Finite Group Databasebeta

← #33158575

Subgroups — #33158575

Order 18688.

726 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#22613781C211yesmaximal, characteristic
2#22611302C211yesmaximal, characteristic
3#22611266C211yesmaximal, characteristic, complemented
4#22611264C211yesmaximal, characteristic, complemented
5#22611074C211yesmaximal, characteristic
6#22610883C211yesmaximal, characteristic, complemented
7#22610666C211yesmaximal, characteristic, complemented
8#22610558C211yesmaximal, characteristic
9#22610551C211yesmaximal, characteristic
10#22610516C211yesmaximal, characteristic, complemented
11#22610516C211yesmaximal, characteristic, complemented
12#22610497C211yesmaximal, characteristic, complemented
13#22610191C211yesmaximal, characteristic
14#22609759C211yesmaximal, characteristic
15C73×#2370C211yesmaximal, characteristic, complemented
16C2×#14556591C2211yescharacteristic
17C2×#14556569—21no—
18C2×C4×D292C2211yescharacteristic
19C2×#14556524C2211yescharacteristic
20C2×#14556522C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×#14556511C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29#17988509—21no—
30#17988500—21no—
31#17988489C2211yescharacteristic
32#17988489C2211yescharacteristic
33#17988485C2211yescharacteristic
34#17988485C2211yescharacteristic
35#17988461—21no—
36#17988349C2211yescharacteristic
37#17988349C2211yescharacteristic
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48C2×#125×C73C2211yescharacteristic
49#389×C73—21no—
50#389×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#387×C73—21no—
53#387×C73—21no—
54C4×C4⋊C4×C73—21no—
55C4×C4⋊C4×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59C22×Dic146—21no—
60C22×D292C2311yescharacteristic
61C22×C4×D73—21no—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556591—22no—
67#14556591—41no—
68#14556569—44no—
69C4×D292—22no—
70C4×D292—41no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×#11924007—21no—
76C2×#11924007—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×#11924005—21no—
82#14556524—22no—
83#14556522—22no—
84#14556522—22no—
85#14556522—41no—
86C4⋊#10596831—41no—
87#14556511—22no—
88#14556511—22no—
89#14556511—41no—
90#14556511Q814yescomplemented
91#14556502—41no—
92#14556498—21no—
93#14556498—21no—
94#125×C73—22no—
95#125×C73—22no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73D411yescharacteristic
101C2×C4⋊C4×C73D411yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C42×C73—21no—
107C2×C42×C73—21no—
108C2×C42×C73—21no—
109C2×C42×C73C2311yescharacteristic
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112#95×C73—21no—
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
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—
132C2×C4×D73—42no—
133C2×C4×D73—42no—
134C2×C4×D73—81no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831C2×Q812yes—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—42no—
153C4⋊Dic73#4112yes—
154#11924007—42no—
155#11924007—42no—
156#11924005—42no—
157#11924005—42no—
158#11924005—42no—
159#11924005—42no—
160#11924005—81no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2411yescharacteristic
172C4⋊C4×C73—24no—
173C4⋊C4×C73—24no—
174C4⋊C4×C73—22no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—41no—
181C4⋊C4×C73—42no—
182C4⋊C4×C73—81no—
183C4⋊C4×C73C2×Q812yes—
184C4⋊C4×C73#4112yes—
185C4⋊C4×C73#4112yes—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—42no—
193C42×C73—81no—
194C42×C73—81no—
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—22no—
208C2×C4×C73—22no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—22no—
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×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73AGL(1,ℤ/8)12yes—
233C2×C4×C73C22×Q811yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C2×C4×C73C2×#4111yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C73H(5,𝔽2)11yescharacteristic
238C2×C4×C732−1+411yescharacteristic
239C2×Dic73—22no—
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—84no—
253Dic146—84no—
254#10596831—22no—
255#10596831—41no—
256#10596831—41no—
257#10596831—41no—
258C22×C73#52511yescharacteristic
259C22×C73#54611yescharacteristic
260C22×C73D4×Q811yescharacteristic
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—41no—
274C4×C73—42no—
275C4×C73—41no—
276C4×C73—42no—
277C4×C73—42no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—81no—
282C4×C73#53311yescharacteristic
283C4×C73#54211yescharacteristic
284C4×C73#55411yescharacteristic
285C4×C73#55611yescharacteristic
286Dic73—42no—
287Dic73—81no—
288Dic73—81no—
289#27026—731nomaximal, Sylow
290C2×C73#246511yescharacteristic
291C2×C73#311511yescharacteristic
292C2×C73#312511yescharacteristic
293C2×C73#331011yescharacteristic
294C2×C73#332611yescharacteristic
295C2×C73#338411yescharacteristic
296C2×C73#338811yescharacteristic
297D73—82no—
298#2452—731no—
299#2370D7311yescharacteristic, complemented
300#2065—731no—
301#2059—731no—
302#2058—731no—
303#2025—731no—
304#1988—731no—
305#1943—731no—
306#1926—731no—
307#1925—731no—
308#1920—731no—
309#1920—731no—
310#1917—731no—
311#1864—731no—
312#1762—731no—
313C73#2702611yescharacteristic, complemented, Sylow
314C2×C4⋊Q8—731no—
315C2×#125C2×D7311yescharacteristic
316C2×C22⋊Q8—1461no—
317C2×C4×D4—731no—
318C2×#107—731no—
319C2×#106—731no—
320C2×#106—731no—
321C2×#106—731no—
322C2×C4⋊C8—731no—
323C2×#102—731no—
324C2×#102—731no—
325C2×#102—731no—
326C2×#102—731no—
327C2×#97—731no—
328#396—1461no—
329#393—1461no—
330#390—731no—
331#390—731no—
332#389—21no—
333#389—731no—
334#389—731no—
335#389C2×D7311yescharacteristic
336#389C2×D7311yescharacteristic
337#387—21no—
338#387—21no—
339#385—1461no—
340C4×C4⋊C4—21no—
341C4×C4⋊C4C2×D7311yescharacteristic
342C4×C4⋊C4C2×D7311yescharacteristic
343C4×C4⋊C4C2×D7311yescharacteristic
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#336—731no—
354#336—731no—
355#336—731no—
356#336—731no—
357C22×Q8—1461no—
358C22×D4—731no—
359C23×C4—1461no—
360C22×C8—731no—
361C22×C8—731no—
362C22×C8—731no—
363C22×C8—731no—
364C4⋊Q8—2921no—
365C4⋊Q8—1462no—
366#125—22no—
367#125—22no—
368C22⋊Q8—2924no—
369C4×D4—2921no—
370C4×D4—1462no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
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⋊C4C22⋊D7311yescharacteristic
382C2×C4⋊C4C22⋊D7311yescharacteristic
383C2×C4⋊C4C22×D7311yescharacteristic
384C2×C4⋊C4C22×D7311yescharacteristic
385C2×C4⋊C4C22×D7311yescharacteristic
386C2×C4⋊C4C22×D7311yescharacteristic
387C2×C22⋊C4—1461no—
388C2×C22⋊C4—1461no—
389C2×C22⋊C4—1461no—
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42C22×D7311yescharacteristic
396C2×C42C22×D7311yescharacteristic
397C2×C42C22×D7311yescharacteristic
398#107—1462no—
399#106—2921no—
400#106—1462no—
401#106—1462no—
402C4⋊C8—2921no—
403#102—2921no—
404#102—734no—
405#102—1462no—
406#102—1462no—
407#97—2921no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1461no—
414#95—1461no—
415#95C22⋊D7311yescharacteristic
416#95C22⋊D7311yescharacteristic
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—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—2922no—
432C22×C4—2922no—
433C22×C4—5841no—
434C22×C4—1461no—
435C22×C4—1461no—
436C22×C4—1461no—
437C22×C4C2×C22⋊D7311yescharacteristic
438C22×C4C2×C22⋊D7311yescharacteristic
439C22×C4C2×C22⋊D7311yescharacteristic
440C22×C4C2×C22⋊D7311yescharacteristic
441C22×C4C2×C22⋊D7311yescharacteristic
442C22×C4C2×C22⋊D7311yescharacteristic
443C22×C4C23×D7311yescharacteristic
444C2×C8—732no—
445C2×C8—1461no—
446C2×C8—1461no—
447C2×C8—1461no—
448C2×C8—1461no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—42no—
466C4⋊C4—81no—
467C4⋊C4—2922no—
468C4⋊C4—2922no—
469C4⋊C4—2922no—
470C4⋊C4—732no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4Q8×D7312yes—
477C4⋊C4#1192402812yes—
478C4⋊C4#1192402812yes—
479C22⋊C4—2922no—
480C22⋊C4—2922no—
481C22⋊C4—2922no—
482C22⋊C4—2922no—
483C22⋊C4—5841no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—81no—
492C42—81no—
493C23—2921no—
494C23—2921no—
495C23—2921no—
496C23—2921no—
497C23—2921no—
498C23—2921no—
499C23—1462no—
500C23C22×C22⋊D7311yescharacteristic
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—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
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—5844no—
544C2×C4—1462no—
545C2×C4#1455661612yes—
546C2×C4C2×Q8×D7311yescharacteristic
547C2×C4#41×D7311yescharacteristic
548C2×C4C2×#1192402811yescharacteristic
549C2×C4C2×#1192402811yescharacteristic
550C2×C4#1455663711yescharacteristic
551C2×C4#1455663911yescharacteristic
552C8—2921no—
553C8—2921no—
554C8—2921no—
555C8—1462no—
556C22—2922no—
557C22—2922no—
558C22—2922no—
559C22—5841no—
560C22—5841no—
561C22—5841no—
562C22—5841no—
563C22#1798909811yescharacteristic
564C22#1798922511yescharacteristic
565C22Q8×C22⋊D7311yescharacteristic
566C22C2×#1455661611yescharacteristic
567C22#1798938511yescharacteristic
568C22#1798939511yescharacteristic
569C22#1798939811yescharacteristic
570C4—22no—
571C4—41no—
572C4—42no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—2922no—
581C4—5841no—
582C4—5841no—
583C4#1798914111yescharacteristic
584C4#1798920911yescharacteristic
585C4#1798929711yescharacteristic
586C4#1798930911yescharacteristic
587C2—5842no—
588C2#2261394611yescharacteristic
589C2#2262008211yescharacteristic
590C2#2262020811yescharacteristic
591C2#2262194611yescharacteristic
592C2#2262217811yescharacteristic
593C2#2262283011yescharacteristic
594C2#2262287011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2370C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#2370D73
hypocenterC73#27026
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #22611266C2semidirect
4. #22611264C2semidirect
6. #22610883C2semidirect
7. #22610666C2semidirect
10. #22610516C2semidirect
11. #22610516C2semidirect
12. #22610497C2semidirect
15. C73×#2370C2semidirect
90. #14556511Q8semidirect
299. #2370D73semidirect
313. C73#27026semidirect

Maximal subgroups

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

subgroupindex
#226137812
#226113022
#226112662
#226112642
#226110742
#226108832
#226106662
#226105582
#226105512
#226105162
#226104972
#226101912
#226097592
C73×#23702
#2702673