Finite Group Databasebeta

← #33144213

Subgroups — #33144213

Order 18688.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22614952C211yesmaximal, characteristic, complemented
2#22612878C211yesmaximal, characteristic
3#22611304C211yesmaximal, characteristic
4#22611304C211yesmaximal, characteristic
5#22611078C211yesmaximal, characteristic
6#22611068C211yesmaximal, characteristic
7#22610886C211yesmaximal, characteristic, complemented
8#22610882C211yesmaximal, characteristic, complemented
9#22610695C211yesmaximal, characteristic, complemented
10#22610517C211yesmaximal, characteristic, complemented
11#22610510C211yesmaximal, characteristic, complemented
12#22610065C211yesmaximal, characteristic, complemented
13#22609942C211yesmaximal, characteristic
14#22609757C211yesmaximal, characteristic
15C73×#1940C211yesmaximal, characteristic, complemented
16C2×#14556591C2211yescharacteristic
17C2×#14556583C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×#14556549—21no—
20C2×#14556523C2211yescharacteristic
21C2×#14556523C2211yescharacteristic
22C2×#14556513C2211yescharacteristic
23C2×#14556513C2211yescharacteristic
24C2×#14556513C2211yescharacteristic
25C2×#14556513C2211yescharacteristic
26#17988520—21no—
27#17988507—21no—
28#17988491—21no—
29#17988489C2211yescharacteristic
30#17988489C2211yescharacteristic
31#17988485C2211yescharacteristic
32#17988485C2211yescharacteristic
33#17988484—21no—
34#17988479—21no—
35#17988479—21no—
36#17988457C2211yescharacteristic
37#17988453C2211yescharacteristic
38#17988444—21no—
39C4×C4⋊Dic73C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
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×D292C2311yescharacteristic
61C22×C4×D73—21no—
62#14556591—22no—
63#14556591—41no—
64#14556583—22no—
65#14556583—41no—
66C4×D292—22no—
67C4×D292Q814yescomplemented
68#14556549—44no—
69C2×C4⋊Dic73—21no—
70C2×C4⋊Dic73—21no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×C4⋊Dic73C2311yescharacteristic
79C2×#11924007—21no—
80C2×#11924007—21no—
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#14556523—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—81no—
123C2×D292—21no—
124C2×D292—21no—
125C2×D292—21no—
126C2×D292—21no—
127C2×D292—21no—
128C2×D292C2×Q812yes—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C2×C4×D73—24no—
137C2×C4×D73—42no—
138C2×C4×D73—42no—
139C4⋊Dic73—21no—
140C4⋊Dic73—21no—
141C4⋊Dic73—21no—
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—42no—
151C4⋊Dic73—42no—
152C4⋊Dic73—81no—
153C4⋊Dic73C2×Q812yes—
154C4⋊Dic73#4112yes—
155C4⋊Dic73#4112yes—
156#11924007—42no—
157#11924007—42no—
158#11924007—42no—
159#11924007—81no—
160#11924005—24no—
161#11924005—42no—
162#11924005—42no—
163#11924005—81no—
164#11924005—81no—
165C4×Dic73—42no—
166C4×Dic73—42no—
167C4×Dic73—81no—
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175C2×C8×C73—21no—
176C2×C8×C73—21no—
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—
187C4⋊C4×C73—22no—
188C4⋊C4×C73—41no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73C2×Q812yes—
194C42×C73#4112yes—
195C23×C73C22×D411yescharacteristic
196C22×D73—22no—
197C22×D73—41no—
198C22×D73—41no—
199C22×D73—41no—
200C22×D73—41no—
201C22×D73—41no—
202C22×D73—41no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
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×C73C22⋊Q812yes—
219C2×C4×C73C22⋊Q812yes—
220C2×C4×C73AGL(1,ℤ/8)12yes—
221C2×C4×C73C22×Q811yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C2×C4×C73C2×#4111yescharacteristic
225C2×C4×C73H(5,𝔽2)11yescharacteristic
226C2×C4×C732−1+411yescharacteristic
227C2×Dic73—22no—
228C2×Dic73—22no—
229C2×Dic73—22no—
230C2×Dic73—41no—
231C2×Dic73—41no—
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—
248D292—22no—
249D292—22no—
250D292—41no—
251D292—41no—
252C4×D73—48no—
253Dic146—84no—
254C8×C73—41no—
255C8×C73—41no—
256C8×C73—41no—
257C8×C73—41no—
258C22×C73C2×C22⋊Q811yescharacteristic
259C22×C73#54611yescharacteristic
260C22×C73#54811yescharacteristic
261C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C73#57511yescharacteristic
263C22×C73#57711yescharacteristic
264C22×C73#57711yescharacteristic
265C2×D73—42no—
266C2×D73—42no—
267C2×D73—42no—
268C2×D73—81no—
269C2×D73—81no—
270C2×D73—81no—
271C2×D73—81no—
272C4×C73—22no—
273C4×C73—22no—
274C4×C73—22no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73#53311yescharacteristic
279C4×C73#54411yescharacteristic
280C4×C73#55511yescharacteristic
281C4×C73#55611yescharacteristic
282Dic73—42no—
283Dic73—42no—
284Dic73—42no—
285Dic73—81no—
286Dic73—81no—
287Dic73—81no—
288Dic73—81no—
289#26032—731nomaximal, Sylow
290C2×C73#243911yescharacteristic
291C2×C73#307711yescharacteristic
292C2×C73#308411yescharacteristic
293C2×C73#330611yescharacteristic
294C2×C73#332111yescharacteristic
295C2×C73#336811yescharacteristic
296C2×C73#337611yescharacteristic
297D73—82no—
298#2550—731no—
299#2354—731no—
300#2065—731no—
301#2065—731no—
302#2025—731no—
303#2023—731no—
304#1989—731no—
305#1988—731no—
306#1948—731no—
307#1940D7311yescharacteristic, complemented
308#1920—731no—
309#1919—731no—
310#1836—731no—
311#1804—731no—
312#1762—731no—
313C73#2603211yescharacteristic, complemented, Sylow
314C2×C4⋊Q8—731no—
315C2×#125—731no—
316C2×C4×D4—731no—
317C2×#117—1461no—
318C2×#106—731no—
319C2×#106—731no—
320C2×C4⋊C8C2×D7311yescharacteristic
321C2×C4⋊C8C2×D7311yescharacteristic
322C2×C4⋊C8C2×D7311yescharacteristic
323C2×#102—731no—
324C2×#102—731no—
325C2×#102—731no—
326C2×#102—731no—
327C2×#97C2×D7311yescharacteristic
328#398—1461no—
329#395—1461no—
330#391—1461no—
331#390—731no—
332#390—731no—
333#389—731no—
334#389—731no—
335#389—1461no—
336#388—1461no—
337#388—1461no—
338#384—731no—
339#382—731no—
340#380—1461no—
341C4×C4⋊C4—731no—
342C4×C4⋊C4—731no—
343C4×C4⋊C4—731no—
344C4×C4⋊C4C2×D7311yescharacteristic
345#340—731no—
346#340—731no—
347#340—731no—
348#340—731no—
349#340—731no—
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355#336C2×D7311yescharacteristic
356#336C2×D7311yescharacteristic
357C22×Q8—1461no—
358C22×D4—731no—
359C23×C4—1461no—
360C22×C8C22×D7311yescharacteristic
361C22×C8C22×D7311yescharacteristic
362C22×C8C22×D7311yescharacteristic
363C22×C8C22×D7311yescharacteristic
364C4⋊Q8—2921no—
365C4⋊Q8—1462no—
366#125—2921no—
367#125—1462no—
368C4×D4—734no—
369C4×D4—1462no—
370#117—2924no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C4⋊C4—1461no—
379C2×C4⋊C4—1461no—
380C2×C4⋊C4—1461no—
381C2×C4⋊C4—1461no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4—1461no—
385C2×C4⋊C4D29211yescharacteristic
386C2×C4⋊C4D29211yescharacteristic
387C2×C22⋊C4—1461no—
388C2×C22⋊C4—1461no—
389C2×C22⋊C4—1461no—
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C42—1461no—
393C2×C42—1461no—
394C2×C42—1461no—
395C2×C42C22×D7311yescharacteristic
396C2×C42C22×D7311yescharacteristic
397C2×C42C22×D7311yescharacteristic
398#106—1462no—
399#106—1462no—
400C4⋊C8—22no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403#102—2921no—
404#102—2921no—
405#102—1462no—
406#102—1462no—
407#97—22no—
408#95—1461no—
409#95—1461no—
410#95—1461no—
411#95—1461no—
412#95—1461no—
413#95—1461no—
414#95—1461no—
415#95D29211yescharacteristic
416#95D29211yescharacteristic
417C24—1461no—
418C2×Q8—2922no—
419C2×Q8—2922no—
420C2×Q8—5841no—
421C2×D4—732no—
422C2×D4—1461no—
423C2×D4—1461no—
424C2×D4—1461no—
425C2×D4—1461no—
426C2×D4—1461no—
427C22×C4—2922no—
428C22×C4—2922no—
429C22×C4—1461no—
430C22×C4—1461no—
431C22×C4—1461no—
432C22×C4—1461no—
433C22×C4—1461no—
434C22×C4—1461no—
435C22×C4—1461no—
436C22×C4—1464no—
437C22×C4C2×D29211yescharacteristic
438C22×C4C2×D29211yescharacteristic
439C22×C4C2×D29211yescharacteristic
440C22×C4C2×D29211yescharacteristic
441C22×C4C2×D29211yescharacteristic
442C22×C4C2×D29211yescharacteristic
443C22×C4C23×D7311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—2922no—
459C4⋊C4—2922no—
460C4⋊C4—2922no—
461C4⋊C4—2922no—
462C4⋊C4—2922no—
463C4⋊C4—5841no—
464C4⋊C4—5841no—
465C4⋊C4—732no—
466C4⋊C4—732no—
467C4⋊C4—732no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C22⋊C4—2922no—
480C22⋊C4—2922no—
481C22⋊C4—5841no—
482C22⋊C4—5841no—
483C22⋊C4—1464no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—2922no—
489C42—2922no—
490C42—5841no—
491C42Q8×D7312yes—
492C42#1192402712yes—
493C23—2921no—
494C23—2921no—
495C23—2921no—
496C23—2921no—
497C23—2921no—
498C23—2921no—
499C23—1462no—
500C23C22×D29211yescharacteristic
501Q8—5844no—
502D4—2921no—
503D4—2921no—
504D4—1462no—
505D4—1462no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
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—2928no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—2921no—
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—1462no—
541C2×C4—1462no—
542C2×C4—1462no—
543C2×C4#1455657112yes—
544C2×C4#1455657112yes—
545C2×C4#1455661912yes—
546C2×C4C2×Q8×D7311yescharacteristic
547C2×C4#41×D7311yescharacteristic
548C2×C4#41×D7311yescharacteristic
549C2×C4C2×#1192402711yescharacteristic
550C2×C4#1455663611yescharacteristic
551C2×C4#1455663911yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—2922no—
557C22—2922no—
558C22—2922no—
559C22—5841no—
560C22—5841no—
561C22—5841no—
562C22—5841no—
563C22C2×#1455657111yescharacteristic
564C22#1798923211yescharacteristic
565C22#1798924911yescharacteristic
566C22C2×#1455661911yescharacteristic
567C22#1798938711yescharacteristic
568C22#1798939911yescharacteristic
569C22#1798939911yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—2922no—
577C4—2922no—
578C4—2922no—
579C4—5841no—
580C4—5841no—
581C4—5841no—
582C4—5841no—
583C4#1798914311yescharacteristic
584C4#1798921411yescharacteristic
585C4#1798930111yescharacteristic
586C4#1798930811yescharacteristic
587C2—5842no—
588C2#2261362011yescharacteristic
589C2#2261973011yescharacteristic
590C2#2261979511yescharacteristic
591C2#2262189411yescharacteristic
592C2#2262211911yescharacteristic
593C2#2262266211yescharacteristic
594C2#2262276011yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#1940C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#1940D73
hypocenterC73#26032
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. #22614952C2semidirect
7. #22610886C2semidirect
8. #22610882C2semidirect
9. #22610695C2semidirect
10. #22610517C2semidirect
11. #22610510C2semidirect
12. #22610065C2semidirect
15. C73×#1940C2semidirect
67. C4×D292Q8semidirect
307. #1940D73semidirect
313. C73#26032semidirect

Maximal subgroups

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

subgroupindex
#226149522
#226128782
#226113042
#226110782
#226110682
#226108862
#226108822
#226106952
#226105172
#226105102
#226100652
#226099422
#226097572
C73×#19402
#2603273