Finite Group Databasebeta

← #34018685

Subgroups — #34018685

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#22626847C211yesmaximal, characteristic
2#22626839C211yesmaximal, characteristic, complemented
3#22625555C211yesmaximal, characteristic, complemented
4#22625546C211yesmaximal, characteristic, complemented
5#22625543C211yesmaximal, characteristic, complemented
6#22625534C211yesmaximal, characteristic, complemented
7#22625526C211yesmaximal, characteristic, complemented
8#22625522C211yesmaximal, characteristic, complemented
9#22625519C211yesmaximal, characteristic, complemented
10#22625514C211yesmaximal, characteristic, complemented
11#22625505C211yesmaximal, characteristic, complemented
12#22625263C211yesmaximal, characteristic
13#22625241C211yesmaximal, characteristic, complemented
14#22625153C211yesmaximal, characteristic, complemented
15#22620004C211yesmaximal, characteristic
16#17989638—21no—
17#17989638—21no—
18#17989637C2211yescharacteristic
19#17989637C2211yescharacteristic
20#17989636C2211yescharacteristic
21#17989636C2211yescharacteristic
22#17989636C2211yescharacteristic
23#17989636C2211yescharacteristic
24#17989614—21no—
25#17989614—21no—
26D4×#10596833C2211yescharacteristic
27D4×#10596833C2211yescharacteristic
28#17989612—21no—
29#17989612—21no—
30#17989609C2211yescharacteristic
31#17989606C2211yescharacteristic
32#17989605C2211yescharacteristic
33#17989604—21no—
34C2×#14556658—21no—
35#17989588C2211yescharacteristic
36#17989451C2211yescharacteristic
37#17989450C2211yescharacteristic
38#17989449C2211yescharacteristic
39#17989448C2211yescharacteristic
40#17989437C2211yescharacteristic
41#17989437C2211yescharacteristic
42#17989437C2211yescharacteristic
43#17989437C2211yescharacteristic
44#17989437C2211yescharacteristic
45#17989437C2211yescharacteristic
46D4⋊#10596833C2211yescharacteristic
47D4⋊#10596833C2211yescharacteristic
48#17989429C2211yescharacteristic
49#17989429C2211yescharacteristic
50#17989428C2211yescharacteristic
51C8×#10596833C2211yescharacteristic
52#17989142C2211yescharacteristic
53C4×#11924027C2211yescharacteristic
54#17988930C411yescharacteristic
55#17988930C411yescharacteristic
56#17988869C411yescharacteristic
57#17988798C411yescharacteristic
58#17988792C411yescharacteristic
59#17988750C411yescharacteristic
60#17988750C411yescharacteristic
61#17988681C2211yescharacteristic
62#17988681C2211yescharacteristic
63#17988678C2211yescharacteristic
64#17988678C2211yescharacteristic
65#17988639C2211yescharacteristic
66#474×C73C411yescharacteristic
67C2×#11924036—21no—
68C22×#10596833—21no—
69C22×#10596833—21no—
70#14556658—21no—
71#14556658—21no—
72#14556658—21no—
73#14556658—21no—
74#14556658—21no—
75#14556658D411yescharacteristic
76#14556658D411yescharacteristic
77C4⋊#10596833—21no—
78C4⋊#10596833—21no—
79C4⋊#10596833—21no—
80C4⋊#10596833C2311yescharacteristic
81C4⋊#10596833C2311yescharacteristic
82C4⋊#10596833C2311yescharacteristic
83C4⋊#10596833C2311yescharacteristic
84#14556648—21no—
85#14556648—21no—
86#14556648D411yescharacteristic
87#14556648D411yescharacteristic
88C22⋊#10596833—21no—
89C22⋊#10596833—21no—
90#14556646—21no—
91#14556646—21no—
92#14556646—21no—
93C4×#10596833—21no—
94C4×#10596833—21no—
95C4×#10596833—21no—
96C4×#10596833—21no—
97C4×#10596833C2311yescharacteristic
98C4×#10596833C2311yescharacteristic
99C4×#10596833C2311yescharacteristic
100C4×#10596833C2311yescharacteristic
101C2×#11924027C2×C411yescharacteristic
102C2×Dic292C2×C411yescharacteristic
103C2×Dic292C2×C411yescharacteristic
104C2×#11924016C2×C411yescharacteristic
105C2×#11924016C2×C411yescharacteristic
106#14556591C2×C411yescharacteristic
107#14556582—21no—
108#14556571C2×C411yescharacteristic
109#14556571C2×C411yescharacteristic
110#14556567—21no—
111Q8×Dic73—21no—
112C4×Dic146C2×C411yescharacteristic
113#14556556C2311yescharacteristic
114#14556556C2311yescharacteristic
115#14556556C2311yescharacteristic
116D4×Dic73C2311yescharacteristic
117C4×C22⋊D73—21no—
118#14556551—21no—
119#14556549—21no—
120#14556549C2×C411yescharacteristic
121#14556547—21no—
122C2×C4×Dic73—21no—
123C42×D73C2311yescharacteristic
124#14556522C2×C411yescharacteristic
125#14556522C2×C411yescharacteristic
126C4⋊#10596831C2×C411yescharacteristic
127#14556516C2×C411yescharacteristic
128#14556516C2×C411yescharacteristic
129#14556514C2×C411yescharacteristic
130#14556514C2×C411yescharacteristic
131#14556514C2×C411yescharacteristic
132#14556514C2×C411yescharacteristic
133#14556503C2×C411yescharacteristic
134#14556503C2×C411yescharacteristic
135C8×Dic73C2311yescharacteristic
136C8×Dic73C2311yescharacteristic
137C4⋊Q8×C73C2×C411yescharacteristic
138C4×D4×C73C2×C411yescharacteristic
139#107×C73C2×C411yescharacteristic
140#107×C73C2×C411yescharacteristic
141C4⋊C8×C73C2×C411yescharacteristic
142#102×C73C2×C411yescharacteristic
143#102×C73C2×C411yescharacteristic
144#11924036—81no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—81no—
152C2×#10596833—81no—
153C2×#10596833C2×D411yescharacteristic
154C2×#10596833C2×D411yescharacteristic
155C2×#10596833C2×D411yescharacteristic
156C2×#10596833C2×D411yescharacteristic
157#11924027—22no—
158#11924027—22no—
159C2×Dic146C22×C411yescharacteristic
160C2×Dic146C22×C411yescharacteristic
161C2×Dic146C22×C411yescharacteristic
162C2×C22⋊D73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C2×C4×D73C22×C411yescharacteristic
166C2×C4×D73C2×D411yescharacteristic
167C2×C4×D73#4111yescharacteristic
168Dic292—22no—
169Dic292—22no—
170#11924016—22no—
171#11924016—22no—
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C22×C411yescharacteristic
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73C22×C411yescharacteristic
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183C22⋊Dic73—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73C2×D411yescharacteristic
193C4×Dic73#4111yescharacteristic
194C4×Dic73C2411yescharacteristic
195C2×Q8×C73—21no—
196C2×D4×C73C22×C411yescharacteristic
197C22×C4×C73—21no—
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C4⋊C4×C73—21no—
201C4⋊C4×C73C22×C411yescharacteristic
202C4⋊C4×C73C22×C411yescharacteristic
203C4⋊C4×C73C22×C411yescharacteristic
204C22⋊C4×C73—21no—
205C42×C73C22×C411yescharacteristic
206C23×C73—21no—
207C22×D73C4×D411yescharacteristic
208Q8×C73—81no—
209D4×C73—21no—
210D4×C73#13112yes—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—81no—
215C2×C4×C73C4×D411yescharacteristic
216C2×C4×C73C4×D411yescharacteristic
217C2×C4×C73C23×C411yescharacteristic
218C22⋊D73—24no—
219C2×Dic73—24no—
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—41no—
225C2×Dic73—41no—
226C2×Dic73C4×D411yescharacteristic
227C2×Dic73C22×D411yescharacteristic
228C2×Dic73C2×#4111yescharacteristic
229C4×D73—21no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—41no—
234Dic146—21no—
235Dic146—21no—
236Dic146—21no—
237Dic146—21no—
238Dic146—21no—
239Dic146#13112yes—
240#10596833—21no—
241#10596833—21no—
242#10596833—21no—
243#10596833—21no—
244#10596833—41no—
245#10596833—41no—
246#10596833—41no—
247#10596833—41no—
248#10596833—41no—
249#10596833—41no—
250C8×C73—21no—
251C8×C73—21no—
252#10596831—21no—
253#10596831—21no—
254C22×C73—22no—
255C22×C73—41no—
256C22×C73—41no—
257C22×C73C2×C4×D411yescharacteristic
258C2×D73—21no—
259C2×D73—21no—
260C2×D73—21no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73C2×#13111yescharacteristic
267C4×C73C2×#13111yescharacteristic
268Dic73—22no—
269Dic73—21no—
270Dic73—21no—
271Dic73—41no—
272Dic73—41no—
273Dic73—41no—
274Dic73#57711yescharacteristic
275Dic73#57811yescharacteristic
276#17921—731nomaximal, Sylow
277C2×C73—42no—
278C2×C73#292911yescharacteristic
279C2×C73#294711yescharacteristic
280C2×C73#295711yescharacteristic
281D73—41no—
282#3107—731no—
283#2988—731no—
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×#41—731no—
300#485—731no—
301#485—731no—
302#475—731no—
303#474#6440811yescharacteristic
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×Q8—731no—
315C8×Q8—731no—
316C4×Q16—731no—
317C4×Q16—731no—
318C4×SD16—731no—
319C4×SD16—731no—
320C8×D4—731no—
321C8×D4—731no—
322C8×D4—1461no—
323C8×D4—1461no—
324#433—1461no—
325#433—1461no—
326#432—731no—
327#431—731no—
328#431—731no—
329#431—731no—
330#431—1461no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—1461no—
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×#41—731no—
350C2×Q16—731no—
351C2×Q16—731no—
352C2×SD16—731no—
353C2×SD16—731no—
354C22×C8—1461no—
355C22×C8—1461no—
356C22×C8—1461no—
357C4⋊Q8—731no—
358C4⋊Q8C2×#6440811yescharacteristic
359#125—1461no—
360C22⋊Q8—731no—
361C22⋊Q8—731no—
362C22⋊Q8—1461no—
363C4×Q8—731no—
364C4×Q8—731no—
365C4×Q8—731no—
366C4×Q8—731no—
367C4×Q8—1461no—
368C4×D4—731no—
369C4×D4—1461no—
370C4×D4—1461no—
371C4×D4C2×#6440811yescharacteristic
372#117—731no—
373#117—1461no—
374#117—1461no—
375C2×C42—731no—
376C2×C42—1461no—
377#107C2×#6440811yescharacteristic
378#107C2×#6440811yescharacteristic
379#106—731no—
380#106—731no—
381C4⋊C8—731no—
382C4⋊C8—731no—
383C4⋊C8—731no—
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⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8C2×#6440811yescharacteristic
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#102C2×#6440811yescharacteristic
404#102C2×#6440811yescharacteristic
405C22⋊C8—731no—
406C22⋊C8—731no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—1461no—
414#97—1461no—
415#97—1461no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8—1461no—
426#41—1462no—
427#41—1462no—
428C2×Q8—21no—
429C2×Q8—731no—
430C2×Q8—731no—
431C2×Q8—731no—
432C2×D4—1461no—
433C2×D4C22×#6440811yescharacteristic
434C22×C4—21no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—1461no—
439C22×C4—1461no—
440Q16—1462no—
441Q16—1462no—
442SD16—1462no—
443SD16—1462no—
444C2×C8—5841no—
445C2×C8—5841no—
446C2×C8—5841no—
447C2×C8—731no—
448C2×C8—731no—
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×C8—1461no—
458C2×C8—1461no—
459C2×C8C22×#6440811yescharacteristic
460C2×C8C22×#6440811yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—731no—
463C4⋊C4—1461no—
464C4⋊C4—1461no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4C22×#6440811yescharacteristic
472C4⋊C4C22×#6440811yescharacteristic
473C4⋊C4C22×#6440811yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C42—731no—
480C42—731no—
481C42—731no—
482C42—1461no—
483C42—1461no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42C22×#6440811yescharacteristic
488C23—21no—
489C23—731no—
490Q8—81no—
491Q8—732no—
492Q8—1461no—
493Q8—1461no—
494Q8—1461no—
495Q8—1461no—
496Q8—1461no—
497D4—21no—
498D4—1464no—
499D4#1455667912yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—81no—
504C2×C4—2921no—
505C2×C4—2921no—
506C2×C4—2921no—
507C2×C4—731no—
508C2×C4—731no—
509C2×C4—731no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1464no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4D4×#6440811yescharacteristic
520C2×C4D4×#6440811yescharacteristic
521C2×C4C23×#6440811yescharacteristic
522C8—21no—
523C8—21no—
524C8—2921no—
525C8—2921no—
526C8—2921no—
527C8—2921no—
528C8—2921no—
529C8—2921no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C22—22no—
537C22—41no—
538C22—41no—
539C22—1461no—
540C22—1461no—
541C22—1461no—
542C22C2×D4×#6440811yescharacteristic
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—2921no—
549C4—2921no—
550C4—2921no—
551C4—731no—
552C4—731no—
553C4—1461no—
554C4—1462no—
555C4—1461no—
556C4D73⋊#13111yescharacteristic
557C4C2×#1455667911yescharacteristic
558C2—42no—
559C2—2921no—
560C2#2262664711yescharacteristic
561C2#2262668911yescharacteristic
562C2#2262670711yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#474×C73C4
socleC22×C73C2×C4×D4
prime radicalC2×#11924027C2×C4
cosocleC4×Dic73C24
hypercenter#474#64408
hypocenterC73#17921
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #22626839C2semidirect
3. #22625555C2semidirect
4. #22625546C2semidirect
5. #22625543C2semidirect
6. #22625534C2semidirect
7. #22625526C2semidirect
8. #22625522C2semidirect
9. #22625519C2semidirect
10. #22625514C2semidirect
11. #22625505C2semidirect
13. #22625241C2semidirect
14. #22625153C2semidirect
297. C73#17921semidirect

Maximal subgroups

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

subgroupindex
#226268472
#226268392
#226255552
#226255462
#226255432
#226255342
#226255262
#226255222
#226255192
#226255142
#226255052
#226252632
#226252412
#226251532
#226200042
#1792173