Finite Group Databasebeta

← C2×#10593313 #11857656

Subgroups — C2×#10593313 #11857656

Order 1152.

1350 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1350 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
2C22×#3788C211yesmaximal, characteristic, complemented
3C2×#63818C211yesmaximal, characteristic, complemented
4C2×#63728C212yesmaximal, complemented
5#10593313C218yesmaximal, direct product factor
6C2×#63727C212yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C3×#235—21no—
9C2×#3811C412yes—
10C2×#3805—21no—
11#64306—22no—
12#64306—22no—
13#64306C414yes—
14#64306C2214yes—
15C2×#3802C2211yescharacteristic
16C2×C4×D32C412yes—
17C2×#3798—21no—
18C2×#3797C2211yescharacteristic
19C2×#3796—21no—
20C22×#622—21no—
21C2×#3788—22no—
22C2×#3788—21no—
23C2×#3788C2212yes—
24C2×#3788C2214yescomplemented
25C2×C3×#208—21no—
26C2×#3712C2212yes—
27#63818—22no—
28#63818C2214yescomplemented
29C2×#3710—21no—
30#63728C2218yescomplemented
31#63727C2218yescomplemented
32C2×D3×#41—61no—
33C2×D3×M16—61no—
34C23×C3⋊D3C2×C411yescharacteristic
35C22×D32C2×C412yes—
36C22×C32×C4D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C412yes—
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D412yes—
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D412yes—
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C4×C3⋊D3C2312yes—
46C2×C3×#67—22no—
47C3×#235—24no—
48C3×#235—24no—
49C2×C3×D12—21no—
50C2×C3×C4×D3—22no—
51C2×C3×Dic6—21no—
52#3811—24no—
53#3811C2×C418yes—
54C2×#627—21no—
55C2×#626—22no—
56C2×#625—21no—
57C2×#624C2×C412yes—
58#3805—24no—
59#3805—24no—
60C2×D3×Dic3—22no—
61#3802—21no—
62#3802—21no—
63#3802C2×C412yes—
64#3802C2312yes—
65C4×D32—24no—
66C4×D32C2×C418yes—
67#3798—24no—
68#3798—24no—
69#3797—21no—
70#3797—21no—
71#3797C2×C412yes—
72#3797C2312yes—
73#3796—24no—
74#3796—24no—
75C2×#622—22no—
76C2×#622—24no—
77#3788—22no—
78#3788—24no—
79#3788C2314yes—
80C3×#208—24no—
81C2×C3×C3⋊C8—22no—
82#3712—22no—
83#3712C2314yes—
84#3710—24no—
85C2×#413—91nomaximal, Sylow
86C2×C3×#41—61no—
87D3×#41—64no—
88D3×#41—64no—
89D3×#41—64no—
90D3×#41—64no—
91C2×#239—61no—
92C2×D3×Q8—61no—
93C2×#237—61no—
94C2×#237—62no—
95C2×D3×D4—61no—
96C2×D3×D4—62no—
97C2×#235—21no—
98C2×#235—62no—
99C22×C4×D3—62no—
100C22×C4×D3—61no—
101C22×C4×D3—61no—
102C2×C3×M16—61no—
103C2×#208—21no—
104D3×M16—64no—
105D3×M16—64no—
106C2×ΓL(1,𝔽25)—62no—
107C2×D3×C8—62no—
108C23×C32C22⋊C411yescharacteristic
109C22×C3⋊D3—42no—
110C22×C3⋊D3C22⋊C411yescharacteristic
111C22×C3⋊D3C22⋊C412yes—
112C22×C3⋊D3C22×C411yescharacteristic
113C22×C3⋊D3C22×C412yes—
114C22×C3×D3—22no—
115C2×D32—22no—
116C2×D32—44no—
117C2×D32C22×C414yes—
118C2×C32×C4C22⋊C411yescharacteristic
119C2×C32×C4C22⋊C412yes—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D412yes—
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C412yes—
124C2×C3⋊Dic3C2×D412yes—
125C2×C3⋊Dic3C2×D411yescharacteristic
126C4×C3⋊D3C22⋊C412yes—
127C4×C3⋊D3C22⋊C412yes—
128C4×C3⋊D3C22⋊C412yes—
129C4×C3⋊D3C22×C411yescharacteristic
130C4×C3⋊D3C22×C412yes—
131C4×C3⋊D3C2×D412yes—
132C4×C3⋊D3C2×D411yescharacteristic
133C4×C3⋊D3C2×D411yescharacteristic
134C4×C3⋊D3C2×D412yes—
135C4×C3⋊D3C2411yescharacteristic
136C3×#67—28no—
137C2×C3×Dic3—22no—
138C3×D12—22no—
139C3×D12—22no—
140C3×C4×D3—28no—
141C3×Dic6—22no—
142C3×Dic6—22no—
143#627—22no—
144#627—22no—
145#626—28no—
146#625—22no—
147#625—22no—
148#624—22no—
149#624C22×C414yes—
150D3×Dic3—28no—
151#622—24no—
152C3×C3⋊C8—24no—
153C22×#41—91no—
154C22×M16—91no—
155C22×M16—91no—
156#413—98no—
157C2×#101—92no—
158C2×#100—92no—
159C23×D3—62no—
160C23×D3—61no—
161C23×D3—61no—
162C3×#41—64no—
163C3×#41—64no—
164C2×C3×Q8—61no—
165C2×C3×D4—61no—
166C2×C3×D4—62no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—62no—
170C2×#67—22no—
171C2×#67—62no—
172C2×#67—62no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—62no—
176#239—64no—
177#239—64no—
178D3×Q8—62no—
179D3×Q8—62no—
180D3×Q8—62no—
181D3×Q8—62no—
182#237—64no—
183#237—64no—
184#237—68no—
185#237—68no—
186D3×D4—62no—
187D3×D4—62no—
188D3×D4—68no—
189D3×D4—62no—
190D3×D4—62no—
191D3×D4—68no—
192#235—24no—
193#235—24no—
194#235—68no—
195#235—68no—
196C2×D12—21no—
197C2×D12—62no—
198C2×C4×D3—22no—
199C2×C4×D3—68no—
200C2×C4×D3—62no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—61no—
216C2×C4×D3—62no—
217C2×C4×D3—68no—
218C2×C4×D3—62no—
219C2×Dic6—21no—
220C2×Dic6—62no—
221C3×M16—64no—
222C2×C3×C8—62no—
223#208—24no—
224C2×C3⋊C8—22no—
225ΓL(1,𝔽25)—64no—
226ΓL(1,𝔽25)—64no—
227D3×C8—68no—
228C22×C32—22no—
229C22×C32C2×C22⋊C412yes—
230C22×C32C2×C22⋊C411yescharacteristic
231C2×C3⋊D3—22no—
232C2×C3⋊D3—22no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3C2×C22⋊C411yescharacteristic
236C2×C3⋊D3C2×C22⋊C412yes—
237C2×C3⋊D3C23×C411yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—44no—
240D32—44no—
241D32—44no—
242C32×C4C2×C22⋊C411yescharacteristic
243C32×C4C2×C22⋊C412yes—
244C32×C4C22×D411yescharacteristic
245C3⋊Dic3C2×C22⋊C412yes—
246C3⋊Dic3C2×C22⋊C411yescharacteristic
247C3⋊Dic3C22×D411yescharacteristic
248C3×Dic3—24no—
249C2×#41—61no—
250C2×#41—94no—
251C2×#41—94no—
252C2×#41—181no—
253C2×#41—181no—
254C2×#41—181no—
255C2×#41—182no—
256C2×#41—182no—
257C22×Q8—91no—
258C22×D4—91no—
259C22×D4—92no—
260C23×C4—92no—
261C23×C4—91no—
262C2×M16—61no—
263C2×M16—92no—
264C2×M16—94no—
265C2×M16—92no—
266C2×M16—94no—
267C2×M16—182no—
268C2×M16—182no—
269C2×M16—181no—
270C22×C8—181no—
271C22×C8—181no—
272#101—98no—
273#100—98no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—62no—
277C22×D3—22no—
278C22×D3—64no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—61no—
286C22×D3—62no—
287C22×D3—64no—
288C22×D3—128no—
289C22×D3—124no—
290C22×D3—124no—
291C3×Q8—62no—
292C3×Q8—62no—
293C3×D4—62no—
294C3×D4—62no—
295C3×D4—68no—
296C2×C3×C4—21no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—68no—
305C2×C3×C4—62no—
306#67—28no—
307#67—68no—
308#67—64no—
309#67—64no—
310C2×Dic3—22no—
311C2×Dic3—61no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—61no—
319C2×Dic3—68no—
320D12—22no—
321D12—22no—
322D12—68no—
323C4×D3—28no—
324C4×D3—64no—
325C4×D3—62no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—61no—
333C4×D3—62no—
334C4×D3—61no—
335C4×D3—62no—
336C4×D3—61no—
337C4×D3—61no—
338C4×D3—62no—
339C4×D3—62no—
340C4×D3—61no—
341C4×D3—61no—
342C4×D3—62no—
343C4×D3—61no—
344C4×D3—61no—
345C4×D3—64no—
346C4×D3—68no—
347Dic6—22no—
348Dic6—22no—
349Dic6—64no—
350Dic6—64no—
351C3×C8—64no—
352C3⋊C8—24no—
353C2×C32—22no—
354C2×C32#41312yescomplemented
355C2×C32C22×C22⋊C411yescharacteristic
356C3⋊D3—21no—
357C3⋊D3—21no—
358C3⋊D3—22no—
359C3×D3—44no—
360C24—92no—
361C24—91no—
362#41—64no—
363#41—64no—
364#41—184no—
365#41—184no—
366#41—184no—
367#41—184no—
368#41—184no—
369#41—184no—
370C2×Q8—61no—
371C2×Q8—92no—
372C2×Q8—92no—
373C2×Q8—181no—
374C2×Q8—181no—
375C2×Q8—181no—
376C2×D4—62no—
377C2×D4—61no—
378C2×D4—92no—
379C2×D4—98no—
380C2×D4—92no—
381C2×D4—182no—
382C2×D4—181no—
383C2×D4—181no—
384C2×D4—181no—
385C2×D4—184no—
386C22×C4—62no—
387C22×C4—92no—
388C22×C4—98no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—92no—
393C22×C4—92no—
394C22×C4—92no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—92no—
398C22×C4—184no—
399C22×C4—182no—
400C22×C4GO+(4,𝔽2)11yescharacteristic
401M16—64no—
402M16—94no—
403M16—94no—
404M16—182no—
405M16—182no—
406M16—184no—
407C2×C8—62no—
408C2×C8—184no—
409C2×C8—184no—
410C2×C8—182no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—64no—
418C22×C3—124no—
419C2×D3—24no—
420C2×D3—44no—
421C2×D3—61no—
422C2×D3—61no—
423C2×D3—62no—
424C2×D3—62no—
425C2×D3—61no—
426C2×D3—61no—
427C2×D3—64no—
428C2×D3—64no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—128no—
432C2×D3—128no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—21no—
443C3×C4—64no—
444Dic3—24no—
445Dic3—61no—
446Dic3—61no—
447Dic3—62no—
448Dic3—62no—
449Dic3—61no—
450Dic3—61no—
451C32C2×#41311yescharacteristic, complemented, Sylow
452C23—62no—
453C23—94no—
454C23—91no—
455C23—91no—
456C23—92no—
457C23—92no—
458C23—182no—
459C23—362no—
460C23—364no—
461C23D32⋊C411yescharacteristic
462Q8—62no—
463Q8—62no—
464Q8—182no—
465Q8—182no—
466D4—68no—
467D4—62no—
468D4—62no—
469D4—188no—
470D4—182no—
471D4—182no—
472C2×C4—62no—
473C2×C4—68no—
474C2×C4—94no—
475C2×C4—92no—
476C2×C4—92no—
477C2×C4—91no—
478C2×C4—91no—
479C2×C4—92no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—91no—
483C2×C4—92no—
484C2×C4—92no—
485C2×C4—92no—
486C2×C4—91no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—182no—
490C2×C4—188no—
491C2×C4D32⋊C412yes—
492C2×C4D32⋊C411yescharacteristic
493C2×C4C2×GO+(4,𝔽2)12yes—
494C2×C4C2×GO+(4,𝔽2)11yescharacteristic
495C8—64no—
496C8—184no—
497C2×C3—22no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—42no—
502C2×C3—42no—
503C2×C3—124no—
504D3—44no—
505D3—62no—
506D3—62no—
507D3—64no—
508D3—121no—
509D3—121no—
510D3—122no—
511C22—22no—
512C22—64no—
513C22—91no—
514C22—91no—
515C22—92no—
516C22—124no—
517C22—182no—
518C22—182no—
519C22—362no—
520C22—362no—
521C22—364no—
522C22—364no—
523C22C2×D32⋊C412yes—
524C22C2×D32⋊C411yescharacteristic
525C4—64no—
526C4—91no—
527C4—92no—
528C4—91no—
529C4C2×D32⋊C412yes—
530C4C2×D32⋊C411yescharacteristic
531C4C22×GO+(4,𝔽2)11yescharacteristic
532C3—21no—
533C3—21no—
534C2—22no—
535C2—124no—
536C2—181no—
537C2—181no—
538C2—182no—
539C2#1059331312yesdirect product factor
540C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊D3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#413
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3788C2semidirect
3. C2×#63818C2semidirect
4. C2×#63728C2semidirect
5. #10593313C2direct (N × H)
6. C2×#63727C2semidirect
24. C2×#3788C22semidirect
28. #63818C22semidirect
30. #63728C22semidirect
31. #63727C22semidirect
354. C2×C32#413semidirect
451. C32C2×#413semidirect
539. C2#10593313direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C22×#37882
C2×#638182
C2×#637282
#105933132
C2×#637272
C2×#4139