Finite Group Databasebeta

← #11779438

Subgroups — #11779438

Order 1152.

542 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 90 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#10596050C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic, complemented
3#10590386C211yesmaximal, characteristic, complemented
4#10590300C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic
8#71156—31nomaximal
9#68246—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64155—21no—
12#64105—22no—
13C4⋊C4×C3⋊D3—21no—
14C4×C4⋊(C3⋊D3)—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64079—21no—
17#64078C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3719—22no—
20C3×#835—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63573—21no—
26#63564—21no—
27#5579—31no—
28#5579—31no—
29#5579—61no—
30C3×#477—31no—
31#5092—31no—
32#5084—31no—
33#5021D311yescharacteristic, complemented
34#4842—31no—
35#4699—31no—
36C3×Q8⋊C8—31no—
37#4535D311yescharacteristic, complemented
38#4483—31no—
39#4481—31no—
40#4481—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—22no—
46C2×#634D412yes—
47C2×C3×Dic6—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C42—21no—
51C32×C42C2311yescharacteristic
52#3752—22no—
53#3752—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—22no—
58#3750—22no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3719—44no—
65#1632—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—21no—
68C3×C4×Q8C2×D311yescharacteristic
69C3×C4×Q8C2×D311yescharacteristic
70#946—62no—
71#946—61no—
72#946—61no—
73C2×#216—62no—
74C2×Dic12—62no—
75#896—62no—
76#896—62no—
77#896—64no—
78D3×C4⋊C4—62no—
79D3×C4⋊C4—61no—
80D3×C4⋊C4—61no—
81C4×D12—31no—
82C4×D12—31no—
83C4×D12—61no—
84C4×D12—61no—
85C4×D12—61no—
86C4×D12—62no—
87#870—61no—
88#870—61no—
89#870—62no—
90#869—31no—
91#869—31no—
92#869—61no—
93#869C2×D311yescharacteristic
94C3×#107—61no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8—31no—
97C3×#103—61no—
98C3×C4×C8—31no—
99#835—21no—
100#821—61no—
101#817—61no—
102#809—61no—
103#808—61no—
104#807—21no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊D3—21no—
109C32×Q8—21no—
110C32×Q8—21no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—22no—
118C4⋊(C3⋊D3)—21no—
119C4⋊(C3⋊D3)Q1612yescomplemented
120C4×C3⋊D3—41no—
121C4×C3⋊D3—41no—
122C4×C3⋊D3—82no—
123#634—42no—
124C2×C3×Dic3—41no—
125C3×Dic6—42no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8—41no—
129#554—91no—
130#494—91no—
131#477—31no—
132#476—91no—
133#333—91no—
134Q8⋊C8—31no—
135D4⋊C8—91no—
136C2×C3×Q8—21no—
137C2×C3×Q8—61no—
138C2×C3×Q8D1211yescharacteristic
139C2×C3×Q8#6711yescharacteristic
140C2×D12—31no—
141C2×D12—31no—
142C2×D12—61no—
143C2×C4×D3—62no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—64no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×Dic6—21no—
150C2×Dic6—32no—
151C2×Dic6—32no—
152C2×Dic6—62no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4D1211yescharacteristic
163C3×C4⋊C4#6711yescharacteristic
164C3×C42—22no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#216—124no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—61no—
182C4⋊Dic3—62no—
183C4⋊Dic3—62no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188Dic3⋊C4—64no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—64no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197Dic12—124no—
198C22×C32#12011yescharacteristic
199C2×C3⋊D3—22no—
200C2×C3⋊D3—41no—
201C2×C3⋊D3—41no—
202C32×C4—21no—
203C32×C4—41no—
204C32×C4—41no—
205C32×C4C2×Q1611yescharacteristic
206C32×C4#13511yescharacteristic
207C32×C4#13711yescharacteristic
208C32×C4#13711yescharacteristic
209C3⋊Dic3—41no—
210C3⋊Dic3—42no—
211C3×Dic3—81no—
212C2×Q16—182no—
213C4⋊Q8—31no—
214C4⋊Q8—91no—
215#125—181no—
216C22⋊Q8—182no—
217C22⋊Q8—181no—
218C4×Q8D3211yescharacteristic
219C4×D4—91no—
220C4×D4—181no—
221C2×C4⋊C4—181no—
222#107—61no—
223#106—181no—
224C4⋊C8—31no—
225C4⋊C8—31no—
226#103—61no—
227#102—181no—
228C4×C8—31no—
229C22×D3—62no—
230C22×D3—61no—
231C22×D3—61no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×Q8—122no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—121no—
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×Dic3—41no—
256C2×Dic3—62no—
257C2×Dic3—64no—
258C2×Dic3—61no—
259C2×Dic3—62no—
260C2×Dic3—61no—
261C2×Dic3—62no—
262D12—32no—
263D12—32no—
264D12—62no—
265D12—62no—
266D12—61no—
267D12—61no—
268C4×D3—122no—
269C4×D3—122no—
270C4×D3—121no—
271C4×D3—121no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—244no—
275C4×D3—242no—
276C4×D3—242no—
277Dic6—42no—
278Dic6—122no—
279Dic6—122no—
280Dic6—242no—
281C3×C8—62no—
282C3×C8—121no—
283C3×C8—121no—
284C3⋊C8—22no—
285C3⋊C8—41no—
286C3⋊C8—41no—
287C2×C32#45111yescharacteristic
288C2×C32#45211yescharacteristic
289C2×C32#45311yescharacteristic
290C3⋊D3—42no—
291C2×Q8—61no—
292C2×Q8—92no—
293C2×Q8#62611yescharacteristic
294C2×D4—91no—
295C22×C4—182no—
296C22×C4—181no—
297Q16—364no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—61no—
301C4⋊C4—21no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—91no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C4⋊C4—181no—
308C4⋊C4—181no—
309C4⋊C4#62611yescharacteristic
310C22⋊C4—182no—
311C22⋊C4—181no—
312C42—21no—
313C42C2×D3211yescharacteristic
314C22×C3—21no—
315C22×C3#88211yescharacteristic
316C22×C3#93711yescharacteristic
317C2×D3—64no—
318C2×D3—62no—
319C2×D3—62no—
320C2×D3—122no—
321C2×D3—122no—
322C2×D3—121no—
323C2×D3—121no—
324C2×D3—121no—
325C2×D3—121no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—41no—
333C3×C4—42no—
334C3×C4—42no—
335C3×C4—41no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—241no—
340C3×C4#90411yescharacteristic
341C3×C4#90911yescharacteristic
342C3×C4#91511yescharacteristic
343C3×C4D3×Q1611yescharacteristic
344C3×C4D3×Q1611yescharacteristic
345C3×C4#91811yescharacteristic
346C3×C4#94211yescharacteristic
347C3×C4#95011yescharacteristic
348Dic3—81no—
349Dic3—124no—
350Dic3—122no—
351Dic3—122no—
352Dic3—121no—
353Dic3—121no—
354Dic3—122no—
355C32#163211yescharacteristic, complemented, Sylow
356C23—181no—
357Q8—21no—
358Q8—21no—
359Q8—122no—
360Q8—362no—
361D4—92no—
362D4—181no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—121no—
366C2×C4—181no—
367C2×C4—182no—
368C2×C4—361no—
369C2×C4—361no—
370C2×C4—722no—
371C2×C4C2×#62611yescharacteristic
372C2×C4#381111yescharacteristic
373C2×C4#381111yescharacteristic
374C8—62no—
375C8—121no—
376C8—121no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3#473311yescharacteristic
381C2×C3#480911yescharacteristic
382C2×C3#482211yescharacteristic
383C2×C3#504711yescharacteristic
384C2×C3#518611yescharacteristic
385C2×C3#519811yescharacteristic
386D3—124no—
387D3—122no—
388D3—122no—
389C22—182no—
390C22—361no—
391C22—361no—
392C22#6398111yescharacteristic
393C4—21no—
394C4—41no—
395C4—41no—
396C4—241no—
397C4—362no—
398C4—361no—
399C4#6382911yescharacteristic
400C4#6383311yescharacteristic
401C4#6394411yescharacteristic
402C4#6395111yescharacteristic
403C3—21no—
404C3#6824611yescharacteristic, complemented
405C3#7115611yescharacteristic, complemented
406C2—362no—
407C2#1059118411yescharacteristic
408C2#1059160311yescharacteristic
409C2#1059166711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4×Q8D32
hypocenterC32#1632
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5021C2semidirect
3. #10590386C2semidirect
5. C3×#4535C2semidirect
6. #10589096C2semidirect
33. #5021D3semidirect
37. #4535D3semidirect
119. C4⋊(C3⋊D3)Q16semidirect
355. C32#1632semidirect
404. C3#68246semidirect
405. C3#71156semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#50212
#105903862
#105903002
C3×#45352
#105890962
#105890822
#711563
#682463