Finite Group Databasebeta

← #33056816

Subgroups — #33056816

Order 18688.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619080C211yesmaximal, characteristic
2#22619026C211yesmaximal, characteristic, complemented
3#22608810C211yesmaximal, characteristic, complemented
4#22608803C211yesmaximal, characteristic, complemented
5#22608803C211yesmaximal, characteristic, complemented
6#22608789C211yesmaximal, characteristic, complemented
7#22608782C211yesmaximal, characteristic, complemented
8#22608782C211yesmaximal, characteristic, complemented
9#22608775C211yesmaximal, characteristic, complemented
10#22608768C211yesmaximal, characteristic, complemented
11#22608698C211yesmaximal, characteristic, complemented
12#22608391C211yesmaximal, characteristic
13#22608386C211yesmaximal, characteristic, complemented
14#22608218C211yesmaximal, characteristic, complemented
15C73×#3172C211yesmaximal, characteristic
16#17988718—21no—
17#17988718—21no—
18#17988718C2211yescharacteristic
19#17988718C2211yescharacteristic
20#17988718C2211yescharacteristic
21Q8×#10596831C2211yescharacteristic
22Q8×#10596831C2211yescharacteristic
23Q8×#10596831C2211yescharacteristic
24#17988665—21no—
25#17988665C2211yescharacteristic
26#17988659—21no—
27D4×#10596831C2211yescharacteristic
28#17988648—21no—
29#17988648—21no—
30#17988648—21no—
31#17988644C2211yescharacteristic
32#17988640C2211yescharacteristic
33#17988614—21no—
34#17988611C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36#17988340C2211yescharacteristic
37#17988340C2211yescharacteristic
38#17988338C2211yescharacteristic
39#17988338C2211yescharacteristic
40Q8⋊#10596831C2211yescharacteristic
41Q8⋊#10596831C2211yescharacteristic
42Q8⋊#10596831C2211yescharacteristic
43Q8⋊#10596831C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48#17988309C2211yescharacteristic
49#17988309C2211yescharacteristic
50#17988309C2211yescharacteristic
51#17988309C2211yescharacteristic
52#533×C73C2211yescharacteristic
53#529×C73C2211yescharacteristic
54#501×C73C411yescharacteristic
55#497×C73C411yescharacteristic
56#491×C73C411yescharacteristic
57#489×C73C411yescharacteristic
58#470×C73C411yescharacteristic
59#470×C73C411yescharacteristic
60#468×C73C411yescharacteristic
61#468×C73C411yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63C4×Q16×C73C2211yescharacteristic
64C4×SD16×C73C2211yescharacteristic
65C4×SD16×C73C2211yescharacteristic
66C4×M16×C73C2211yescharacteristic
67C2×#11924012—21no—
68C2×#11924012—21no—
69C22×#10596831—21no—
70C22×#10596831—21no—
71C4⋊#10596831—21no—
72C4⋊#10596831—21no—
73C4⋊#10596831—21no—
74C4⋊#10596831—21no—
75C4⋊#10596831—21no—
76C4⋊#10596831—21no—
77C4⋊#10596831—21no—
78C4⋊#10596831D411yescharacteristic
79C4⋊#10596831D411yescharacteristic
80C4⋊#10596831C2311yescharacteristic
81C4⋊#10596831C2311yescharacteristic
82C4⋊#10596831C2311yescharacteristic
83C4⋊#10596831C2311yescharacteristic
84C22⋊#10596831—21no—
85C22⋊#10596831—21no—
86C22⋊#10596831—21no—
87C22⋊#10596831D411yescharacteristic
88C22⋊#10596831D411yescharacteristic
89#14556502—21no—
90#14556502—21no—
91#14556502—21no—
92#14556502—21no—
93C4×#10596831—21no—
94C4×#10596831—21no—
95C4×#10596831—21no—
96C4×#10596831—21no—
97C4×#10596831C2311yescharacteristic
98C4×#10596831C2311yescharacteristic
99C4×#10596831C2311yescharacteristic
100C4×#10596831C2311yescharacteristic
101C2×Q16×C73C2×C411yescharacteristic
102C2×Q16×C73C2×C411yescharacteristic
103C2×SD16×C73C2×C411yescharacteristic
104C2×SD16×C73C2×C411yescharacteristic
105C2×M16×C73C2×C411yescharacteristic
106C2×M16×C73C2×C411yescharacteristic
107C4⋊Q8×C73C2×C411yescharacteristic
108C4⋊Q8×C73C2×C411yescharacteristic
109#126×C73—21no—
110#125×C73—21no—
111#125×C73C2×C411yescharacteristic
112#124×C73C2×C411yescharacteristic
113#123×C73—21no—
114C22⋊Q8×C73—21no—
115C22⋊Q8×C73C2×C411yescharacteristic
116C22⋊Q8×C73C2×C411yescharacteristic
117C22⋊Q8×C73C2×C411yescharacteristic
118#121×C73C2×C411yescharacteristic
119C4×Q8×C73—21no—
120C4×Q8×C73C2311yescharacteristic
121C4×Q8×C73C2311yescharacteristic
122C4×Q8×C73C2311yescharacteristic
123C4×D4×C73—21no—
124C4×D4×C73C2311yescharacteristic
125#117×C73—21no—
126#117×C73—21no—
127C2×C42×C73C2311yescharacteristic
128#107×C73C2×C411yescharacteristic
129#107×C73C2×C411yescharacteristic
130#106×C73C2×C411yescharacteristic
131#106×C73C2×C411yescharacteristic
132#103×C73C2×C411yescharacteristic
133#103×C73C2×C411yescharacteristic
134#103×C73C2×C411yescharacteristic
135#103×C73C2×C411yescharacteristic
136#103×C73C2×C411yescharacteristic
137#103×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140#97×C73C2×C411yescharacteristic
141#97×C73C2×C411yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924012—81no—
145#11924012—81no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—42no—
153C2×#10596831—81no—
154C2×#10596831C2×D411yescharacteristic
155C2×#10596831C2×D411yescharacteristic
156C2×#10596831C2×D411yescharacteristic
157C2×#10596831C2×D411yescharacteristic
158C2×Q8×C73—21no—
159C2×Q8×C73C22×C411yescharacteristic
160C2×Q8×C73C22×C411yescharacteristic
161C2×Q8×C73C22×C411yescharacteristic
162C2×D4×C73—21no—
163C2×D4×C73C22×C411yescharacteristic
164C22×C4×C73—21no—
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73#4111yescharacteristic
168Q16×C73—41no—
169Q16×C73—41no—
170SD16×C73—41no—
171SD16×C73—41no—
172M16×C73—41no—
173M16×C73—41no—
174C2×C8×C73C22×C411yescharacteristic
175C2×C8×C73C22×C411yescharacteristic
176C2×C8×C73C22×C411yescharacteristic
177C2×C8×C73C22×C411yescharacteristic
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73C22×C411yescharacteristic
190C4⋊C4×C73C22×C411yescharacteristic
191C4⋊C4×C73C22×C411yescharacteristic
192C4⋊C4×C73C22×C411yescharacteristic
193C22⋊C4×C73—21no—
194C22⋊C4×C73—21no—
195C22⋊C4×C73—21no—
196C22⋊C4×C73—21no—
197C22⋊C4×C73—21no—
198C22⋊C4×C73—21no—
199C22⋊C4×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73C22×C411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73#4111yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C23×C73C4×D411yescharacteristic
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73—81no—
216D4×C73—21no—
217D4×C73—21no—
218D4×C73—81no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73C4×D411yescharacteristic
234C2×C4×C73C4×D411yescharacteristic
235C2×C4×C73C4×D411yescharacteristic
236C2×C4×C73C23×C411yescharacteristic
237C2×C4×C73C22×D411yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243#10596831—22no—
244#10596831—21no—
245#10596831—21no—
246#10596831—21no—
247#10596831—21no—
248#10596831—41no—
249#10596831—41no—
250#10596831—41no—
251#10596831—41no—
252#10596831—41no—
253C22×C73—21no—
254C22×C73—21no—
255C22×C73—21no—
256C22×C73—41no—
257C22×C73—41no—
258C22×C73—41no—
259C22×C73C2×C4×D411yescharacteristic
260C4×C73—21no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73—21no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73#56811yescharacteristic
272C4×C73#56811yescharacteristic
273C4×C73#57711yescharacteristic
274C4×C73#57811yescharacteristic
275#17988—731nomaximal, Sylow
276C2×C73—41no—
277C2×C73—81no—
278C2×C73#293211yescharacteristic
279C2×C73#294711yescharacteristic
280C2×C73#295611yescharacteristic
281#3172D7311yescharacteristic
282#2993—731no—
283#2985—731no—
284#1588—731no—
285#1587—731no—
286#1587—731no—
287#1585—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1582—731no—
292#1569—731no—
293#1494—731no—
294#1493—731no—
295#1451—731no—
296C73#1798811yescharacteristic, complemented, Sylow
297#533C2×D7311yescharacteristic
298#529C2×D7311yescharacteristic
299#501Dic7311yescharacteristic
300#497Dic7311yescharacteristic
301#491Dic7311yescharacteristic
302#489Dic7311yescharacteristic
303#470Dic7311yescharacteristic
304#470Dic7311yescharacteristic
305#468Dic7311yescharacteristic
306#468Dic7311yescharacteristic
307#446—731no—
308#446—731no—
309#446—731no—
310#446—1461no—
311#446—1461no—
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8—731no—
315C4×Q16C2×D7311yescharacteristic
316C4×Q16C2×D7311yescharacteristic
317C4×SD16C2×D7311yescharacteristic
318C4×SD16C2×D7311yescharacteristic
319#436—731no—
320#436—1461no—
321#435—1461no—
322C8×D4—731no—
323#433—1461no—
324#433—1461no—
325#433—1461no—
326#432—731no—
327#431—731no—
328#424—1461no—
329#423—731no—
330C4×M16C2×D7311yescharacteristic
331C2×C4×C8—731no—
332#335—731no—
333#335—731no—
334#334—731no—
335#334—731no—
336Q8⋊C8—731no—
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342D4⋊C8—731no—
343D4⋊C8—731no—
344#322—731no—
345#322—731no—
346#322—731no—
347#322—731no—
348C2×Q16C2×Dic7311yescharacteristic
349C2×Q16C2×Dic7311yescharacteristic
350C2×SD16C2×Dic7311yescharacteristic
351C2×SD16C2×Dic7311yescharacteristic
352C2×M16—1461no—
353C2×M16—1461no—
354C2×M16C2×Dic7311yescharacteristic
355C2×M16C2×Dic7311yescharacteristic
356C22×C8—1461no—
357C22×C8—1461no—
358C4⋊Q8C2×Dic7311yescharacteristic
359C4⋊Q8C2×Dic7311yescharacteristic
360#126—21no—
361#125—21no—
362#125C2×Dic7311yescharacteristic
363#124C2×Dic7311yescharacteristic
364#123—21no—
365C22⋊Q8—21no—
366C22⋊Q8C2×Dic7311yescharacteristic
367C22⋊Q8C2×Dic7311yescharacteristic
368C22⋊Q8C2×Dic7311yescharacteristic
369#121C2×Dic7311yescharacteristic
370C4×Q8—21no—
371C4×Q8C22×D7311yescharacteristic
372C4×Q8C22×D7311yescharacteristic
373C4×Q8C22×D7311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D7311yescharacteristic
376#117—21no—
377#117—21no—
378C2×C42C22×D7311yescharacteristic
379#107C2×Dic7311yescharacteristic
380#107C2×Dic7311yescharacteristic
381#106C2×Dic7311yescharacteristic
382#106C2×Dic7311yescharacteristic
383C4⋊C8—731no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396#103C2×Dic7311yescharacteristic
397#103C2×Dic7311yescharacteristic
398#103C2×Dic7311yescharacteristic
399#103C2×Dic7311yescharacteristic
400#103C2×Dic7311yescharacteristic
401#103C2×Dic7311yescharacteristic
402#102C2×Dic7311yescharacteristic
403#102C2×Dic7311yescharacteristic
404C22⋊C8—731no—
405C22⋊C8—731no—
406C22⋊C8—1461no—
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409#97—1461no—
410#97—1461no—
411#97—1461no—
412#97—1461no—
413#97C2×Dic7311yescharacteristic
414#97C2×Dic7311yescharacteristic
415C4×C8—731no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—1461no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C2×Q8—21no—
426C2×Q8C22×Dic7311yescharacteristic
427C2×Q8C22×Dic7311yescharacteristic
428C2×Q8C22×Dic7311yescharacteristic
429C2×D4—21no—
430C2×D4C22×Dic7311yescharacteristic
431C22×C4—21no—
432C22×C4C22×Dic7311yescharacteristic
433C22×C4D4×D7311yescharacteristic
434C22×C4#1192402711yescharacteristic
435Q16—41no—
436Q16—41no—
437SD16—41no—
438SD16—41no—
439M16—41no—
440M16—41no—
441M16—5841no—
442M16—5841no—
443C2×C8—2922no—
444C2×C8—5841no—
445C2×C8—731no—
446C2×C8—731no—
447C2×C8—731no—
448C2×C8—731no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8C22×Dic7311yescharacteristic
456C2×C8C22×Dic7311yescharacteristic
457C2×C8C22×Dic7311yescharacteristic
458C2×C8C22×Dic7311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4C22×Dic7311yescharacteristic
471C4⋊C4C22×Dic7311yescharacteristic
472C4⋊C4C22×Dic7311yescharacteristic
473C4⋊C4C22×Dic7311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42C22×Dic7311yescharacteristic
485C42D4×D7311yescharacteristic
486C42#1192402711yescharacteristic
487C42C23×D7311yescharacteristic
488C23—21no—
489C23D4×Dic7311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—81no—
497D4—21no—
498D4—21no—
499D4—81no—
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—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4D4×Dic7311yescharacteristic
515C2×C4D4×Dic7311yescharacteristic
516C2×C4D4×Dic7311yescharacteristic
517C2×C4C23×Dic7311yescharacteristic
518C2×C4C2×D4×D7311yescharacteristic
519C2×C4C2×#1192402711yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—2921no—
525C8—2921no—
526C8—2921no—
527C8—2921no—
528C8—2921no—
529C8—1462no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×D4×Dic7311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4#1798935411yescharacteristic
553C4#1798935411yescharacteristic
554C4#1798939611yescharacteristic
555C4#1798940311yescharacteristic
556C2—41no—
557C2—81no—
558C2#2261864911yescharacteristic
559C2#2261877511yescharacteristic
560C2#2261884111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#3172C2
socleC22×C73C2×C4×D4
prime radical#121×C73C2×C4
cosocleC42×C73C24
hypercenter#3172D73
hypocenterC73#17988
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3172

Complements

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

NH ≅ G/Ntype
2. #22619026C2semidirect
3. #22608810C2semidirect
4. #22608803C2semidirect
5. #22608803C2semidirect
6. #22608789C2semidirect
7. #22608782C2semidirect
8. #22608782C2semidirect
9. #22608775C2semidirect
10. #22608768C2semidirect
11. #22608698C2semidirect
13. #22608386C2semidirect
14. #22608218C2semidirect
296. C73#17988semidirect

Maximal subgroups

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

subgroupindex
#226190802
#226190262
#226088102
#226088032
#226087892
#226087822
#226087752
#226087682
#226086982
#226083912
#226083862
#226082182
C73×#31722
#1798873