Finite Group Databasebeta

← #33056094

Subgroups — #33056094

Order 18688.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620000C211yesmaximal, characteristic
2#22619041C211yesmaximal, characteristic
3#22619022C211yesmaximal, characteristic, complemented
4#22608803C211yesmaximal, characteristic, complemented
5#22608787C211yesmaximal, characteristic, complemented
6#22608778C211yesmaximal, characteristic, complemented
7#22608770C211yesmaximal, characteristic, complemented
8#22608748C211yesmaximal, characteristic, complemented
9#22608741C211yesmaximal, characteristic, complemented
10C8×#11924017C211yesmaximal, characteristic, complemented
11#22608715C211yesmaximal, characteristic, complemented
12#22608364C211yesmaximal, characteristic
13#22608332C211yesmaximal, characteristic, complemented
14#22608230C211yesmaximal, characteristic, complemented
15C8×Q16×C73C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×#11924029C2211yescharacteristic
18#17988930C411yescharacteristic
19#17988926C411yescharacteristic
20#17988870C411yescharacteristic
21#17988866C411yescharacteristic
22#17988795C411yescharacteristic
23#17988791C411yescharacteristic
24#17988752C411yescharacteristic
25#17988748C411yescharacteristic
26#17988718C2211yescharacteristic
27#17988717—21no—
28#17988716—21no—
29#17988714C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31C8×Dic146C2211yescharacteristic
32C4×#11924018C2211yescharacteristic
33C4×#11924017C2211yescharacteristic
34C4×#11924015C2211yescharacteristic
35C8×D292—21no—
36C8×D292C2211yescharacteristic
37#17988652—21no—
38#17988652C2211yescharacteristic
39#17988647—21no—
40#17988646—21no—
41#17988643C2211yescharacteristic
42#17988638—21no—
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45#17988638C2211yescharacteristic
46C4⋊C8×D73—21no—
47C4⋊C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988338C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988309C2211yescharacteristic
60C8×Q8×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#11924029C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×C8×D73—21no—
72C2×C8×D73—21no—
73C2×C8×D73—21no—
74#14556590C2×C411yescharacteristic
75#14556589C2×C411yescharacteristic
76#14556581—21no—
77#14556571C2×C411yescharacteristic
78#14556569—21no—
79#14556567C2×C411yescharacteristic
80Q8×Dic73C2×C411yescharacteristic
81C4×Dic146—21no—
82C4×Dic146C2311yescharacteristic
83C4×D292—21no—
84C4×D292C2311yescharacteristic
85#14556553—21no—
86#14556553C2×C411yescharacteristic
87#14556549—21no—
88#14556549C2×C411yescharacteristic
89#14556548—21no—
90C42×D73—21no—
91C42×D73C2311yescharacteristic
92#14556524C2×C411yescharacteristic
93#14556523C2×C411yescharacteristic
94#14556522C2×C411yescharacteristic
95C4⋊#10596831—21no—
96C4⋊#10596831—21no—
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
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#14556503D411yescharacteristic
120#14556503D411yescharacteristic
121#14556502—21no—
122#14556501—21no—
123#14556501—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
139C4×C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924029—22no—
145#11924029—22no—
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—22no—
158#11924015—22no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C8×D73—81no—
167C8×D73—81no—
168C8×D73—81no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924005—21no—
179#11924005—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73C22×C411yescharacteristic
187C4×Dic73C2×D411yescharacteristic
188C4×Dic73#4111yescharacteristic
189C2×Q8×C73C22×C411yescharacteristic
190C2×Q8×C73C22×C411yescharacteristic
191Q16×C73—22no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73C22×C411yescharacteristic
196C2×C8×C73C22×C411yescharacteristic
197C2×C8×C73C2×D411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73C22×C411yescharacteristic
202C4⋊C4×C73C22×C411yescharacteristic
203C42×C73—21no—
204C42×C73—21no—
205C42×C73C2411yescharacteristic
206C22×D73—21no—
207C22×D73C4×D411yescharacteristic
208Q8×C73—21no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73#13112yes—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73C23×C411yescharacteristic
217C2×C4×C73C22×D411yescharacteristic
218C2×C4×C73C2×#4111yescharacteristic
219C2×Dic73—21no—
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73C4×D411yescharacteristic
223C2×Dic73C4×D411yescharacteristic
224C2×Dic73C4×D411yescharacteristic
225D292—24no—
226D292—21no—
227D292#13112yes—
228C4×D73—24no—
229C4×D73—21no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—41no—
234C4×D73—41no—
235C4×D73—41no—
236C4×D73—81no—
237Dic146—21no—
238Dic146—21no—
239Dic146—81no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—41no—
245C8×C73—41no—
246C8×C73—41no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254C22×C73C2×C4×D411yescharacteristic
255C2×D73—21no—
256C2×D73—22no—
257C2×D73—21no—
258C2×D73—21no—
259C2×D73—41no—
260C2×D73—41no—
261C4×C73—22no—
262C4×C73—21no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73C2×#13111yescharacteristic
267C4×C73C2×#13111yescharacteristic
268C4×C73#57711yescharacteristic
269C4×C73#57811yescharacteristic
270Dic73—21no—
271Dic73—21no—
272Dic73—21no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276#17921—731nomaximal, Sylow
277C2×C73#292911yescharacteristic
278C2×C73#294711yescharacteristic
279C2×C73#295711yescharacteristic
280D73—41no—
281D73—42no—
282#3107—731no—
283#2988—731no—
284#2985—731no—
285#1587—731no—
286#1585—731no—
287#1584—731no—
288#1582—731no—
289#1579—731no—
290SD16⋊C8—731no—
291C8×Q16D7311yescharacteristic, complemented
292C8×SD16—731no—
293#1573—731no—
294#1488—731no—
295#1481—731no—
296#1454—731no—
297C73#1792111yescharacteristic, complemented, Sylow
298#533—731no—
299C4×#41—731no—
300#485—731no—
301#485—731no—
302#475—731no—
303#474—731no—
304#462—731no—
305#461—731no—
306#452—731no—
307#452—731no—
308#446—731no—
309#446—731no—
310#446—1461no—
311#446—1461no—
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8C2×D7311yescharacteristic
315C8×Q8C2×D7311yescharacteristic
316C4×Q16—731no—
317C4×Q16C2×D7311yescharacteristic
318C4×SD16—731no—
319C4×SD16—731no—
320C8×D4—731no—
321C8×D4—731no—
322C8×D4—1461no—
323C8×D4—1461no—
324#433—1461no—
325#433—1461no—
326#432—731no—
327#431—731no—
328#431—731no—
329#431—731no—
330#431—1461no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—1461no—
333#335—731no—
334#335C2×D7311yescharacteristic
335#334—731no—
336#334—731no—
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8C2×D7311yescharacteristic
342Q8⋊C8C2×D7311yescharacteristic
343D4⋊C8—731no—
344D4⋊C8—731no—
345#322—731no—
346#322—731no—
347#322—731no—
348C82C2×D7311yescharacteristic
349C2×#41—731no—
350C2×Q16—731no—
351C2×Q16C4×D7311yescharacteristic
352C2×SD16—731no—
353C2×SD16—731no—
354C22×C8—1461no—
355C22×C8—1461no—
356C22×C8—1461no—
357C4⋊Q8—731no—
358C4⋊Q8—731no—
359#125—1461no—
360C22⋊Q8—731no—
361C22⋊Q8—731no—
362C22⋊Q8—1461no—
363C4×Q8—731no—
364C4×Q8—731no—
365C4×Q8—1461no—
366C4×Q8C22×D7311yescharacteristic
367C4×Q8C22×D7311yescharacteristic
368C4×D4—731no—
369C4×D4—731no—
370C4×D4—1461no—
371C4×D4—1461no—
372#117—731no—
373#117—1461no—
374#117—1461no—
375C2×C42—731no—
376C2×C42—1461no—
377#107—731no—
378#107C4×D7311yescharacteristic
379#106—731no—
380#106—731no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—731no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8C22×D7311yescharacteristic
396C4⋊C8C22×D7311yescharacteristic
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103C4×D7311yescharacteristic
402#103C4×D7311yescharacteristic
403#102—731no—
404#102—731no—
405C22⋊C8—731no—
406C22⋊C8—731no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—1461no—
414#97—1461no—
415#97—1461no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426#41—1462no—
427#41—1462no—
428C2×Q8—731no—
429C2×Q8—1461no—
430C2×Q8C2×C4×D7311yescharacteristic
431C2×Q8C2×C4×D7311yescharacteristic
432C2×D4—731no—
433C2×D4—1461no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4—1461no—
440Q16—22no—
441Q16—1462no—
442SD16—1462no—
443SD16—1462no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—5841no—
448C2×C8—5841no—
449C2×C8—5841no—
450C2×C8—731no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8C2×C4×D7311yescharacteristic
458C2×C8C2×C4×D7311yescharacteristic
459C2×C8D4×D7311yescharacteristic
460C2×C8D4×D7311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—731no—
464C4⋊C4—731no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4C2×C4×D7311yescharacteristic
473C4⋊C4C2×C4×D7311yescharacteristic
474C22⋊C4—1461no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C42—21no—
480C42—21no—
481C42—731no—
482C42—731no—
483C42—731no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42C23×D7311yescharacteristic
488C23—731no—
489C23—1461no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—5841no—
494Q8—1461no—
495Q8—1461no—
496Q8#1455659712yes—
497D4—732no—
498D4—1464no—
499D4—1461no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—2921no—
505C2×C4—2921no—
506C2×C4—2921no—
507C2×C4—5841no—
508C2×C4—731no—
509C2×C4—731no—
510C2×C4—731no—
511C2×C4—1464no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4C22×C4×D7311yescharacteristic
520C2×C4C2×D4×D7311yescharacteristic
521C2×C4#41×D7311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—2921no—
530C8—2921no—
531C8—2921no—
532C8—1461no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C22—2921no—
537C22—2921no—
538C22—1461no—
539C22—1461no—
540C22—1462no—
541C22—1461no—
542C22C4×D4×D7311yescharacteristic
543C4—21no—
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—2921no—
549C4—2921no—
550C4—2921no—
551C4—1461no—
552C4—1461no—
553C4—1461no—
554C4#131×D7311yescharacteristic
555C4C2×#1455659711yescharacteristic
556C4#1798939411yescharacteristic
557C4#1798940011yescharacteristic
558C2—2922no—
559C2—2921no—
560C2#2261862011yescharacteristic
561C2#2261876911yescharacteristic
562C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC8×Q16×C73C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924029C2×C4
cosocleC42×C73C24
hypercenterC8×Q16D73
hypocenterC73#17921
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
3. #22619022C2semidirect
4. #22608803C2semidirect
5. #22608787C2semidirect
6. #22608778C2semidirect
7. #22608770C2semidirect
8. #22608748C2semidirect
9. #22608741C2semidirect
10. C8×#11924017C2semidirect
11. #22608715C2semidirect
13. #22608332C2semidirect
14. #22608230C2semidirect
15. C8×Q16×C73C2semidirect
291. C8×Q16D73semidirect
297. C73#17921semidirect

Maximal subgroups

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

subgroupindex
#226200002
#226190412
#226190222
#226088032
#226087872
#226087782
#226087702
#226087482
#226087412
C8×#119240172
#226087152
#226083642
#226083322
#226082302
C8×Q16×C732
#1792173