Finite Group Databasebeta

← #33158590

Subgroups — #33158590

Order 18688.

690 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613803C211yesmaximal, characteristic
2#22611316C211yesmaximal, characteristic
3#22611269C211yesmaximal, characteristic, complemented
4#22611266C211yesmaximal, characteristic, complemented
5#22611074C211yesmaximal, characteristic
6#22610888C211yesmaximal, characteristic, complemented
7#22610671C211yesmaximal, characteristic, complemented
8#22610558C211yesmaximal, characteristic
9#22610551C211yesmaximal, characteristic
10#22610509C211yesmaximal, characteristic, complemented
11#22610502C211yesmaximal, characteristic, complemented
12#22610497C211yesmaximal, characteristic, complemented
13#22610191C211yesmaximal, characteristic
14#22609759C211yesmaximal, characteristic
15C73×#2370C211yesmaximal, characteristic, complemented
16C2×#14556583C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18C2×#14556524C2211yescharacteristic
19C2×#14556524C2211yescharacteristic
20C2×#14556522C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×#14556511C2211yescharacteristic
24C2×#14556511C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556502C2211yescharacteristic
28#17988522—21no—
29#17988511—21no—
30#17988489C2211yescharacteristic
31#17988489C2211yescharacteristic
32#17988485C2211yescharacteristic
33#17988485C2211yescharacteristic
34#17988458—21no—
35#17988446—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×D292C2311yescharacteristic
60C22×C4×D73—21no—
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65#14556583—22no—
66#14556583—41no—
67C4×D292—22no—
68C4×D292—41no—
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×#11924007—21no—
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×#11924005—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81#14556524—22no—
82#14556524—41no—
83#14556522—22no—
84#14556522—22no—
85C4⋊#10596831—41no—
86#14556511—22no—
87#14556511—22no—
88#14556511—41no—
89#14556511Q814yes—
90#14556502—41no—
91#14556498—21no—
92#14556498—21no—
93#125×C73—22no—
94#125×C73—22no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73D411yescharacteristic
100C2×C4⋊C4×C73D411yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C42×C73—21no—
106C2×C42×C73—21no—
107C2×C42×C73—21no—
108C2×C42×C73C2311yescharacteristic
109C2×C42×C73C2311yescharacteristic
110C2×C42×C73C2311yescharacteristic
111#95×C73—21no—
112#95×C73—21no—
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73D411yescharacteristic
117#95×C73D411yescharacteristic
118C23×D73—21no—
119C2×D292—21no—
120C2×D292—21no—
121C2×D292—21no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292C2×Q812yes—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C2×C4×D73—42no—
129C2×C4×D73—42no—
130C2×C4×D73—81no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831C2×Q812yes—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73#4112yes—
149#11924007—42no—
150#11924007—42no—
151#11924007—81no—
152#11924007—81no—
153#11924005—42no—
154#11924005—42no—
155#11924005—81no—
156#11924005—81no—
157#11924005—81no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73C2×D411yescharacteristic
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2411yescharacteristic
169C4⋊C4×C73—24no—
170C4⋊C4×C73—24no—
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—41no—
177C4⋊C4×C73—41no—
178C4⋊C4×C73—42no—
179C4⋊C4×C73—81no—
180C4⋊C4×C73C2×Q812yes—
181C4⋊C4×C73#4112yes—
182C4⋊C4×C73#4112yes—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—42no—
190C42×C73—81no—
191C42×C73—81no—
192C23×C73C22×D411yescharacteristic
193C22×D73—22no—
194C22×D73—41no—
195C22×D73—41no—
196C22×D73—41no—
197C22×D73—41no—
198C22×D73—41no—
199C22×D73—41no—
200C2×C4×C73—21no—
201C2×C4×C73—21no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—22no—
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×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
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×C73C22×Q811yescharacteristic
231C2×C4×C73C2×#4111yescharacteristic
232C2×C4×C73C2×#4111yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C2×C4×C73H(5,𝔽2)11yescharacteristic
235C2×C4×C732−1+411yescharacteristic
236C2×Dic73—22no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245D292—22no—
246D292—22no—
247D292—41no—
248D292—41no—
249C4×D73—84no—
250#10596831—22no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254C22×C73#52511yescharacteristic
255C22×C73#54611yescharacteristic
256C22×C73D4×Q811yescharacteristic
257C22×C73#57511yescharacteristic
258C22×C73#57511yescharacteristic
259C22×C73#57611yescharacteristic
260C22×C73#57711yescharacteristic
261C2×D73—42no—
262C2×D73—42no—
263C2×D73—42no—
264C2×D73—81no—
265C2×D73—81no—
266C2×D73—81no—
267C2×D73—81no—
268C4×C73—41no—
269C4×C73—42no—
270C4×C73—41no—
271C4×C73—42no—
272C4×C73—42no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—81no—
278C4×C73#53311yescharacteristic
279C4×C73#54211yescharacteristic
280C4×C73#55411yescharacteristic
281C4×C73#55611yescharacteristic
282Dic73—42no—
283Dic73—81no—
284Dic73—81no—
285#27027—731nomaximal, Sylow
286C2×C73#246511yescharacteristic
287C2×C73#311111yescharacteristic
288C2×C73#311911yescharacteristic
289C2×C73#330911yescharacteristic
290C2×C73#332311yescharacteristic
291C2×C73#338811yescharacteristic
292C2×C73#338911yescharacteristic
293D73—82no—
294#2454—731no—
295#2370D7311yescharacteristic, complemented
296#2067—731no—
297#2059—731no—
298#2059—731no—
299#2025—731no—
300#1989—731no—
301#1944—731no—
302#1926—731no—
303#1925—731no—
304#1919—731no—
305#1918—731no—
306#1917—731no—
307#1864—731no—
308#1762—731no—
309C73#2702711yescharacteristic, complemented, Sylow
310C2×#125—731no—
311C2×#125C2×D7311yescharacteristic
312C2×C4×D4—731no—
313C2×#107—731no—
314C2×#107—731no—
315C2×#106—731no—
316C2×#106—731no—
317C2×C4⋊C8—731no—
318C2×#102—731no—
319C2×#102—731no—
320C2×#102—731no—
321C2×#102—731no—
322C2×#97—731no—
323#399—1461no—
324#396—1461no—
325#390—731no—
326#390—731no—
327#389—21no—
328#389—731no—
329#389—731no—
330#389C2×D7311yescharacteristic
331#389C2×D7311yescharacteristic
332#387—21no—
333#387—21no—
334#385—1461no—
335#380—1461no—
336C4×C4⋊C4—21no—
337C4×C4⋊C4C2×D7311yescharacteristic
338C4×C4⋊C4C2×D7311yescharacteristic
339C4×C4⋊C4C2×D7311yescharacteristic
340C4×C4⋊C4C2×D7311yescharacteristic
341#340—731no—
342#340—731no—
343#340—731no—
344#340—731no—
345#340—731no—
346#340—731no—
347#340—731no—
348#340—731no—
349#336—731no—
350#336—731no—
351#336—731no—
352#336—731no—
353C22×D4—731no—
354C23×C4—1461no—
355C22×C8—731no—
356C22×C8—731no—
357C22×C8—731no—
358C22×C8—731no—
359#125—22no—
360#125—22no—
361#125—2921no—
362#125—1462no—
363C4×D4—2921no—
364C4×D4—1462no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—1461no—
373C2×C4⋊C4—1461no—
374C2×C4⋊C4—1461no—
375C2×C4⋊C4—1461no—
376C2×C4⋊C4C22⋊D7311yescharacteristic
377C2×C4⋊C4C22⋊D7311yescharacteristic
378C2×C4⋊C4C22×D7311yescharacteristic
379C2×C4⋊C4C22×D7311yescharacteristic
380C2×C4⋊C4C22×D7311yescharacteristic
381C2×C4⋊C4C22×D7311yescharacteristic
382C2×C22⋊C4—1461no—
383C2×C22⋊C4—1461no—
384C2×C22⋊C4—1461no—
385C2×C22⋊C4—1461no—
386C2×C22⋊C4—1461no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C22×D7311yescharacteristic
391C2×C42C22×D7311yescharacteristic
392C2×C42C22×D7311yescharacteristic
393#107—2921no—
394#107—1462no—
395#106—1462no—
396#106—1462no—
397C4⋊C8—2921no—
398#102—2921no—
399#102—734no—
400#102—1462no—
401#102—1462no—
402#97—2921no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—1461no—
409#95—1461no—
410#95C22⋊D7311yescharacteristic
411#95C22⋊D7311yescharacteristic
412C24—1461no—
413C2×D4—732no—
414C2×D4—1461no—
415C2×D4—1461no—
416C2×D4—1461no—
417C2×D4—1461no—
418C2×D4—1461no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—2922no—
424C22×C4—2922no—
425C22×C4—5841no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1461no—
429C22×C4C2×C22⋊D7311yescharacteristic
430C22×C4C2×C22⋊D7311yescharacteristic
431C22×C4C2×C22⋊D7311yescharacteristic
432C22×C4C2×C22⋊D7311yescharacteristic
433C22×C4C2×C22⋊D7311yescharacteristic
434C22×C4C2×C22⋊D7311yescharacteristic
435C22×C4C23×D7311yescharacteristic
436C2×C8—732no—
437C2×C8—1461no—
438C2×C8—1461no—
439C2×C8—1461no—
440C2×C8—1461no—
441C2×C8—1461no—
442C2×C8—1461no—
443C2×C8—1461no—
444C2×C8—1461no—
445C2×C8—1461no—
446C2×C8—1461no—
447C2×C8—1461no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—42no—
458C4⋊C4—81no—
459C4⋊C4—2922no—
460C4⋊C4—2922no—
461C4⋊C4—5841no—
462C4⋊C4—5841no—
463C4⋊C4—732no—
464C4⋊C4—1461no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4Q8×D7312yes—
470C4⋊C4#1192402812yes—
471C4⋊C4#1192402812yes—
472C22⋊C4—2922no—
473C22⋊C4—2922no—
474C22⋊C4—5841no—
475C22⋊C4—5841no—
476C22⋊C4—5841no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—42no—
484C42—81no—
485C42—81no—
486C23—2921no—
487C23—2921no—
488C23—2921no—
489C23—2921no—
490C23—2921no—
491C23—2921no—
492C23—1462no—
493C23C22×C22⋊D7311yescharacteristic
494D4—2921no—
495D4—2921no—
496D4—1462no—
497D4—1462no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
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—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
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—5844no—
537C2×C4—1462no—
538C2×C4C2×Q8×D7311yescharacteristic
539C2×C4#41×D7311yescharacteristic
540C2×C4C2×#1192402811yescharacteristic
541C2×C4C2×#1192402811yescharacteristic
542C2×C4#1455663711yescharacteristic
543C2×C4#1455663911yescharacteristic
544C8—2921no—
545C8—2921no—
546C8—2921no—
547C8—1462no—
548C22—2922no—
549C22—2922no—
550C22—2922no—
551C22—5841no—
552C22—5841no—
553C22—5841no—
554C22—5841no—
555C22#1798909811yescharacteristic
556C22#1798922511yescharacteristic
557C22Q8×C22⋊D7311yescharacteristic
558C22#1798938511yescharacteristic
559C22#1798938511yescharacteristic
560C22#1798939011yescharacteristic
561C22#1798939511yescharacteristic
562C4—41no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—2922no—
573C4—5841no—
574C4—5841no—
575C4#1798914111yescharacteristic
576C4#1798920911yescharacteristic
577C4#1798929711yescharacteristic
578C4#1798930911yescharacteristic
579C2—5842no—
580C2#2261394611yescharacteristic
581C2#2262004011yescharacteristic
582C2#2262013011yescharacteristic
583C2#2262193111yescharacteristic
584C2#2262214111yescharacteristic
585C2#2262287011yescharacteristic
586C2#2262288511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2370C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#2370D73
hypocenterC73#27027
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. #22611269C2semidirect
4. #22611266C2semidirect
6. #22610888C2semidirect
7. #22610671C2semidirect
10. #22610509C2semidirect
11. #22610502C2semidirect
12. #22610497C2semidirect
15. C73×#2370C2semidirect
295. #2370D73semidirect
309. C73#27027semidirect

Maximal subgroups

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

subgroupindex
#226138032
#226113162
#226112692
#226112662
#226110742
#226108882
#226106712
#226105582
#226105512
#226105092
#226105022
#226104972
#226101912
#226097592
C73×#23702
#2702773