Finite Group Databasebeta

← #33057255

Subgroups — #33057255

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620013C211yesmaximal, characteristic
2#22619093C211yesmaximal, characteristic
3#22619018C211yesmaximal, characteristic, complemented
4#22608841C211yesmaximal, characteristic, complemented
5#22608835C211yesmaximal, characteristic, complemented
6#22608783C211yesmaximal, characteristic, complemented
7#22608783C211yesmaximal, characteristic, complemented
8#22608776C211yesmaximal, characteristic, complemented
9#22608769C211yesmaximal, characteristic, complemented
10#22608751C211yesmaximal, characteristic, complemented
11#22608745C211yesmaximal, characteristic, complemented
12#22608716C211yesmaximal, characteristic, complemented
13#22608392C211yesmaximal, characteristic
14C2×#17988319C211yesmaximal, characteristic, complemented
15C73×#1452C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C2×C4×Dic146C2211yescharacteristic
18#17988918C411yescharacteristic
19#17988901C411yescharacteristic
20#17988895C411yescharacteristic
21#17988895C411yescharacteristic
22#17988810C411yescharacteristic
23#17988810C411yescharacteristic
24#17988745C411yescharacteristic
25#17988728C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988717C2211yescharacteristic
28#17988717C2211yescharacteristic
29#17988716—21no—
30#17988716—21no—
31C8×Dic146C2211yescharacteristic
32C8×Dic146C2211yescharacteristic
33C8×Dic146C2211yescharacteristic
34C4×Dic292C2211yescharacteristic
35C4×Dic292C2211yescharacteristic
36C4×#11924017C2211yescharacteristic
37C4×#11924017C2211yescharacteristic
38#17988666C2211yescharacteristic
39#17988655—21no—
40C8×D292C2211yescharacteristic
41#17988650—21no—
42#17988647—21no—
43#17988644C2211yescharacteristic
44#17988641—21no—
45#17988637—21no—
46#17988612—21no—
47C2×C4⋊#10596831C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988338C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988319C2211yescharacteristic
57#17988319C2211yescharacteristic
58#17988316C2211yescharacteristic
59#17988316C2211yescharacteristic
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic
64#322×C73C2211yescharacteristic
65#322×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C22×Dic146C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×Dic292C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×#11924017C2×C411yescharacteristic
72C2×#11924011—21no—
73C22×#10596831—21no—
74C2×C8×D73—21no—
75#14556585—21no—
76#14556583C2×C411yescharacteristic
77#14556579C2×C411yescharacteristic
78#14556574—21no—
79#14556570C2×C411yescharacteristic
80#14556565C2×C411yescharacteristic
81C4×Dic146—21no—
82C4×Dic146—21no—
83C4×Dic146C2×C411yescharacteristic
84C4×Dic146C2×C411yescharacteristic
85C4×Dic146C2311yescharacteristic
86C4×Dic146C2311yescharacteristic
87C4×Dic146C2311yescharacteristic
88C4×D292C2311yescharacteristic
89C4×C22⋊D73—21no—
90#14556548—21no—
91C2×C4⋊Dic73C2×C411yescharacteristic
92C2×#11924007—21no—
93C2×C4×Dic73—21no—
94#14556525C2×C411yescharacteristic
95#14556525C2×C411yescharacteristic
96#14556523C2×C411yescharacteristic
97#14556523C2×C411yescharacteristic
98C4⋊#10596831—21no—
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102C4⋊#10596831C2311yescharacteristic
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556520—21no—
108#14556520—21no—
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556516C2×C411yescharacteristic
112#14556516C2×C411yescharacteristic
113#14556516C2×C411yescharacteristic
114#14556516C2×C411yescharacteristic
115#14556513C2×C411yescharacteristic
116#14556513C2×C411yescharacteristic
117C22⋊#10596831—21no—
118#14556503—21no—
119#14556503—21no—
120#14556502—21no—
121#14556501—21no—
122#14556501—21no—
123#14556501—21no—
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C22×C8×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C22⋊C8×C73C2×C411yescharacteristic
134C22⋊C8×C73C2×C411yescharacteristic
135C22⋊C8×C73D411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137C4×C8×C73—21no—
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—22no—
145C2×Dic146—21no—
146C2×Dic146—41no—
147C2×Dic146C22×C411yescharacteristic
148C2×Dic146C22×C411yescharacteristic
149C2×Dic146C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C2×C4×D73—21no—
155Dic292—22no—
156Dic292—41no—
157#11924017—22no—
158#11924017—41no—
159#11924011—81no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—81no—
165C8×D73—81no—
166C4⋊Dic73—21no—
167C4⋊Dic73C22×C411yescharacteristic
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170C4⋊Dic73C22×C411yescharacteristic
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179C22⋊Dic73—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73#4111yescharacteristic
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—42no—
195C2×C8×C73C22×C411yescharacteristic
196C2×C8×C73C22×C411yescharacteristic
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C42×C73C22×C411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73#4111yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73C4×D411yescharacteristic
208C22×D73—21no—
209C2×C4×C73—22no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73C4×D411yescharacteristic
215C2×C4×C73C4×D411yescharacteristic
216C2×C4×C73C4×D411yescharacteristic
217C2×C4×C73C23×C411yescharacteristic
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C22⋊D73—42no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—42no—
229C2×Dic73—42no—
230D292—21no—
231D292—21no—
232C4×D73—41no—
233C4×D73—41no—
234Dic146—21no—
235Dic146—21no—
236Dic146—21no—
237Dic146—21no—
238Dic146—21no—
239Dic146—42no—
240Dic146#13112yes—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—41no—
250C8×C73—41no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255C22×C73—21no—
256C22×C73—21no—
257C22×C73#44412yes—
258C22×C73C2×C4×D411yescharacteristic
259C2×D73—41no—
260C2×D73—41no—
261C2×D73—41no—
262C4×C73—21no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73—21no—
266C4×C73C2×#13111yescharacteristic
267C4×C73#56811yescharacteristic
268C4×C73#57711yescharacteristic
269C4×C73#57811yescharacteristic
270Dic73—22no—
271Dic73—41no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276Dic73—41no—
277#18023—731nomaximal, Sylow
278C2×C73—22no—
279C2×C73#293311yescharacteristic
280C2×C73#294711yescharacteristic
281C2×C73C2×#44411yescharacteristic
282D73—81no—
283#3108—731no—
284#2994—731no—
285#2984—731no—
286#1593—731no—
287#1592—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1582—731no—
292#1579—731no—
293SD16⋊C8—731no—
294#1573—731no—
295#1494—731no—
296C2×Q8⋊C8—731no—
297#1452D7311yescharacteristic, complemented
298C73#1802311yescharacteristic, complemented, Sylow
299#529—731no—
300C2×C4×Q8—731no—
301#483—731no—
302#480—731no—
303#479—731no—
304#479—731no—
305#464—731no—
306#464—731no—
307#451—731no—
308#448—731no—
309#446—731no—
310#446—731no—
311#446—731no—
312#446—1461no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C4×Q16—731no—
318C4×Q16—731no—
319C4×SD16—731no—
320C4×SD16—731no—
321#436—731no—
322#435—1461no—
323C8×D4—731no—
324C8×D4—1461no—
325#433—1461no—
326#432—731no—
327#432—1461no—
328#431—1461no—
329#431C2×D7311yescharacteristic
330#431C2×D7311yescharacteristic
331#424—1461no—
332C2×C4⋊C8—731no—
333C2×C4×C8C2×D7311yescharacteristic
334#335—731no—
335#335—731no—
336#334—731no—
337#334—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8—731no—
344D4⋊C8—731no—
345D4⋊C8—731no—
346#322C2×D7311yescharacteristic
347#322C2×D7311yescharacteristic
348#322C2×D7311yescharacteristic
349#322C2×D7311yescharacteristic
350C22×Q8—731no—
351C2×Q16—731no—
352C2×Q16—731no—
353C2×SD16—731no—
354C2×SD16—731no—
355C2×M16—1461no—
356C22×C8—21no—
357C22×C8—1461no—
358C22×C8—1461no—
359#126—1461no—
360#125—731no—
361#124—731no—
362#123—1461no—
363C22⋊Q8—731no—
364#121—731no—
365C4×Q8—731no—
366C4×Q8—731no—
367C4×Q8—731no—
368C4×Q8—731no—
369C4×Q8—731no—
370C4×Q8—1461no—
371C4×Q8—1461no—
372C4×D4—731no—
373C4×D4—1461no—
374#117—1461no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—1461no—
377C2×C42—1461no—
378C2×C42C22×D7311yescharacteristic
379#107—731no—
380#107—731no—
381#106—731no—
382#106—731no—
383C4⋊C8—731no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—1461no—
388C4⋊C8—1461no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8C4×D7311yescharacteristic
395C4⋊C8C4×D7311yescharacteristic
396C4⋊C8D29211yescharacteristic
397C4⋊C8D29211yescharacteristic
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#103—731no—
404#102—731no—
405#102—731no—
406C22⋊C8—1461no—
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409C22⋊C8C4×D7311yescharacteristic
410C22⋊C8C4×D7311yescharacteristic
411C22⋊C8D29211yescharacteristic
412C22⋊C8D29211yescharacteristic
413#97—1461no—
414#97—1461no—
415#97—1461no—
416#97—1461no—
417C4×C8—21no—
418C4×C8—1461no—
419C4×C8—1461no—
420C4×C8—1461no—
421C4×C8C22×D7311yescharacteristic
422C4×C8C22×D7311yescharacteristic
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426C4×C8C22×D7311yescharacteristic
427C2×Q8—2921no—
428C2×Q8—731no—
429C2×Q8—731no—
430C2×Q8—731no—
431C2×Q8—1462no—
432C2×Q8—1461no—
433C2×D4—731no—
434C2×D4—1461no—
435C22×C4—1461no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4C2×C4×D7311yescharacteristic
439C22×C4C2×D29211yescharacteristic
440C22×C4#1192402811yescharacteristic
441Q16—2921no—
442Q16—1462no—
443SD16—2921no—
444SD16—1462no—
445M16—5841no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—5841no—
450C2×C8—5841no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8C2×C4×D7311yescharacteristic
456C2×C8C2×C4×D7311yescharacteristic
457C2×C8C2×C4×D7311yescharacteristic
458C2×C8C2×C4×D7311yescharacteristic
459C2×C8C2×D29211yescharacteristic
460C2×C8C2×D29211yescharacteristic
461C2×C8C2×D29211yescharacteristic
462C2×C8C2×D29211yescharacteristic
463C4⋊C4—731no—
464C4⋊C4—731no—
465C4⋊C4—731no—
466C4⋊C4—731no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42—1461no—
485C42—1461no—
486C42C2×C4×D7311yescharacteristic
487C42C2×D29211yescharacteristic
488C42#1192402811yescharacteristic
489C42C23×D7311yescharacteristic
490C23—1461no—
491C23C4×D29211yescharacteristic
492Q8—2922no—
493Q8—732no—
494Q8—1461no—
495Q8—1461no—
496Q8—1461no—
497Q8—1461no—
498Q8—1461no—
499D4—2922no—
500D4—1461no—
501D4—1461no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—2922no—
508C2×C4—2922no—
509C2×C4—2921no—
510C2×C4—2921no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4C4×D29211yescharacteristic
519C2×C4C4×D29211yescharacteristic
520C2×C4C4×D29211yescharacteristic
521C2×C4C22×C4×D7311yescharacteristic
522C2×C4C22×D29211yescharacteristic
523C2×C4C2×#1192402811yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—2921no—
535C8—2921no—
536C8—2921no—
537C8—2921no—
538C22—21no—
539C22—21no—
540C22—2921no—
541C22—2921no—
542C22—2921no—
543C22#1798871012yes—
544C22C2×C4×D29211yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—2921no—
550C4—2921no—
551C4—2921no—
552C4—2921no—
553C4—2921no—
554C4—2921no—
555C4—1462no—
556C4#131×D7311yescharacteristic
557C4#1798935211yescharacteristic
558C4#1798939911yescharacteristic
559C4#1798940411yescharacteristic
560C2—22no—
561C2—5841no—
562C2#2261865911yescharacteristic
563C2#2261877611yescharacteristic
564C2C2×#1798871011yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1452C2
socleC22×C73C2×C4×D4
prime radical#14556565C2×C4
cosocleC42×C73C24
hypercenter#1452D73
hypocenterC73#18023
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1452

Complements

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

NH ≅ G/Ntype
3. #22619018C2semidirect
4. #22608841C2semidirect
5. #22608835C2semidirect
6. #22608783C2semidirect
7. #22608783C2semidirect
8. #22608776C2semidirect
9. #22608769C2semidirect
10. #22608751C2semidirect
11. #22608745C2semidirect
12. #22608716C2semidirect
14. C2×#17988319C2semidirect
15. C73×#1452C2semidirect
297. #1452D73semidirect
298. C73#18023semidirect

Maximal subgroups

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

subgroupindex
#226200132
#226190932
#226190182
#226088412
#226088352
#226087832
#226087762
#226087692
#226087512
#226087452
#226087162
#226083922
C2×#179883192
C73×#14522
#1802373