Finite Group Databasebeta

← C2×#10593323 #11858167

Subgroups — C2×#10593323 #11858167

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
1C22×#3798C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3C2×#63818C211yesmaximal, characteristic, complemented
4#10593323C218yesmaximal, direct product factor
5C2×#63731C214yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×C3×C4×D3—21no—
8C22×#627C411yescharacteristic, complemented
9C22×#626—21no—
10C22×#625C411yescharacteristic, complemented
11C2×#3798—21no—
12C2×#3798—22no—
13C2×#3798—21no—
14C2×#3798—22no—
15C2×#3798C414yescomplemented
16C2×#3798C412yescomplemented
17C2×#3798C2212yes—
18C2×#3798C2214yes—
19C2×C22⋊#157—21no—
20#64286—22no—
21#64286C2214yescomplemented
22C2×C4⋊#157—21no—
23C2×C4×#157C2212yescomplemented
24C2×C3×#208—21no—
25C2×#3712C2212yescomplemented
26#63818—22no—
27#63818C2214yescomplemented
28C2×#3710—21no—
29#63731C22116yescomplemented
30C22×#235—61no—
31C2×D3×M16—61no—
32C23×C3⋊D3D411yescharacteristic
33C23×C3×D3—21no—
34C22×#157—22no—
35C22×C32×C4D411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C412yes—
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D412yes—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C4×C3⋊D3C2312yes—
45C22×C3×Dic3—21no—
46C2×C3×C4×D3—24no—
47C2×C3×C4×D3—22no—
48C2×C3×C4×D3—22no—
49C2×C3×C4×D3—24no—
50C2×#627—22no—
51C2×#627—21no—
52C2×#627C2×C412yes—
53C2×#627C2×C414yescomplemented
54C2×#626—24no—
55C2×#626—22no—
56C2×#626—22no—
57C2×#626—24no—
58C2×#625—22no—
59C2×#625—21no—
60C2×#625C2×C412yes—
61C2×#625C2×C414yescomplemented
62#3798—24no—
63#3798—24no—
64#3798—24no—
65#3798—22no—
66#3798—22no—
67#3798—24no—
68#3798—24no—
69#3798C2×C414yes—
70#3798C2×C418yescomplemented
71#3798C2314yes—
72C22⋊#157—24no—
73C4⋊#157—24no—
74C4×#157—22no—
75C4×#157C2314yescomplemented
76C3×#208—24no—
77C2×C3×C3⋊C8—22no—
78#3712—22no—
79#3712C2314yescomplemented
80#3710—24no—
81C2×#421—91nomaximal, Sylow
82C23×C3×C4—61no—
83C22×#67—61no—
84C22×#67—61no—
85C2×#235—62no—
86C2×#235—64no—
87C2×#235—62no—
88C2×#235—64no—
89C2×#235—64no—
90C2×#235—62no—
91C2×#235—62no—
92C2×#235—64no—
93C22×D12—61no—
94C22×C4×D3—21no—
95C22×C4×D3—61no—
96C22×C4×D3—61no—
97C22×Dic6—61no—
98C2×C3×M16—61no—
99C2×#208—21no—
100D3×M16—64no—
101D3×M16—64no—
102C2×ΓL(1,𝔽25)—62no—
103C2×D3×C8—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—
111C22×C3×D3—24no—
112C22×C3×D3—44no—
113C2×#157—24no—
114C2×#157—44no—
115C2×C32×C4C22⋊C412yes—
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D412yes—
119C2×C3⋊Dic3C22⋊C412yes—
120C2×C3⋊Dic3C22⋊C411yescharacteristic
121C2×C3⋊Dic3C22×C411yescharacteristic
122C2×C3⋊Dic3C22×C412yes—
123C4×C3⋊D3C22⋊C412yes—
124C4×C3⋊D3C22⋊C412yes—
125C4×C3⋊D3C22⋊C412yes—
126C4×C3⋊D3C22×C411yescharacteristic
127C4×C3⋊D3C22×C412yes—
128C4×C3⋊D3C2×D411yescharacteristic
129C4×C3⋊D3C2×D412yes—
130C4×C3⋊D3C2×D412yes—
131C4×C3⋊D3C2×D411yescharacteristic
132C4×C3⋊D3C2411yescharacteristic
133C2×C3×Dic3—22no—
134C2×C3×Dic3—24no—
135C3×C4×D3—24no—
136C3×C4×D3—28no—
137C3×C4×D3—24no—
138#627—22no—
139#627—24no—
140#627C22×C414yes—
141#626—24no—
142#626—28no—
143#626—24no—
144#625—22no—
145#625—24no—
146#625C22×C414yes—
147C3×C3⋊C8—24no—
148C22×#41—91no—
149C22×M16—91no—
150C2×#117—91no—
151#421—98no—
152C2×#104—94no—
153C24×C3—61no—
154C23×D3—21no—
155C23×D3—61no—
156C23×D3—61no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—64no—
160C22×C3×C4—62no—
161C22×C3×C4—64no—
162C22×C3×C4—62no—
163C22×C3×C4—61no—
164C2×#67—62no—
165C2×#67—64no—
166C2×#67—62no—
167C2×#67—64no—
168C2×#67—62no—
169C2×#67—64no—
170C2×#67—64no—
171C2×#67—62no—
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175#235—64no—
176#235—68no—
177#235—64no—
178#235—68no—
179#235—68no—
180#235—68no—
181#235—68no—
182#235—64no—
183#235—64no—
184#235—68no—
185C2×D12—62no—
186C2×D12—64no—
187C2×D12—62no—
188C2×D12—64no—
189C2×C4×D3—24no—
190C2×C4×D3—22no—
191C2×C4×D3—24no—
192C2×C4×D3—22no—
193C2×C4×D3—61no—
194C2×C4×D3—61no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—61no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×C4×D3—62no—
207C2×C4×D3—61no—
208C2×C4×D3—62no—
209C2×Dic6—62no—
210C2×Dic6—64no—
211C2×Dic6—64no—
212C2×Dic6—62no—
213C3×M16—64no—
214C2×C3×C8—62no—
215#208—24no—
216C2×C3⋊C8—22no—
217ΓL(1,𝔽25)—64no—
218ΓL(1,𝔽25)—64no—
219D3×C8—68no—
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—48no—
232C2×C3×D3—44no—
233#157—44no—
234C32×C4C2×C22⋊C411yescharacteristic
235C32×C4C2×C22⋊C412yes—
236C32×C4C22×D411yescharacteristic
237C3⋊Dic3C2×C22⋊C411yescharacteristic
238C3⋊Dic3C2×C22⋊C412yes—
239C3⋊Dic3C23×C411yescharacteristic
240C3×Dic3—24no—
241C2×#41—92no—
242C2×#41—94no—
243C2×#41—92no—
244C2×#41—94no—
245C2×#41—182no—
246C2×#41—181no—
247C2×#41—181no—
248C2×#41—182no—
249C22×Q8—91no—
250C22×D4—91no—
251C22×D4—181no—
252C23×C4—61no—
253C23×C4—91no—
254C2×M16—61no—
255C2×M16—92no—
256C2×M16—94no—
257C2×M16—182no—
258C22×C8—181no—
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—
268C23×C3—64no—
269C23×C3—124no—
270C22×D3—22no—
271C22×D3—24no—
272C22×D3—44no—
273C22×D3—61no—
274C22×D3—61no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—61no—
278C22×D3—62no—
279C22×D3—61no—
280C22×D3—62no—
281C22×D3—124no—
282C22×D3—124no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—64no—
292C2×C3×C4—64no—
293C2×C3×C4—68no—
294C2×C3×C4—62no—
295C2×C3×C4—64no—
296#67—64no—
297#67—64no—
298#67—68no—
299#67—64no—
300#67—64no—
301#67—68no—
302C2×Dic3—22no—
303C2×Dic3—24no—
304C2×Dic3—62no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—62no—
308C2×Dic3—61no—
309C2×Dic3—62no—
310C2×Dic3—61no—
311C2×Dic3—62no—
312D12—64no—
313D12—68no—
314D12—64no—
315C4×D3—24no—
316C4×D3—24no—
317C4×D3—28no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—62no—
321C4×D3—62no—
322C4×D3—62no—
323C4×D3—62no—
324C4×D3—62no—
325C4×D3—61no—
326C4×D3—61no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—61no—
330C4×D3—61no—
331C4×D3—62no—
332C4×D3—62no—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3—62no—
336C4×D3—61no—
337C4×D3—61no—
338Dic6—64no—
339Dic6—64no—
340Dic6—68no—
341C3×C8—64no—
342C3⋊C8—24no—
343C2×C32—22no—
344C2×C32#42112yescomplemented
345C2×C32C22×C22⋊C411yescharacteristic
346C3⋊D3—22no—
347C3⋊D3—21no—
348C3⋊D3—21no—
349C3×D3—44no—
350C24—61no—
351C24—91no—
352#41—94no—
353#41—94no—
354#41—98no—
355#41—184no—
356#41—182no—
357#41—182no—
358#41—184no—
359#41—184no—
360#41—184no—
361#41—184no—
362C2×Q8—92no—
363C2×Q8—94no—
364C2×Q8—182no—
365C2×Q8—181no—
366C2×D4—92no—
367C2×D4—94no—
368C2×D4—182no—
369C2×D4—182no—
370C2×D4—184no—
371C2×D4—184no—
372C2×D4—182no—
373C2×D4—181no—
374C22×C4—61no—
375C22×C4—64no—
376C22×C4—62no—
377C22×C4—64no—
378C22×C4—62no—
379C22×C4—91no—
380C22×C4—92no—
381C22×C4—92no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—92no—
386C22×C4—91no—
387C22×C4—92no—
388C22×C4—182no—
389C22×C4GO+(4,𝔽2)11yescharacteristic
390M16—64no—
391M16—94no—
392M16—182no—
393C2×C8—62no—
394C2×C8—184no—
395C4⋊C4—184no—
396C22⋊C4—184no—
397C42—94no—
398C42—182no—
399C22×C3—24no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—22no—
404C22×C3—42no—
405C22×C3—64no—
406C22×C3—128no—
407C22×C3—124no—
408C2×D3—24no—
409C2×D3—48no—
410C2×D3—44no—
411C2×D3—62no—
412C2×D3—62no—
413C2×D3—61no—
414C2×D3—61no—
415C2×D3—61no—
416C2×D3—61no—
417C2×D3—64no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—124no—
422C2×D3—124no—
423C2×D3—124no—
424C2×D3—124no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—22no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—64no—
432Dic3—24no—
433Dic3—62no—
434Dic3—61no—
435Dic3—61no—
436Dic3—62no—
437Dic3—61no—
438Dic3—61no—
439C32C2×#42111yescharacteristic, complemented, Sylow
440C23—64no—
441C23—62no—
442C23—91no—
443C23—91no—
444C23—92no—
445C23—92no—
446C23—124no—
447C23—362no—
448C23D32⋊C411yescharacteristic
449Q8—94no—
450Q8—184no—
451Q8—182no—
452D4—94no—
453D4—184no—
454D4—188no—
455D4—184no—
456D4—184no—
457D4—182no—
458C2×C4—64no—
459C2×C4—62no—
460C2×C4—64no—
461C2×C4—68no—
462C2×C4—64no—
463C2×C4—92no—
464C2×C4—91no—
465C2×C4—92no—
466C2×C4—91no—
467C2×C4—91no—
468C2×C4—92no—
469C2×C4—91no—
470C2×C4—91no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—91no—
474C2×C4—92no—
475C2×C4—92no—
476C2×C4—92no—
477C2×C4—184no—
478C2×C4—364no—
479C2×C4D32⋊C411yescharacteristic
480C2×C4D32⋊C412yes—
481C2×C4C2×GO+(4,𝔽2)12yes—
482C2×C4C2×GO+(4,𝔽2)11yescharacteristic
483C8—64no—
484C2×C3—24no—
485C2×C3—22no—
486C2×C3—22no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—42no—
490C2×C3—124no—
491D3—44no—
492D3—64no—
493D3—121no—
494D3—121no—
495D3—122no—
496D3—121no—
497D3—121no—
498C22—22no—
499C22—64no—
500C22—91no—
501C22—92no—
502C22—91no—
503C22—128no—
504C22—124no—
505C22—182no—
506C22—182no—
507C22—362no—
508C22—362no—
509C22C2×D32⋊C412yes—
510C22C2×D32⋊C411yescharacteristic
511C4—64no—
512C4—91no—
513C4—92no—
514C4—91no—
515C4—364no—
516C4C2×D32⋊C412yes—
517C4C2×D32⋊C411yescharacteristic
518C4C22×GO+(4,𝔽2)11yescharacteristic
519C3—21no—
520C3—21no—
521C2—22no—
522C2—124no—
523C2—181no—
524C2—182no—
525C2—181no—
526C2#1059332312yesdirect product factor
527C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC22×#3798C2
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. C2×#63818C2semidirect
4. #10593323C2direct (N × H)
5. C2×#63731C2semidirect
8. C22×#627C4semidirect
10. C22×#625C4semidirect
15. C2×#3798C4semidirect
16. C2×#3798C4semidirect
21. #64286C22semidirect
23. C2×C4×#157C22semidirect
25. C2×#3712C22semidirect
27. #63818C22semidirect
29. #63731C22semidirect
53. C2×#627C2×C4semidirect
61. C2×#625C2×C4semidirect
70. #3798C2×C4semidirect
75. C4×#157C23semidirect
79. #3712C23semidirect
344. C2×C32#421semidirect
439. C32C2×#421semidirect
526. C2#10593323direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37982
C2×#642862
C2×#638182
#105933232
C2×#637312
C2×#4219