Finite Group Databasebeta

← #33056555

Subgroups — #33056555

Order 18688.

614 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620495C211yesmaximal, characteristic
2#22618906C211yesmaximal, characteristic, complemented
3#22608843C211yesmaximal, characteristic, complemented
4#22608838C211yesmaximal, characteristic, complemented
5#22608833C211yesmaximal, characteristic, complemented
6#22608831C211yesmaximal, characteristic, complemented
7#22608753C211yesmaximal, characteristic, complemented
8#22608748C211yesmaximal, characteristic, complemented
9#22608743C211yesmaximal, characteristic, complemented
10#22608741C211yesmaximal, characteristic, complemented
11#22608692C211yesmaximal, characteristic, complemented
12#22608391C211yesmaximal, characteristic, complemented
13#22608389C211yesmaximal, characteristic, complemented
14C2×#17988309C211yesmaximal, characteristic, complemented
15C73×#2966C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988986C411yescharacteristic
18#17988969C411yescharacteristic
19#17988944C411yescharacteristic
20#17988941C411yescharacteristic
21#17988826C411yescharacteristic
22#17988821C411yescharacteristic
23#17988818C411yescharacteristic
24#17988814C411yescharacteristic
25#17988717C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924018C2211yescharacteristic
28C4×#11924015C2211yescharacteristic
29C4×#11924016C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988658—21no—
33C8×D292C2211yescharacteristic
34C8×C22⋊D73—21no—
35#17988646—21no—
36#17988644C2211yescharacteristic
37#17988541—21no—
38C2×C4×#10596831C2211yescharacteristic
39C2×C4×#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46#17988317C2211yescharacteristic
47#17988317C2211yescharacteristic
48D4⋊#10596831C2211yescharacteristic
49D4⋊#10596831C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988309C2211yescharacteristic
55#17988309C2211yescharacteristic
56#529×C73C2211yescharacteristic
57#446×C73C2211yescharacteristic
58C8×Q8×C73C2211yescharacteristic
59#436×C73C2211yescharacteristic
60#435×C73—21no—
61C8×D4×C73—21no—
62C8×D4×C73C2211yescharacteristic
63#433×C73—21no—
64#432×C73C2211yescharacteristic
65#405×C73—21no—
66C2×C4×C8×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924011—21no—
72C22×#10596831—21no—
73C22×#10596831C2×C411yescharacteristic
74C22×#10596831C2×C411yescharacteristic
75C2×C8×D73—21no—
76#14556585—21no—
77#14556583C2×C411yescharacteristic
78#14556579C2×C411yescharacteristic
79#14556574—21no—
80#14556570C2×C411yescharacteristic
81#14556565C2×C411yescharacteristic
82C4×Dic146C2311yescharacteristic
83C4×D292C2311yescharacteristic
84C4×C22⋊D73—21no—
85#14556548—21no—
86#14556524C2×C411yescharacteristic
87#14556524C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90C4⋊#10596831C2311yescharacteristic
91C4⋊#10596831C2311yescharacteristic
92#14556520—21no—
93#14556520—21no—
94#14556515C2×C411yescharacteristic
95#14556515C2×C411yescharacteristic
96#14556514C2×C411yescharacteristic
97#14556514C2×C411yescharacteristic
98#14556512C2×C411yescharacteristic
99#14556512C2×C411yescharacteristic
100#14556511C2×C411yescharacteristic
101#14556511C2×C411yescharacteristic
102C22⋊#10596831—21no—
103#14556503—21no—
104#14556503—21no—
105#14556502—21no—
106#14556501—21no—
107C4×#10596831—21no—
108C4×#10596831C2×C411yescharacteristic
109C4×#10596831C2×C411yescharacteristic
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C8×Dic73—21no—
115C2×M16×C73—21no—
116C22×C8×C73—21no—
117C22×C8×C73D411yescharacteristic
118C22×C8×C73D411yescharacteristic
119#126×C73—21no—
120#125×C73C2×C411yescharacteristic
121#124×C73C2×C411yescharacteristic
122#123×C73—21no—
123C22⋊Q8×C73C2×C411yescharacteristic
124#121×C73C2×C411yescharacteristic
125C4×Q8×C73C2311yescharacteristic
126C4×D4×C73—21no—
127C4×D4×C73C2311yescharacteristic
128#117×C73—21no—
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73—21no—
137#97×C73—21no—
138#97×C73—21no—
139C4×C8×C73—21no—
140C4×C8×C73D411yescharacteristic
141C4×C8×C73D411yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292C22×C411yescharacteristic
146C2×C22⋊D73—21no—
147C2×C4×D73—21no—
148#11924018—22no—
149#11924016—22no—
150#11924015—22no—
151#11924013—22no—
152#11924011—42no—
153C2×#10596831—22no—
154C2×#10596831—22no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—42no—
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C8×D73—42no—
165C4⋊Dic73C22×C411yescharacteristic
166C4⋊Dic73C22×C411yescharacteristic
167#11924007—21no—
168#11924007—21no—
169#11924007—21no—
170#11924007—21no—
171C22⋊Dic73—21no—
172#11924005—21no—
173#11924005—21no—
174#11924005—21no—
175#11924005—21no—
176C4×Dic73—21no—
177C2×Q8×C73C22×C411yescharacteristic
178C2×D4×C73—21no—
179C2×D4×C73C22×C411yescharacteristic
180C22×C4×C73—21no—
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73#4111yescharacteristic
184M16×C73—42no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—41no—
188C2×C8×C73—41no—
189C2×C8×C73—42no—
190C2×C8×C73C2×D411yescharacteristic
191C2×C8×C73C2×D411yescharacteristic
192C2×C8×C73C2×D411yescharacteristic
193C2×C8×C73C2×D411yescharacteristic
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—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C42×C73—21no—
206C42×C73C22×C411yescharacteristic
207C42×C73C2×D411yescharacteristic
208C42×C73#4111yescharacteristic
209C42×C73C2411yescharacteristic
210C23×C73—21no—
211C23×C73C4×D411yescharacteristic
212C22×D73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215D4×C73—21no—
216D4×C73—21no—
217D4×C73—42no—
218C2×C4×C73—22no—
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—41no—
227C2×C4×C73—41no—
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C23×C411yescharacteristic
232C2×C4×C73C22×D411yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C22⋊D73—42no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238D292—21no—
239D292—21no—
240C4×D73—41no—
241C4×D73—41no—
242Dic146—21no—
243Dic146—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—41no—
249C8×C73—41no—
250#10596831—21no—
251#10596831—21no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831—41no—
256#10596831#13112yes—
257#10596831#13112yes—
258C22×C73—21no—
259C22×C73—21no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73—41no—
263C22×C73#44412yes—
264C22×C73C2×C4×D411yescharacteristic
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C4×C73—21no—
269C4×C73—21no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73C2×#13111yescharacteristic
276C4×C73C2×#13111yescharacteristic
277C4×C73#57511yescharacteristic
278C4×C73#57511yescharacteristic
279Dic73—41no—
280Dic73—41no—
281Dic73—41no—
282#17963—731nomaximal, Sylow
283C2×C73—22no—
284C2×C73—81no—
285C2×C73#293111yescharacteristic
286C2×C73#294311yescharacteristic
287C2×C73C2×#44411yescharacteristic
288D73—81no—
289#3168—731no—
290#2966—731no—
291#2966D7311yescharacteristic, complemented
292#1594—731no—
293#1593—731no—
294#1592—731no—
295#1592—731no—
296#1580—731no—
297#1579—731no—
298SD16⋊C8—731no—
299SD16⋊C8—731no—
300#1568—731no—
301#1494—731no—
302#1494—731no—
303C2×#322—731no—
304C73#1796311yescharacteristic, complemented, Sylow
305#529—731no—
306#529C2×D7311yescharacteristic
307#499—731no—
308#495—731no—
309#488—731no—
310#488—731no—
311#467—731no—
312#466—731no—
313#465—731no—
314#465—731no—
315#446—731no—
316#446C2×D7311yescharacteristic
317C8×Q8—731no—
318C8×Q8C2×D7311yescharacteristic
319C4×Q16—731no—
320C4×SD16—731no—
321C4×SD16—731no—
322C4×D8—731no—
323#436—731no—
324#436C2×D7311yescharacteristic
325#435—21no—
326#435—1461no—
327C8×D4—21no—
328C8×D4—731no—
329C8×D4—1461no—
330C8×D4C2×D7311yescharacteristic
331#433—21no—
332#433—1461no—
333#432—731no—
334#432C2×D7311yescharacteristic
335#405—21no—
336#405—1461no—
337C2×C4×C8—731no—
338C2×C4×C8—731no—
339C2×C4×C8C2×D7311yescharacteristic
340#335—731no—
341#335—731no—
342#334—731no—
343#334—731no—
344Q8⋊C8—731no—
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348D4⋊C8—731no—
349D4⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352#322—731no—
353#322—731no—
354#322—731no—
355#322—731no—
356C2×Q16—731no—
357C2×SD16—731no—
358C2×SD16—731no—
359C2×D8—731no—
360C2×M16—21no—
361C2×M16—1461no—
362C22×C8—21no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—1461no—
366C22×C8—1461no—
367C22×C8C22⋊D7311yescharacteristic
368C22×C8C22⋊D7311yescharacteristic
369#126—21no—
370#126—1461no—
371#125—731no—
372#125C4×D7311yescharacteristic
373#124—731no—
374#124C4×D7311yescharacteristic
375#123—21no—
376#123—1461no—
377C22⋊Q8—731no—
378C22⋊Q8C4×D7311yescharacteristic
379#121—731no—
380#121C4×D7311yescharacteristic
381C4×Q8—731no—
382C4×Q8C22×D7311yescharacteristic
383C4×D4—21no—
384C4×D4—731no—
385C4×D4—1461no—
386C4×D4C22×D7311yescharacteristic
387#117—21no—
388#117—1461no—
389C2×C42C22×D7311yescharacteristic
390#107—731no—
391#107—731no—
392#106—731no—
393#106—731no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8C22×D7311yescharacteristic
401C4⋊C8C22×D7311yescharacteristic
402#103—731no—
403#103—731no—
404#103—731no—
405#103—731no—
406#102—731no—
407#102—731no—
408#102—731no—
409#102—731no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—1461no—
414C22⋊C8—1461no—
415C22⋊C8—1461no—
416#97—21no—
417#97—21no—
418#97—1461no—
419#97—1461no—
420C4×C8—21no—
421C4×C8—731no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—1461no—
428C4×C8—1461no—
429C4×C8C22⋊D7311yescharacteristic
430C4×C8C22⋊D7311yescharacteristic
431C4×C8C22×D7311yescharacteristic
432C4×C8C22×D7311yescharacteristic
433C2×Q8—731no—
434C2×Q8C2×C4×D7311yescharacteristic
435C2×D4—21no—
436C2×D4—731no—
437C2×D4—1461no—
438C2×D4C2×C4×D7311yescharacteristic
439C22×C4—21no—
440C22×C4—1461no—
441C22×C4C2×C4×D7311yescharacteristic
442C22×C4C2×C22⋊D7311yescharacteristic
443C22×C4#1192402811yescharacteristic
444Q16—1462no—
445SD16—1462no—
446SD16—1462no—
447D8—1462no—
448M16—42no—
449M16—2922no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—41no—
453C2×C8—41no—
454C2×C8—42no—
455C2×C8—2922no—
456C2×C8—2922no—
457C2×C8—731no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1462no—
466C2×C8—1462no—
467C2×C8C2×C22⋊D7311yescharacteristic
468C2×C8C2×C22⋊D7311yescharacteristic
469C2×C8C2×C22⋊D7311yescharacteristic
470C2×C8C2×C22⋊D7311yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4C2×C4×D7311yescharacteristic
482C4⋊C4C2×C4×D7311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—21no—
494C42—1461no—
495C42C2×C4×D7311yescharacteristic
496C42C2×C22⋊D7311yescharacteristic
497C42#1192402811yescharacteristic
498C42C23×D7311yescharacteristic
499C23—21no—
500C23—1461no—
501C23C4×C22⋊D7311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1461no—
505Q8—1461no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—2922no—
510D4—1461no—
511D4—1461no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4C4×C22⋊D7311yescharacteristic
528C2×C4C4×C22⋊D7311yescharacteristic
529C2×C4C4×C22⋊D7311yescharacteristic
530C2×C4C22×C4×D7311yescharacteristic
531C2×C4C22×C22⋊D7311yescharacteristic
532C2×C4C2×#1192402811yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—2921no—
540C8—2921no—
541C8—2921no—
542C8—2921no—
543C8—732no—
544C8—732no—
545C8—1461no—
546C8—1461no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—2921no—
553C22—2921no—
554C22—2921no—
555C22#1798870712yes—
556C22C2×C4×C22⋊D7311yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—2921no—
565C4—2921no—
566C4—2921no—
567C4#131×D7311yescharacteristic
568C4#131×D7311yescharacteristic
569C4#1798938511yescharacteristic
570C4#1798938511yescharacteristic
571C2—22no—
572C2—81no—
573C2—5841no—
574C2#2261864111yescharacteristic
575C2#2261872911yescharacteristic
576C2C2×#1798870711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2966C2
socleC22×C73C2×C4×D4
prime radical#17988821C4
cosocleC42×C73C24
hypercenter#2966D73
hypocenterC73#17963
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #22618906C2semidirect
3. #22608843C2semidirect
4. #22608838C2semidirect
5. #22608833C2semidirect
6. #22608831C2semidirect
7. #22608753C2semidirect
8. #22608748C2semidirect
9. #22608743C2semidirect
10. #22608741C2semidirect
11. #22608692C2semidirect
12. #22608391C2semidirect
13. #22608389C2semidirect
14. C2×#17988309C2semidirect
15. C73×#2966C2semidirect
291. #2966D73semidirect
304. C73#17963semidirect

Maximal subgroups

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

subgroupindex
#226204952
#226189062
#226088432
#226088382
#226088332
#226088312
#226087532
#226087482
#226087432
#226087412
#226086922
#226083912
#226083892
C2×#179883092
C73×#29662
#1796373