Finite Group Databasebeta

← #11868848

Subgroups — #11868848

Order 1152.

716 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 115 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#10593966C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic, complemented
3#10593729C211yesmaximal, characteristic, complemented
4#10593394C212yesmaximal, complemented
5#10593391C212yesmaximal, complemented
6#10593385C212yesmaximal, complemented
7#10593367C212yesmaximal, complemented
8#10593360C212yesmaximal
9#10593357C212yesmaximal, complemented
10C2×#3798C2211yescharacteristic
11C2×#3797—21no—
12C2×#3788C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14C3×#872—21no—
15C3×#869—21no—
16#63919—21no—
17#63919C2212yes—
18#63902C2211yescharacteristic
19#63902C2211yescharacteristic
20#63900—21no—
21#63900C2212yes—
22#63881—21no—
23#63881—21no—
24C4×D3×Dic3—21no—
25#63874C2211yescharacteristic
26#63873C2212yes—
27#63838C2211yescharacteristic
28#63838C2211yescharacteristic
29#63779C2212yes—
30#63779C2212yes—
31#63743C2214yes—
32#63742C2214yes—
33#63740C2214yes—
34#63739C2214yes—
35D3×C4⋊Q8—61no—
36#5522—61no—
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3C2311yescharacteristic
40C2×C3×C4×D3—21no—
41C2×C3×Dic6—22no—
42C2×#627—22no—
43C2×#627C2311yescharacteristic
44C2×#626—21no—
45C2×#625C2311yescharacteristic
46C2×#624—22no—
47C2×D3×Dic3—21no—
48C2×D3×Dic3—21no—
49#3798—22no—
50#3798Q814yescomplemented
51#3797—44no—
52C2×#622C2314yes—
53#3788—24no—
54C32×C42D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3C2311yescharacteristic
57C4×C3⋊Dic3C2311yescharacteristic
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—22no—
61C3×C4⋊Dic3—22no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65#3724—22no—
66#3724C2311yescharacteristic
67#3724C2311yescharacteristic
68#3724C2314yes—
69#3722—21no—
70Dic32—21no—
71Dic32—21no—
72#3079—91nomaximal, Sylow
73C2×D3×Q8—62no—
74C2×#235—61no—
75C3×C4⋊Q8—61no—
76C3×#117—61no—
77#944—62no—
78C2×C4×Dic3—61no—
79#893—61no—
80#893—61no—
81D3×C4⋊C4—62no—
82D3×C4⋊C4—62no—
83#888—62no—
84#888—62no—
85#887—61no—
86#887—61no—
87#67⋊C4—61no—
88#67⋊C4—61no—
89#67⋊C4—61no—
90#67⋊C4—61no—
91#872—21no—
92#872—61no—
93C42×D3—61no—
94C42×D3—61no—
95C42×D3—61no—
96#869—21no—
97C22×C3⋊D3C2×D411yescharacteristic
98C22×C3×D3—21no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3C2×D411yescharacteristic
103C2×C3⋊Dic3C2×D411yescharacteristic
104C2×C3⋊Dic3C2411yescharacteristic
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107C4×C3⋊D3C2×Q812yes—
108C4×C3⋊D3#4112yes—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—24no—
113C3×C4×D3—24no—
114C3×Dic6—44no—
115#627—21no—
116#627—44no—
117#627C2×Q812yescomplemented
118#626—24no—
119#625—21no—
120#625C2×Q812yescomplemented
121#624—44no—
122D3×Dic3—42no—
123D3×Dic3—42no—
124#622—24no—
125C2×C4⋊Q8—91no—
126C4×#41—91no—
127#477—92no—
128#476—92no—
129#475—92no—
130#474—92no—
131#428—92no—
132#423—91no—
133#417—92no—
134C2×C3×Q8—62no—
135C22×C3×C4—61no—
136C2×#67—61no—
137C2×#67—61no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140D3×Q8—128no—
141#235—64no—
142#235—64no—
143C2×D12—61no—
144C2×C4×D3—21no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×C4×D3—64no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×Dic6—22no—
155C2×Dic6—61no—
156C2×Dic6—64no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—62no—
160C3×C4⋊C4—62no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—61no—
166(C2×D3)⋊C4—21no—
167(C2×D3)⋊C4—21no—
168(C2×D3)⋊C4—61no—
169(C2×D3)⋊C4—61no—
170C4⋊Dic3—22no—
171C4⋊Dic3—22no—
172Dic3⋊C4—21no—
173Dic3⋊C4—21no—
174Dic3⋊C4—61no—
175Dic3⋊C4—61no—
176Dic3⋊C4—64no—
177Dic3⋊C4—64no—
178C4×Dic3—21no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C22×C32C22×D411yescharacteristic
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3C22⋊Q812yes—
193C2×C3×D3—22no—
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4C22⋊Q812yes—
199C3⋊Dic3AGL(1,ℤ/8)12yes—
200C3⋊Dic3#13712yes—
201C3⋊Dic3C22×Q811yescharacteristic
202C3⋊Dic3C2×#4111yescharacteristic
203C3×Dic3—22no—
204C3×Dic3—41no—
205C3×Dic3—44no—
206C3×Dic3—41no—
207C2×#41—91no—
208C22×Q8—181no—
209C2×M16—92no—
210C4⋊Q8—61no—
211C4⋊Q8—92no—
212C4⋊Q8—92no—
213C4⋊Q8—181no—
214C4×Q8—91no—
215C4×Q8—91no—
216C4×D4—91no—
217C4×D4—91no—
218C4×D4—181no—
219C4×D4—181no—
220#117—61no—
221#117—91no—
222C2×C4⋊C4—92no—
223C2×C4⋊C4—181no—
224C2×C42—91no—
225C2×C42—181no—
226#107—94no—
227#106—94no—
228C4⋊C8—92no—
229C4⋊C8—92no—
230#103—94no—
231#102—94no—
232C23×C3—61no—
233C22×D3—21no—
234C22×D3—61no—
235C22×D3—61no—
236C3×Q8—124no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—64no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—64no—
248#67—62no—
249#67—64no—
250#67—62no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—24no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—122no—
262C2×Dic3—122no—
263D12—64no—
264C4×D3—24no—
265C4×D3—62no—
266C4×D3—62no—
267C4×D3—62no—
268C4×D3—62no—
269C4×D3—64no—
270C4×D3—64no—
271C4×D3—122no—
272C4×D3—122no—
273C4×D3—128no—
274C4×D3—122no—
275C4×D3—122no—
276Dic6—44no—
277Dic6—62no—
278Dic6—62no—
279Dic6—128no—
280C2×C32C2×C22⋊Q811yescharacteristic
281C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
282C2×C32C2×#13711yescharacteristic
283C3⋊D3—22no—
284C3×D3—42no—
285#41—94no—
286#41—182no—
287C2×Q8—62no—
288C2×Q8—91no—
289C2×Q8—182no—
290C2×Q8—364no—
291C2×D4—91no—
292C2×D4—181no—
293C22×C4—61no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4—182no—
298C22×C4—181no—
299C22×C4—181no—
300M16—184no—
301C2×C8—94no—
302C4⋊C4—62no—
303C4⋊C4—62no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4—94no—
307C4⋊C4—91no—
308C4⋊C4—91no—
309C4⋊C4—182no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C22⋊C4—181no—
313C42—61no—
314C42—91no—
315C42—91no—
316C42—91no—
317C42—181no—
318C42—181no—
319C42GO+(4,𝔽2)11yescharacteristic
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—62no—
323C22×C3—121no—
324C22×C3—121no—
325C2×D3—22no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—62no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—121no—
333C2×D3—121no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—62no—
341C3×C4—124no—
342C3×C4—121no—
343C3×C4—121no—
344Dic3—22no—
345Dic3—44no—
346Dic3—41no—
347Dic3—41no—
348Dic3—61no—
349Dic3—61no—
350Dic3—62no—
351Dic3—62no—
352Dic3—61no—
353Dic3—61no—
354Dic3—62no—
355Dic3—62no—
356C32#307911yescharacteristic, complemented, Sylow
357C23—61no—
358C23—91no—
359Q8—92no—
360Q8—124no—
361Q8—181no—
362Q8—364no—
363D4—92no—
364D4—184no—
365D4—181no—
366C2×C4—61no—
367C2×C4—64no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—64no—
371C2×C4—91no—
372C2×C4—91no—
373C2×C4—91no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—362no—
379C2×C4—362no—
380C2×C4—364no—
381C2×C4C2×GO+(4,𝔽2)11yescharacteristic
382C2×C4C2×GO+(4,𝔽2)11yescharacteristic
383C2×C4C2×GO+(4,𝔽2)11yescharacteristic
384C8—184no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—122no—
392D3—42no—
393D3—64no—
394D3—122no—
395C22—62no—
396C22—92no—
397C22—121no—
398C22—121no—
399C22—181no—
400C22—181no—
401C22C22×GO+(4,𝔽2)11yescharacteristic
402C4—21no—
403C4—21no—
404C4—62no—
405C4—91no—
406C4—91no—
407C4—92no—
408C4—92no—
409C4—124no—
410C4—121no—
411C4—121no—
412C4D32⋊Q812yes—
413C3—21no—
414C3—21no—
415C2—122no—
416C2—182no—
417C2C2×D32⋊Q811yescharacteristic
418C2#1059650111yescharacteristic
419C2#1059650511yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3798C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#3079
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593909C2semidirect
3. #10593729C2semidirect
4. #10593394C2semidirect
5. #10593391C2semidirect
6. #10593385C2semidirect
7. #10593367C2semidirect
9. #10593357C2semidirect
50. #3798Q8semidirect
117. #627C2×Q8semidirect
120. #625C2×Q8semidirect
356. C32#3079semidirect

Maximal subgroups

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

subgroupindex
#105939662
#105939092
#105937292
#105933942
#105933912
#105933852
#105933672
#105933602
#105933572
#30799