Finite Group Databasebeta

← C2×#10593298 #11861073

Subgroups — C2×#10593298 #11861073

Order 1152.

730 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#64223C211yesmaximal, characteristic
2C2×#63805C211yesmaximal, characteristic, complemented
3C2×#63803C211yesmaximal, characteristic, complemented
4C2×#63767C211yesmaximal, characteristic, complemented
5C2×#63733C211yesmaximal, characteristic, complemented
6C2×#63731C211yesmaximal, characteristic, complemented
7C2×#63731C211yesmaximal, characteristic, complemented
8#10593298C218yesmaximal, direct product factor
9C2×#3798C2211yescharacteristic
10C2×#3798C2211yescharacteristic
11C2×C4×#157C2211yescharacteristic
12C2×#3787C2211yescharacteristic
13C2×#3776C411yescharacteristic, complemented
14C2×#3775C411yescharacteristic, complemented
15C2×#3775C411yescharacteristic, complemented
16C2×#3774C411yescharacteristic, complemented
17#64223C414yescomplemented
18#64223C2214yes—
19C2×C8×C3⋊D3C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)—21no—
21C2×C3×D3×C8—21no—
22C2×#3712C2211yescharacteristic
23C2×#3712C2211yescharacteristic
24C2×#3711—21no—
25C2×D3×C3⋊C8—21no—
26#63805—22no—
27#63805C2214yescomplemented
28#63803—22no—
29#63803C2214yescomplemented
30#63767C2214yescomplemented
31#63733C2214yescomplemented
32#63731C2214yescomplemented
33#63731C2214yescomplemented
34C2×#907—61no—
35C2×#901—61no—
36C22×#157—21no—
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×C3×C4×D3—21no—
39C2×C3×C4×D3—21no—
40C2×#627C2×C411yescharacteristic
41C2×#627C2×C411yescharacteristic
42C2×#626—21no—
43C2×#626—21no—
44C2×#625C2×C411yescharacteristic
45C2×#625C2×C411yescharacteristic
46#3798—21no—
47#3798—21no—
48#3798—21no—
49#3798—21no—
50#3798C2×C412yes—
51#3798C2×C412yes—
52#3798C2312yes—
53#3798C2312yes—
54C2×#622C2×C411yescharacteristic
55C2×#622C2×C411yescharacteristic
56C4×#157—21no—
57C4×#157C2312yes—
58#3787C2×C412yes—
59#3787C2312yes—
60#3776C2×C414yescomplemented
61#3775C2×C414yescomplemented
62#3775C2×C414yescomplemented
63#3774C2×C414yescomplemented
64C2×C32×C8D411yescharacteristic
65C2×C3⋊(C3⋊C8)D411yescharacteristic
66C8×C3⋊D3D412yes—
67C8×C3⋊D3C2312yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C3×ΓL(1,𝔽25)—24no—
71C3×D3×C8—24no—
72#3712—21no—
73#3712—21no—
74#3712C2312yes—
75#3712C2312yes—
76#3711—24no—
77D3×C3⋊C8—24no—
78C2×#444—91nomaximal, Sylow
79C2×#235—61no—
80C2×#235—61no—
81C2×C3×M16—61no—
82C22×C3×C8—61no—
83C2×#208—61no—
84C22×C3⋊C8—61no—
85#907—64no—
86#907—64no—
87#901—64no—
88#901—64no—
89C2×ΓL(1,𝔽25)—21no—
90C2×ΓL(1,𝔽25)—61no—
91C2×ΓL(1,𝔽25)—61no—
92C2×ΓL(1,𝔽25)—61no—
93C2×D3×C8—21no—
94C2×D3×C8—61no—
95C2×D3×C8—61no—
96C2×D3×C8—61no—
97C22×C3⋊D3#4111yescharacteristic
98C22×C3×D3—21no—
99C22×C3×D3—21no—
100C2×#157—22no—
101C2×#157—42no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C3⋊Dic3C22×C411yescharacteristic
104C4×C3⋊D3C22×C411yescharacteristic
105C4×C3⋊D3C2×D411yescharacteristic
106C4×C3⋊D3#4111yescharacteristic
107C4×C3⋊D3C2411yescharacteristic
108C2×C3×Dic3—21no—
109C2×C3×Dic3—21no—
110C3×C4×D3—22no—
111C3×C4×D3—22no—
112C3×C4×D3—22no—
113C3×C4×D3—22no—
114#627—21no—
115#627—21no—
116#627C22×C412yes—
117#627C22×C412yes—
118#626—22no—
119#626—22no—
120#626—22no—
121#626—22no—
122#625—21no—
123#625—21no—
124#625C22×C412yes—
125#625C22×C412yes—
126#622C22×C412yes—
127#622C22×C412yes—
128C32×C8C2×D412yes—
129C3⋊(C3⋊C8)C2×D412yes—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—22no—
132C2×#135—91no—
133C2×#131—91no—
134C2×#131—91no—
135#444—98no—
136C2×#108—91no—
137C2×#104—91no—
138C2×#104—91no—
139C2×#97—91no—
140C22×C3×C4—61no—
141C22×C3×C4—61no—
142C2×#67—61no—
143C2×#67—61no—
144C2×#67—61no—
145C2×#67—61no—
146#235—62no—
147#235—62no—
148#235—62no—
149#235—62no—
150#235—62no—
151#235—62no—
152#235—62no—
153#235—62no—
154C2×D12—61no—
155C2×D12—61no—
156C2×C4×D3—21no—
157C2×C4×D3—21no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C3×M16—64no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—64no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168#208—64no—
169C2×C3⋊C8—21no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8—61no—
173C2×C3⋊C8—64no—
174ΓL(1,𝔽25)—24no—
175ΓL(1,𝔽25)—62no—
176ΓL(1,𝔽25)—62no—
177ΓL(1,𝔽25)—62no—
178ΓL(1,𝔽25)—62no—
179ΓL(1,𝔽25)—64no—
180D3×C8—24no—
181D3×C8—62no—
182D3×C8—62no—
183D3×C8—62no—
184D3×C8—62no—
185D3×C8—64no—
186C22×C32C4×D411yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3C4×D411yescharacteristic
189C2×C3⋊D3C2×#4111yescharacteristic
190C2×C3×D3—22no—
191C2×C3×D3—22no—
192C2×C3×D3—42no—
193C2×C3×D3—42no—
194#157—42no—
195C32×C4C4×D411yescharacteristic
196C32×C4C22×D411yescharacteristic
197C3⋊Dic3C4×D411yescharacteristic
198C3⋊Dic3C23×C411yescharacteristic
199C3×Dic3—22no—
200C3×Dic3—22no—
201C2×#41—91no—
202C2×#41—91no—
203#135—94no—
204#135—94no—
205C2×Q16—91no—
206C2×SD16—91no—
207C2×SD16—91no—
208C2×D8—91no—
209#131—94no—
210#131—94no—
211#131—182no—
212#131—182no—
213C2×M16—61no—
214C2×M16—91no—
215C2×M16—91no—
216C2×M16—181no—
217C22×C8—61no—
218C22×C8—91no—
219C22×C8—91no—
220C22×C8—181no—
221C2×C42—91no—
222#108—94no—
223#104—94no—
224#104—94no—
225#97—94no—
226C23×C3—61no—
227C23×C3—61no—
228C22×D3—21no—
229C22×D3—21no—
230C22×D3—61no—
231C22×D3—61no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4—62no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240#67—62no—
241#67—62no—
242#67—62no—
243#67—62no—
244#67—62no—
245#67—62no—
246#67—62no—
247#67—62no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252D12—62no—
253D12—62no—
254D12—62no—
255D12—62no—
256C4×D3—22no—
257C4×D3—22no—
258C4×D3—22no—
259C4×D3—22no—
260C4×D3—61no—
261C4×D3—61no—
262C4×D3—61no—
263C4×D3—61no—
264C4×D3—61no—
265C4×D3—61no—
266C4×D3—61no—
267C4×D3—61no—
268Dic6—62no—
269Dic6—62no—
270Dic6—62no—
271Dic6—62no—
272C3×C8—22no—
273C3×C8—22no—
274C3×C8—62no—
275C3×C8—62no—
276C3⋊C8—22no—
277C3⋊C8—22no—
278C3⋊C8—62no—
279C3⋊C8—62no—
280C2×C32#44412yescomplemented
281C2×C32C2×C4×D411yescharacteristic
282C3⋊D3—21no—
283C3⋊D3—21no—
284C3×D3—42no—
285C3×D3—42no—
286#41—92no—
287#41—92no—
288#41—92no—
289#41—92no—
290#41—181no—
291#41—181no—
292#41—181no—
293#41—181no—
294C2×Q8—91no—
295C2×Q8—91no—
296C2×D4—91no—
297C2×D4—91no—
298C2×D4—181no—
299C2×D4—181no—
300C22×C4—61no—
301C22×C4—61no—
302C22×C4—91no—
303C22×C4—181no—
304Q16—94no—
305SD16—94no—
306SD16—94no—
307D8—94no—
308M16—64no—
309M16—92no—
310M16—92no—
311M16—181no—
312M16—181no—
313M16—184no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—64no—
317C2×C8—92no—
318C2×C8—91no—
319C2×C8—91no—
320C2×C8—92no—
321C2×C8—91no—
322C2×C8—92no—
323C2×C8—92no—
324C2×C8—184no—
325C2×C8GO+(4,𝔽2)11yescharacteristic
326C42—92no—
327C42—181no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—62no—
331C22×C3—62no—
332C22×C3—122no—
333C22×C3—122no—
334C2×D3—22no—
335C2×D3—22no—
336C2×D3—42no—
337C2×D3—42no—
338C2×D3—61no—
339C2×D3—61no—
340C2×D3—61no—
341C2×D3—61no—
342C2×D3—122no—
343C2×D3—122no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—62no—
349C3×C4—62no—
350Dic3—22no—
351Dic3—22no—
352Dic3—61no—
353Dic3—61no—
354Dic3—61no—
355Dic3—61no—
356C32C2×#44411yescharacteristic, complemented, Sylow
357C23—61no—
358C23—61no—
359C23—91no—
360Q8—92no—
361Q8—92no—
362Q8—181no—
363Q8—181no—
364D4—92no—
365D4—92no—
366D4—182no—
367D4—182no—
368D4—182no—
369D4—182no—
370D4—181no—
371D4—181no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—91no—
379C2×C4—91no—
380C2×C4—91no—
381C2×C4—91no—
382C2×C4—91no—
383C2×C4—182no—
384C2×C4—362no—
385C2×C4C2×GO+(4,𝔽2)11yescharacteristic
386C8—62no—
387C8—62no—
388C8—92no—
389C8—92no—
390C8—92no—
391C8C2×GO+(4,𝔽2)12yes—
392C2×C3—22no—
393C2×C3—22no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—122no—
397C2×C3—122no—
398D3—42no—
399D3—42no—
400D3—121no—
401D3—121no—
402D3—121no—
403D3—121no—
404C22—62no—
405C22—62no—
406C22—91no—
407C22—91no—
408C22—122no—
409C22—122no—
410C22—182no—
411C22C4×GO+(4,𝔽2)11yescharacteristic
412C4—62no—
413C4—62no—
414C4—91no—
415C4—91no—
416C4—362no—
417C4C4×GO+(4,𝔽2)11yescharacteristic
418C4C22×GO+(4,𝔽2)11yescharacteristic
419C3—21no—
420C3—21no—
421C2—122no—
422C2—122no—
423C2—181no—
424C2—181no—
425C2#1059329812yesdirect product factor
426C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC2×#64223C2
cosocleC4×C3⋊D3C24
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#444
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63805C2semidirect
3. C2×#63803C2semidirect
4. C2×#63767C2semidirect
5. C2×#63733C2semidirect
6. C2×#63731C2semidirect
7. C2×#63731C2semidirect
8. #10593298C2direct (N × H)
13. C2×#3776C4semidirect
14. C2×#3775C4semidirect
15. C2×#3775C4semidirect
16. C2×#3774C4semidirect
17. #64223C4semidirect
27. #63805C22semidirect
29. #63803C22semidirect
30. #63767C22semidirect
31. #63733C22semidirect
32. #63731C22semidirect
33. #63731C22semidirect
60. #3776C2×C4semidirect
61. #3775C2×C4semidirect
62. #3775C2×C4semidirect
63. #3774C2×C4semidirect
280. C2×C32#444semidirect
356. C32C2×#444semidirect
425. C2#10593298direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642232
C2×#638052
C2×#638032
C2×#637672
C2×#637332
C2×#637312
#105932982
C2×#4449