Finite Group Databasebeta

← #11792206

Subgroups — #11792206

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5816C211yesmaximal, characteristic
2C2×C3×#944C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic
4C2×#63663C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic
6#10591099C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71868—31nomaximal
9#71795—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#947—21no—
16C3×#946—22no—
17C3×#944—22no—
18C3×#944—21no—
19C3×#944—22no—
20C3×#929—22no—
21C3×#926C2211yescharacteristic
22C2×C3×Dic3⋊C4—22no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×#3718—21no—
25#63827—22no—
26#63827—22no—
27C2×#3715—21no—
28#63663—22no—
29#63569—22no—
30#63565—22no—
31C3×#536—31no—
32C2×C3×C4⋊Q8—31no—
33C2×#951—31no—
34#5816D311yescharacteristic
35C2×#944D311yescharacteristic, complemented
36C2×#942—31no—
37C2×#837—31no—
38C2×#836—31no—
39C2×#836—31no—
40C2×#836—61no—
41#5225—31no—
42#5004—31no—
43C2×#805—31no—
44#4532—31no—
45#4523—31no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C22×C32×C4D412yes—
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6D412yes—
69C2×C3×Dic6D411yescharacteristic
70#3748—21no—
71#3748—21no—
72#3748—21no—
73#3748D412yes—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)—21no—
76C3×#217—21no—
77C3×(C2×D3)⋊C4—24no—
78C3×C4⋊Dic3D412yes—
79C3×Dic3⋊C4—28no—
80C3×Dic3⋊C4—24no—
81C3×C4×Dic3—21no—
82C3×C4×Dic3—21no—
83C3×C4×Dic3D412yes—
84#3718—24no—
85#3715—24no—
86#2005—91noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—21no—
89C22×C3×Q8—31no—
90C22×C3×Q8C2×D311yescharacteristic
91C22×C3×Q8C2×D311yescharacteristic
92C2×#235C2×D311yescharacteristic
93C22×Dic6C2×D311yescharacteristic
94C3×C4⋊Q8—62no—
95C3×C4⋊Q8—62no—
96C3×C4⋊Q8—61no—
97C3×#124—61no—
98C3×#123—62no—
99C3×C22⋊Q8—62no—
100C3×#117—31no—
101C2×C3×C4⋊C4—62no—
102C2×C3×C42—31no—
103#951—62no—
104#951—62no—
105#947—21no—
106#946—22no—
107#944—22no—
108#944—21no—
109#944—22no—
110C2×#216—61no—
111C2×#216—61no—
112#942—62no—
113#942—62no—
114C2×#215—61no—
115C2×#214—61no—
116#929—22no—
117#926C2×D311yescharacteristic
118C2×Dic3⋊C4—22no—
119C2×C4×Dic3C2×D311yescharacteristic
120C2×#208—31no—
121C2×#208—31no—
122C2×#208—31no—
123C2×#208—31no—
124C2×#208—61no—
125C2×#208—61no—
126#837—62no—
127#836—62no—
128#836—62no—
129#836—64no—
130#835—62no—
131#810—62no—
132#805—62no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C32×Q8—41no—
136C32×Q8—41no—
137C32×Q8—41no—
138C32×Q8—41no—
139C2×C32×C4—22no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C3×#67—41no—
149C3×#67—41no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—22no—
164C3×Dic6—21no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C3⋊(C3⋊C8)—22no—
168C3⋊(C3⋊C8)—41no—
169C2×#137—91no—
170#536—31no—
171C2×C4⋊Q8—31no—
172C2×#104—91no—
173#419—91no—
174C2×#101—91no—
175#339—91no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—32no—
195C2×C3×Q8—31no—
196C2×C3×Q8—41no—
197C2×C3×Q8—41no—
198C2×C3×Q8—41no—
199C2×C3×Q8—41no—
200C2×C3×Q8—61no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204C2×C3×Q8—61no—
205C2×C3×D4—31no—
206C2×C3×D4—61no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4#6712yes—
213C22×C3×C4#6712yes—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C2×#67—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219#235—21no—
220#235—21no—
221#235—21no—
222#235—21no—
223C2×D12#6711yescharacteristic
224C2×C4×D3—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6#6711yescharacteristic
231C2×Dic6#6712yes—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—68no—
234C3×C4⋊C4—64no—
235C3×C22⋊C4—64no—
236C3×C22⋊C4—61no—
237C3×C42—32no—
238C3×C42—61no—
239C3×C42—61no—
240#217—21no—
241#216—64no—
242#216—64no—
243#215—64no—
244#214—64no—
245(C2×D3)⋊C4—24no—
246C4⋊Dic3#6712yes—
247Dic3⋊C4—28no—
248Dic3⋊C4—24no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C4×Dic3#6712yes—
252#208—32no—
253#208—32no—
254#208—62no—
255#208—61no—
256#208—61no—
257#208—62no—
258#208—61no—
259#208—61no—
260#208—61no—
261#208—61no—
262#208—121no—
263#208—121no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—121no—
269C2×C3⋊C8—121no—
270C22×C32—22no—
271C22×C32#12011yescharacteristic
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C2×C3×D3—41no—
275C2×C3×D3—42no—
276C32×C4—42no—
277C32×C4#12011yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12711yescharacteristic
281C3×Dic3—24no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C3×Dic3—42no—
285C2×#41—31no—
286C22×Q8—31no—
287C22×Q8D3211yescharacteristic
288#137—182no—
289#137—182no—
290C2×Q16—181no—
291C2×SD16—181no—
292C2×M16—91no—
293C2×M16—91no—
294C4⋊Q8—62no—
295C4⋊Q8—62no—
296C4⋊Q8—61no—
297#124—61no—
298#123—62no—
299C22⋊Q8—62no—
300#117—31no—
301C2×C4⋊C4—62no—
302C2×C42—31no—
303#104—182no—
304#103—182no—
305#101—182no—
306C23×C3—21no—
307C23×C3—61no—
308C23×C3C2×#6711yescharacteristic
309C23×C3C2×#6711yescharacteristic
310C22×D3—21no—
311C3×Q8—42no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—42no—
315C3×Q8—41no—
316C3×Q8—41no—
317C3×Q8—41no—
318C3×Q8—41no—
319C3×Q8—41no—
320C3×Q8—41no—
321C3×Q8—41no—
322C3×Q8—41no—
323C3×Q8—62no—
324C3×Q8—61no—
325C3×Q8—62no—
326C3×Q8—61no—
327C3×Q8—121no—
328C3×Q8—121no—
329C3×D4—61no—
330C3×D4—61no—
331C3×D4—121no—
332C3×D4—121no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—64no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4—121no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369#67—41no—
370#67—41no—
371C2×Dic3—24no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376C2×Dic3—41no—
377C2×Dic3—41no—
378D12—21no—
379D12—21no—
380C4×D3—41no—
381C4×D3—41no—
382Dic6—22no—
383Dic6—21no—
384Dic6—22no—
385Dic6—21no—
386Dic6—41no—
387Dic6—41no—
388C3⋊C8—62no—
389C3⋊C8—62no—
390C3⋊C8—122no—
391C3⋊C8—122no—
392C3⋊C8—121no—
393C3⋊C8—121no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32#39211yescharacteristic
397C2×C32#45612yes—
398C3×D3—81no—
399#41—61no—
400#41—61no—
401#41—61no—
402#41—61no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—31no—
410C2×Q8—32no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8—61no—
416C2×D4—31no—
417C2×D4—61no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4#62512yes—
422C22×C4C2×D3211yescharacteristic
423Q16—184no—
424SD16—184no—
425M16—92no—
426M16—181no—
427M16—181no—
428M16—181no—
429C2×C8—181no—
430C2×C8—181no—
431C4⋊C4—32no—
432C4⋊C4—68no—
433C4⋊C4—64no—
434C22⋊C4—64no—
435C22⋊C4—61no—
436C42—32no—
437C42—61no—
438C42—61no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—42no—
445C22×C3—121no—
446C22×C3—122no—
447C22×C3#93711yescharacteristic
448C22×C3#93711yescharacteristic
449C22×C3#93911yescharacteristic
450C22×C3#93911yescharacteristic
451C22×C3#95311yescharacteristic
452C22×C3#95311yescharacteristic
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—44no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—64no—
463C3×C4—121no—
464C3×C4—122no—
465C3×C4—122no—
466C3×C4#93711yescharacteristic
467C3×C4#93711yescharacteristic
468C3×C4#93811yescharacteristic
469C3×C4#93811yescharacteristic
470C3×C4#93911yescharacteristic
471C3×C4#93911yescharacteristic
472C3×C4#94011yescharacteristic
473C3×C4#94011yescharacteristic
474Dic3—24no—
475Dic3—42no—
476Dic3—41no—
477Dic3—42no—
478C32#200511yescharacteristic, complemented, Sylow
479C23—61no—
480C23C2×#62511yescharacteristic
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—62no—
486Q8—61no—
487Q8—62no—
488Q8—61no—
489Q8—121no—
490Q8—121no—
491D4—61no—
492D4—61no—
493D4—121no—
494D4—121no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—64no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—61no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4#380511yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4#381111yescharacteristic
513C8—182no—
514C8—361no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—22no—
520C2×C3—21no—
521C2×C3—41no—
522C2×C3—41no—
523C2×C3—241no—
524C2×C3#509512yes—
525C2×C3#522311yescharacteristic
526C2×C3#522311yescharacteristic
527C2×C3#524612yes—
528D3—81no—
529C22—22no—
530C22—122no—
531C22—121no—
532C22#6397611yescharacteristic
533C22#6397611yescharacteristic
534C22#6398011yescharacteristic
535C4—42no—
536C4—64no—
537C4—122no—
538C4—121no—
539C4—122no—
540C4#6397011yescharacteristic
541C4#6397011yescharacteristic
542C4#6397911yescharacteristic
543C4#6398311yescharacteristic
544C3—21no—
545C3#7179511yescharacteristic, complemented
546C3#7186811yescharacteristic, complemented
547C2—21no—
548C2—21no—
549C2—241no—
550C2#1059164812yes—
551C2#1059172311yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC22×Q8D32
hypocenterC32#2005
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#944C2semidirect
4. C2×#63663C2semidirect
6. #10591099C2semidirect
7. #10589161C2semidirect
35. C2×#944D3semidirect
478. C32#2005semidirect
545. C3#71795semidirect
546. C3#71868semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C2×C3×#9442
C2×#638272
C2×#636632
C2×#635692
#105910992
#105891612
#718683
#717953