Finite Group Databasebeta

← #33056808

Subgroups — #33056808

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#22620531C211yesmaximal, characteristic
2#22619076C211yesmaximal, characteristic
3#22619026C211yesmaximal, characteristic, complemented
4#22608806C211yesmaximal, characteristic, complemented
5#22608805C211yesmaximal, characteristic, complemented
6#22608799C211yesmaximal, characteristic, complemented
7#22608791C211yesmaximal, characteristic, complemented
8#22608784C211yesmaximal, characteristic, complemented
9#22608778C211yesmaximal, characteristic, complemented
10#22608771C211yesmaximal, characteristic, complemented
11#22608770C211yesmaximal, characteristic, complemented
12#22608696C211yesmaximal, characteristic, complemented
13#22608392C211yesmaximal, characteristic
14#22608220C211yesmaximal, characteristic, complemented
15C73×#1493C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988993C411yescharacteristic
18#17988979C411yescharacteristic
19#17988955C411yescharacteristic
20#17988949C411yescharacteristic
21#17988843C411yescharacteristic
22#17988843C411yescharacteristic
23#17988835C411yescharacteristic
24#17988835C411yescharacteristic
25#17988718—21no—
26#17988718—21no—
27#17988718C2211yescharacteristic
28#17988718C2211yescharacteristic
29#17988714C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31Q8×#10596831C2211yescharacteristic
32#17988711C2211yescharacteristic
33C4×#11924018C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924015C2211yescharacteristic
36C4×#11924015C2211yescharacteristic
37#17988664C2211yescharacteristic
38#17988663—21no—
39#17988656—21no—
40#17988652C2211yescharacteristic
41#17988648—21no—
42#17988648—21no—
43#17988647—21no—
44#17988644C2211yescharacteristic
45#17988640C2211yescharacteristic
46#17988612—21no—
47C4×#11924012C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59#17988308C2211yescharacteristic
60#533×C73C2211yescharacteristic
61#423×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924012C2×C411yescharacteristic
72C2×#11924012C2×C411yescharacteristic
73C2×#11924011—21no—
74C2×C8×D73—21no—
75#14556585—21no—
76#14556583C2×C411yescharacteristic
77#14556579C2×C411yescharacteristic
78#14556574—21no—
79#14556570C2×C411yescharacteristic
80#14556565C2×C411yescharacteristic
81C4×Dic146C2311yescharacteristic
82C4×D292C2311yescharacteristic
83C4×C22⋊D73—21no—
84#14556548—21no—
85#14556524C2×C411yescharacteristic
86#14556524C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89C4⋊#10596831—21no—
90C4⋊#10596831—21no—
91C4⋊#10596831—21no—
92C4⋊#10596831—21no—
93C4⋊#10596831D411yescharacteristic
94C4⋊#10596831D411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556515C2×C411yescharacteristic
100#14556515C2×C411yescharacteristic
101#14556515C2×C411yescharacteristic
102#14556515C2×C411yescharacteristic
103#14556514C2×C411yescharacteristic
104#14556514C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831D411yescharacteristic
109C22⋊#10596831D411yescharacteristic
110#14556503—21no—
111#14556503—21no—
112#14556502—21no—
113#14556502—21no—
114#14556502—21no—
115#14556502C2×C411yescharacteristic
116#14556502C2×C411yescharacteristic
117#14556501—21no—
118C4×#10596831—21no—
119C4×#10596831—21no—
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C2×M16×C73—21no—
126C22×C8×C73—21no—
127C4⋊Q8×C73C2×C411yescharacteristic
128C4⋊Q8×C73C2×C411yescharacteristic
129#125×C73—21no—
130C22⋊Q8×C73—21no—
131C22⋊Q8×C73C2×C411yescharacteristic
132C22⋊Q8×C73C2×C411yescharacteristic
133C4×Q8×C73—21no—
134C4×Q8×C73C2311yescharacteristic
135C4×Q8×C73C2311yescharacteristic
136#117×C73—21no—
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—21no—
139C4⋊C8×C73C2311yescharacteristic
140C4⋊C8×C73C2311yescharacteristic
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292C22×C411yescharacteristic
146C2×C22⋊D73—21no—
147C2×C4×D73—21no—
148#11924018—41no—
149#11924018—41no—
150#11924015—41no—
151#11924015—41no—
152#11924012—41no—
153#11924012—41no—
154#11924011—81no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831C22×C411yescharacteristic
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C2×D411yescharacteristic
162C2×#10596831C2×D411yescharacteristic
163C2×#10596831C2×D411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C8×D73—81no—
166C4⋊Dic73C22×C411yescharacteristic
167C4⋊Dic73C22×C411yescharacteristic
168#11924007—21no—
169#11924007—21no—
170#11924007—21no—
171#11924007—21no—
172C22⋊Dic73—21no—
173#11924005—21no—
174#11924005—21no—
175#11924005—21no—
176#11924005—21no—
177C4×Dic73—21no—
178C2×Q8×C73—21no—
179C2×Q8×C73C22×C411yescharacteristic
180C2×Q8×C73C22×C411yescharacteristic
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73#4111yescharacteristic
184M16×C73—81no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—42no—
190C4⋊C4×C73—21no—
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×C73C22×C411yescharacteristic
198C4⋊C4×C73C22×C411yescharacteristic
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73C22×C411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73#4111yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73C4×D411yescharacteristic
208C22×D73—21no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—81no—
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—21no—
222C2×C4×C73—41no—
223C2×C4×C73C4×D411yescharacteristic
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C23×C411yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C2×C4×C73C2×#4111yescharacteristic
229C22⋊D73—81no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233D292—21no—
234D292—21no—
235C4×D73—41no—
236C4×D73—41no—
237Dic146—21no—
238Dic146—21no—
239C8×C73—22no—
240C8×C73—41no—
241C8×C73—41no—
242C8×C73—41no—
243#10596831—21no—
244#10596831—21no—
245#10596831—21no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—41no—
252#10596831—41no—
253C22×C73—21no—
254C22×C73—21no—
255C22×C73—21no—
256C22×C73C2×C4×D411yescharacteristic
257C2×D73—41no—
258C2×D73—41no—
259C2×D73—41no—
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#56811yescharacteristic
269C4×C73#56811yescharacteristic
270C4×C73#57711yescharacteristic
271C4×C73#57811yescharacteristic
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275#17988—731nomaximal, Sylow
276C2×C73—41no—
277C2×C73#293211yescharacteristic
278C2×C73#294711yescharacteristic
279C2×C73#295611yescharacteristic
280D73—81no—
281#3172—731no—
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#1493D7311yescharacteristic, complemented
295#1451—731no—
296C73#1798811yescharacteristic, complemented, Sylow
297#533C2×D7311yescharacteristic
298#529—731no—
299#501—731no—
300#497—731no—
301#491—731no—
302#489—731no—
303#470—731no—
304#470—731no—
305#468—731no—
306#468—731no—
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×Q16—731no—
316C4×Q16—731no—
317C4×SD16—731no—
318C4×SD16—731no—
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#423C2×D7311yescharacteristic
330C4×M16—731no—
331C2×C4×C8C2×D7311yescharacteristic
332#335—731no—
333#335—731no—
334#334—731no—
335#334—731no—
336Q8⋊C8—731no—
337Q8⋊C8—731no—
338Q8⋊C8C2×D7311yescharacteristic
339Q8⋊C8C2×D7311yescharacteristic
340Q8⋊C8C2×D7311yescharacteristic
341Q8⋊C8C2×D7311yescharacteristic
342D4⋊C8—731no—
343D4⋊C8—731no—
344#322—731no—
345#322—731no—
346#322—731no—
347#322—731no—
348C2×Q16—731no—
349C2×Q16—731no—
350C2×SD16—731no—
351C2×SD16—731no—
352C2×M16—21no—
353C2×M16—731no—
354C2×M16—731no—
355C2×M16—1461no—
356C22×C8—21no—
357C22×C8—1461no—
358C4⋊Q8C4×D7311yescharacteristic
359C4⋊Q8C4×D7311yescharacteristic
360#126—1461no—
361#125—21no—
362#125—731no—
363#124—731no—
364#123—1461no—
365C22⋊Q8—21no—
366C22⋊Q8—731no—
367C22⋊Q8C4×D7311yescharacteristic
368C22⋊Q8C4×D7311yescharacteristic
369#121—731no—
370C4×Q8—21no—
371C4×Q8—731no—
372C4×Q8C22×D7311yescharacteristic
373C4×Q8C22×D7311yescharacteristic
374C4×D4—731no—
375C4×D4—1461no—
376#117—21no—
377#117—1461no—
378C2×C42C22×D7311yescharacteristic
379#107—731no—
380#107—731no—
381#106—731no—
382#106—731no—
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⋊C8—1461no—
394C4⋊C8C22×D7311yescharacteristic
395C4⋊C8C22×D7311yescharacteristic
396#103—731no—
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#102—731no—
403#102—731no—
404C22⋊C8—731no—
405C22⋊C8—731no—
406C22⋊C8—1461no—
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409#97—731no—
410#97—731no—
411#97—1461no—
412#97—1461no—
413#97—1461no—
414#97—1461no—
415C4×C8—21no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C2×Q8—21no—
426C2×Q8—731no—
427C2×Q8C2×C4×D7311yescharacteristic
428C2×Q8C2×C4×D7311yescharacteristic
429C2×D4—731no—
430C2×D4—1461no—
431C22×C4—1461no—
432C22×C4C2×C4×D7311yescharacteristic
433C22×C4D4×D7311yescharacteristic
434C22×C4#1192402711yescharacteristic
435Q16—2921no—
436Q16—2921no—
437SD16—2921no—
438SD16—2921no—
439M16—81no—
440M16—2921no—
441M16—2921no—
442M16—5841no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—5841no—
449C2×C8—731no—
450C2×C8—731no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—1461no—
458C2×C8—1461no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—731no—
467C4⋊C4—731no—
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—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—21no—
482C42—21no—
483C42—1461no—
484C42C2×C4×D7311yescharacteristic
485C42D4×D7311yescharacteristic
486C42#1192402711yescharacteristic
487C42C23×D7311yescharacteristic
488C23—1461no—
489C23#1455655111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—1461no—
496Q8—1461no—
497D4—5841no—
498D4—1461no—
499D4—1461no—
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—41no—
509C2×C4—2921no—
510C2×C4—2921no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4#1455655111yescharacteristic
515C2×C4#1455655111yescharacteristic
516C2×C4#1455655111yescharacteristic
517C2×C4C22×C4×D7311yescharacteristic
518C2×C4C2×D4×D7311yescharacteristic
519C2×C4C2×#1192402711yescharacteristic
520C8—22no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—2921no—
525C8—2921no—
526C8—1461no—
527C8—1461no—
528C8—1461no—
529C8—1461no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—2921no—
538C22—2921no—
539C22—2921no—
540C22C2×#1455655111yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—2921no—
550C4—2921no—
551C4—2921no—
552C4#1798935211yescharacteristic
553C4#1798935211yescharacteristic
554C4#1798939311yescharacteristic
555C4#1798940011yescharacteristic
556C2—41no—
557C2—5841no—
558C2#2261864611yescharacteristic
559C2#2261876811yescharacteristic
560C2#2261883711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1493C2
socleC22×C73C2×C4×D4
prime radical#14556565C2×C4
cosocleC42×C73C24
hypercenter#1493D73
hypocenterC73#17988
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #22619026C2semidirect
4. #22608806C2semidirect
5. #22608805C2semidirect
6. #22608799C2semidirect
7. #22608791C2semidirect
8. #22608784C2semidirect
9. #22608778C2semidirect
10. #22608771C2semidirect
11. #22608770C2semidirect
12. #22608696C2semidirect
14. #22608220C2semidirect
15. C73×#1493C2semidirect
294. #1493D73semidirect
296. C73#17988semidirect

Maximal subgroups

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

subgroupindex
#226205312
#226190762
#226190262
#226088062
#226088052
#226087992
#226087912
#226087842
#226087782
#226087712
#226087702
#226086962
#226083922
#226082202
C73×#14932
#1798873