Finite Group Databasebeta

← #11778402

Subgroups — #11778402

Order 1152.

621 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 621 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594979C211yesmaximal, characteristic
2#10592930C211yesmaximal, characteristic, complemented
3C3×#5228C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic, complemented
5#10589152C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic, complemented
8#70981—31nomaximal
9#70973—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3752—21no—
12C2×#3752C2211yescharacteristic
13C2×C3×#216—21no—
14C2×C3×#215—21no—
15C3×#930C2211yescharacteristic
16C3×#924C2211yescharacteristic
17#63981—21no—
18#67⋊Dic3—21no—
19#63907—21no—
20#63890—21no—
21#63886—21no—
22#63848—21no—
23#63658—21no—
24#63658C2211yescharacteristic
25C3×#835—21no—
26C3×#835—21no—
27C3×#830C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5644—31no—
30#5617—31no—
31C3×#451—31no—
32C3×#448—31no—
33#5231—31no—
34#5231—31no—
35#5231—61no—
36#5228D311yescharacteristic, complemented
37#5227D311yescharacteristic, complemented
38#4538—31no—
39#4537—31no—
40#4470—31no—
41#4468—31no—
42#4468—31no—
43#4467—31no—
44C23×C3⋊D3D411yescharacteristic
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—42no—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3D411yescharacteristic
52C2×C3×#67—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#626—21no—
56C2×#626—21no—
57C2×D3×Dic3—21no—
58#3752—21no—
59#3752—21no—
60#3752—42no—
61C3×#217—21no—
62C3×#216—42no—
63C3×#215—42no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72#3722—21no—
73(C2×D3)⋊Dic3—21no—
74Dic32—21no—
75#1606—91noSylow
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C2×D311yescharacteristic
79C2×C3×Q16—61no—
80C2×C3×SD16—61no—
81C3×C22⋊Q8—31no—
82C3×#121—31no—
83#947—61no—
84C2×#216—21no—
85C2×#215—21no—
86#939—61no—
87#937—61no—
88D4×Dic3—61no—
89#930C2×D311yescharacteristic
90C2×(C2×D3)⋊C4—31no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—62no—
96#924C2×D311yescharacteristic
97#898—61no—
98#898—61no—
99#895—61no—
100#894—61no—
101#886—61no—
102#885—61no—
103#882—61no—
104#67⋊C4—61no—
105C3×#103—61no—
106C3×#103—61no—
107C3×C22⋊C8—31no—
108C3×C22⋊C8—31no—
109#835—21no—
110#835—21no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—61no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116C3⋊#95—62no—
117#830C2×D311yescharacteristic
118#830C2×D311yescharacteristic
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3×D3—21no—
126C32×Q8—22no—
127C32×Q8—22no—
128C32×Q8—41no—
129C32×Q8—41no—
130C2×C32×C4—22no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C3×#67—41no—
142C3×#67—41no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C3×D12—41no—
147C3×Dic6—41no—
148#626—81no—
149#626—81no—
150D3×Dic3—81no—
151C3×C3⋊C8—41no—
152C3×C3⋊C8—41no—
153#538—91no—
154#451—31no—
155#448—31no—
156#393—91no—
157#328—91no—
158#327—91no—
159#323—91no—
160C23×D3—31no—
161C23×D3—31no—
162C23×D3—61no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—31no—
168C2×C3×Q8—41no—
169C2×C3×Q8—41no—
170C2×C3×Q8—42no—
171C2×C3×Q8—42no—
172C2×C3×Q8—44no—
173C2×C3×D4—31no—
174C2×C3×D4—61no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—21no—
182C2×#67—61no—
183C2×#67—61no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—62no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12#6711yescharacteristic
194C2×C4×D3—61no—
195C2×Dic6#6711yescharacteristic
196C3×Q16—122no—
197C3×SD16—122no—
198C2×C3×C8—61no—
199C2×C3×C8—61no—
200C3×C4⋊C4—31no—
201C3×C4⋊C4—31no—
202C3×C4⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205#217—21no—
206#217—61no—
207#216—42no—
208#215—42no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—121no—
220(C2×D3)⋊C4—121no—
221(C2×D3)⋊C4—122no—
222(C2×D3)⋊C4—122no—
223(C2×D3)⋊C4—124no—
224C4⋊Dic3—61no—
225C4⋊Dic3#6711yescharacteristic
226C4⋊Dic3#6711yescharacteristic
227Dic3⋊C4—21no—
228Dic3⋊C4—61no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12011yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32#13711yescharacteristic
238C2×C3⋊D3—42no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—41no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—81no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—41no—
246C32×C4—21no—
247C32×C4—21no—
248C32×C4—42no—
249C3⋊Dic3—41no—
250C3⋊Dic3—81no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—41no—
254C22×Q8D3211yescharacteristic
255C2×Q16—61no—
256C2×SD16—61no—
257#126—181no—
258#124—181no—
259#123—181no—
260C22⋊Q8—31no—
261#121—31no—
262#121—181no—
263#120—181no—
264C4×D4—181no—
265C2×C22⋊C4—91no—
266C2×C22⋊C4—181no—
267#103—61no—
268#103—61no—
269C22⋊C8—31no—
270C22⋊C8—31no—
271#95—91no—
272#95—181no—
273C23×C3—21no—
274C23×C3—61no—
275C23×C3D3×D411yescharacteristic
276C23×C3D3×D411yescharacteristic
277C22×D3—21no—
278C22×D3—62no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—121no—
286C22×D3—121no—
287C22×D3—121no—
288C22×D3—121no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—122no—
292C22×D3—122no—
293C3×Q8—22no—
294C3×Q8—22no—
295C3×Q8—22no—
296C3×Q8—22no—
297C3×Q8—42no—
298C3×Q8—42no—
299C3×Q8—41no—
300C3×Q8—41no—
301C3×Q8—41no—
302C3×Q8—41no—
303C3×Q8—42no—
304C3×Q8—42no—
305C3×Q8—121no—
306C3×D4—121no—
307C3×D4—121no—
308C3×D4—121no—
309C2×C3×C4—24no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—42no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330#67—41no—
331#67—41no—
332#67—241no—
333#67—241no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—122no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—122no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—241no—
353D12—41no—
354D12—241no—
355D12—241no—
356C4×D3—241no—
357Dic6—41no—
358C3×C8—121no—
359C3×C8—121no—
360C3⋊C8—41no—
361C3⋊C8—41no—
362C2×C32—21no—
363C2×C32—21no—
364C2×C32#45211yescharacteristic
365C2×C32#45511yescharacteristic
366C2×C32B(4,𝔽2)11yescharacteristic
367C3⋊D3—81no—
368C3×D3—81no—
369C24—91no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—31no—
373C2×Q8—42no—
374C2×D4—31no—
375C2×D4—61no—
376C2×D4—181no—
377C2×D4—181no—
378C22×C4—21no—
379C22×C4—91no—
380C22×C4—181no—
381C22×C4—181no—
382C22×C4C2×D3211yescharacteristic
383Q16—122no—
384SD16—122no—
385C2×C8—61no—
386C2×C8—61no—
387C4⋊C4—31no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—181no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—181no—
394C22⋊C4—181no—
395C22⋊C4—181no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—362no—
399C42—181no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3#91511yescharacteristic
413C22×C3#91611yescharacteristic
414C22×C3#91811yescharacteristic
415C22×C3#91911yescharacteristic
416C22×C3#93711yescharacteristic
417C22×C3#93711yescharacteristic
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—124no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—241no—
432C2×D3—241no—
433C2×D3—242no—
434C2×D3—241no—
435C2×D3—241no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—44no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—121no—
446C3×C4—121no—
447C3×C4—121no—
448Dic3—41no—
449Dic3—41no—
450Dic3—41no—
451Dic3—121no—
452Dic3—121no—
453Dic3—241no—
454Dic3—242no—
455Dic3—241no—
456Dic3—241no—
457C32#160611yescharacteristic, complemented, Sylow
458C23—61no—
459C23—181no—
460C23—181no—
461C23—181no—
462C23—361no—
463C23—361no—
464C23#381111yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—41no—
468Q8—41no—
469Q8—121no—
470D4—121no—
471D4—121no—
472D4—121no—
473D4—721no—
474D4—721no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—181no—
483C2×C4—361no—
484C2×C4—361no—
485C2×C4—361no—
486C2×C4—361no—
487C2×C4—721no—
488C2×C4D3×#6711yescharacteristic
489C2×C4D3×#6711yescharacteristic
490C8—121no—
491C8—121no—
492C2×C3—22no—
493C2×C3—22no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—241no—
502C2×C3#503211yescharacteristic
503C2×C3#503211yescharacteristic
504C2×C3#517311yescharacteristic
505C2×C3#518711yescharacteristic
506C2×C3#520211yescharacteristic
507C2×C3#520211yescharacteristic
508D3—81no—
509D3—242no—
510D3—241no—
511D3—241no—
512C22—21no—
513C22—21no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—362no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22—721no—
522C22#6395011yescharacteristic
523C22#6395111yescharacteristic
524C22#6398311yescharacteristic
525C4—21no—
526C4—21no—
527C4—42no—
528C4—121no—
529C4—121no—
530C4—121no—
531C4—361no—
532C4—721no—
533C3—21no—
534C3#7097311yescharacteristic, complemented
535C3#7098111yescharacteristic, complemented
536C2—21no—
537C2—21no—
538C2—241no—
539C2—721no—
540C2#1059165611yescharacteristic
541C2#1059165811yescharacteristic
542C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radical#10594979C2
hypercenterC22×Q8D32
hypocenterC32#1606
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #10592930C2semidirect
3. C3×#5228C2semidirect
4. C3×#5227C2semidirect
5. #10589152C2semidirect
6. #10589150C2semidirect
7. #10589146C2semidirect
36. #5228D3semidirect
37. #5227D3semidirect
457. C32#1606semidirect
534. C3#70973semidirect
535. C3#70981semidirect

Maximal subgroups

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

subgroupindex
#105949792
#105929302
C3×#52282
C3×#52272
#105891522
#105891502
#105891462
#709813
#709733