Finite Group Databasebeta

← #11882255

Subgroups — #11882255

Order 1152.

895 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 895 conjugacy classes of subgroups — too many to draw. Only its 164 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#10596199C211yesmaximal, characteristic, complemented
2#10593972C211yesmaximal, characteristic
3C3×#5083C212yesmaximal, complemented
4#10591630C212yesmaximal, complemented
5#10591622C212yesmaximal, complemented
6#10591591C214yesmaximal, complemented
7#10590331C211yesmaximal, characteristic, complemented
8#10590268C212yesmaximal, complemented
9#80438—32nomaximal
10C2×#3798—21no—
11C32×C4⋊Q8C2211yescharacteristic
12#64155C2212yes—
13Q8×C3⋊Dic3C2212yes—
14#64106—21no—
15#64101—21no—
16#64099—21no—
17#64096—21no—
18C42×C3⋊D3C2211yescharacteristic
19#64078C2211yescharacteristic
20C2×C3×#215C2214yes—
21C3×C4×D12C2212yes—
22#63919C2211yescharacteristic
23#63916C2212yes—
24#63915—21no—
25#63914C2211yescharacteristic
26#63912—21no—
27C4×#625—21no—
28C2×#3710C2212yes—
29C3×#835C2214yes—
30C3×C4⋊(C3⋊C8)C2212yes—
31#63573C2214yes—
32#63572C2212yes—
33#63563C2214yes—
34#5728—32no—
35#5728—61no—
36#5548—32no—
37C3×#461—32no—
38#5171—34no—
39#5163—34no—
40#5083D312yescomplemented
41#5008—32no—
42#4842—32no—
43D3×C4⋊C8—32no—
44#4807—34no—
45#4791—34no—
46C2×C32×Q8C2312yes—
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×#634—21no—
51C2×C3×D12C2312yes—
52C2×C3×C4×D3—22no—
53C2×#627—21no—
54C2×#626—22no—
55C2×#625—21no—
56C2×#625—21no—
57#3798—44no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4—21no—
60C32×C42C2311yescharacteristic
61#3752—22no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—22no—
64C4⋊(C3⋊Dic3)C2312yes—
65#3750—22no—
66C4×C3⋊Dic3—22no—
67C4×C3⋊Dic3D411yescharacteristic
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3C2311yescharacteristic
70C3×#215—44no—
71C3×(C2×D3)⋊C4—22no—
72C3×C4⋊Dic3C2312yes—
73C2×C3×C3⋊C8C2314yes—
74#3724—21no—
75(C2×D3)⋊Dic3—22no—
76#3710—42no—
77#3246—91noSylow
78C2×#235—62no—
79C2×C3×SD16—34no—
80C3×C4⋊Q8—21no—
81C3×C4⋊Q8C2×D312yes—
82C3×C4×D4—32no—
83#946—34no—
84#946—62no—
85Q8×Dic3—34no—
86Q8×Dic3—62no—
87C2×#215C2×D314yes—
88#940—32no—
89#938—32no—
90C4×#67—62no—
91C2×D3×C8—34no—
92#897—62no—
93#897—62no—
94#895—32no—
95#892—62no—
96#892—62no—
97#890—62no—
98#890—62no—
99#888—32no—
100#887—62no—
101#887—62no—
102#885—62no—
103#884—62no—
104C4×D12C2×D312yes—
105C42×D3—32no—
106C42×D3—61no—
107#869—32no—
108#869—61no—
109C3×C4⋊C8—32no—
110C3×#103—34no—
111#835C2×D314yes—
112#832—34no—
113#821—34no—
114#817—34no—
115Dic3⋊C8—34no—
116#808—34no—
117C4⋊(C3⋊C8)C2×D312yes—
118C22×C3⋊D3C2×D411yescharacteristic
119C22×C3×D3—22no—
120C32×Q8—22no—
121C32×Q8—22no—
122C2×C32×C4—22no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3C2×D411yescharacteristic
128C2×C3⋊Dic3C2×D411yescharacteristic
129C2×C3⋊Dic3C2×D411yescharacteristic
130C4×C3⋊D3—21no—
131C4×C3⋊D3—21no—
132C4×C3⋊D3—41no—
133C4×C3⋊D3SD1614yescomplemented
134#634—42no—
135C2×C3×Dic3—22no—
136C3×D12—22no—
137C3×D12—22no—
138C3×C4×D3—44no—
139#627—42no—
140#626—44no—
141#625—42no—
142#625—42no—
143C3×C3⋊C8—24no—
144#533—91no—
145#532—91no—
146#476—92no—
147#475—92no—
148#465—94no—
149#461—32no—
150#460—92no—
151C2×C4⋊C8—91no—
152C2×C3×Q8—22no—
153C2×C3×Q8C22×D314yes—
154C2×C3×D4—32no—
155C22×C3×C4—62no—
156C2×#67—62no—
157C2×#67—62no—
158C2×#67—62no—
159#235—128no—
160C2×D12—62no—
161C2×D12C22×D312yes—
162C2×C4×D3—22no—
163C2×C4×D3—32no—
164C2×C4×D3—32no—
165C2×C4×D3—32no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×Dic6—62no—
170C2×Dic6—62no—
171C2×Dic6—62no—
172C3×SD16—124no—
173C2×C3×C8—34no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—32no—
179C3×C22⋊C4—62no—
180C3×C42—21no—
181C3×C42C22×D312yes—
182#217—62no—
183#215—44no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—62no—
186(C2×D3)⋊C4—64no—
187(C2×D3)⋊C4—64no—
188C4⋊Dic3—34no—
189C4⋊Dic3—62no—
190C4⋊Dic3—64no—
191C4⋊Dic3—62no—
192C4⋊Dic3—64no—
193C4⋊Dic3—62no—
194C4⋊Dic3C22×D312yes—
195Dic3⋊C4—62no—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198C4×Dic3—32no—
199C4×Dic3—32no—
200C4×Dic3—32no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—64no—
205C4×Dic3—64no—
206C2×C3⋊C8C22×D314yes—
207D3×C8—124no—
208C22×C32C22×D411yescharacteristic
209C2×C3⋊D3—21no—
210C2×C3⋊D3—21no—
211C2×C3⋊D3C2×SD1612yes—
212C2×C3×D3—42no—
213C2×C3×D3—42no—
214C2×C3×D3—42no—
215C32×C4—21no—
216C32×C4—42no—
217C32×C4C2×SD1612yes—
218C32×C4H(5,𝔽2)11yescharacteristic
219C32×C42−1+411yescharacteristic
220C3⋊Dic3—21no—
221C3⋊Dic3—21no—
222C3⋊Dic3—42no—
223C3⋊Dic3C2×SD1612yes—
224C3×Dic3—42no—
225C2×#41—181no—
226C2×SD16—34no—
227C22×C8—92no—
228C4⋊Q8—91no—
229C4⋊Q8—91no—
230C4⋊Q8D3211yescharacteristic
231#127—91no—
232#125—181no—
233#124—181no—
234C22⋊Q8—92no—
235C22⋊Q8—181no—
236#121—92no—
237#121—181no—
238C4×Q8—92no—
239C4×Q8—181no—
240C4×D4—32no—
241C4×D4—181no—
242#117—181no—
243C2×C42—91no—
244#106—94no—
245C4⋊C8—32no—
246C4⋊C8—92no—
247#103—34no—
248#102—94no—
249C23×C3—62no—
250C22×D3—22no—
251C22×D3—32no—
252C22×D3—61no—
253C3×Q8—24no—
254C3×Q8—24no—
255C3×Q8—42no—
256C3×Q8—42no—
257C3×D4—62no—
258C3×D4—62no—
259C2×C3×C4—24no—
260C2×C3×C4—24no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—62no—
265C2×C3×C4—124no—
266C2×C3×C4D3×D412yes—
267C2×C3×C4D3×D412yes—
268C2×C3×C4C23×D312yes—
269#67—124no—
270#67—124no—
271#67—124no—
272C2×Dic3—22no—
273C2×Dic3—32no—
274C2×Dic3—32no—
275C2×Dic3—32no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—64no—
280C2×Dic3—64no—
281D12—22no—
282D12—22no—
283D12—124no—
284C4×D3—38no—
285C4×D3—44no—
286C4×D3—64no—
287C4×D3—62no—
288C4×D3—62no—
289C4×D3—121no—
290C4×D3—121no—
291C4×D3—122no—
292C4×D3—122no—
293Dic6—124no—
294Dic6—124no—
295Dic6—124no—
296C3×C8—64no—
297C3⋊C8—24no—
298C2×C32#53711yescharacteristic
299C2×C32C22×SD1611yescharacteristic
300C2×C32#57511yescharacteristic
301C3⋊D3—22no—
302C3×D3—82no—
303#41—364no—
304C2×Q8—181no—
305C2×Q8—181no—
306C2×Q8C2×D3212yes—
307C2×D4—32no—
308C2×D4—182no—
309C2×D4—181no—
310C2×D4—181no—
311C22×C4—62no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—91no—
315SD16—124no—
316C2×C8—34no—
317C2×C8—362no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—32no—
321C4⋊C4—92no—
322C4⋊C4—182no—
323C4⋊C4—182no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C22⋊C4—62no—
327C22⋊C4—182no—
328C22⋊C4—182no—
329C42—91no—
330C42—91no—
331C42—91no—
332C42—182no—
333C42C2×D3211yescharacteristic
334C22×C3—21no—
335C22×C3—122no—
336C22×C3—122no—
337C22×C3—122no—
338C22×C3C2×D3×D412yes—
339C2×D3—34no—
340C2×D3—42no—
341C2×D3—42no—
342C2×D3—42no—
343C2×D3—62no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—121no—
347C2×D3—121no—
348C3×C4—22no—
349C3×C4—22no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—22no—
353C3×C4—44no—
354C3×C4—44no—
355C3×C4—122no—
356C3×C4D3×SD1614yes—
357C3×C4#100412yes—
358C3×C4#101012yes—
359Dic3—34no—
360Dic3—42no—
361Dic3—62no—
362Dic3—62no—
363Dic3—62no—
364Dic3—121no—
365Dic3—121no—
366Dic3—124no—
367Dic3—124no—
368C32#324611yescharacteristic, complemented, Sylow
369C23—62no—
370C23—91no—
371Q8—22no—
372Q8—22no—
373Q8—362no—
374Q8—362no—
375D4—62no—
376D4—62no—
377D4—362no—
378D4—364no—
379D4—362no—
380C2×C4—22no—
381C2×C4—62no—
382C2×C4—91no—
383C2×C4—94no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—124no—
387C2×C4—181no—
388C2×C4—181no—
389C2×C4—182no—
390C2×C4—361no—
391C2×C4#381111yescharacteristic
392C2×C4#381111yescharacteristic
393C2×C4C22×D3211yescharacteristic
394C8—64no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—242no—
399C2×C3#560812yes—
400C2×C3C2×D3×SD1612yes—
401C2×C3#577712yes—
402D3—64no—
403D3—82no—
404D3—122no—
405C22—92no—
406C22—122no—
407C22—122no—
408C22—122no—
409C22—181no—
410C22—181no—
411C22C2×#381111yescharacteristic
412C4—21no—
413C4—42no—
414C4—92no—
415C4—122no—
416C4—181no—
417C4—181no—
418C4—362no—
419C4#6394012yes—
420C4#6430911yescharacteristic
421C4#6431311yescharacteristic
422C3—21no—
423C3#8043812yescomplemented
424C2—182no—
425C2—242no—
426C2#1059524011yescharacteristic
427C2C2×#6394011yescharacteristic
428C2#1059532311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593972C2
hypercenterC4⋊Q8D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C3×#5083C2semidirect
4. #10591630C2semidirect
5. #10591622C2semidirect
6. #10591591C2semidirect
7. #10590331C2semidirect
8. #10590268C2semidirect
40. #5083D3semidirect
133. C4×C3⋊D3SD16semidirect
368. C32#3246semidirect
423. C3#80438semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105939722
C3×#50832
#105916302
#105916222
#105915912
#105903312
#105902682
#804383