Finite Group Databasebeta

← #11775330

Subgroups — #11775330

Order 1152.

709 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 709 conjugacy classes of subgroups — too many to draw. Only its 94 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⋊D3×C22⋊Q8C211yesmaximal, characteristic
2#10591219C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4C3×#4538C212yesmaximal, complemented
5#10589154C212yesmaximal, complemented
6#68336—32nomaximal
7C2×Q8×C3⋊D3C411yescharacteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C32×C22⋊Q8C2211yescharacteristic
10#64155C411yescharacteristic, complemented
11#64133C2211yescharacteristic
12#64106C411yescharacteristic, complemented
13#64105—21no—
14C4⋊C4×C3⋊D3—21no—
15C4⋊C4×C3⋊D3C411yescharacteristic, complemented
16C22⋊C4×C3⋊D3—21no—
17#64087—21no—
18C2×#3722—21no—
19C2×#3712—21no—
20C3×C3⋊#95C2212yes—
21C3×#830C2212yes—
22#63579—21no—
23#63557—21no—
24D3×C22⋊Q8—32no—
25D3×C22⋊Q8—61no—
26#4726—32no—
27#4664—32no—
28C3×#328—32no—
29#4538D312yescomplemented
30#4467—32no—
31#4452—32no—
32C23×C3⋊D3D411yescharacteristic
33C2×C32×Q8C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36Q8×C3⋊D3—42no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—42no—
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3C2×C411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×#634—21no—
45C2×#634C2×C411yescharacteristic
46C22×C3×Dic3—22no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50#3757—21no—
51#3752—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56#3750—21no—
57#3750—21no—
58C2×C3×C3⋊C8—22no—
59#3722—42no—
60#3712—42no—
61#1511—91noSylow
62C2×D3×Q8—32no—
63C2×D3×Q8—61no—
64C22×C4×D3—32no—
65C22×C4×D3—61no—
66C3×C22⋊Q8—21no—
67C3×C22⋊Q8C2×D312yes—
68#946—32no—
69#946—61no—
70C2×(C2×D3)⋊C4—62no—
71#924—32no—
72#924—61no—
73C2×ΓL(1,𝔽25)—62no—
74#897—32no—
75#897—61no—
76#896—62no—
77#896—62no—
78D3×C4⋊C4—32no—
79D3×C4⋊C4—61no—
80D3×C4⋊C4—62no—
81D3×C4⋊C4—62no—
82D3×C22⋊C4—62no—
83D3×C22⋊C4—62no—
84#878—62no—
85#878—62no—
86C3×C22⋊C8—32no—
87C3×#95—32no—
88C3⋊#95—62no—
89C3⋊#95C2×D312yes—
90#830C2×D312yes—
91(C2×D3)⋊C8—62no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3—41no—
96C22×C3⋊D3C22⋊C411yescharacteristic
97C22×C3⋊D3C22⋊C411yescharacteristic
98C32×Q8—41no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C4×C3⋊D3—22no—
110C4×C3⋊D3—22no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3—41no—
113C4×C3⋊D3—42no—
114C4×C3⋊D3—42no—
115#634—42no—
116#634—41no—
117C2×C3×Dic3—42no—
118C2×C3×Dic3—42no—
119C2×C3×Dic3—42no—
120C3×C3⋊C8—42no—
121C2×C22⋊Q8—91no—
122#407—91no—
123#381—91no—
124#328—32no—
125#328—92no—
126C23×D3—32no—
127C23×D3—61no—
128C2×C3×Q8—21no—
129C2×C3×Q8C4×D312yes—
130C22×C3×C4—21no—
131C22×C3×C4—62no—
132C22×C3×C4C22×D312yes—
133C22×Dic3—22no—
134C22×Dic3—32no—
135C22×Dic3—61no—
136D3×Q8—124no—
137D3×Q8—124no—
138C2×C4×D3—32no—
139C2×C4×D3—32no—
140C2×C4×D3—32no—
141C2×C4×D3—32no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—124no—
151C2×C4×D3—124no—
152C2×Dic6—32no—
153C2×Dic6—61no—
154C2×Dic6—62no—
155C2×Dic6—62no—
156C2×C3×C8—62no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4C4×D312yes—
161C3×C22⋊C4—22no—
162C3×C22⋊C4—22no—
163#217—62no—
164#217—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—124no—
170C4⋊Dic3—32no—
171C4⋊Dic3—61no—
172C4⋊Dic3—62no—
173C4⋊Dic3—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179Dic3⋊C4—62no—
180C2×C3⋊C8—22no—
181ΓL(1,𝔽25)—124no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32C2×C22⋊C411yescharacteristic
185C22×C32#13712yes—
186C2×C3⋊D3—21no—
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3—21no—
191C2×C3⋊D3—44no—
192C2×C3⋊D3#9912yes—
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—41no—
196C32×C4—41no—
197C3⋊Dic3—21no—
198C3⋊Dic3—21no—
199C3⋊Dic3—41no—
200C3⋊Dic3—41no—
201C3×Dic3—82no—
202C22×Q8—91no—
203C23×C4—91no—
204C2×M16—181no—
205C22⋊Q8—91no—
206C22⋊Q8—91no—
207C22⋊Q8—91no—
208C22⋊Q8—181no—
209C22⋊Q8—181no—
210C22⋊Q8D3211yescharacteristic
211C2×C4⋊C4—91no—
212C2×C4⋊C4—181no—
213C2×C22⋊C4—181no—
214C2×C22⋊C4—181no—
215C22⋊C8—32no—
216C22⋊C8—181no—
217#95—32no—
218#95—181no—
219C23×C3—21no—
220C23×C3D3×D412yes—
221C22×D3—32no—
222C22×D3—32no—
223C22×D3—61no—
224C22×D3—61no—
225C22×D3—64no—
226C22×D3—64no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—122no—
230C22×D3—122no—
231C22×D3—122no—
232C3×Q8—42no—
233C3×Q8—42no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—122no—
243C2×C3×C4—122no—
244C2×C3×C4—122no—
245C2×C3×C4C2×C4×D312yes—
246C2×C3×C4D3×D412yes—
247C2×Dic3—32no—
248C2×Dic3—32no—
249C2×Dic3—42no—
250C2×Dic3—42no—
251C2×Dic3—42no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—122no—
259C2×Dic3—122no—
260C4×D3—64no—
261C4×D3—64no—
262C4×D3—64no—
263C4×D3—122no—
264C4×D3—122no—
265C4×D3—122no—
266C4×D3—122no—
267C4×D3—122no—
268C4×D3—124no—
269C4×D3—124no—
270C4×D3—124no—
271C4×D3—124no—
272Dic6—124no—
273Dic6—124no—
274Dic6—122no—
275Dic6—122no—
276C3×C8—122no—
277C3⋊C8—42no—
278C2×C32—22no—
279C2×C32C2×#9911yescharacteristic
280C2×C32#41911yescharacteristic
281C2×C32#42111yescharacteristic
282C3⋊D3—22no—
283C3⋊D3—41no—
284C24—91no—
285C2×Q8—91no—
286C2×Q8—181no—
287C2×Q8—362no—
288C2×Q8#62411yescharacteristic
289C22×C4—62no—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—181no—
296C22×C4—181no—
297C22×C4—362no—
298C22×C4C2×D3211yescharacteristic
299M16—362no—
300C2×C8—62no—
301C4⋊C4—21no—
302C4⋊C4—91no—
303C4⋊C4—181no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4#62411yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—181no—
310C22⋊C4—181no—
311C22⋊C4—181no—
312C22⋊C4—362no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3D3×C22⋊C412yes—
320C22×C3#91512yes—
321C22×C3#91812yes—
322C2×D3—34no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—121no—
333C2×D3—121no—
334C2×D3—124no—
335C2×D3—124no—
336C2×D3—128no—
337C3×C4—22no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—41no—
341C3×C4—42no—
342C3×C4—42no—
343C3×C4—42no—
344C3×C4—42no—
345C3×C4—242no—
346Dic3—62no—
347Dic3—62no—
348Dic3—62no—
349Dic3—82no—
350Dic3—121no—
351Dic3—122no—
352Dic3—122no—
353Dic3—122no—
354Dic3—122no—
355C32#151111yescharacteristic, complemented, Sylow
356C23—91no—
357C23—91no—
358C23—182no—
359C23—182no—
360C23—361no—
361C23#381111yescharacteristic
362Q8—41no—
363Q8—361no—
364Q8—362no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—122no—
371C2×C4—122no—
372C2×C4—122no—
373C2×C4—182no—
374C2×C4—182no—
375C2×C4—181no—
376C2×C4—181no—
377C2×C4—361no—
378C2×C4—361no—
379C2×C4—362no—
380C2×C4—362no—
381C2×C4—361no—
382C2×C4C2×#62411yescharacteristic
383C2×C4#381111yescharacteristic
384C8—122no—
385C2×C3—22no—
386C2×C3—22no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—42no—
391C2×C3D3×#9912yes—
392C2×C3#480212yes—
393C2×C3#482112yes—
394D3—64no—
395D3—64no—
396D3—122no—
397D3—122no—
398C22—21no—
399C22—21no—
400C22—92no—
401C22—181no—
402C22—181no—
403C22—181no—
404C22—181no—
405C22—181no—
406C22—364no—
407C22#6395112yes—
408C22#6397411yescharacteristic
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—181no—
414C4—181no—
415C4—242no—
416C4—361no—
417C4—361no—
418C3—21no—
419C3#6833612yescomplemented
420C2—22no—
421C2—182no—
422C2—361no—
423C2#1059152711yescharacteristic
424C2#1059156211yescharacteristic
425C2#1059167211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1511
LCSG ▷ C2×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
4. C3×#4538C2semidirect
5. #10589154C2semidirect
7. C2×Q8×C3⋊D3C4semidirect
10. #64155C4semidirect
12. #64106C4semidirect
15. C4⋊C4×C3⋊D3C4semidirect
29. #4538D3semidirect
355. C32#1511semidirect
419. C3#68336semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
#105912192
#105911592
C3×#45382
#105891542
#683363