Finite Group Databasebeta

← #11778817

Subgroups — #11778817

Order 1152.

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

normal subgroups only

This group has 456 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#10592743C211yesmaximal, characteristic
3#10591226C211yesmaximal, characteristic
4#10591103C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#71899—31nomaximal
9#68331—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—
20#63662—21no—
21#63657C2211yescharacteristic
22#63634—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27#63575—21no—
28#63566—21no—
29C3×#544—31no—
30#5623D311yescharacteristic
31#5044—31no—
32#5044—31no—
33#5044—31no—
34#5044—61no—
35#4986—31no—
36#4722—31no—
37#4659—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—
71#1617—91noSylow
72C3×C4⋊Q8—61no—
73C3×C4⋊Q8—61no—
74C3×#125—61no—
75C3×#125—61no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—31no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×#117—61no—
82C2×C3×C4⋊C4—31no—
83#944—21no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—61no—
87#924C2×D311yescharacteristic
88C2×Dic3⋊C4C2×D311yescharacteristic
89#889—21no—
90#889—21no—
91#888—21no—
92#878—21no—
93#877—21no—
94C3×C22⋊C8—31no—
95C3×#95—31no—
96#835—61no—
97#835—62no—
98#835—61no—
99#835—61no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95C2×D311yescharacteristic
105#830—31no—
106#830—31no—
107#830—61no—
108#830C2×D311yescharacteristic
109#818—61no—
110#816—61no—
111#807—61no—
112#807—62no—
113#807—61no—
114#807—61no—
115C23×C32C2×D411yescharacteristic
116C32×Q8—41no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—42no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3Q1612yes—
134C3×Dic6—41no—
135C3×Dic6—81no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—41no—
138#544—31no—
139#484—91no—
140#484—91no—
141#400—91no—
142#328—31no—
143#328—91no—
144#324—91no—
145C2×C3×Q8—21no—
146C2×C3×Q8—31no—
147C2×C3×Q8—61no—
148C2×C3×Q8D1211yescharacteristic
149C2×C3×Q8#6711yescharacteristic
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—21no—
157C22×Dic3—61no—
158C22×Dic3—61no—
159C22×Dic3—121no—
160C22×Dic3#6711yescharacteristic
161C22×Dic3#6711yescharacteristic
162C2×Dic6—21no—
163C2×Dic6#6711yescharacteristic
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—41no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
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⋊C4D1211yescharacteristic
179C3×C4⋊C4#6711yescharacteristic
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—41no—
183C3×C22⋊C4—61no—
184C3×C42—61no—
185C3×C42—61no—
186#217—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—62no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—121no—
194C4⋊Dic3#6711yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32#12011yescharacteristic
211C22×C32C2×Q1611yescharacteristic
212C22×C32#13711yescharacteristic
213C32×C4—21no—
214C32×C4—21no—
215C32×C4—41no—
216C32×C4—41no—
217C3⋊Dic3—81no—
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223C4⋊Q8—61no—
224C4⋊Q8—61no—
225#125—61no—
226#125—61no—
227C22⋊Q8—31no—
228C22⋊Q8—61no—
229C22⋊Q8D3211yescharacteristic
230#117—61no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—91no—
233#107—181no—
234#107—181no—
235#103—181no—
236#103—181no—
237C22⋊C8—31no—
238C22⋊C8—91no—
239#95—31no—
240#95—181no—
241#95—181no—
242C23×C3—21no—
243C23×C3D3×D411yescharacteristic
244C23×C3C2×#6711yescharacteristic
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—42no—
248C3×Q8—121no—
249C3×Q8—241no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—32no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—42no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—41no—
284C2×Dic3—122no—
285C2×Dic3—122no—
286C2×Dic3—122no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289C2×Dic3—242no—
290C2×Dic3#21612yes—
291Dic6—41no—
292Dic6—81no—
293C3×C8—121no—
294C3⋊C8—41no—
295C3⋊C8—122no—
296C3⋊C8—121no—
297C3⋊C8—121no—
298C2×C32—21no—
299C2×C32—21no—
300C2×C32#45111yescharacteristic
301C2×C32#45411yescharacteristic
302C2×C32#45811yescharacteristic
303C2×Q8—31no—
304C2×Q8—61no—
305C2×Q8#62611yescharacteristic
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—61no—
309C22×C4—181no—
310C22×C4C2×D3211yescharacteristic
311C2×C8—61no—
312C2×C8—181no—
313C4⋊C4—21no—
314C4⋊C4—31no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4#62611yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—61no—
328C42—61no—
329C42—61no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3#88211yescharacteristic
340C22×C3#91511yescharacteristic
341C22×C3D3×Q1611yescharacteristic
342C22×C3#94211yescharacteristic
343C22×C3C2×#21611yescharacteristic
344C22×C3#95311yescharacteristic
345C3×C4—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—62no—
356C3×C4—81no—
357C3×C4—81no—
358C3×C4—121no—
359C3×C4—121no—
360C3×C4—121no—
361C3×C4—241no—
362Dic3—22no—
363Dic3—41no—
364Dic3—41no—
365Dic3—41no—
366Dic3—81no—
367Dic3—242no—
368Dic3—241no—
369Dic3—241no—
370C32#161711yescharacteristic, complemented, Sylow
371C23D3×#6711yescharacteristic
372Q8—41no—
373Q8—121no—
374Q8—241no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—32no—
378C2×C4—41no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—362no—
389C2×C4—361no—
390C2×C4C2×#62611yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C8—121no—
393C8—361no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3#474211yescharacteristic
404C2×C3#480911yescharacteristic
405C2×C3#482711yescharacteristic
406C2×C3#522811yescharacteristic
407C2×C3#524311yescharacteristic
408C2×C3#524511yescharacteristic
409C22—21no—
410C22—21no—
411C22D3×#21611yescharacteristic
412C22#6394611yescharacteristic
413C22#6397711yescharacteristic
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—62no—
419C4—121no—
420C4—121no—
421C4—121no—
422C4—241no—
423C4—721no—
424C3—21no—
425C3#6833111yescharacteristic, complemented
426C3#7189911yescharacteristic, complemented
427C2—21no—
428C2—21no—
429C2#1059153411yescharacteristic
430C2#1059159511yescharacteristic
431C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#1617
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
370. C32#1617semidirect
425. C3#68331semidirect
426. C3#71899semidirect

Maximal subgroups

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

subgroupindex
C3×#56232
#105927432
#105912262
#105911032
C3×#45382
#105891532
#105891472
#718993
#683313