Finite Group Databasebeta

← #33057128

Subgroups — #33057128

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620000C211yesmaximal, characteristic
2#22618950C211yesmaximal, characteristic
3#22618879C211yesmaximal, characteristic, complemented
4#22608831C211yesmaximal, characteristic, complemented
5#22608820C211yesmaximal, characteristic, complemented
6#22608811C211yesmaximal, characteristic, complemented
7#22608778C211yesmaximal, characteristic, complemented
8#22608771C211yesmaximal, characteristic, complemented
9#22608748C211yesmaximal, characteristic, complemented
10Q16×#10596831C211yesmaximal, characteristic, complemented
11#22608713C211yesmaximal, characteristic, complemented
12#22608402C211yesmaximal, characteristic, complemented
13#22608317C211yesmaximal, characteristic
14#22608227C211yesmaximal, characteristic, complemented
15C73×#1587C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×#11924029C2211yescharacteristic
18#17988930C411yescharacteristic
19#17988926C411yescharacteristic
20#17988870C411yescharacteristic
21#17988866C411yescharacteristic
22#17988795C411yescharacteristic
23#17988791C411yescharacteristic
24#17988752C411yescharacteristic
25#17988748C411yescharacteristic
26#17988715—21no—
27#17988714—21no—
28#17988714C2211yescharacteristic
29Q8×#10596831C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31C8×Dic146C2211yescharacteristic
32C4×#11924018C2211yescharacteristic
33C4×#11924017C2211yescharacteristic
34C4×#11924015C2211yescharacteristic
35#17988666—21no—
36#17988666C2211yescharacteristic
37#17988664—21no—
38#17988664C2211yescharacteristic
39#17988643—21no—
40#17988643C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988612—21no—
44C4⋊C8×D73C2211yescharacteristic
45#17988544—21no—
46C4×#11924011—21no—
47C4×#11924011C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924029C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924011—21no—
72C2×#11924011—21no—
73C2×#11924011D411yescharacteristic
74C2×#11924011D411yescharacteristic
75C2×C8×D73—21no—
76#14556590C2×C411yescharacteristic
77#14556589C2×C411yescharacteristic
78#14556581—21no—
79#14556571C2×C411yescharacteristic
80#14556569—21no—
81#14556567C2×C411yescharacteristic
82Q8×Dic73C2×C411yescharacteristic
83C4×Dic146—21no—
84C4×Dic146C2311yescharacteristic
85C4×D292—21no—
86C4×D292C2311yescharacteristic
87#14556553—21no—
88#14556553C2×C411yescharacteristic
89#14556549—21no—
90#14556549C2×C411yescharacteristic
91#14556548—21no—
92C42×D73—21no—
93C42×D73C2311yescharacteristic
94#14556524C2×C411yescharacteristic
95#14556523C2×C411yescharacteristic
96#14556522C2×C411yescharacteristic
97C4⋊#10596831—21no—
98C4⋊#10596831—21no—
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520C2×C411yescharacteristic
106#14556520C2×C411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556515C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503C2×C411yescharacteristic
118#14556503C2×C411yescharacteristic
119#14556501—21no—
120#14556501—21no—
121#14556501D411yescharacteristic
122#14556501D411yescharacteristic
123C4×#10596831—21no—
124C4×#10596831—21no—
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C4×#10596831C2311yescharacteristic
128C8×Dic73—21no—
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
144#11924029—22no—
145#11924029—41no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×D292—21no—
149C2×D292C22×C411yescharacteristic
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73C22×C411yescharacteristic
154C2×C4×D73C2×D411yescharacteristic
155C2×C4×D73#4111yescharacteristic
156#11924018—22no—
157#11924017—41no—
158#11924015—41no—
159#11924011—22no—
160#11924011—41no—
161#11924011—42no—
162#11924011—42no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C8×D73—42no—
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#11924007—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73C22×C411yescharacteristic
189C4×Dic73C2×D411yescharacteristic
190C4×Dic73#4111yescharacteristic
191C2×Q8×C73C22×C411yescharacteristic
192C2×Q8×C73C22×C411yescharacteristic
193Q16×C73—22no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73C22×C411yescharacteristic
204C4⋊C4×C73C22×C411yescharacteristic
205C42×C73—21no—
206C42×C73—21no—
207C42×C73C2411yescharacteristic
208C22×D73—21no—
209C22×D73C4×D411yescharacteristic
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73#13112yes—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73C23×C411yescharacteristic
219C2×C4×C73C22×D411yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73C4×D411yescharacteristic
225C2×Dic73C4×D411yescharacteristic
226C2×Dic73C4×D411yescharacteristic
227D292—21no—
228D292—21no—
229D292—42no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—21no—
234C4×D73—41no—
235C4×D73—42no—
236C4×D73—41no—
237C4×D73—41no—
238C4×D73—81no—
239Dic146—21no—
240Dic146—21no—
241Dic146—81no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—41no—
247C8×C73—41no—
248C8×C73—41no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831#13712yes—
256C22×C73C2×C4×D411yescharacteristic
257C2×D73—21no—
258C2×D73—21no—
259C2×D73—21no—
260C2×D73—41no—
261C2×D73—41no—
262C2×D73—41no—
263C4×C73—22no—
264C4×C73—21no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73C2×#13111yescharacteristic
269C4×C73#56811yescharacteristic
270C4×C73C2×#13711yescharacteristic
271C4×C73#57511yescharacteristic
272Dic73—21no—
273Dic73—21no—
274Dic73—21no—
275Dic73—41no—
276Dic73—41no—
277Dic73—41no—
278#18013—731nomaximal, Sylow
279C2×C73#293311yescharacteristic
280C2×C73C4×#13711yescharacteristic
281C2×C73#295711yescharacteristic
282D73—41no—
283D73—81no—
284#3107—731no—
285#2971—731no—
286#2962—731no—
287#1592—731no—
288#1590—731no—
289#1588—731no—
290#1587D7311yescharacteristic, complemented
291#1584—731no—
292#1583—731no—
293#1579—731no—
294C8×Q16—731no—
295#1573—731no—
296#1497—731no—
297#1477—731no—
298#1453—731no—
299C73#1801311yescharacteristic, complemented, Sylow
300#533—731no—
301C4×#41—731no—
302#485—731no—
303#485—731no—
304#475—731no—
305#474—731no—
306#462—731no—
307#461—731no—
308#452—731no—
309#452—731no—
310#446—731no—
311#446—1461no—
312#446—1461no—
313#446C2×D7311yescharacteristic
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C8×Q8C2×D7311yescharacteristic
318C4×Q16—731no—
319C4×Q16C2×D7311yescharacteristic
320C4×SD16—731no—
321C4×SD16—731no—
322#436—731no—
323#436—731no—
324#436—1461no—
325#436—1461no—
326#432—731no—
327#432—1461no—
328#431—731no—
329#431—731no—
330#424—1461no—
331C2×C4⋊C8—731no—
332#405—1461no—
333C4×M16—731no—
334C4×M16—1461no—
335#335—731no—
336#335—731no—
337#334—731no—
338#334C2×D7311yescharacteristic
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8C2×D7311yescharacteristic
344Q8⋊C8C2×D7311yescharacteristic
345D4⋊C8—731no—
346D4⋊C8—731no—
347#322—731no—
348#322—731no—
349#322C2×D7311yescharacteristic
350C82—731no—
351C2×#41—731no—
352C2×Q16—731no—
353C2×Q16C4×D7311yescharacteristic
354C2×SD16—731no—
355C2×SD16—731no—
356C2×M16—731no—
357C2×M16—731no—
358C2×M16—1461no—
359C2×M16—1461no—
360C22×C8—1461no—
361C4⋊Q8—731no—
362C4⋊Q8—731no—
363#125—1461no—
364C22⋊Q8—731no—
365C22⋊Q8—731no—
366C22⋊Q8—1461no—
367C4×Q8—731no—
368C4×Q8—731no—
369C4×Q8—1461no—
370C4×Q8C22×D7311yescharacteristic
371C4×Q8C22×D7311yescharacteristic
372C4×D4—731no—
373C4×D4—731no—
374C4×D4—1461no—
375C4×D4—1461no—
376#117—731no—
377#117—1461no—
378#117—1461no—
379C2×C42—731no—
380C2×C42—1461no—
381#107—731no—
382#107C4×D7311yescharacteristic
383#106—731no—
384#106—731no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8C22×D7311yescharacteristic
398C4⋊C8C22×D7311yescharacteristic
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#103C4×D7311yescharacteristic
404#103C4×D7311yescharacteristic
405#102—731no—
406#102—731no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—21no—
414#97—731no—
415#97—731no—
416#97—1461no—
417#97—1461no—
418C4×C8—21no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8C22×D7311yescharacteristic
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428#41—2921no—
429#41—1462no—
430C2×Q8—731no—
431C2×Q8—1461no—
432C2×Q8C2×C4×D7311yescharacteristic
433C2×Q8C2×C4×D7311yescharacteristic
434C2×D4—731no—
435C2×D4—1461no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4—1461no—
442Q16—22no—
443Q16—1462no—
444SD16—2921no—
445SD16—2921no—
446M16—2922no—
447M16—2921no—
448M16—2922no—
449M16—1462no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—2922no—
454C2×C8—731no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—731no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8C2×C4×D7311yescharacteristic
462C2×C8C2×C4×D7311yescharacteristic
463C2×C8D4×D7311yescharacteristic
464C2×C8D4×D7311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—731no—
468C4⋊C4—731no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4C2×C4×D7311yescharacteristic
477C4⋊C4C2×C4×D7311yescharacteristic
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C22⋊C4—1461no—
482C22⋊C4—1461no—
483C42—21no—
484C42—21no—
485C42—731no—
486C42—731no—
487C42—731no—
488C42—1461no—
489C42—1461no—
490C42—1461no—
491C42C23×D7311yescharacteristic
492C23—731no—
493C23—1461no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—5841no—
498Q8—1461no—
499Q8—1461no—
500Q8#1455659912yes—
501D4—2922no—
502D4—1461no—
503D4—1461no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—2922no—
509C2×C4—2921no—
510C2×C4—2921no—
511C2×C4—2921no—
512C2×C4—5841no—
513C2×C4—731no—
514C2×C4—731no—
515C2×C4—731no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4C22×C4×D7311yescharacteristic
524C2×C4C2×D4×D7311yescharacteristic
525C2×C4#41×D7311yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—2921no—
534C8—2921no—
535C8—2921no—
536C8—732no—
537C8—1461no—
538C8—1461no—
539C8—1461no—
540C22—2921no—
541C22—2921no—
542C22—2921no—
543C22—1461no—
544C22—1461no—
545C22—1461no—
546C22C4×D4×D7311yescharacteristic
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—2921no—
553C4—2921no—
554C4—2921no—
555C4—1461no—
556C4—1461no—
557C4—1461no—
558C4C2×#1455659911yescharacteristic
559C4#1798935211yescharacteristic
560C4#137×D7311yescharacteristic
561C4#1798938611yescharacteristic
562C2—2921no—
563C2—5841no—
564C2#2261865711yescharacteristic
565C2#2261874711yescharacteristic
566C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1587C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924029C2×C4
cosocleC42×C73C24
hypercenter#1587D73
hypocenterC73#18013
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
3. #22618879C2semidirect
4. #22608831C2semidirect
5. #22608820C2semidirect
6. #22608811C2semidirect
7. #22608778C2semidirect
8. #22608771C2semidirect
9. #22608748C2semidirect
10. Q16×#10596831C2semidirect
11. #22608713C2semidirect
12. #22608402C2semidirect
14. #22608227C2semidirect
15. C73×#1587C2semidirect
290. #1587D73semidirect
299. C73#18013semidirect

Maximal subgroups

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

subgroupindex
#226200002
#226189502
#226188792
#226088312
#226088202
#226088112
#226087782
#226087712
#226087482
Q16×#105968312
#226087132
#226084022
#226083172
#226082272
C73×#15872
#1801373