Finite Group Databasebeta

← #33057121

Subgroups — #33057121

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619996C211yesmaximal, characteristic
2#22618949C211yesmaximal, characteristic
3#22608831C211yesmaximal, characteristic, complemented
4#22608821C211yesmaximal, characteristic, complemented
5#22608809C211yesmaximal, characteristic, complemented
6#22608800C211yesmaximal, characteristic, complemented
7#22608779C211yesmaximal, characteristic, complemented
8#22608774C211yesmaximal, characteristic, complemented
9#22608748C211yesmaximal, characteristic, complemented
10C8×#11924018C211yesmaximal, characteristic, complemented
11#22608714C211yesmaximal, characteristic, complemented
12#22608404C211yesmaximal, characteristic, complemented
13#22608316C211yesmaximal, characteristic
14#22608228C211yesmaximal, characteristic, complemented
15C73×#2962C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988925C411yescharacteristic
18#17988925C411yescharacteristic
19#17988869C411yescharacteristic
20#17988864C411yescharacteristic
21#17988794C411yescharacteristic
22#17988789C411yescharacteristic
23#17988747C411yescharacteristic
24#17988747C411yescharacteristic
25C8×Dic146C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924018C2211yescharacteristic
28C4×#11924018C2211yescharacteristic
29C4×#11924015C2211yescharacteristic
30C4×#11924015C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988666C2211yescharacteristic
33#17988663—21no—
34#17988663—21no—
35#17988644C2211yescharacteristic
36#17988642—21no—
37#17988640C2211yescharacteristic
38#17988640C2211yescharacteristic
39#17988539—21no—
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46Q8⋊#10596831C2211yescharacteristic
47Q8⋊#10596831C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56#533×C73C2211yescharacteristic
57#446×C73—21no—
58#446×C73—21no—
59#446×C73C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C8×Q8×C73C2211yescharacteristic
63#424×C73—21no—
64C2×C4⋊C8×C73C2211yescharacteristic
65#405×C73—21no—
66C4×M16×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924015C2×C411yescharacteristic
72C2×#11924011—21no—
73C2×#11924011—21no—
74C4×Dic146C2×C411yescharacteristic
75C4×Dic146C2311yescharacteristic
76C4×D292C2×C411yescharacteristic
77C4×D292C2311yescharacteristic
78C4×C22⋊D73—21no—
79C4×C22⋊D73—21no—
80#14556550C2×C411yescharacteristic
81#14556548—21no—
82C42×D73—21no—
83#14556524C2×C411yescharacteristic
84#14556524C2×C411yescharacteristic
85#14556522C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87C4⋊#10596831—21no—
88C4⋊#10596831C2×C411yescharacteristic
89C4⋊#10596831C2×C411yescharacteristic
90C4⋊#10596831C2311yescharacteristic
91C4⋊#10596831C2311yescharacteristic
92#14556520—21no—
93#14556520—21no—
94#14556515C2×C411yescharacteristic
95#14556515C2×C411yescharacteristic
96#14556515C2×C411yescharacteristic
97#14556515C2×C411yescharacteristic
98#14556514C2×C411yescharacteristic
99#14556514C2×C411yescharacteristic
100#14556511C2×C411yescharacteristic
101#14556511C2×C411yescharacteristic
102C22⋊#10596831—21no—
103C22⋊#10596831—21no—
104C22⋊#10596831C2×C411yescharacteristic
105C22⋊#10596831C2×C411yescharacteristic
106#14556503—21no—
107#14556503—21no—
108#14556502—21no—
109C4×#10596831C2311yescharacteristic
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C8×Dic73—21no—
114C8×Dic73—21no—
115C2×M16×C73D411yescharacteristic
116C2×M16×C73D411yescharacteristic
117C22×C8×C73—21no—
118C4⋊Q8×C73C2×C411yescharacteristic
119C4⋊Q8×C73C2×C411yescharacteristic
120#125×C73—21no—
121C22⋊Q8×C73—21no—
122C22⋊Q8×C73C2×C411yescharacteristic
123C22⋊Q8×C73C2×C411yescharacteristic
124C4×Q8×C73—21no—
125C4×Q8×C73C2311yescharacteristic
126C4×Q8×C73C2311yescharacteristic
127#117×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—21no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73—21no—
133C4⋊C8×C73—21no—
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136#97×C73—21no—
137#97×C73—21no—
138#97×C73D411yescharacteristic
139#97×C73D411yescharacteristic
140C4×C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—41no—
146C2×Dic146C22×C411yescharacteristic
147C2×D292C22×C411yescharacteristic
148C2×C22⋊D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152#11924018—22no—
153#11924018—22no—
154#11924015—41no—
155#11924015—41no—
156#11924011—42no—
157#11924011—42no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C4⋊Dic73C22×C411yescharacteristic
167C4⋊Dic73C22×C411yescharacteristic
168#11924007—21no—
169#11924007—21no—
170C22⋊Dic73—21no—
171#11924005—21no—
172#11924005—21no—
173C4×Dic73—21no—
174C4×Dic73—21no—
175C4×Dic73—21no—
176C2×Q8×C73—21no—
177C2×Q8×C73C22×C411yescharacteristic
178C2×Q8×C73C22×C411yescharacteristic
179C22×C4×C73C22×C411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73#4111yescharacteristic
182M16×C73—22no—
183M16×C73—41no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—42no—
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
190C2×C8×C73C2×D411yescharacteristic
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73C22×C411yescharacteristic
199C4⋊C4×C73C22×C411yescharacteristic
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73C22×C411yescharacteristic
205C42×C73C2×D411yescharacteristic
206C42×C73#4111yescharacteristic
207C42×C73C2411yescharacteristic
208C23×C73C4×D411yescharacteristic
209C22×D73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—81no—
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×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C23×C411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C22⋊D73—42no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234D292—21no—
235D292—21no—
236C4×D73—42no—
237C4×D73—41no—
238C4×D73—41no—
239C4×D73—81no—
240Dic146—21no—
241Dic146#13112yes—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—41no—
246C8×C73—41no—
247C8×C73#13712yes—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831—41no—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73C2×C4×D411yescharacteristic
260C2×D73—41no—
261C2×D73—41no—
262C2×D73—41no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73—21no—
266C4×C73—21no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73C2×#13111yescharacteristic
272C4×C73#56811yescharacteristic
273C4×C73C2×#13711yescharacteristic
274C4×C73#57511yescharacteristic
275Dic73—22no—
276Dic73—41no—
277Dic73—41no—
278#18013—731nomaximal, Sylow
279C2×C73—41no—
280C2×C73#293311yescharacteristic
281C2×C73C4×#13711yescharacteristic
282C2×C73#295711yescharacteristic
283D73—81no—
284#3107—731no—
285#2971—731no—
286#2962D7311yescharacteristic, complemented
287#1592—731no—
288#1590—731no—
289#1588—731no—
290#1587—731no—
291#1584—731no—
292#1583—731no—
293#1579—731no—
294C8×Q16—731no—
295#1573—731no—
296#1497—731no—
297#1477—731no—
298#1453—731no—
299C73#1801311yescharacteristic, complemented, Sylow
300#533C2×D7311yescharacteristic
301C4×#41—731no—
302#485—731no—
303#485—731no—
304#475—731no—
305#474—731no—
306#462—731no—
307#461—731no—
308#452—731no—
309#452—731no—
310#446—21no—
311#446—21no—
312#446C2×D7311yescharacteristic
313#446C2×D7311yescharacteristic
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8C2×D7311yescharacteristic
317C8×Q8C2×D7311yescharacteristic
318C4×Q16—731no—
319C4×Q16—731no—
320C4×SD16—731no—
321C4×SD16—731no—
322#436—731no—
323#436—731no—
324#436—1461no—
325#436—1461no—
326#432—731no—
327#432—1461no—
328#431—731no—
329#431—731no—
330#424—21no—
331C2×C4⋊C8C2×D7311yescharacteristic
332#405—21no—
333C4×M16—1461no—
334C4×M16C2×D7311yescharacteristic
335#335—731no—
336#335—731no—
337#334—731no—
338#334—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8—731no—
344Q8⋊C8—731no—
345D4⋊C8—731no—
346D4⋊C8—731no—
347#322—731no—
348#322—731no—
349#322—731no—
350C82—731no—
351C2×#41—731no—
352C2×Q16—731no—
353C2×Q16—731no—
354C2×SD16—731no—
355C2×SD16—731no—
356C2×M16—1461no—
357C2×M16—1461no—
358C2×M16C22⋊D7311yescharacteristic
359C2×M16C22⋊D7311yescharacteristic
360C22×C8—21no—
361C4⋊Q8C4×D7311yescharacteristic
362C4⋊Q8C4×D7311yescharacteristic
363#125—21no—
364C22⋊Q8—21no—
365C22⋊Q8C4×D7311yescharacteristic
366C22⋊Q8C4×D7311yescharacteristic
367C4×Q8—21no—
368C4×Q8—731no—
369C4×Q8—731no—
370C4×Q8C22×D7311yescharacteristic
371C4×Q8C22×D7311yescharacteristic
372C4×D4—731no—
373C4×D4—731no—
374C4×D4—1461no—
375C4×D4—1461no—
376#117—21no—
377#117—731no—
378#117—1461no—
379C2×C42—1461no—
380C2×C42C22×D7311yescharacteristic
381#107—731no—
382#107—731no—
383#106—731no—
384#106—731no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—731no—
391C4⋊C8—731no—
392C4⋊C8—731no—
393C4⋊C8—731no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8C22×D7311yescharacteristic
398C4⋊C8C22×D7311yescharacteristic
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#103—731no—
404#103—731no—
405#102—731no—
406#102—731no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—21no—
414#97—21no—
415#97—1461no—
416#97C22⋊D7311yescharacteristic
417#97C22⋊D7311yescharacteristic
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—1461no—
425C4×C8—1461no—
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428#41—2921no—
429#41—1462no—
430C2×Q8—21no—
431C2×Q8—731no—
432C2×Q8C2×C4×D7311yescharacteristic
433C2×Q8C2×C4×D7311yescharacteristic
434C2×D4—731no—
435C2×D4—1461no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4C2×C4×D7311yescharacteristic
440C22×C4C2×C22⋊D7311yescharacteristic
441C22×C4#1192402811yescharacteristic
442Q16—1462no—
443Q16—1462no—
444SD16—2921no—
445SD16—2921no—
446M16—22no—
447M16—41no—
448M16—2922no—
449M16—2922no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8C2×C22⋊D7311yescharacteristic
462C2×C8C2×C22⋊D7311yescharacteristic
463C2×C8C2×C22⋊D7311yescharacteristic
464C2×C8C2×C22⋊D7311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—731no—
473C4⋊C4—731no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4C2×C4×D7311yescharacteristic
477C4⋊C4C2×C4×D7311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—1461no—
481C22⋊C4—1461no—
482C22⋊C4—1461no—
483C42—21no—
484C42—21no—
485C42—1461no—
486C42—1461no—
487C42—1461no—
488C42C2×C4×D7311yescharacteristic
489C42C2×C22⋊D7311yescharacteristic
490C42#1192402811yescharacteristic
491C42C23×D7311yescharacteristic
492C23—1461no—
493C23C4×C22⋊D7311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—732no—
500Q8—1461no—
501D4—2922no—
502D4—1461no—
503D4—1461no—
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—41no—
513C2×C4—2922no—
514C2×C4—2921no—
515C2×C4—2921no—
516C2×C4—5841no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4C4×C22⋊D7311yescharacteristic
521C2×C4C4×C22⋊D7311yescharacteristic
522C2×C4C4×C22⋊D7311yescharacteristic
523C2×C4C22×C4×D7311yescharacteristic
524C2×C4C22×C22⋊D7311yescharacteristic
525C2×C4C2×#1192402811yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—2921no—
532C8—2921no—
533C8—2921no—
534C8—2921no—
535C8—1461no—
536C8—1461no—
537C8—1461no—
538C8—1461no—
539C8#1455662212yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—2921no—
544C22—2921no—
545C22—2921no—
546C22C2×C4×C22⋊D7311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—2921no—
556C4—2921no—
557C4—1462no—
558C4#131×D7311yescharacteristic
559C4#1798935211yescharacteristic
560C4C2×#1455662211yescharacteristic
561C4#1798938511yescharacteristic
562C2—41no—
563C2—5841no—
564C2#2261865311yescharacteristic
565C2C4×#1455662211yescharacteristic
566C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2962C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C2×C4
cosocleC42×C73C24
hypercenter#2962D73
hypocenterC73#18013
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #22608831C2semidirect
4. #22608821C2semidirect
5. #22608809C2semidirect
6. #22608800C2semidirect
7. #22608779C2semidirect
8. #22608774C2semidirect
9. #22608748C2semidirect
10. C8×#11924018C2semidirect
11. #22608714C2semidirect
12. #22608404C2semidirect
14. #22608228C2semidirect
15. C73×#2962C2semidirect
286. #2962D73semidirect
299. C73#18013semidirect

Maximal subgroups

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

subgroupindex
#226199962
#226189492
#226088312
#226088212
#226088092
#226088002
#226087792
#226087742
#226087482
C8×#119240182
#226087142
#226084042
#226083162
#226082282
C73×#29622
#1801373