Finite Group Databasebeta

← C2×#10593324 #11858168

Subgroups — C2×#10593324 #11858168

Order 1152.

1366 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1366 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64306C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3C22×#3712C211yesmaximal, characteristic, complemented
4#10593324C218yesmaximal, direct product factor
5C2×#63731C214yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C3×#235—21no—
8C2×#3811—21no—
9C2×#3805C412yescomplemented
10#64306—22no—
11#64306—22no—
12#64306C414yescomplemented
13#64306C2214yes—
14C2×#3802C411yescharacteristic, complemented
15C2×C4×D32—21no—
16C2×#3798C2212yes—
17C2×#3797C411yescharacteristic, complemented
18C2×#3796—21no—
19C2×C22⋊#157—21no—
20#64286—22no—
21#64286C2214yescomplemented
22C2×C4⋊#157—21no—
23C2×C4×#157C2212yescomplemented
24C22×C3×C3⋊C8—21no—
25C2×#3712—21no—
26C2×#3712—22no—
27C2×#3712C2212yescomplemented
28C2×#3712C2214yescomplemented
29#63731C22116yescomplemented
30C2×D3×#41—61no—
31C22×ΓL(1,𝔽25)—61no—
32C23×C3⋊D3D411yescharacteristic
33C22×D32—21no—
34C22×#157—22no—
35C22×C32×C4D411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3C2×C412yes—
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D412yes—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C4×C3⋊D3C2312yes—
45C2×C3×#67—22no—
46C3×#235—24no—
47C3×#235—24no—
48C2×C3×D12—21no—
49C2×C3×C4×D3—22no—
50C2×C3×Dic6—21no—
51#3811—24no—
52#3811—24no—
53C2×#627C2×C412yes—
54C2×#626—22no—
55C2×#625C2×C412yes—
56C2×#624—21no—
57#3805—24no—
58#3805C2×C418yescomplemented
59C2×D3×Dic3—22no—
60#3802—22no—
61#3802C2×C414yescomplemented
62C4×D32—24no—
63C4×D32—24no—
64#3798—22no—
65#3798—22no—
66#3798C2×C414yes—
67#3798C2314yes—
68#3797—22no—
69#3797C2×C414yescomplemented
70#3796—24no—
71#3796—24no—
72C22⋊#157—24no—
73C4⋊#157—24no—
74C4×#157—22no—
75C4×#157C2314yescomplemented
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8—24no—
78#3712—22no—
79#3712—24no—
80#3712C2314yescomplemented
81C2×#421—91nomaximal, Sylow
82C2×C3×#41—61no—
83D3×#41—64no—
84D3×#41—64no—
85D3×#41—64no—
86D3×#41—64no—
87C2×#239—61no—
88C2×D3×Q8—61no—
89C2×#237—62no—
90C2×#237—61no—
91C2×D3×D4—61no—
92C2×D3×D4—62no—
93C2×#235—21no—
94C2×#235—62no—
95C22×C4×D3—61no—
96C22×C4×D3—61no—
97C22×C4×D3—62no—
98C22×C3×C8—61no—
99C22×C3⋊C8—21no—
100C2×ΓL(1,𝔽25)—62no—
101C2×ΓL(1,𝔽25)—64no—
102C2×ΓL(1,𝔽25)—64no—
103C2×ΓL(1,𝔽25)—62no—
104C23×C32C22⋊C411yescharacteristic
105C22×C3⋊D3—42no—
106C22×C3⋊D3C22⋊C411yescharacteristic
107C22×C3⋊D3C22⋊C412yes—
108C22×C3⋊D3C2×D411yescharacteristic
109C22×C3⋊D3C2×D412yes—
110C22×C3×D3—22no—
111C2×D32—24no—
112C2×D32—44no—
113C2×#157—24no—
114C2×#157—44no—
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22⋊C412yes—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D412yes—
119C2×C3⋊Dic3C22⋊C411yescharacteristic
120C2×C3⋊Dic3C22⋊C412yes—
121C2×C3⋊Dic3C22×C412yes—
122C2×C3⋊Dic3C22×C411yescharacteristic
123C4×C3⋊D3C22⋊C412yes—
124C4×C3⋊D3C22⋊C412yes—
125C4×C3⋊D3C22⋊C412yes—
126C4×C3⋊D3C22×C412yes—
127C4×C3⋊D3C22×C411yescharacteristic
128C4×C3⋊D3C2×D411yescharacteristic
129C4×C3⋊D3C2×D412yes—
130C4×C3⋊D3C2×D411yescharacteristic
131C4×C3⋊D3C2×D412yes—
132C4×C3⋊D3C2411yescharacteristic
133C3×#67—28no—
134C2×C3×Dic3—22no—
135C3×D12—24no—
136C3×C4×D3—24no—
137C3×C4×D3—24no—
138C3×Dic6—24no—
139#627—22no—
140#627C22×C414yes—
141#626—24no—
142#626—24no—
143#625—22no—
144#625C22×C414yes—
145#624—24no—
146D3×Dic3—28no—
147C3×C3⋊C8—24no—
148C22×#41—91no—
149C22×M16—91no—
150C2×#117—91no—
151#421—98no—
152C2×#104—94no—
153C23×D3—61no—
154C23×D3—61no—
155C23×D3—62no—
156C3×#41—64no—
157C3×#41—64no—
158C2×C3×Q8—61no—
159C2×C3×D4—61no—
160C2×C3×D4—62no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—62no—
164C2×#67—22no—
165C2×#67—62no—
166C2×#67—62no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170#239—64no—
171#239—64no—
172D3×Q8—64no—
173D3×Q8—64no—
174#237—68no—
175#237—64no—
176#237—64no—
177#237—68no—
178D3×D4—64no—
179D3×D4—64no—
180D3×D4—68no—
181D3×D4—68no—
182#235—24no—
183#235—24no—
184#235—64no—
185#235—64no—
186#235—64no—
187#235—64no—
188C2×D12—21no—
189C2×D12—62no—
190C2×C4×D3—22no—
191C2×C4×D3—62no—
192C2×C4×D3—61no—
193C2×C4×D3—62no—
194C2×C4×D3—61no—
195C2×C4×D3—61no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—61no—
204C2×C4×D3—62no—
205C2×C4×D3—61no—
206C2×C4×D3—62no—
207C2×C4×D3—68no—
208C2×C4×D3—68no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×Dic6—21no—
212C2×Dic6—62no—
213C2×C3×C8—64no—
214C2×C3×C8—62no—
215C2×C3⋊C8—24no—
216C2×C3⋊C8—22no—
217ΓL(1,𝔽25)—64no—
218ΓL(1,𝔽25)—68no—
219ΓL(1,𝔽25)—64no—
220C22×C32—22no—
221C22×C32C2×C22⋊C412yes—
222C22×C32C2×C22⋊C411yescharacteristic
223C2×C3⋊D3—22no—
224C2×C3⋊D3—22no—
225C2×C3⋊D3—42no—
226C2×C3⋊D3—42no—
227C2×C3⋊D3C2×C22⋊C412yes—
228C2×C3⋊D3C2×C22⋊C411yescharacteristic
229C2×C3⋊D3C22×D411yescharacteristic
230C2×C3×D3—24no—
231C2×C3×D3—44no—
232D32—48no—
233#157—44no—
234C32×C4C2×C22⋊C412yes—
235C32×C4C2×C22⋊C411yescharacteristic
236C32×C4C22×D411yescharacteristic
237C3⋊Dic3C2×C22⋊C412yes—
238C3⋊Dic3C2×C22⋊C411yescharacteristic
239C3⋊Dic3C23×C411yescharacteristic
240C3×Dic3—24no—
241C2×#41—61no—
242C2×#41—92no—
243C2×#41—92no—
244C2×#41—94no—
245C2×#41—94no—
246C2×#41—181no—
247C2×#41—182no—
248C2×#41—182no—
249C22×Q8—91no—
250C22×D4—91no—
251C22×D4—181no—
252C23×C4—91no—
253C23×C4—181no—
254C2×M16—92no—
255C2×M16—94no—
256C2×M16—182no—
257C2×M16—181no—
258C22×C8—61no—
259#117—94no—
260#117—182no—
261C2×C4⋊C4—181no—
262C2×C22⋊C4—181no—
263C2×C42—92no—
264#104—916no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—62no—
268C22×D3—22no—
269C22×D3—61no—
270C22×D3—62no—
271C22×D3—61no—
272C22×D3—62no—
273C22×D3—61no—
274C22×D3—62no—
275C22×D3—61no—
276C22×D3—62no—
277C22×D3—68no—
278C22×D3—128no—
279C22×D3—124no—
280C22×D3—124no—
281C3×Q8—64no—
282C3×D4—64no—
283C3×D4—68no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—64no—
293C2×C3×C4—64no—
294C2×C3×C4—62no—
295#67—28no—
296#67—64no—
297#67—64no—
298#67—64no—
299#67—64no—
300C2×Dic3—22no—
301C2×Dic3—61no—
302C2×Dic3—62no—
303C2×Dic3—61no—
304C2×Dic3—62no—
305C2×Dic3—61no—
306C2×Dic3—62no—
307C2×Dic3—61no—
308C2×Dic3—62no—
309C2×Dic3—68no—
310D12—24no—
311D12—64no—
312D12—64no—
313C4×D3—24no—
314C4×D3—24no—
315C4×D3—62no—
316C4×D3—62no—
317C4×D3—62no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—62no—
321C4×D3—62no—
322C4×D3—61no—
323C4×D3—61no—
324C4×D3—62no—
325C4×D3—62no—
326C4×D3—61no—
327C4×D3—61no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—61no—
331C4×D3—61no—
332C4×D3—62no—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3—68no—
336C4×D3—68no—
337Dic6—24no—
338Dic6—64no—
339Dic6—64no—
340C3×C8—64no—
341C3⋊C8—24no—
342C2×C32—22no—
343C2×C32#42112yescomplemented
344C2×C32C22×C22⋊C411yescharacteristic
345C3⋊D3—22no—
346C3⋊D3—21no—
347C3⋊D3—21no—
348C3×D3—44no—
349C24—91no—
350C24—181no—
351#41—64no—
352#41—64no—
353#41—94no—
354#41—94no—
355#41—98no—
356#41—182no—
357#41—182no—
358#41—184no—
359#41—184no—
360#41—184no—
361C2×Q8—61no—
362C2×Q8—92no—
363C2×Q8—94no—
364C2×Q8—182no—
365C2×D4—62no—
366C2×D4—61no—
367C2×D4—94no—
368C2×D4—92no—
369C2×D4—182no—
370C2×D4—182no—
371C2×D4—184no—
372C2×D4—184no—
373C22×C4—62no—
374C22×C4—91no—
375C22×C4—92no—
376C22×C4—92no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—92no—
381C22×C4—91no—
382C22×C4—92no—
383C22×C4—184no—
384C22×C4—184no—
385C22×C4—181no—
386C22×C4—182no—
387C22×C4—182no—
388C22×C4GO+(4,𝔽2)11yescharacteristic
389M16—94no—
390M16—184no—
391M16—182no—
392C2×C8—64no—
393C2×C8—62no—
394C4⋊C4—184no—
395C22⋊C4—184no—
396C42—94no—
397C42—182no—
398C22×C3—24no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—22no—
403C22×C3—42no—
404C22×C3—64no—
405C22×C3—124no—
406C2×D3—24no—
407C2×D3—44no—
408C2×D3—62no—
409C2×D3—61no—
410C2×D3—61no—
411C2×D3—62no—
412C2×D3—61no—
413C2×D3—61no—
414C2×D3—64no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—1216no—
419C2×D3—124no—
420C2×D3—124no—
421C2×D3—124no—
422C2×D3—124no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—64no—
430Dic3—24no—
431Dic3—61no—
432Dic3—61no—
433Dic3—62no—
434Dic3—62no—
435Dic3—61no—
436Dic3—61no—
437C32C2×#42111yescharacteristic, complemented, Sylow
438C23—62no—
439C23—91no—
440C23—91no—
441C23—92no—
442C23—92no—
443C23—184no—
444C23—362no—
445C23—364no—
446C23D32⋊C411yescharacteristic
447Q8—64no—
448Q8—94no—
449Q8—182no—
450D4—68no—
451D4—64no—
452D4—94no—
453D4—184no—
454D4—184no—
455D4—182no—
456C2×C4—62no—
457C2×C4—64no—
458C2×C4—64no—
459C2×C4—91no—
460C2×C4—91no—
461C2×C4—92no—
462C2×C4—92no—
463C2×C4—91no—
464C2×C4—92no—
465C2×C4—91no—
466C2×C4—91no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—92no—
471C2×C4—91no—
472C2×C4—92no—
473C2×C4—184no—
474C2×C4—188no—
475C2×C4—184no—
476C2×C4—364no—
477C2×C4D32⋊C411yescharacteristic
478C2×C4D32⋊C412yes—
479C2×C4C2×GO+(4,𝔽2)12yes—
480C2×C4C2×GO+(4,𝔽2)11yescharacteristic
481C8—64no—
482C2×C3—24no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—42no—
488C2×C3—124no—
489D3—44no—
490D3—64no—
491D3—121no—
492D3—121no—
493D3—122no—
494D3—121no—
495D3—121no—
496C22—22no—
497C22—64no—
498C22—91no—
499C22—92no—
500C22—91no—
501C22—124no—
502C22—182no—
503C22—182no—
504C22—362no—
505C22—362no—
506C22—368no—
507C22C2×D32⋊C412yes—
508C22C2×D32⋊C411yescharacteristic
509C4—64no—
510C4—92no—
511C4—91no—
512C4—91no—
513C4—364no—
514C4C2×D32⋊C411yescharacteristic
515C4C2×D32⋊C412yes—
516C4C22×GO+(4,𝔽2)11yescharacteristic
517C3—21no—
518C3—21no—
519C2—22no—
520C2—124no—
521C2—181no—
522C2—182no—
523C2—181no—
524C2#1059332412yesdirect product factor
525C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#421
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. C22×#3712C2semidirect
4. #10593324C2direct (N × H)
5. C2×#63731C2semidirect
9. C2×#3805C4semidirect
12. #64306C4semidirect
14. C2×#3802C4semidirect
17. C2×#3797C4semidirect
21. #64286C22semidirect
23. C2×C4×#157C22semidirect
27. C2×#3712C22semidirect
28. C2×#3712C22semidirect
29. #63731C22semidirect
58. #3805C2×C4semidirect
61. #3802C2×C4semidirect
69. #3797C2×C4semidirect
75. C4×#157C23semidirect
80. #3712C23semidirect
343. C2×C32#421semidirect
437. C32C2×#421semidirect
524. C2#10593324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642862
C22×#37122
#105933242
C2×#637312
C2×#4219