypocenterC73#26036
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. #22614957C2semidirect
7. #22610882C2semidirect
8. #22610878C2semidirect
9. #22610701C2semidirect
10. #22610524C2semidirect
11. #22610510C2semidirect
12. #22610065C2semidirect
15. C73×#1940C2semidirect
69. C4×D292Q8semidirect
310. #1940D73semidirect
316. C73#26036semidirect

Maximal subgroups

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

subgroupindex
#226149572
#226129022
#226113182
#226113042
#226110682
#226108822
#226108782
#226107012
#226105242
#226105102
#226100652
#226099322
#226097572
C73×#19402
#2603673