Finite Group Databasebeta

← #33056161

Subgroups — #33056161

Order 18688.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619951C211yesmaximal, characteristic
2#22619076C211yesmaximal, characteristic, complemented
3#22619040C211yesmaximal, characteristic, complemented
4#22608801C211yesmaximal, characteristic, complemented
5#22608794C211yesmaximal, characteristic, complemented
6#22608773C211yesmaximal, characteristic, complemented
7#22608766C211yesmaximal, characteristic, complemented
8#22608754C211yesmaximal, characteristic, complemented
9#22608749C211yesmaximal, characteristic, complemented
10#22608730C211yesmaximal, characteristic, complemented
11#22608730C211yesmaximal, characteristic, complemented
12#22608368C211yesmaximal, characteristic, complemented
13#22608342C211yesmaximal, characteristic, complemented
14#22608226C211yesmaximal, characteristic, complemented
15C73×#1570C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C4×#11924028C2211yescharacteristic
18#17988929C411yescharacteristic
19#17988912C411yescharacteristic
20#17988895C411yescharacteristic
21#17988888C411yescharacteristic
22#17988810C411yescharacteristic
23#17988803C411yescharacteristic
24#17988751C411yescharacteristic
25#17988734C411yescharacteristic
26#17988714C2211yescharacteristic
27#17988711C2211yescharacteristic
28#17988711C2211yescharacteristic
29#17988711C2211yescharacteristic
30C4×Dic292C2211yescharacteristic
31C4×#11924017C2211yescharacteristic
32C4×#11924017C2211yescharacteristic
33C4×D584C2211yescharacteristic
34#17988664C2211yescharacteristic
35#17988663—21no—
36#17988656—21no—
37#17988652C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988652C2211yescharacteristic
40C8×C22⋊D73—21no—
41C8×C22⋊D73—21no—
42#17988647—21no—
43#17988640C2211yescharacteristic
44#17988639—21no—
45#17988612—21no—
46C4⋊C8×D73—21no—
47C4×#11924012C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50#17988317C2211yescharacteristic
51#17988317C2211yescharacteristic
52#17988314C2211yescharacteristic
53#17988314C2211yescharacteristic
54#17988314C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#431×C73C2211yescharacteristic
61#423×C73C2211yescharacteristic
62C2×C4⋊C8×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64#334×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×#11924012—21no—
73C2×#11924011—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77#14556585—21no—
78#14556583C2×C411yescharacteristic
79#14556579C2×C411yescharacteristic
80#14556574—21no—
81#14556570C2×C411yescharacteristic
82#14556565C2×C411yescharacteristic
83C4×Dic146C2×C411yescharacteristic
84C4×Dic146C2311yescharacteristic
85C4×Dic146C2311yescharacteristic
86C4×D292C2×C411yescharacteristic
87C4×D292C2311yescharacteristic
88C4×D292C2311yescharacteristic
89C4×C22⋊D73—21no—
90C4×C22⋊D73—21no—
91C4×C22⋊D73—21no—
92#14556550C2×C411yescharacteristic
93#14556548—21no—
94#14556548—21no—
95C42×D73—21no—
96#14556525C2×C411yescharacteristic
97#14556525C2×C411yescharacteristic
98#14556523C2×C411yescharacteristic
99#14556523C2×C411yescharacteristic
100C4⋊#10596831D411yescharacteristic
101C4⋊#10596831D411yescharacteristic
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556516C2×C411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556513C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115C22⋊#10596831D411yescharacteristic
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556502—21no—
121#14556501—21no—
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×M16×C73—21no—
130C22×C8×C73—21no—
131C2×C42×C73C2311yescharacteristic
132C4⋊C8×C73—21no—
133C4⋊C8×C73—21no—
134C4⋊C8×C73C2×C411yescharacteristic
135C4⋊C8×C73C2×C411yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C4⋊C8×C73C2311yescharacteristic
140C22⋊C8×C73C2×C411yescharacteristic
141C22⋊C8×C73C2×C411yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—22no—
146C2×Dic146C22×C411yescharacteristic
147C2×Dic146C22×C411yescharacteristic
148C2×D292C22×C411yescharacteristic
149C2×D292C22×C411yescharacteristic
150C2×C22⋊D73—21no—
151C2×C22⋊D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156Dic292—22no—
157#11924017—22no—
158#11924017—22no—
159D584—22no—
160#11924012—42no—
161#11924011—81no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C8×D73—81no—
169C8×D73—81no—
170C8×D73—81no—
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174C4⋊Dic73C22×C411yescharacteristic
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181C22⋊Dic73—21no—
182C22⋊Dic73—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73#4111yescharacteristic
196M16×C73—81no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—81no—
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C42×C73C22×C411yescharacteristic
207C42×C73C2×D411yescharacteristic
208C42×C73#4111yescharacteristic
209C42×C73C2411yescharacteristic
210C23×C73C4×D411yescharacteristic
211C22×D73—21no—
212C22×D73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—41no—
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×D411yescharacteristic
220C2×C4×C73C4×D411yescharacteristic
221C2×C4×C73C23×C411yescharacteristic
222C2×C4×C73C22×D411yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C22⋊D73—24no—
225C22⋊D73—81no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232D292—21no—
233D292—21no—
234D292—21no—
235D292#13112yes—
236C4×D73—24no—
237C4×D73—41no—
238C4×D73—41no—
239C4×D73—41no—
240C4×D73—41no—
241C4×D73—81no—
242Dic146—21no—
243Dic146—21no—
244Dic146—21no—
245Dic146#13112yes—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254#10596831—22no—
255#10596831—21no—
256#10596831—21no—
257#10596831—21no—
258#10596831—21no—
259#10596831—41no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73C2×C4×D411yescharacteristic
264C2×D73—22no—
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—41no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73C2×#13111yescharacteristic
275C4×C73C2×#13111yescharacteristic
276C4×C73#57711yescharacteristic
277C4×C73#57711yescharacteristic
278Dic73—22no—
279Dic73—41no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284#17927—731nomaximal, Sylow
285C2×C73—41no—
286C2×C73#292911yescharacteristic
287C2×C73#295211yescharacteristic
288C2×C73#295611yescharacteristic
289D73—42no—
290D73—81no—
291#3102—731no—
292#2993—731no—
293#2988—731no—
294#1587—731no—
295#1586—731no—
296#1583—731no—
297#1582—731no—
298#1580—731no—
299#1579—731no—
300C8×SD16—731no—
301C8×SD16—731no—
302#1570D7311yescharacteristic, complemented
303#1489—731no—
304#1483—731no—
305#1453—731no—
306C73#1792711yescharacteristic, complemented, Sylow
307#529—731no—
308C4×#41—731no—
309#485—731no—
310#482—731no—
311#479—731no—
312#478—731no—
313#464—731no—
314#463—731no—
315#452—731no—
316#449—731no—
317#446—731no—
318C8×Q8—731no—
319C8×Q8—731no—
320C8×Q8—731no—
321C4×Q16—731no—
322C4×SD16—731no—
323C4×SD16—731no—
324C4×D8—731no—
325#436—731no—
326#436—1461no—
327#435—1461no—
328C8×D4—731no—
329C8×D4—731no—
330C8×D4—731no—
331C8×D4—1461no—
332C8×D4—1461no—
333#433—1461no—
334#431—731no—
335#431—1461no—
336#431C2×D7311yescharacteristic
337#424—1461no—
338#423C2×D7311yescharacteristic
339C2×C4⋊C8—1461no—
340C2×C4⋊C8C2×D7311yescharacteristic
341C4×M16—731no—
342#334C2×D7311yescharacteristic
343#334C2×D7311yescharacteristic
344#334C2×D7311yescharacteristic
345#334C2×D7311yescharacteristic
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349Q8⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8—731no—
353D4⋊C8—731no—
354#322—731no—
355#322—731no—
356#322—731no—
357C82—731no—
358C2×#41—731no—
359C2×Q16—731no—
360C2×SD16—731no—
361C2×SD16—731no—
362C2×D8—731no—
363C2×M16—21no—
364C2×M16—1461no—
365C2×M16—1461no—
366C22×C8—21no—
367C22×C8—1461no—
368C22×C8—1461no—
369C22×C8—1461no—
370#126—1461no—
371#125—731no—
372#124—731no—
373#123—1461no—
374C22⋊Q8—731no—
375#121—731no—
376C4×Q8—731no—
377C4×Q8—731no—
378C4×Q8—731no—
379C4×D4—731no—
380C4×D4—731no—
381C4×D4—731no—
382C4×D4—1461no—
383C4×D4—1461no—
384C4×D4—1461no—
385#117—731no—
386#117—1461no—
387#117—1461no—
388C2×C42—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⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8C4×D7311yescharacteristic
403C4⋊C8C4×D7311yescharacteristic
404C4⋊C8C22×D7311yescharacteristic
405C4⋊C8C22×D7311yescharacteristic
406C4⋊C8C22×D7311yescharacteristic
407C4⋊C8C22×D7311yescharacteristic
408#103—731no—
409#103—731no—
410#103—731no—
411#103—731no—
412#102—731no—
413#102—731no—
414#102—731no—
415#102—731no—
416C22⋊C8—731no—
417C22⋊C8—731no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8C4×D7311yescharacteristic
423C22⋊C8C4×D7311yescharacteristic
424#97—1461no—
425#97—1461no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8—1461no—
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435#41—1462no—
436#41—1462no—
437C2×Q8—731no—
438C2×Q8—731no—
439C2×D4—731no—
440C2×D4—731no—
441C2×D4—1461no—
442C2×D4—1461no—
443C22×C4—1461no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4C2×C4×D7311yescharacteristic
448C22×C4D4×D7311yescharacteristic
449C22×C4#1192402911yescharacteristic
450Q16—1462no—
451SD16—1462no—
452SD16—1462no—
453D8—1462no—
454M16—81no—
455M16—2922no—
456M16—5841no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—5841no—
463C2×C8—5841no—
464C2×C8—5841no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8C2×C4×D7311yescharacteristic
472C2×C8C2×C4×D7311yescharacteristic
473C2×C8C2×C4×D7311yescharacteristic
474C2×C8C2×C4×D7311yescharacteristic
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—731no—
478C4⋊C4—731no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C22⋊C4—1461no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—1461no—
494C42—1461no—
495C42—1461no—
496C42—1461no—
497C42C2×C4×D7311yescharacteristic
498C42D4×D7311yescharacteristic
499C42#1192402911yescharacteristic
500C42C23×D7311yescharacteristic
501C23—1461no—
502C23—1461no—
503C23#1455655311yescharacteristic
504Q8—732no—
505Q8—1461no—
506Q8—1461no—
507Q8—1461no—
508D4—5841no—
509D4—732no—
510D4—1464no—
511D4—1461no—
512D4—1461no—
513D4—1461no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—2921no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—2921no—
523C2×C4—5841no—
524C2×C4—1464no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4#1455655311yescharacteristic
532C2×C4#1455655311yescharacteristic
533C2×C4#1455655311yescharacteristic
534C2×C4C22×C4×D7311yescharacteristic
535C2×C4C2×D4×D7311yescharacteristic
536C2×C4C2×#1192402911yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—2921no—
546C8—1462no—
547C8—1461no—
548C8—1461no—
549C8—1461no—
550C8—1461no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—2921no—
555C22—2921no—
556C22—2921no—
557C22—2921no—
558C22—2921no—
559C22—1462no—
560C22C2×#1455655311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—2921no—
566C4—2921no—
567C4—2921no—
568C4—2921no—
569C4—2921no—
570C4—1462no—
571C4#131×D7311yescharacteristic
572C4#131×D7311yescharacteristic
573C4#1798939311yescharacteristic
574C4#1798939311yescharacteristic
575C2—41no—
576C2—2922no—
577C2—5841no—
578C2#2261862411yescharacteristic
579C2#2261881411yescharacteristic
580C2#2261884011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1570C2
socleC22×C73C2×C4×D4
prime radical#17988734C4
cosocleC42×C73C24
hypercenter#1570D73
hypocenterC73#17927
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
2. #22619076C2semidirect
3. #22619040C2semidirect
4. #22608801C2semidirect
5. #22608794C2semidirect
6. #22608773C2semidirect
7. #22608766C2semidirect
8. #22608754C2semidirect
9. #22608749C2semidirect
10. #22608730C2semidirect
11. #22608730C2semidirect
12. #22608368C2semidirect
13. #22608342C2semidirect
14. #22608226C2semidirect
15. C73×#1570C2semidirect
302. #1570D73semidirect
306. C73#17927semidirect

Maximal subgroups

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

subgroupindex
#226199512
#226190762
#226190402
#226088012
#226087942
#226087732
#226087662
#226087542
#226087492
#226087302
#226083682
#226083422
#226082262
C73×#15702
#1792773