Finite Group Databasebeta

← #11775060

Subgroups — #11775060

Order 1152.

723 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 723 conjugacy classes of subgroups — too many to draw. Only its 102 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#10596067C211yesmaximal, characteristic
2#10591257C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4C3×#4537C212yesmaximal, complemented
5#10589151C212yesmaximal, complemented
6#68277—32nomaximal
7C2×#3830—21no—
8C32×#121C2211yescharacteristic
9#64149C411yescharacteristic, complemented
10#64148—21no—
11D4×C3⋊Dic3C411yescharacteristic, complemented
12#64139C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64102C411yescharacteristic, complemented
15#64097C411yescharacteristic, complemented
16#64094—21no—
17#64090—21no—
18C2×#3724—21no—
19C2×Dic32—21no—
20C3×C3⋊#95C2212yes—
21C3×#830C2212yes—
22#63572—21no—
23#63553—21no—
24#5596—32no—
25#5596—61no—
26#4718—32no—
27#4649—32no—
28C3×#327—32no—
29#4537D312yescomplemented
30#4470—32no—
31#4451—32no—
32C2×C32×D4—21no—
33C2×C32×D4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×#638—21no—
36C2×#638—21no—
37C2×#638—21no—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41#3830—42no—
42#3830—42no—
43C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×#634—21no—
46C22×C3×Dic3—22no—
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C22⋊C4—21no—
49#3757—21no—
50#3752—21no—
51#3752—21no—
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53#3750—21no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C2×C3×C3⋊C8—22no—
59#3724—24no—
60Dic32—42no—
61#1502—91noSylow
62C2×#237—62no—
63C2×#237—62no—
64C3×#121—21no—
65C3×#121C2×D312yes—
66#940—32no—
67#940—61no—
68#939—62no—
69#939—62no—
70D4×Dic3—32no—
71D4×Dic3—61no—
72#930—32no—
73#930—61no—
74C2×Dic3⋊C4—62no—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—61no—
77C2×C4×Dic3—62no—
78#893—32no—
79#893—61no—
80#888—32no—
81#888—61no—
82#885—62no—
83#885—62no—
84#67⋊C4—62no—
85#67⋊C4—62no—
86C3×C22⋊C8—32no—
87C3×#95—32no—
88C3⋊#95C2×D312yes—
89#830C2×D312yes—
90Dic3⋊C8—62no—
91C8×Dic3—62no—
92C23×C32—21no—
93C23×C32C2×D411yescharacteristic
94C22×C3⋊D3—21no—
95C32×D4—41no—
96C32×D4—41no—
97C32×D4—41no—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102#638—41no—
103#638—41no—
104#638—42no—
105#638—42no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—42no—
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C2×C3⋊Dic3C22⋊C411yescharacteristic
112C2×C3⋊Dic3C22⋊C411yescharacteristic
113C2×C3⋊Dic3D812yes—
114C2×C3⋊Dic3SD1612yes—
115C4⋊(C3⋊D3)—41no—
116C4×C3⋊D3—42no—
117#634—42no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C3×C3⋊C8—42no—
122#532—91no—
123#431—91no—
124C4×C4⋊C4—91no—
125#327—32no—
126#327—92no—
127C2×C3×D4—22no—
128C2×C3×D4—22no—
129C2×C3×D4—21no—
130C2×C3×D4C4×D312yes—
131C22×C3×C4—21no—
132C22×C3×C4—62no—
133C22×C3×C4C22×D312yes—
134C2×#67—62no—
135C2×#67—62no—
136C2×#67—62no—
137C2×#67—62no—
138C2×#67—62no—
139C2×#67—62no—
140C22×Dic3—22no—
141C22×Dic3—32no—
142C22×Dic3—32no—
143C22×Dic3—61no—
144C22×Dic3—61no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147#237—124no—
148#237—124no—
149#237—124no—
150#237—124no—
151C2×D12—32no—
152C2×D12—61no—
153C2×C4×D3—62no—
154C2×C4×D3—62no—
155C2×Dic6—62no—
156C2×Dic6—62no—
157C2×C3×C8—62no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4C4×D312yes—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—22no—
162#217—62no—
163#217—62no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168C4⋊Dic3—32no—
169C4⋊Dic3—61no—
170Dic3⋊C4—68no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173C4×Dic3—32no—
174C4×Dic3—32no—
175C4×Dic3—32no—
176C4×Dic3—32no—
177C4×Dic3—61no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—124no—
182C2×C3⋊C8—22no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—41no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32C2×C22⋊C411yescharacteristic
189C22×C32C2×D811yescharacteristic
190C22×C32C2×SD1611yescharacteristic
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—41no—
197C3⋊Dic3—21no—
198C3⋊Dic3—41no—
199C3⋊Dic3#10212yes—
200C3⋊Dic3#10212yes—
201C3⋊Dic3#10412yes—
202C3×Dic3—44no—
203C2×#41—181no—
204C4⋊Q8—91no—
205#127—91no—
206#124—181no—
207#121—91no—
208#121—181no—
209#121D3211yescharacteristic
210C4×D4—91no—
211C4×D4—91no—
212C4×D4—181no—
213C2×C4⋊C4—181no—
214C2×C42—91no—
215C2×C42—181no—
216C4⋊C8—181no—
217C22⋊C8—32no—
218C4×C8—181no—
219#95—32no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—21no—
223C23×C3D3×D412yes—
224C22×D3—62no—
225C22×D3—62no—
226C3×D4—42no—
227C3×D4—42no—
228C3×D4—42no—
229C3×D4—42no—
230C3×D4—42no—
231C3×D4—42no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—64no—
239C2×C3×C4—122no—
240C2×C3×C4—122no—
241C2×C3×C4C2×C4×D312yes—
242C2×C3×C4D3×D412yes—
243#67—124no—
244#67—124no—
245#67—124no—
246#67—124no—
247#67—122no—
248#67—122no—
249#67—122no—
250#67—122no—
251C2×Dic3—24no—
252C2×Dic3—32no—
253C2×Dic3—32no—
254C2×Dic3—32no—
255C2×Dic3—34no—
256C2×Dic3—34no—
257C2×Dic3—32no—
258C2×Dic3—42no—
259C2×Dic3—42no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—61no—
266C2×Dic3—64no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—122no—
270C2×Dic3—124no—
271C2×Dic3—124no—
272D12—122no—
273D12—122no—
274C4×D3—124no—
275C4×D3—124no—
276Dic6—124no—
277Dic6—124no—
278C3×C8—122no—
279C3⋊C8—42no—
280C2×C32—21no—
281C2×C32—21no—
282C2×C32—81no—
283C2×C32#41011yescharacteristic
284C2×C32C2×#10211yescharacteristic
285C2×C32C2×#10411yescharacteristic
286C3⋊D3—81no—
287#41—362no—
288#41—362no—
289C2×Q8—181no—
290C2×D4—21no—
291C2×D4—91no—
292C2×D4—181no—
293C2×D4—181no—
294C2×D4—181no—
295C2×D4#62411yescharacteristic
296C22×C4—62no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—181no—
300C22×C4—181no—
301C22×C4C2×D3211yescharacteristic
302C2×C8—62no—
303C4⋊C4—91no—
304C4⋊C4—181no—
305C4⋊C4—184no—
306C4⋊C4#62411yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—181no—
309C22⋊C4—181no—
310C22⋊C4—181no—
311C42—91no—
312C42—91no—
313C42—91no—
314C42—91no—
315C42—362no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3D3×C22⋊C412yes—
330C22×C3D3×D812yes—
331C22×C3D3×SD1612yes—
332C2×D3—122no—
333C2×D3—122no—
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—122no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—41no—
342C3×C4—42no—
343C3×C4—42no—
344C3×C4—124no—
345Dic3—34no—
346Dic3—34no—
347Dic3—34no—
348Dic3—44no—
349Dic3—62no—
350Dic3—62no—
351Dic3—62no—
352Dic3—62no—
353Dic3—121no—
354Dic3—122no—
355Dic3—122no—
356C32#150211yescharacteristic, complemented, Sylow
357C23—21no—
358C23—181no—
359C23#381111yescharacteristic
360Q8—362no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—361no—
365D4—362no—
366D4—362no—
367D4—361no—
368D4—361no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—64no—
372C2×C4—92no—
373C2×C4—92no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—122no—
379C2×C4—122no—
380C2×C4—182no—
381C2×C4—181no—
382C2×C4—362no—
383C2×C4—362no—
384C2×C4C2×#62411yescharacteristic
385C2×C4#381111yescharacteristic
386C8—122no—
387C2×C3—22no—
388C2×C3—22no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—82no—
395C2×C3—82no—
396C2×C3#474012yes—
397C2×C3D3×#10212yes—
398C2×C3D3×#10412yes—
399D3—242no—
400D3—242no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—361no—
407C22—361no—
408C22—361no—
409C22#6392611yescharacteristic
410C22#6393011yescharacteristic
411C22#6397411yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—92no—
416C4—92no—
417C4—92no—
418C4—124no—
419C4—181no—
420C4—361no—
421C3—21no—
422C3#6827712yescomplemented
423C2—21no—
424C2—21no—
425C2—81no—
426C2—721no—
427C2#1059141611yescharacteristic
428C2#1059152911yescharacteristic
429C2#1059167111yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radical#10596067C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1502
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591257C2semidirect
3. #10591061C2semidirect
4. C3×#4537C2semidirect
5. #10589151C2semidirect
9. #64149C4semidirect
11. D4×C3⋊Dic3C4semidirect
14. #64102C4semidirect
15. #64097C4semidirect
29. #4537D3semidirect
356. C32#1502semidirect
422. C3#68277semidirect

Maximal subgroups

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

subgroupindex
#105960672
#105912572
#105910612
C3×#45372
#105891512
#682773