Finite Group Databasebeta

← #33056089

Subgroups — #33056089

Order 18688.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620002C211yesmaximal, characteristic
2#22619025C211yesmaximal, characteristic, complemented
3#22608802C211yesmaximal, characteristic, complemented
4#22608788C211yesmaximal, characteristic, complemented
5#22608781C211yesmaximal, characteristic, complemented
6#22608767C211yesmaximal, characteristic, complemented
7#22608748C211yesmaximal, characteristic, complemented
8#22608743C211yesmaximal, characteristic, complemented
9C8×#11924018C211yesmaximal, characteristic, complemented
10C8×#11924016C211yesmaximal, characteristic, complemented
11#22608714C211yesmaximal, characteristic, complemented
12#22608365C211yesmaximal, characteristic
13#22608333C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#2988C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17#17988928C411yescharacteristic
18#17988928C411yescharacteristic
19#17988872C411yescharacteristic
20#17988867C411yescharacteristic
21#17988797C411yescharacteristic
22#17988792C411yescharacteristic
23#17988749C411yescharacteristic
24#17988749C411yescharacteristic
25#17988717C2211yescharacteristic
26#17988717C2211yescharacteristic
27#17988716—21no—
28#17988716—21no—
29C8×Dic146C2211yescharacteristic
30C8×Dic146C2211yescharacteristic
31C4×#11924018C2211yescharacteristic
32C4×#11924018C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34C4×#11924016C2211yescharacteristic
35#17988645—21no—
36#17988645—21no—
37#17988644C2211yescharacteristic
38#17988640C2211yescharacteristic
39#17988640C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46#17988317C2211yescharacteristic
47#17988317C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50D4⋊#10596831C2211yescharacteristic
51D4⋊#10596831C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56C4×#41×C73C2211yescharacteristic
57C8×Q8×C73C2211yescharacteristic
58C8×Q8×C73C2211yescharacteristic
59C8×D4×C73—21no—
60C8×D4×C73—21no—
61C8×D4×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#431×C73—21no—
64#431×C73C2211yescharacteristic
65C2×C4⋊C8×C73—21no—
66C2×C4⋊C8×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71#14556591C2×C411yescharacteristic
72#14556591C2×C411yescharacteristic
73#14556583—21no—
74#14556570—21no—
75#14556570C2×C411yescharacteristic
76#14556570C2×C411yescharacteristic
77C4×Dic146—21no—
78C4×Dic146C2311yescharacteristic
79C4×Dic146C2311yescharacteristic
80#14556550—21no—
81#14556524C2×C411yescharacteristic
82#14556524C2×C411yescharacteristic
83#14556522C2×C411yescharacteristic
84#14556522C2×C411yescharacteristic
85C4⋊#10596831—21no—
86C4⋊#10596831C2×C411yescharacteristic
87C4⋊#10596831C2×C411yescharacteristic
88C4⋊#10596831C2311yescharacteristic
89C4⋊#10596831C2311yescharacteristic
90#14556520—21no—
91#14556520—21no—
92#14556520—21no—
93#14556520—21no—
94#14556515C2×C411yescharacteristic
95#14556515C2×C411yescharacteristic
96#14556514C2×C411yescharacteristic
97#14556514C2×C411yescharacteristic
98#14556514C2×C411yescharacteristic
99#14556514C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102C22⋊#10596831—21no—
103C22⋊#10596831—21no—
104C22⋊#10596831C2×C411yescharacteristic
105C22⋊#10596831C2×C411yescharacteristic
106#14556502—21no—
107#14556501—21no—
108#14556501—21no—
109C4×#10596831C2311yescharacteristic
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C8×Dic73—21no—
114C8×Dic73—21no—
115C2×#41×C73C2×C411yescharacteristic
116C22×C8×C73—21no—
117C22×C8×C73—21no—
118C22×C8×C73—21no—
119C4×Q8×C73C2×C411yescharacteristic
120C4×Q8×C73C2311yescharacteristic
121C4×D4×C73—21no—
122C4×D4×C73—21no—
123C4×D4×C73C2×C411yescharacteristic
124C4×D4×C73C2311yescharacteristic
125#117×C73—21no—
126#117×C73C2×C411yescharacteristic
127C2×C42×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—21no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73D411yescharacteristic
133C4⋊C8×C73D411yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73D411yescharacteristic
139C22⋊C8×C73D411yescharacteristic
140C4×C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×Dic146C22×C411yescharacteristic
147#11924018—22no—
148#11924018—22no—
149#11924016—22no—
150#11924016—22no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831C22×C411yescharacteristic
156C2×#10596831C22×C411yescharacteristic
157C2×#10596831C22×C411yescharacteristic
158C2×#10596831C22×C411yescharacteristic
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73C22×C411yescharacteristic
163C4⋊Dic73C22×C411yescharacteristic
164#11924007—21no—
165#11924007—21no—
166#11924007—21no—
167#11924007—21no—
168C22⋊Dic73—21no—
169C22⋊Dic73—21no—
170C4×Dic73—21no—
171C4×Dic73—21no—
172#41×C73—22no—
173#41×C73—22no—
174C2×Q8×C73C22×C411yescharacteristic
175C2×D4×C73—21no—
176C2×D4×C73C22×C411yescharacteristic
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73C22×C411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73#4111yescharacteristic
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—81no—
186C2×C8×C73—81no—
187C2×C8×C73—81no—
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
190C2×C8×C73C2×D411yescharacteristic
191C2×C8×C73C2×D411yescharacteristic
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73C22×C411yescharacteristic
195C4⋊C4×C73C22×C411yescharacteristic
196C22⋊C4×C73—21no—
197C22⋊C4×C73—21no—
198C22⋊C4×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73C22×C411yescharacteristic
203C42×C73C2×D411yescharacteristic
204C42×C73#4111yescharacteristic
205C42×C73C2411yescharacteristic
206C23×C73—21no—
207C23×C73C4×D411yescharacteristic
208Q8×C73—21no—
209Q8×C73#13112yes—
210D4×C73—24no—
211D4×C73—21no—
212D4×C73#13112yes—
213C2×C4×C73—24no—
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—81no—
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C4×D411yescharacteristic
228C2×C4×C73C23×C411yescharacteristic
229C2×C4×C73C22×D411yescharacteristic
230C2×C4×C73C2×#4111yescharacteristic
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235Dic146—21no—
236Dic146—21no—
237Dic146—21no—
238Dic146—21no—
239Dic146—81no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—41no—
245C8×C73—41no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—41no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254C22×C73—21no—
255C22×C73—22no—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73C2×C4×D411yescharacteristic
261C4×C73—21no—
262C4×C73—22no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73—21no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73C2×#13111yescharacteristic
269C4×C73C2×#13111yescharacteristic
270C4×C73#57711yescharacteristic
271C4×C73#57811yescharacteristic
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276#17921—731nomaximal, Sylow
277C2×C73—41no—
278C2×C73—42no—
279C2×C73#292911yescharacteristic
280C2×C73#294711yescharacteristic
281C2×C73#295711yescharacteristic
282#3107—731no—
283#2988D7311yescharacteristic
284#2985—731no—
285#1587—731no—
286#1585—731no—
287#1584—731no—
288#1582—731no—
289#1579—731no—
290SD16⋊C8—731no—
291C8×Q16—731no—
292C8×SD16—731no—
293#1573—731no—
294#1488—731no—
295#1481—731no—
296#1454—731no—
297C73#1792111yescharacteristic, complemented, Sylow
298#533—731no—
299C4×#41C2×D7311yescharacteristic
300#485—731no—
301#485—731no—
302#475—731no—
303#474—731no—
304#462—731no—
305#461—731no—
306#452—731no—
307#452—731no—
308#446—731no—
309#446—731no—
310#446—1461no—
311#446—1461no—
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8C2×D7311yescharacteristic
315C8×Q8C2×D7311yescharacteristic
316C4×Q16—731no—
317C4×Q16—731no—
318C4×SD16—731no—
319C4×SD16—731no—
320C8×D4—21no—
321C8×D4—21no—
322C8×D4C2×D7311yescharacteristic
323C8×D4C2×D7311yescharacteristic
324#433—1461no—
325#433—1461no—
326#432—731no—
327#431—21no—
328#431—731no—
329#431—731no—
330#431C2×D7311yescharacteristic
331C2×C4⋊C8—21no—
332C2×C4⋊C8C2×D7311yescharacteristic
333#335—731no—
334#335—731no—
335#334—731no—
336#334—731no—
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343D4⋊C8—731no—
344D4⋊C8—731no—
345#322—731no—
346#322—731no—
347#322—731no—
348C82—731no—
349C2×#41C4×D7311yescharacteristic
350C2×Q16—731no—
351C2×Q16—731no—
352C2×SD16—731no—
353C2×SD16—731no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C4⋊Q8—731no—
358C4⋊Q8—731no—
359#125—1461no—
360C22⋊Q8—731no—
361C22⋊Q8—731no—
362C22⋊Q8—1461no—
363C4×Q8—731no—
364C4×Q8—731no—
365C4×Q8—1461no—
366C4×Q8C4×D7311yescharacteristic
367C4×Q8C22×D7311yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4C4×D7311yescharacteristic
371C4×D4C22×D7311yescharacteristic
372#117—21no—
373#117—1461no—
374#117C4×D7311yescharacteristic
375C2×C42—21no—
376C2×C42C22×D7311yescharacteristic
377#107—731no—
378#107—731no—
379#106—731no—
380#106—731no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—1461no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8C22⋊D7311yescharacteristic
394C4⋊C8C22⋊D7311yescharacteristic
395C4⋊C8C22×D7311yescharacteristic
396C4⋊C8C22×D7311yescharacteristic
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#102—731no—
404#102—731no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8C22⋊D7311yescharacteristic
412C22⋊C8C22⋊D7311yescharacteristic
413#97—1461no—
414#97—1461no—
415#97—1461no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426#41—22no—
427#41—22no—
428C2×Q8—731no—
429C2×Q8—731no—
430C2×Q8—1461no—
431C2×Q8C2×C4×D7311yescharacteristic
432C2×D4—21no—
433C2×D4C2×C4×D7311yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C2×C4×D7311yescharacteristic
438C22×C4C2×C22⋊D7311yescharacteristic
439C22×C4#1192402811yescharacteristic
440Q16—1462no—
441Q16—1462no—
442SD16—1462no—
443SD16—1462no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8—81no—
449C2×C8—731no—
450C2×C8—731no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8C2×C22⋊D7311yescharacteristic
458C2×C8C2×C22⋊D7311yescharacteristic
459C2×C8C2×C22⋊D7311yescharacteristic
460C2×C8C2×C22⋊D7311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—731no—
464C4⋊C4—731no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4C2×C4×D7311yescharacteristic
473C4⋊C4C2×C4×D7311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—1461no—
483C42—1461no—
484C42C2×C4×D7311yescharacteristic
485C42C2×C22⋊D7311yescharacteristic
486C42#1192402811yescharacteristic
487C42C23×D7311yescharacteristic
488C23—21no—
489C23C4×C22⋊D7311yescharacteristic
490Q8—21no—
491Q8—5841no—
492Q8—1461no—
493Q8—1461no—
494Q8—1461no—
495Q8—1461no—
496Q8#1455659712yes—
497D4—24no—
498D4—21no—
499D4#1455659712yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4C4×C22⋊D7311yescharacteristic
517C2×C4C4×C22⋊D7311yescharacteristic
518C2×C4C4×C22⋊D7311yescharacteristic
519C2×C4C22×C4×D7311yescharacteristic
520C2×C4C22×C22⋊D7311yescharacteristic
521C2×C4C2×#1192402811yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—2921no—
529C8—2921no—
530C8—2921no—
531C8—2921no—
532C8—1461no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C22—21no—
537C22—22no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22C2×C4×C22⋊D7311yescharacteristic
543C4—21no—
544C4—22no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—2921no—
551C4—2921no—
552C4—2921no—
553C4—2921no—
554C4C2×#1455659711yescharacteristic
555C4C2×#1455659711yescharacteristic
556C4#1798939811yescharacteristic
557C4#1798940211yescharacteristic
558C2—41no—
559C2—42no—
560C2#2261862511yescharacteristic
561C2#2261877011yescharacteristic
562C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2988C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×C73C2×C4
cosocleC42×C73C24
hypercenter#2988D73
hypocenterC73#17921
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2988

Complements

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

NH ≅ G/Ntype
2. #22619025C2semidirect
3. #22608802C2semidirect
4. #22608788C2semidirect
5. #22608781C2semidirect
6. #22608767C2semidirect
7. #22608748C2semidirect
8. #22608743C2semidirect
9. C8×#11924018C2semidirect
10. C8×#11924016C2semidirect
11. #22608714C2semidirect
13. #22608333C2semidirect
14. #22608231C2semidirect
297. C73#17921semidirect

Maximal subgroups

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

subgroupindex
#226200022
#226190252
#226088022
#226087882
#226087812
#226087672
#226087482
#226087432
C8×#119240182
C8×#119240162
#226087142
#226083652
#226083332
#226082312
C73×#29882
#1792173