Finite Group Databasebeta

← #11778591

Subgroups — #11778591

Order 1152.

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

normal subgroups only

This group has 523 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#10596094C211yesmaximal, characteristic
2C3×#5043C211yesmaximal, characteristic
3#10591358C211yesmaximal, characteristic
4#10591124C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic
7#10589148C211yesmaximal, characteristic
8#71175—31nomaximal
9#68329—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11#64153—21no—
12#64133C2211yescharacteristic
13C2×#3750C2211yescharacteristic
14#64098—21no—
15#64098—21no—
16#64097—21no—
17#64087—21no—
18#64086—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×Dic3⋊Dic3—21no—
21C3×#835—21no—
22C3×C3⋊#95C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#808—21no—
26#63579—21no—
27#63573—21no—
28#63567—21no—
29#5623—31no—
30#5623—31no—
31#5623—61no—
32C3×#483—31no—
33#5043D311yescharacteristic
34#4983—31no—
35#4971—31no—
36#4721—31no—
37#4661—31no—
38C3×#328—31no—
39#4538D311yescharacteristic
40#4469—31no—
41#4469—31no—
42#4467—31no—
43#4452—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×#634—21no—
49C2×#634D411yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55#3757—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59#3750—21no—
60#3750—21no—
61#3750—21no—
62#3750—21no—
63#3750—21no—
64#3750—21no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—42no—
72#1611—91noSylow
73C3×C22⋊Q8—21no—
74C3×C22⋊Q8C2×D311yescharacteristic
75C3×C22⋊Q8C2×D311yescharacteristic
76C2×C3×C4⋊C4—31no—
77#944—62no—
78#944—61no—
79#944—61no—
80C2×C4⋊Dic3—61no—
81C2×C4⋊Dic3C2×D311yescharacteristic
82#924—31no—
83#924—31no—
84#924—61no—
85C2×Dic3⋊C4—31no—
86C2×Dic3⋊C4—31no—
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—61no—
89#889—61no—
90#889—61no—
91#889—62no—
92#889—62no—
93#889—61no—
94#889—61no—
95#888—61no—
96#888—61no—
97#888—62no—
98#878—61no—
99#878—61no—
100#878—62no—
101#877—61no—
102#877—61no—
103#877—62no—
104C3×#106—61no—
105C3×#103—61no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8—31no—
108C3×#95—31no—
109#835—21no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#817—61no—
116#816—61no—
117#810—61no—
118#808—21no—
119#808—61no—
120C23×C32C2×D411yescharacteristic
121C32×Q8—41no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3SD1612yes—
134#634—41no—
135#634—81no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144#544—91no—
145#483—31no—
146#483—91no—
147#398—91no—
148#328—31no—
149#328—91no—
150#324—91no—
151C2×C3×Q8—21no—
152C2×C3×Q8D1211yescharacteristic
153C2×C3×Q8#6711yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×Dic3—21no—
160C22×Dic3—21no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—31no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C2×Dic6—31no—
168C2×Dic6—31no—
169C2×Dic6—61no—
170C2×Dic6—62no—
171C2×Dic6—61no—
172C2×Dic6—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4D1211yescharacteristic
182C3×C4⋊C4#6711yescharacteristic
183C3×C22⋊C4—22no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186#217—62no—
187#217—61no—
188#217—61no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—31no—
192C4⋊Dic3—31no—
193C4⋊Dic3—61no—
194C4⋊Dic3—62no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—122no—
198Dic3⋊C4—62no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—62no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—62no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—62no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—62no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—122no—
220C4×Dic3—62no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—62no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32#12011yescharacteristic
231C22×C32C2×SD1611yescharacteristic
232C22×C32#13711yescharacteristic
233C32×C4—21no—
234C32×C4—21no—
235C32×C4—41no—
236C32×C4—41no—
237C3⋊Dic3—22no—
238C3⋊Dic3—41no—
239C3⋊Dic3—41no—
240C3⋊Dic3—41no—
241C3×Dic3—42no—
242C3×Dic3—81no—
243C4⋊Q8—181no—
244C4⋊Q8—181no—
245#125—181no—
246#125—181no—
247C22⋊Q8—91no—
248C22⋊Q8—181no—
249C22⋊Q8D3211yescharacteristic
250#117—181no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—181no—
254#106—61no—
255#106—181no—
256#103—61no—
257#103—181no—
258C22⋊C8—31no—
259C22⋊C8—31no—
260#95—31no—
261#95—181no—
262C23×C3—21no—
263C23×C3D3×D411yescharacteristic
264C23×C3D3×D411yescharacteristic
265C3×Q8—41no—
266C3×Q8—41no—
267C3×Q8—81no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—62no—
279C2×C3×C4—81no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×Dic3—22no—
290C2×Dic3—32no—
291C2×Dic3—32no—
292C2×Dic3—41no—
293C2×Dic3—41no—
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—241no—
316Dic6—121no—
317Dic6—121no—
318Dic6—241no—
319Dic6—242no—
320Dic6—241no—
321Dic6—241no—
322C3×C8—121no—
323C3×C8—121no—
324C3⋊C8—41no—
325C3⋊C8—41no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32#44811yescharacteristic
329C2×C32#45611yescharacteristic
330C2×C32#45811yescharacteristic
331C2×Q8—91no—
332C2×Q8—181no—
333C2×Q8#62611yescharacteristic
334C22×C4—61no—
335C22×C4—61no—
336C22×C4—91no—
337C22×C4—91no—
338C22×C4C2×D3211yescharacteristic
339C2×C8—61no—
340C2×C8—61no—
341C4⋊C4—21no—
342C4⋊C4—61no—
343C4⋊C4—61no—
344C4⋊C4—91no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4—362no—
354C4⋊C4#62611yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—181no—
357C42—181no—
358C42—181no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3#88211yescharacteristic
369C22×C3D3×SD1611yescharacteristic
370C22×C3D3×SD1611yescharacteristic
371C22×C3#91511yescharacteristic
372C22×C3#91811yescharacteristic
373C22×C3#93711yescharacteristic
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—42no—
381C3×C4—42no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—122no—
387C3×C4—241no—
388Dic3—42no—
389Dic3—64no—
390Dic3—62no—
391Dic3—62no—
392Dic3—81no—
393Dic3—122no—
394Dic3—122no—
395Dic3—122no—
396Dic3—121no—
397Dic3—121no—
398Dic3—121no—
399Dic3—121no—
400Dic3—121no—
401Dic3—121no—
402C32#161111yescharacteristic, complemented, Sylow
403C23#381111yescharacteristic
404Q8—41no—
405Q8—361no—
406Q8—721no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—62no—
411C2×C4—92no—
412C2×C4—121no—
413C2×C4—121no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—181no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—181no—
422C2×C4—361no—
423C2×C4C2×#62611yescharacteristic
424C2×C4#381111yescharacteristic
425C8—121no—
426C8—121no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3#474211yescharacteristic
437C2×C3#480611yescharacteristic
438C2×C3#482611yescharacteristic
439C2×C3#505311yescharacteristic
440C2×C3#517011yescharacteristic
441C2×C3#520511yescharacteristic
442C22—21no—
443C22—21no—
444C22#6394011yescharacteristic
445C22#6395111yescharacteristic
446C22#6398111yescharacteristic
447C4—21no—
448C4—21no—
449C4—41no—
450C4—41no—
451C4—122no—
452C4—182no—
453C4—241no—
454C4—361no—
455C4—361no—
456C4—361no—
457C3—21no—
458C3#6832911yescharacteristic, complemented
459C3#7117511yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2#1059153511yescharacteristic
463C2#1059159211yescharacteristic
464C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#1611
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
402. C32#1611semidirect
458. C3#68329semidirect
459. C3#71175semidirect

Maximal subgroups

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

subgroupindex
#105960942
C3×#50432
#105913582
#105911242
C3×#45382
#105891542
#105891482
#711753
#683293