Finite Group Databasebeta

← #33057397

Subgroups — #33057397

Order 18688.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619951C211yesmaximal, characteristic
2#22619093C211yesmaximal, characteristic, complemented
3#22619060C211yesmaximal, characteristic, complemented
4#22608835C211yesmaximal, characteristic, complemented
5#22608817C211yesmaximal, characteristic, complemented
6#22608811C211yesmaximal, characteristic, complemented
7#22608811C211yesmaximal, characteristic, complemented
8#22608783C211yesmaximal, characteristic, complemented
9#22608762C211yesmaximal, characteristic, complemented
10#22608745C211yesmaximal, characteristic, complemented
11C8×Dic292C211yesmaximal, characteristic, complemented
12#22608706C211yesmaximal, characteristic, complemented
13#22608397C211yesmaximal, characteristic, complemented
14#22608319C211yesmaximal, characteristic, complemented
15C73×#1454C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C4×#11924028C2211yescharacteristic
18#17988929C411yescharacteristic
19#17988912C411yescharacteristic
20#17988895C411yescharacteristic
21#17988888C411yescharacteristic
22#17988810C411yescharacteristic
23#17988803C411yescharacteristic
24#17988751C411yescharacteristic
25#17988734C411yescharacteristic
26#17988717C2211yescharacteristic
27C8×Dic146C2211yescharacteristic
28C8×Dic146C2211yescharacteristic
29C8×Dic146C2211yescharacteristic
30C4×Dic292C2211yescharacteristic
31C4×#11924017C2211yescharacteristic
32C4×#11924017C2211yescharacteristic
33C4×D584C2211yescharacteristic
34#17988666C2211yescharacteristic
35#17988666C2211yescharacteristic
36#17988666C2211yescharacteristic
37#17988662—21no—
38#17988662—21no—
39#17988655—21no—
40C8×D292C2211yescharacteristic
41#17988650—21no—
42#17988647—21no—
43#17988639—21no—
44#17988612—21no—
45#17988611C2211yescharacteristic
46#17988609—21no—
47C2×C4⋊#10596831C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988340C2211yescharacteristic
51#17988340C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988316C2211yescharacteristic
57#17988316C2211yescharacteristic
58#17988316C2211yescharacteristic
59#17988316C2211yescharacteristic
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic
64#322×C73C2211yescharacteristic
65#322×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×#11924012—21no—
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×#11924011—21no—
76C22×#10596831—21no—
77C2×C8×D73—21no—
78#14556585—21no—
79#14556583C2×C411yescharacteristic
80#14556579C2×C411yescharacteristic
81#14556574—21no—
82#14556570C2×C411yescharacteristic
83#14556565C2×C411yescharacteristic
84C4×Dic146C2×C411yescharacteristic
85C4×Dic146C2311yescharacteristic
86C4×Dic146C2311yescharacteristic
87C4×D292C2×C411yescharacteristic
88C4×D292C2311yescharacteristic
89C4×D292C2311yescharacteristic
90C4×C22⋊D73—21no—
91C4×C22⋊D73—21no—
92C4×C22⋊D73—21no—
93#14556550C2×C411yescharacteristic
94#14556548—21no—
95#14556548—21no—
96C42×D73—21no—
97#14556525C2×C411yescharacteristic
98#14556525C2×C411yescharacteristic
99#14556523C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101C4⋊#10596831—21no—
102C4⋊#10596831—21no—
103C4⋊#10596831C2311yescharacteristic
104C4⋊#10596831C2311yescharacteristic
105C4⋊#10596831C2311yescharacteristic
106C4⋊#10596831C2311yescharacteristic
107#14556520—21no—
108#14556520—21no—
109#14556520—21no—
110#14556520—21no—
111#14556516C2×C411yescharacteristic
112#14556516C2×C411yescharacteristic
113#14556516C2×C411yescharacteristic
114#14556516C2×C411yescharacteristic
115#14556513C2×C411yescharacteristic
116#14556513C2×C411yescharacteristic
117#14556513C2×C411yescharacteristic
118#14556513C2×C411yescharacteristic
119#14556503—21no—
120#14556503—21no—
121#14556503—21no—
122#14556503—21no—
123#14556501—21no—
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73—21no—
129C4⋊C8×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C22⋊C8×C73—21no—
134C22⋊C8×C73C2×C411yescharacteristic
135C22⋊C8×C73C2×C411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137C22⋊C8×C73D411yescharacteristic
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—41no—
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—41no—
159D584—41no—
160#11924012—81no—
161#11924011—81no—
162#11924011—81no—
163#11924011—81no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—81no—
169C8×D73—81no—
170C4⋊Dic73C22×C411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180C22⋊Dic73—21no—
181C22⋊Dic73—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73#4111yescharacteristic
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C2×C8×C73C2×D411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73C4×D411yescharacteristic
210C22×D73—21no—
211C22×D73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—41no—
217C2×C4×C73C4×D411yescharacteristic
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×D411yescharacteristic
220C2×C4×C73C23×C411yescharacteristic
221C2×C4×C73C22×D411yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C22⋊D73—42no—
224C22⋊D73—42no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231D292—21no—
232D292—21no—
233D292—21no—
234D292—21no—
235C4×D73—42no—
236C4×D73—42no—
237C4×D73—41no—
238C4×D73—41no—
239C4×D73—41no—
240C4×D73—41no—
241Dic146—21no—
242Dic146—21no—
243Dic146—21no—
244Dic146#13112yes—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—21no—
252C8×C73—21no—
253C8×C73—41no—
254C8×C73—41no—
255#10596831—41no—
256#10596831—41no—
257#10596831—41no—
258#10596831—41no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73C2×C4×D411yescharacteristic
263C2×D73—41no—
264C2×D73—41no—
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C4×C73—21no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73C2×#13111yescharacteristic
274C4×C73#56811yescharacteristic
275C4×C73#57611yescharacteristic
276C4×C73#57811yescharacteristic
277Dic73—22no—
278Dic73—41no—
279Dic73—41no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283#18033—731nomaximal, Sylow
284C2×C73—41no—
285C2×C73#293311yescharacteristic
286C2×C73#295111yescharacteristic
287C2×C73#295511yescharacteristic
288D73—81no—
289D73—81no—
290#3102—731no—
291#2994—731no—
292#2991—731no—
293#1592—731no—
294#1589—731no—
295#1588—731no—
296#1588—731no—
297#1584—731no—
298#1581—731no—
299SD16⋊C8—731no—
300C8×Q16—731no—
301#1571—731no—
302#1495—731no—
303#1477—731no—
304#1454D7311yescharacteristic, complemented
305C73#1803311yescharacteristic, complemented, Sylow
306#529—731no—
307C4×#41—731no—
308#485—731no—
309#482—731no—
310#479—731no—
311#478—731no—
312#464—731no—
313#463—731no—
314#452—731no—
315#449—731no—
316#446—731no—
317C8×Q8—731no—
318C8×Q8—731no—
319C8×Q8—731no—
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16—731no—
323C4×D8—731no—
324#436—731no—
325#436—731no—
326#436—731no—
327#436—1461no—
328#436—1461no—
329#435—1461no—
330C8×D4—731no—
331C8×D4—1461no—
332#433—1461no—
333#431—1461no—
334#431C2×D7311yescharacteristic
335#431C2×D7311yescharacteristic
336#431C2×D7311yescharacteristic
337#424—1461no—
338#423—731no—
339#423—1461no—
340C2×C4⋊C8—731no—
341#335—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349D4⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8—731no—
353#322C2×D7311yescharacteristic
354#322C2×D7311yescharacteristic
355#322C2×D7311yescharacteristic
356C82C2×D7311yescharacteristic
357C2×#41—731no—
358C2×Q16—731no—
359C2×SD16—731no—
360C2×SD16—731no—
361C2×D8—731no—
362C2×M16—1461no—
363C2×M16—1461no—
364C2×M16—1461no—
365C2×M16—1461no—
366C22×C8—1461no—
367C22×C8—1461no—
368#126—1461no—
369#125—731no—
370#124—731no—
371#123—1461no—
372C22⋊Q8—731no—
373#121—731no—
374C4×Q8—731no—
375C4×Q8—731no—
376C4×Q8—731no—
377C4×D4—731no—
378C4×D4—731no—
379C4×D4—731no—
380C4×D4—1461no—
381C4×D4—1461no—
382C4×D4—1461no—
383#117—731no—
384#117—1461no—
385#117—1461no—
386C2×C42—1461no—
387C2×C42C22×D7311yescharacteristic
388#107—731no—
389#107—731no—
390#106—731no—
391#106—731no—
392C4⋊C8—21no—
393C4⋊C8—731no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—1461no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8C4×D7311yescharacteristic
404C4⋊C8C4×D7311yescharacteristic
405C4⋊C8D29211yescharacteristic
406C4⋊C8D29211yescharacteristic
407#103—731no—
408#103—731no—
409#103—731no—
410#103—731no—
411#102—731no—
412#102—731no—
413#102—731no—
414#102—731no—
415C22⋊C8—21no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420C22⋊C8C4×D7311yescharacteristic
421C22⋊C8C4×D7311yescharacteristic
422C22⋊C8D29211yescharacteristic
423C22⋊C8D29211yescharacteristic
424#97—1461no—
425C4×C8—1461no—
426C4×C8—1461no—
427C4×C8—1461no—
428C4×C8C22×D7311yescharacteristic
429C4×C8C22×D7311yescharacteristic
430C4×C8C22×D7311yescharacteristic
431C4×C8C22×D7311yescharacteristic
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434#41—2921no—
435#41—1462no—
436C2×Q8—731no—
437C2×Q8—731no—
438C2×D4—731no—
439C2×D4—731no—
440C2×D4—1461no—
441C2×D4—1461no—
442C22×C4—1461no—
443C22×C4—1461no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4C2×C4×D7311yescharacteristic
447C22×C4C2×D29211yescharacteristic
448C22×C4#1192402811yescharacteristic
449Q16—1462no—
450SD16—2921no—
451SD16—1462no—
452D8—2921no—
453M16—5841no—
454M16—5841no—
455M16—5841no—
456M16—5841no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—5841no—
460C2×C8—5841no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8C2×C4×D7311yescharacteristic
466C2×C8C2×C4×D7311yescharacteristic
467C2×C8C2×C4×D7311yescharacteristic
468C2×C8C2×C4×D7311yescharacteristic
469C2×C8C2×D29211yescharacteristic
470C2×C8C2×D29211yescharacteristic
471C2×C8C2×D29211yescharacteristic
472C2×C8C2×D29211yescharacteristic
473C4⋊C4—731no—
474C4⋊C4—731no—
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C22⋊C4—1461no—
484C22⋊C4—1461no—
485C22⋊C4—1461no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C42—1461no—
492C42—1461no—
493C42—1461no—
494C42—1461no—
495C42C2×C4×D7311yescharacteristic
496C42C2×D29211yescharacteristic
497C42#1192402811yescharacteristic
498C42C23×D7311yescharacteristic
499C23—1461no—
500C23—1461no—
501C23C4×D29211yescharacteristic
502Q8—732no—
503Q8—1461no—
504Q8—1461no—
505Q8—1461no—
506D4—2922no—
507D4—2922no—
508D4—1461no—
509D4—1461no—
510D4—1461no—
511D4—1461no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—2922no—
518C2×C4—2922no—
519C2×C4—2921no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—2921no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4C4×D29211yescharacteristic
530C2×C4C4×D29211yescharacteristic
531C2×C4C4×D29211yescharacteristic
532C2×C4C22×C4×D7311yescharacteristic
533C2×C4C22×D29211yescharacteristic
534C2×C4C2×#1192402811yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—2921no—
546C8—2921no—
547C8—2921no—
548C8—2921no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—2921no—
553C22—2921no—
554C22—2921no—
555C22—2921no—
556C22—2921no—
557C22—2921no—
558C22C2×C4×D29211yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—2921no—
564C4—2921no—
565C4—2921no—
566C4—2921no—
567C4—2921no—
568C4—1462no—
569C4#131×D7311yescharacteristic
570C4#1798935211yescharacteristic
571C4#1798939211yescharacteristic
572C4#1798940411yescharacteristic
573C2—41no—
574C2—5841no—
575C2—5841no—
576C2#2261865911yescharacteristic
577C2#2261880811yescharacteristic
578C2#2261883511yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1454C2
socleC22×C73C2×C4×D4
prime radical#17988734C4
cosocleC42×C73C24
hypercenter#1454D73
hypocenterC73#18033
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #22619093C2semidirect
3. #22619060C2semidirect
4. #22608835C2semidirect
5. #22608817C2semidirect
6. #22608811C2semidirect
7. #22608811C2semidirect
8. #22608783C2semidirect
9. #22608762C2semidirect
10. #22608745C2semidirect
11. C8×Dic292C2semidirect
12. #22608706C2semidirect
13. #22608397C2semidirect
14. #22608319C2semidirect
15. C73×#1454C2semidirect
304. #1454D73semidirect
305. C73#18033semidirect

Maximal subgroups

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

subgroupindex
#226199512
#226190932
#226190602
#226088352
#226088172
#226088112
#226087832
#226087622
#226087452
C8×Dic2922
#226087062
#226083972
#226083192
C73×#14542
#1803373