Finite Group Databasebeta

← #11778705

Subgroups — #11778705

Order 1152.

593 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 593 conjugacy classes of subgroups — too many to draw. Only its 82 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#10596105C211yesmaximal, characteristic
2C3×#5044C211yesmaximal, characteristic, complemented
3#10591350C211yesmaximal, characteristic
4#10591135C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic
8#71176—31nomaximal
9#68322—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11#64155—21no—
12C2×#3752C2211yescharacteristic
13#64133C2211yescharacteristic
14#64106—21no—
15#64105—21no—
16#64105—21no—
17C22⋊C4×C3⋊D3—21no—
18#64087—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×Dic3⋊Dic3—21no—
21C2×#3722—21no—
22C3×#835—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#807—21no—
27#63575—21no—
28#63567—21no—
29#5634—31no—
30#5634—31no—
31#5634—61no—
32C3×#484—31no—
33#5044D311yescharacteristic, complemented
34#4993—31no—
35#4970—31no—
36#4722—31no—
37#4677—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4468—31no—
41#4468—31no—
42#4467—31no—
43#4452—31no—
44C23×C3⋊D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×#634—21no—
51C2×#634D411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C22⋊C4—21no—
57#3757—21no—
58#3752—21no—
59#3752—21no—
60#3752—21no—
61#3752—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)D411yescharacteristic
64#3750—21no—
65#3750—21no—
66#3750—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—42no—
72#3722—42no—
73#1614—91noSylow
74C3×C22⋊Q8—21no—
75C3×C22⋊Q8C2×D311yescharacteristic
76C3×C22⋊Q8C2×D311yescharacteristic
77C2×C3×C4⋊C4—31no—
78#946—62no—
79#946—61no—
80#946—61no—
81C2×(C2×D3)⋊C4—31no—
82C2×(C2×D3)⋊C4—31no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3C2×D311yescharacteristic
88#924—31no—
89#924—31no—
90#924—61no—
91C2×Dic3⋊C4—61no—
92#897—61no—
93#897—61no—
94#897—62no—
95#896—61no—
96#896—61no—
97#896—62no—
98#896—62no—
99#896—61no—
100#896—61no—
101D3×C22⋊C4—61no—
102D3×C22⋊C4—61no—
103D3×C22⋊C4—62no—
104#878—61no—
105#878—61no—
106#878—62no—
107C3×#107—61no—
108C3×#103—61no—
109C3×C22⋊C8—31no—
110C3×C22⋊C8—31no—
111C3×#95—31no—
112#835—21no—
113C3⋊#95C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#830C2×D311yescharacteristic
116#818—61no—
117#816—61no—
118#810—61no—
119#807—21no—
120#807—61no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3Q1612yes—
127C32×Q8—41no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—41no—
137C4×C3⋊D3—81no—
138C4×C3⋊D3—81no—
139#634—41no—
140#634—81no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×C3⋊C8—41no—
148C3×C3⋊C8—41no—
149#543—91no—
150#484—31no—
151#484—91no—
152#399—91no—
153#328—31no—
154#328—91no—
155#323—91no—
156C23×D3—31no—
157C23×D3—31no—
158C23×D3—61no—
159C2×C3×Q8—21no—
160C2×C3×Q8D1211yescharacteristic
161C2×C3×Q8#6711yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—61no—
172C2×C4×D3—62no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—62no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×Dic6—31no—
179C2×Dic6—31no—
180C2×Dic6—61no—
181C2×Dic6—62no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4D1211yescharacteristic
193C3×C4⋊C4#6711yescharacteristic
194C3×C22⋊C4—22no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197#217—62no—
198#217—61no—
199#217—61no—
200(C2×D3)⋊C4—62no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—62no—
207(C2×D3)⋊C4—62no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—122no—
213(C2×D3)⋊C4—122no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—31no—
217C4⋊Dic3—31no—
218C4⋊Dic3—61no—
219C4⋊Dic3—62no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—122no—
223Dic3⋊C4—62no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—62no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229Dic3⋊C4—62no—
230Dic3⋊C4—61no—
231Dic3⋊C4—61no—
232Dic3⋊C4—122no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32#12011yescharacteristic
238C22×C32C2×Q1611yescharacteristic
239C22×C32#13711yescharacteristic
240C2×C3⋊D3—22no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C2×C3⋊D3—42no—
244C2×C3⋊D3—81no—
245C32×C4—21no—
246C32×C4—21no—
247C32×C4—41no—
248C32×C4—41no—
249C3⋊Dic3—41no—
250C3⋊Dic3—41no—
251C3⋊Dic3—41no—
252C3×Dic3—42no—
253C3×Dic3—81no—
254C22⋊Q8—91no—
255C22⋊Q8—181no—
256C22⋊Q8—181no—
257C22⋊Q8—181no—
258C22⋊Q8—181no—
259C22⋊Q8—181no—
260C22⋊Q8D3211yescharacteristic
261C2×C4⋊C4—31no—
262C2×C4⋊C4—181no—
263C2×C22⋊C4—91no—
264C2×C22⋊C4—181no—
265C2×C22⋊C4—181no—
266#107—61no—
267#107—181no—
268#103—61no—
269#103—181no—
270C22⋊C8—31no—
271C22⋊C8—31no—
272#95—31no—
273C23×C3—21no—
274C23×C3D3×D411yescharacteristic
275C23×C3D3×D411yescharacteristic
276C22×D3—32no—
277C22×D3—32no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—62no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—121no—
286C22×D3—121no—
287C22×D3—121no—
288C22×D3—121no—
289C22×D3—241no—
290C22×D3—241no—
291C3×Q8—41no—
292C3×Q8—41no—
293C3×Q8—81no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—62no—
305C2×C3×C4—81no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C2×D1211yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—241no—
333C4×D3—242no—
334C4×D3—242no—
335C4×D3—241no—
336C4×D3—241no—
337C4×D3—241no—
338C4×D3—241no—
339Dic6—121no—
340Dic6—121no—
341Dic6—241no—
342Dic6—242no—
343Dic6—241no—
344Dic6—241no—
345C3×C8—121no—
346C3×C8—121no—
347C3⋊C8—41no—
348C3⋊C8—41no—
349C2×C32—21no—
350C2×C32—21no—
351C2×C32#45111yescharacteristic
352C2×C32#45311yescharacteristic
353C2×C32#45811yescharacteristic
354C3⋊D3—42no—
355C24—91no—
356C2×Q8—91no—
357C2×Q8—181no—
358C2×Q8#62611yescharacteristic
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—91no—
362C22×C4—181no—
363C22×C4—181no—
364C22×C4C2×D3211yescharacteristic
365C2×C8—61no—
366C2×C8—61no—
367C4⋊C4—21no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—91no—
371C4⋊C4—181no—
372C4⋊C4—181no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C4⋊C4—362no—
376C4⋊C4#62611yescharacteristic
377C22⋊C4—21no—
378C22⋊C4—181no—
379C22⋊C4—181no—
380C22⋊C4—181no—
381C22⋊C4—181no—
382C22⋊C4—181no—
383C22⋊C4—362no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3#88211yescharacteristic
394C22×C3#91511yescharacteristic
395C22×C3D3×Q1611yescharacteristic
396C22×C3D3×Q1611yescharacteristic
397C22×C3#91811yescharacteristic
398C22×C3#93711yescharacteristic
399C2×D3—64no—
400C2×D3—62no—
401C2×D3—62no—
402C2×D3—122no—
403C2×D3—122no—
404C2×D3—121no—
405C2×D3—121no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—122no—
409C2×D3—122no—
410C2×D3—242no—
411C2×D3—241no—
412C2×D3—241no—
413C2×D3—242no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—41no—
419C3×C4—41no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—122no—
427C3×C4—241no—
428Dic3—42no—
429Dic3—81no—
430Dic3—122no—
431Dic3—122no—
432Dic3—122no—
433Dic3—121no—
434Dic3—121no—
435Dic3—121no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439C32#161411yescharacteristic, complemented, Sylow
440C23—92no—
441C23—181no—
442C23—181no—
443C23—361no—
444C23—361no—
445C23#381111yescharacteristic
446Q8—41no—
447Q8—361no—
448Q8—721no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—62no—
453C2×C4—121no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—361no—
462C2×C4—721no—
463C2×C4—721no—
464C2×C4C2×#62611yescharacteristic
465C2×C4#381111yescharacteristic
466C8—121no—
467C8—121no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—41no—
476C2×C3—41no—
477C2×C3#474211yescharacteristic
478C2×C3#480911yescharacteristic
479C2×C3#482211yescharacteristic
480C2×C3#505311yescharacteristic
481C2×C3#518611yescharacteristic
482C2×C3#519811yescharacteristic
483D3—124no—
484D3—122no—
485D3—122no—
486C22—21no—
487C22—21no—
488C22—182no—
489C22—362no—
490C22—361no—
491C22—361no—
492C22—721no—
493C22#6394411yescharacteristic
494C22#6395111yescharacteristic
495C22#6398111yescharacteristic
496C4—21no—
497C4—21no—
498C4—41no—
499C4—41no—
500C4—122no—
501C4—241no—
502C4—361no—
503C4—361no—
504C4—361no—
505C3—21no—
506C3#6832211yescharacteristic, complemented
507C3#7117611yescharacteristic, complemented
508C2—21no—
509C2—21no—
510C2—362no—
511C2#1059153511yescharacteristic
512C2#1059160311yescharacteristic
513C2#1059166711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C3⋊D3D4
hypercenterC22⋊Q8D32
hypocenterC32#1614
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. C3×#5044C2semidirect
4. #10591135C2semidirect
5. C3×#4538C2semidirect
6. #10589154C2semidirect
33. #5044D3semidirect
39. #4538D3semidirect
439. C32#1614semidirect
506. C3#68322semidirect
507. C3#71176semidirect

Maximal subgroups

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

subgroupindex
#105961052
C3×#50442
#105913502
#105911352
C3×#45382
#105891542
#105891462
#711763
#683223