Finite Group Databasebeta

← #33056852

Subgroups — #33056852

Order 18688.

576 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620504C211yesmaximal, characteristic
2#22619083C211yesmaximal, characteristic, complemented
3#22619079C211yesmaximal, characteristic, complemented
4#22608809C211yesmaximal, characteristic, complemented
5#22608806C211yesmaximal, characteristic, complemented
6#22608791C211yesmaximal, characteristic, complemented
7#22608786C211yesmaximal, characteristic, complemented
8#22608782C211yesmaximal, characteristic, complemented
9#22608762C211yesmaximal, characteristic, complemented
10#22608759C211yesmaximal, characteristic, complemented
11#22608688C211yesmaximal, characteristic, complemented
12#22608395C211yesmaximal, characteristic, complemented
13#22608395C211yesmaximal, characteristic, complemented
14#22608222C211yesmaximal, characteristic, complemented
15C73×#1584C211yesmaximal, characteristic, complemented
16#17989124C2211yescharacteristic
17#17989124C2211yescharacteristic
18#17988988C411yescharacteristic
19#17988972C411yescharacteristic
20#17988943C411yescharacteristic
21#17988943C411yescharacteristic
22#17988825C411yescharacteristic
23#17988824C411yescharacteristic
24#17988819C411yescharacteristic
25#17988819C411yescharacteristic
26#17988718C2211yescharacteristic
27Q8×#10596831C2211yescharacteristic
28C4×#11924015C2211yescharacteristic
29C4×#11924015C2211yescharacteristic
30C4×D584C2211yescharacteristic
31#17988666—21no—
32#17988666C2211yescharacteristic
33#17988664—21no—
34#17988664C2211yescharacteristic
35#17988660—21no—
36#17988657—21no—
37C8×D292C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988649—21no—
40#17988646—21no—
41#17988638C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988612—21no—
44#17988612—21no—
45#17988609C2211yescharacteristic
46#17988609C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988339C2211yescharacteristic
51Q8⋊#10596831C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53#17988316C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988308C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924015C2×C411yescharacteristic
68C2×#11924015C2×C411yescharacteristic
69C2×D584C2×C411yescharacteristic
70C2×#11924011—21no—
71C2×#11924011—21no—
72C2×#11924011—21no—
73C2×#11924011—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76C2×C8×D73C2×C411yescharacteristic
77C2×C8×D73C2×C411yescharacteristic
78#14556586—21no—
79#14556586—21no—
80#14556582C2×C411yescharacteristic
81#14556582C2×C411yescharacteristic
82#14556580C2×C411yescharacteristic
83#14556580C2×C411yescharacteristic
84#14556576—21no—
85#14556576—21no—
86#14556567C2×C411yescharacteristic
87#14556567C2×C411yescharacteristic
88#14556566C2×C411yescharacteristic
89#14556566C2×C411yescharacteristic
90C4×D292—21no—
91C4×D292—21no—
92C4×D292C2311yescharacteristic
93C4×D292C2311yescharacteristic
94#14556548—21no—
95#14556548—21no—
96C42×D73C2311yescharacteristic
97#14556525C2×C411yescharacteristic
98#14556522C2×C411yescharacteristic
99#14556522C2×C411yescharacteristic
100C4⋊#10596831—21no—
101C4⋊#10596831—21no—
102C4⋊#10596831C2311yescharacteristic
103C4⋊#10596831C2311yescharacteristic
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556520D411yescharacteristic
108#14556520D411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556515C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556511C2×C411yescharacteristic
114#14556511C2×C411yescharacteristic
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503D411yescharacteristic
121#14556503D411yescharacteristic
122#14556502—21no—
123C4×#10596831—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73C2×C411yescharacteristic
128C8×Dic73C2×C411yescharacteristic
129C2×Q16×C73C2×C411yescharacteristic
130C4×Q8×C73C2311yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132#107×C73C2×C411yescharacteristic
133C4⋊C8×C73—21no—
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#103×C73C2×C411yescharacteristic
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×D292—21no—
145C2×D292—21no—
146C2×D292C22×C411yescharacteristic
147C2×D292C22×C411yescharacteristic
148C2×C4×D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73C22×C411yescharacteristic
151C2×C4×D73C2×D411yescharacteristic
152C2×C4×D73#4111yescharacteristic
153#11924015—41no—
154#11924015—41no—
155D584—41no—
156#11924011—81no—
157#11924011—81no—
158#11924011—81no—
159#11924011—81no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C8×D73—41no—
168C8×D73—41no—
169C8×D73—81no—
170C8×D73—81no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C22×C411yescharacteristic
174C4⋊Dic73C22×C411yescharacteristic
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924005—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189C4×Dic73C22×C411yescharacteristic
190C4×Dic73C2×D411yescharacteristic
191C4×Dic73#4111yescharacteristic
192C2×Q8×C73C22×C411yescharacteristic
193C2×Q8×C73C22×C411yescharacteristic
194Q16×C73—41no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73C22×C411yescharacteristic
205C4⋊C4×C73C22×C411yescharacteristic
206C42×C73—21no—
207C42×C73—21no—
208C42×C73C2411yescharacteristic
209C22×D73—21no—
210C22×D73—21no—
211C22×D73C4×D411yescharacteristic
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73C23×C411yescharacteristic
221C2×C4×C73C22×D411yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73C4×D411yescharacteristic
226C2×Dic73C4×D411yescharacteristic
227C2×Dic73C4×D411yescharacteristic
228D292—21no—
229D292—21no—
230D292—21no—
231D292—21no—
232D292—81no—
233D292—81no—
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—21no—
237C4×D73—21no—
238C4×D73—41no—
239C4×D73—41no—
240C4×D73—41no—
241C4×D73—41no—
242C4×D73—41no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—21no—
254#10596831—41no—
255#10596831—41no—
256#10596831—41no—
257C22×C73C2×C4×D411yescharacteristic
258C2×D73—21no—
259C2×D73—21no—
260C2×D73—21no—
261C2×D73—41no—
262C2×D73—41no—
263C2×D73—41no—
264C2×D73—41no—
265C2×D73—41no—
266C2×D73—41no—
267C4×C73—21no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73#56811yescharacteristic
273C4×C73#56811yescharacteristic
274C4×C73#57611yescharacteristic
275C4×C73#57811yescharacteristic
276Dic73—21no—
277Dic73—21no—
278Dic73—21no—
279Dic73—41no—
280Dic73—41no—
281#17992—731nomaximal, Sylow
282C2×C73#293211yescharacteristic
283C2×C73#295111yescharacteristic
284C2×C73#295711yescharacteristic
285D73—41no—
286D73—81no—
287D73—81no—
288#3168—731no—
289#2993—731no—
290#2993—731no—
291#1588—731no—
292#1588—731no—
293#1585—731no—
294#1585—731no—
295#1584—731no—
296#1584D7311yescharacteristic, complemented
297#1581—731no—
298#1581—731no—
299#1567—731no—
300#1495—731no—
301#1495—731no—
302#1452—731no—
303C73#1799211yescharacteristic, complemented, Sylow
304#529—731no—
305#529—731no—
306#499—731no—
307#495—731no—
308#488—731no—
309#488—731no—
310#467—731no—
311#466—731no—
312#465—731no—
313#465—731no—
314#446—731no—
315#446C2×D7311yescharacteristic
316C8×Q8—731no—
317C8×Q8C2×D7311yescharacteristic
318C4×Q16C2×D7311yescharacteristic
319C4×SD16—731no—
320C4×SD16—731no—
321C4×D8—731no—
322#436—731no—
323#436—731no—
324#436—1461no—
325#436—1461no—
326#435—1461no—
327#435—1461no—
328C8×D4—731no—
329C8×D4—731no—
330#433—1461no—
331#433—1461no—
332#431—731no—
333#431—731no—
334#424—1461no—
335#424—1461no—
336#423—731no—
337#423—731no—
338C2×C4×C8—731no—
339#335—731no—
340#335—731no—
341#335—731no—
342#335C2×D7311yescharacteristic
343Q8⋊C8—731no—
344Q8⋊C8—731no—
345Q8⋊C8C2×D7311yescharacteristic
346Q8⋊C8C2×D7311yescharacteristic
347D4⋊C8—731no—
348D4⋊C8—731no—
349D4⋊C8—731no—
350D4⋊C8—731no—
351#322—731no—
352#322—731no—
353#322—731no—
354#322C2×D7311yescharacteristic
355C2×Q16C4×D7311yescharacteristic
356C2×SD16—731no—
357C2×SD16—731no—
358C2×D8—731no—
359C2×M16—1461no—
360C2×M16—1461no—
361C2×M16—1461no—
362C2×M16—1461no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—1461no—
366C22×C8—1461no—
367#126—1461no—
368#126—1461no—
369#125—731no—
370#125—731no—
371#124—731no—
372#124—731no—
373#123—1461no—
374#123—1461no—
375C22⋊Q8—731no—
376C22⋊Q8—731no—
377#121—731no—
378#121—731no—
379C4×Q8C22×D7311yescharacteristic
380C4×Q8C22×D7311yescharacteristic
381C4×D4—731no—
382C4×D4—731no—
383C4×D4—1461no—
384C4×D4—1461no—
385#117—1461no—
386#117—1461no—
387C2×C42—731no—
388#107—731no—
389#107C4×D7311yescharacteristic
390#106—731no—
391#106—731no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8C22×D7311yescharacteristic
404C4⋊C8C22×D7311yescharacteristic
405#103—731no—
406#103—731no—
407#103C4×D7311yescharacteristic
408#103C4×D7311yescharacteristic
409#102—731no—
410#102—731no—
411#102—731no—
412#102—731no—
413C22⋊C8—731no—
414C22⋊C8—731no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420#97—21no—
421#97—1461no—
422C4×C8—21no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—1461no—
429C4×C8C22×D7311yescharacteristic
430C4×C8C22×D7311yescharacteristic
431C4×C8C22×D7311yescharacteristic
432C2×Q8C2×C4×D7311yescharacteristic
433C2×Q8C2×C4×D7311yescharacteristic
434C2×D4—731no—
435C2×D4—731no—
436C2×D4—1461no—
437C2×D4—1461no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—1461no—
442C22×C4—1461no—
443Q16—41no—
444SD16—2921no—
445SD16—2921no—
446D8—2921no—
447M16—5841no—
448M16—5841no—
449M16—5841no—
450M16—5841no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—2921no—
455C2×C8—2921no—
456C2×C8—5841no—
457C2×C8—5841no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—731no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8C2×C4×D7311yescharacteristic
466C2×C8C2×C4×D7311yescharacteristic
467C2×C8D4×D7311yescharacteristic
468C2×C8D4×D7311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—731no—
472C4⋊C4—731no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4C2×C4×D7311yescharacteristic
480C4⋊C4C2×C4×D7311yescharacteristic
481C22⋊C4—1461no—
482C22⋊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—21no—
492C42—21no—
493C42—731no—
494C42—731no—
495C42—731no—
496C42C23×D7311yescharacteristic
497C23—731no—
498C23—1461no—
499C23—1461no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504D4—5841no—
505D4—5841no—
506D4—1461no—
507D4—1461no—
508D4—1461no—
509D4—1461no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—2921no—
515C2×C4—2921no—
516C2×C4—2921no—
517C2×C4—2921no—
518C2×C4—2921no—
519C2×C4—731no—
520C2×C4—731no—
521C2×C4—731no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4C22×C4×D7311yescharacteristic
529C2×C4C2×D4×D7311yescharacteristic
530C2×C4#41×D7311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—2921no—
539C8—2921no—
540C8—2921no—
541C8—1461no—
542C8—1461no—
543C8—1461no—
544C8—1461no—
545C22—2921no—
546C22—2921no—
547C22—2921no—
548C22—2921no—
549C22—2921no—
550C22—2921no—
551C22—1461no—
552C22—1461no—
553C22—1461no—
554C22C4×D4×D7311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—2921no—
561C4—2921no—
562C4—1461no—
563C4—1461no—
564C4—1461no—
565C4#1798935211yescharacteristic
566C4#1798935311yescharacteristic
567C4#1798938911yescharacteristic
568C4#1798940011yescharacteristic
569C2—2921no—
570C2—5841no—
571C2—5841no—
572C2#2261864511yescharacteristic
573C2#2261880611yescharacteristic
574C2#2261884511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1584C2
socleC22×C73C2×C4×D4
prime radical#17988824C4
cosocleC42×C73C24
hypercenter#1584D73
hypocenterC73#17992
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
2. #22619083C2semidirect
3. #22619079C2semidirect
4. #22608809C2semidirect
5. #22608806C2semidirect
6. #22608791C2semidirect
7. #22608786C2semidirect
8. #22608782C2semidirect
9. #22608762C2semidirect
10. #22608759C2semidirect
11. #22608688C2semidirect
12. #22608395C2semidirect
13. #22608395C2semidirect
14. #22608222C2semidirect
15. C73×#1584C2semidirect
296. #1584D73semidirect
303. C73#17992semidirect

Maximal subgroups

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

subgroupindex
#226205042
#226190832
#226190792
#226088092
#226088062
#226087912
#226087862
#226087822
#226087622
#226087592
#226086882
#226083952
#226082222
C73×#15842
#1799273