Finite Group Databasebeta

← #11778590

Subgroups — #11778590

Order 1152.

472 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#5623C211yesmaximal, characteristic
2#10592742C211yesmaximal, characteristic
3#10591353C211yesmaximal, characteristic
4#10591126C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#71898—31nomaximal
9#68329—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#944—21no—
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×#889—21no—
16C3×#889—21no—
17C3×#888—21no—
18C3×#878—21no—
19C3×#877—21no—
20C2×Dic3⋊Dic3—21no—
21#63662—21no—
22#63657C2211yescharacteristic
23#63635—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27#63573—21no—
28#63566—21no—
29C3×#544—31no—
30#5623D311yescharacteristic
31#5043—31no—
32#5043—31no—
33#5043—31no—
34#5043—61no—
35#4981—31no—
36#4721—31no—
37#4661—31no—
38C3×#328—31no—
39#4538—31no—
40#4538D311yescharacteristic
41#4528—31no—
42#4469—31no—
43#4452—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6—21no—
51C2×C3×Dic6D411yescharacteristic
52C32×C4⋊C4—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—42no—
72#1611—91noSylow
73C3×C4⋊Q8—61no—
74C3×C4⋊Q8—61no—
75C3×#125—61no—
76C3×#125—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8—31no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C22⋊Q8C2×D311yescharacteristic
82C3×#117—61no—
83C2×C3×C4⋊C4—31no—
84#944—21no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—61no—
88C2×C4⋊Dic3—61no—
89#924C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4C2×D311yescharacteristic
92#889—21no—
93#889—21no—
94#888—21no—
95#878—21no—
96#877—21no—
97C3×C22⋊C8—31no—
98C3×#95—31no—
99#835—61no—
100#835—62no—
101#835—61no—
102#835—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#817—61no—
111#816—61no—
112#808—61no—
113#808—62no—
114#808—61no—
115#808—61no—
116C23×C32C2×D411yescharacteristic
117C32×Q8—41no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3SD1612yes—
136C3×Dic6—41no—
137C3×Dic6—81no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140#544—31no—
141#483—91no—
142#483—91no—
143#398—91no—
144#328—31no—
145#328—91no—
146#324—91no—
147C2×C3×Q8—21no—
148C2×C3×Q8—31no—
149C2×C3×Q8—61no—
150C2×C3×Q8D1211yescharacteristic
151C2×C3×Q8#6711yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—121no—
162C22×Dic3#6711yescharacteristic
163C22×Dic3#6711yescharacteristic
164C2×Dic6—21no—
165C2×Dic6#6711yescharacteristic
166C2×C3×C8—61no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—41no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4D1211yescharacteristic
181C3×C4⋊C4#6711yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—41no—
185C3×C22⋊C4—61no—
186C3×C42—61no—
187C3×C42—61no—
188#217—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3—62no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—121no—
196C4⋊Dic3—122no—
197C4⋊Dic3#6711yescharacteristic
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—122no—
206C4×Dic3—21no—
207C4×Dic3—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32#12011yescharacteristic
215C22×C32C2×SD1611yescharacteristic
216C22×C32#13711yescharacteristic
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—41no—
221C3⋊Dic3—81no—
222C3×Dic3—22no—
223C3×Dic3—42no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C4⋊Q8—61no—
228C4⋊Q8—61no—
229#125—61no—
230#125—61no—
231C22⋊Q8—31no—
232C22⋊Q8—61no—
233C22⋊Q8D3211yescharacteristic
234#117—61no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—181no—
238#106—181no—
239#106—181no—
240#103—181no—
241#103—181no—
242C22⋊C8—31no—
243C22⋊C8—91no—
244#95—31no—
245#95—181no—
246C23×C3—21no—
247C23×C3D3×D411yescharacteristic
248C23×C3C2×#6711yescharacteristic
249C3×Q8—41no—
250C3×Q8—41no—
251C3×Q8—42no—
252C3×Q8—121no—
253C3×Q8—241no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—32no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—42no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—62no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4—121no—
275C2×C3×C4C2×D1211yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—22no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—122no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C2×Dic3—121no—
294C2×Dic3—121no—
295C2×Dic3—241no—
296C2×Dic3—241no—
297C2×Dic3#21512yes—
298Dic6—41no—
299Dic6—81no—
300C3×C8—121no—
301C3⋊C8—41no—
302C3⋊C8—122no—
303C3⋊C8—121no—
304C3⋊C8—121no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32#44811yescharacteristic
308C2×C32#45611yescharacteristic
309C2×C32#45811yescharacteristic
310C2×Q8—31no—
311C2×Q8—61no—
312C2×Q8#62611yescharacteristic
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—61no—
316C22×C4—181no—
317C22×C4C2×D3211yescharacteristic
318C2×C8—61no—
319C2×C8—181no—
320C4⋊C4—21no—
321C4⋊C4—31no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—362no—
333C4⋊C4#62611yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—61no—
336C42—61no—
337C42—61no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3#88211yescharacteristic
348C22×C3D3×SD1611yescharacteristic
349C22×C3#91811yescharacteristic
350C22×C3C2×#21511yescharacteristic
351C22×C3#94211yescharacteristic
352C22×C3#95311yescharacteristic
353C3×C4—22no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—62no—
364C3×C4—81no—
365C3×C4—81no—
366C3×C4—122no—
367C3×C4—121no—
368C3×C4—121no—
369C3×C4—121no—
370Dic3—22no—
371Dic3—42no—
372Dic3—41no—
373Dic3—41no—
374Dic3—41no—
375Dic3—242no—
376Dic3—241no—
377Dic3—241no—
378C32#161111yescharacteristic, complemented, Sylow
379C23D3×#6711yescharacteristic
380Q8—41no—
381Q8—121no—
382Q8—241no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—32no—
386C2×C4—41no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—62no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—121no—
394C2×C4—121no—
395C2×C4—121no—
396C2×C4—361no—
397C2×C4—361no—
398C2×C4—361no—
399C2×C4C2×#62611yescharacteristic
400C2×C4D3×#6711yescharacteristic
401C8—121no—
402C8—361no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3#474211yescharacteristic
413C2×C3#480611yescharacteristic
414C2×C3#482611yescharacteristic
415C2×C3#522711yescharacteristic
416C2×C3#524311yescharacteristic
417C2×C3#524611yescharacteristic
418C22—21no—
419C22—21no—
420C22D3×#21511yescharacteristic
421C22#6394811yescharacteristic
422C22#6397711yescharacteristic
423C4—21no—
424C4—21no—
425C4—41no—
426C4—41no—
427C4—62no—
428C4—122no—
429C4—121no—
430C4—121no—
431C4—121no—
432C4—721no—
433C3—21no—
434C3#6832911yescharacteristic, complemented
435C3#7189811yescharacteristic, complemented
436C2—21no—
437C2—21no—
438C2#1059153411yescharacteristic
439C2#1059158411yescharacteristic
440C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
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
378. C32#1611semidirect
434. C3#68329semidirect
435. C3#71898semidirect

Maximal subgroups

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

subgroupindex
C3×#56232
#105927422
#105913532
#105911262
C3×#45382
#105891532
#105891472
#718983
#683293