Finite Group Databasebeta

← C4×#1007⋊C3 #11923185

Subgroups — C4×#1007⋊C3 #11923185

Order 1152.

779 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 779 conjugacy classes of subgroups — too many to draw. Only its 115 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×#1007⋊C3C211yesmaximal, characteristic
2C2×C3×C4×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3#5812⋊C3C211yesmaximal, characteristic, complemented
4#5572⋊C3C211yesmaximal, characteristic, complemented
5C4×D3×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
6#5574⋊C3C211yesmaximal, characteristic, complemented
7C4×C3⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
8C4×#1007C311yesmaximal, characteristic, complemented
9C4×2−1+4⋊C3—31nomaximal
10C22×C3×SL(2,𝔽3)C2211yescharacteristic
11#1007⋊C3C414yesdirect product factor
12C2×D3×SL(2,𝔽3)C2211yescharacteristic
13C2×C3⋊(#41⋊C3)C2211yescharacteristic
14C3×C4×#67—41nomaximal
15C3×C4×SL(2,𝔽3)C2211yescharacteristic
16C3×C4×SL(2,𝔽3)C2211yescharacteristic
17Dic3×SL(2,𝔽3)C2211yescharacteristic
18Dic3×SL(2,𝔽3)C2211yescharacteristic
19C2×#1007C2×C311yescharacteristic
20C2×2−1+4⋊C3—31no—
21C2×C3×C4×Q8C2×C311yescharacteristic, complemented
22#5812C2×C311yescharacteristic, complemented
23#5574—31no—
24#5574C2×C311yescharacteristic, complemented
25C4×#239—31no—
26C4×#239C2×C311yescharacteristic, complemented
27#5572—31no—
28#5572C2×C311yescharacteristic, complemented
29C4×D3×Q8—31no—
30C4×D3×Q8C2×C311yescharacteristic, complemented
31#5504—31no—
32#5504—31no—
33C4×#235—31no—
34C4×#235—31no—
35#520⋊C3—31no—
36#519⋊C3—31no—
37#519⋊C3—31no—
38C4×#41⋊C3—31no—
39C2×C4×SL(2,𝔽3)—21no—
40C2×C4×SL(2,𝔽3)—31no—
41C2×C4×SL(2,𝔽3)D311yescharacteristic, complemented
42C22×C32×C4—41no—
43C2×C3×#67—41no—
44C2×C3×C4×D3—41no—
45C2×C3×SL(2,𝔽3)C2×C412yescomplemented
46C2×C3×SL(2,𝔽3)C2311yescharacteristic
47D3×SL(2,𝔽3)C2×C412yescomplemented
48C3⋊(#41⋊C3)C2×C412yescomplemented
49C3×#217—41no—
50C3×(C2×D3)⋊C4—41no—
51C3×Dic3⋊C4—41no—
52C3×C4×Dic3—41no—
53C4×2−1+4—31noSylow
54C22×C3×Q8C22×C311yescharacteristic
55#1007—34no—
56#1007C3×C414yescomplemented
57C2×#239—31no—
58C2×#239C22×C311yescharacteristic
59C2×D3×Q8—31no—
60C2×D3×Q8C22×C311yescharacteristic
61C2×#235—31no—
62C2×#235—31no—
632−1+4⋊C3—34no—
64C2×#41⋊C3—31no—
65C22×SL(2,𝔽3)—21no—
66C22×SL(2,𝔽3)—31no—
67C22×SL(2,𝔽3)C2×D311yescharacteristic
68C3×C4×Q8—31no—
69C3×C4×Q8—31no—
70C3×C4×Q8C22×C311yescharacteristic
71C3×C4×Q8C22×C311yescharacteristic
72C3×C4×D4—121no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C42—31no—
75Q8×Dic3—31no—
76Q8×Dic3—31no—
77Q8×Dic3C22×C311yescharacteristic
78Q8×Dic3C22×C311yescharacteristic
79C4×#67—32no—
80C4×#67—31no—
81C4×#67—31no—
82C4×#67—31no—
83C4×#67A411yescharacteristic
84#926—31no—
85#926—31no—
86#893—32no—
87#893—31no—
88#893—31no—
89#892—32no—
90#892—31no—
91#892—31no—
92D3×C4⋊C4—31no—
93D3×C4⋊C4—32no—
94D3×C4⋊C4—31no—
95#887—32no—
96#887—31no—
97#887—31no—
98C4×D12—31no—
99C4×D12—31no—
100C4×D12—31no—
101C4×D12—31no—
102#872—32no—
103#872—31no—
104#872—31no—
105C42×D3—32no—
106C42×D3—31no—
107C42×D3—31no—
108C4×Dic6—31no—
109C4×Dic6—31no—
110C4×Dic6—31no—
111C4×Dic6—31no—
112C4×SL(2,𝔽3)—21no—
113C4×SL(2,𝔽3)—21no—
114C4×SL(2,𝔽3)—31no—
115C4×SL(2,𝔽3)—31no—
116C4×SL(2,𝔽3)C2×D311yescharacteristic
117C4×SL(2,𝔽3)C2×D311yescharacteristic
118C23×C32—41no—
119C22×C3×D3—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—82no—
123C3×#67—44no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C3×C4×D3—82no—
128C3×SL(2,𝔽3)C22×C411yescharacteristic
129C2×2−1+4—31no—
130#520—31no—
131#520—91no—
132#520—91no—
133#520—91no—
134#519—31no—
135#519—31no—
136#519—91no—
137C4×#41—31no—
138C4×#41—91no—
139C4×#41—91no—
140C4×#41—91no—
141C2×C4×Q8—31no—
142C2×C4×Q8—91no—
143C2×C4×Q8C3×D311yescharacteristic, complemented
144C2×C3×Q8—31no—
145C2×C3×Q8—32no—
146C2×C3×Q8C2×C3×C412yescomplemented
147C2×C3×Q8C23×C311yescharacteristic
148C2×C3×D4—121no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—41no—
152C22×C3×C4—81no—
153C22×C3×C4—121no—
154C22×C3×C4C2×A411yescharacteristic
155C2×#67—31no—
156C2×#67C2×A411yescharacteristic
157#239—34no—
158#239—34no—
159#239—32no—
160#239C2×C3×C412yescomplemented
161D3×Q8—34no—
162D3×Q8—32no—
163D3×Q8—34no—
164D3×Q8C2×C3×C412yescomplemented
165#235—34no—
166#235—34no—
167#235—34no—
168#235—34no—
169C2×D12—31no—
170C2×D12—31no—
171C2×C4×D3—32no—
172C2×C4×D3—31no—
173C2×C4×D3—31no—
174C2×C4×D3—31no—
175C2×C4×D3—32no—
176C2×C4×D3—31no—
177C2×C4×D3—31no—
178C2×C4×D3C2×A411yescharacteristic
179C2×Dic6—31no—
180C2×Dic6—31no—
181#41⋊C3—32no—
182C2×SL(2,𝔽3)—22no—
183C2×SL(2,𝔽3)—21no—
184C2×SL(2,𝔽3)—32no—
185C2×SL(2,𝔽3)C4×D312yescomplemented
186C2×SL(2,𝔽3)C22×D311yescharacteristic
187C3×C4⋊C4—31no—
188C3×C4⋊C4—31no—
189C3×C4⋊C4—32no—
190C3×C4⋊C4—121no—
191C3×C22⋊C4—121no—
192C3×C22⋊C4—121no—
193C3×C42—31no—
194C3×C42—31no—
195C3×C42—31no—
196C3×C42—31no—
197C3×C42—121no—
198#217—31no—
199#217C2×A411yescharacteristic
200(C2×D3)⋊C4—32no—
201(C2×D3)⋊C4—31no—
202(C2×D3)⋊C4—31no—
203(C2×D3)⋊C4—31no—
204(C2×D3)⋊C4C2×A411yescharacteristic
205C4⋊Dic3—31no—
206C4⋊Dic3—31no—
207C4⋊Dic3—31no—
208C4⋊Dic3—31no—
209Dic3⋊C4—32no—
210Dic3⋊C4—31no—
211Dic3⋊C4—31no—
212Dic3⋊C4—31no—
213Dic3⋊C4C2×A411yescharacteristic
214C4×Dic3—32no—
215C4×Dic3—32no—
216C4×Dic3—31no—
217C4×Dic3—31no—
218C4×Dic3—31no—
219C4×Dic3—31no—
220C4×Dic3—31no—
221C4×Dic3C2×A411yescharacteristic
222C22×C32—42no—
223C22×C32—41no—
224C22×C32—81no—
225C22×C32—81no—
226C2×C3×D3—42no—
227C2×C3×D3—81no—
228C2×C3×D3—81no—
229C32×C4—42no—
230C32×C4—81no—
231C3×Dic3—42no—
232C3×Dic3—81no—
233C3×Dic3—81no—
2342−1+4—34no—
2352−1+4—94no—
236C2×#41—31no—
237C2×#41—91no—
238C2×#41—91no—
239C2×#41—91no—
240C22×Q8—31no—
241C22×Q8—91no—
242C22×Q8C2×C3×D311yescharacteristic
243C4×Q8—31no—
244C4×Q8—31no—
245C4×Q8—31no—
246C4×Q8—31no—
247C4×Q8—91no—
248C4×Q8—91no—
249C4×Q8—91no—
250C4×Q8—91no—
251C4×Q8—92no—
252C4×Q8—91no—
253C4×Q8—91no—
254C4×Q8—91no—
255C4×Q8—91no—
256C4×Q8C2×C3×D311yescharacteristic
257C4×Q8C2×C3×D311yescharacteristic
258C4×D4—31no—
259C4×D4—91no—
260C4×D4—91no—
261C4×D4—91no—
262C4×D4—91no—
263C4×D4—91no—
264C4×D4—92no—
265C4×D4—91no—
266C4×D4—91no—
267C4×D4—92no—
268C4×D4—91no—
269C4×D4—91no—
270#117—91no—
271#117—91no—
272#117—92no—
273#117—91no—
274#117—92no—
275#117—91no—
276#117—91no—
277#117—91no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—92no—
281C2×C4⋊C4—91no—
282C2×C42—31no—
283C2×C42—91no—
284C2×C42—91no—
285C2×C42—92no—
286C23×C3—41no—
287C23×C3—81no—
288C23×C3—121no—
289C23×C3C22×A411yescharacteristic
290C22×D3—31no—
291C22×D3C22×A411yescharacteristic
292C3×Q8—32no—
293C3×Q8—31no—
294C3×Q8—32no—
295C3×Q8C22×C3×C411yescharacteristic
296C3×D4—124no—
297C2×C3×C4—22no—
298C2×C3×C4—32no—
299C2×C3×C4—32no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—31no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—82no—
307C2×C3×C4—84no—
308C2×C3×C4—81no—
309C2×C3×C4—81no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—242no—
315C2×C3×C4C22×A411yescharacteristic
316C2×C3×C4C22×A411yescharacteristic
317#67—34no—
318#67C4×A414yes—
319C2×Dic3—31no—
320C2×Dic3—31no—
321C2×Dic3—31no—
322C2×Dic3C22×A411yescharacteristic
323C2×Dic3C22×A411yescharacteristic
324C2×Dic3C22×A411yescharacteristic
325D12—32no—
326D12—32no—
327D12—34no—
328C4×D3—22no—
329C4×D3—38no—
330C4×D3—32no—
331C4×D3—32no—
332C4×D3—32no—
333C4×D3—32no—
334C4×D3—62no—
335C4×D3—121no—
336C4×D3—121no—
337C4×D3—122no—
338Dic6—32no—
339Dic6—34no—
340Dic6—32no—
341SL(2,𝔽3)—21no—
342SL(2,𝔽3)C2×C4×D311yescharacteristic
343C2×C32—41no—
344C2×C32—41no—
345C2×C32—41no—
346C2×C32—82no—
347C3×D3—82no—
348#41—32no—
349#41—94no—
350#41—94no—
351#41—94no—
352#41—94no—
353#41—94no—
354#41—94no—
355#41—92no—
356C2×Q8—31no—
357C2×Q8—32no—
358C2×Q8—32no—
359C2×Q8—91no—
360C2×Q8—91no—
361C2×Q8—94no—
362C2×Q8—94no—
363C2×Q8—92no—
364C2×Q8C3×C4×D312yescomplemented
365C2×Q8C22×C3×D311yescharacteristic
366C2×D4—31no—
367C2×D4—91no—
368C2×D4—91no—
369C2×D4—91no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—31no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—92no—
377C22×C4—91no—
378C22×C4—92no—
379C22×C4—91no—
380C22×C4D3×A411yescharacteristic
381C4⋊C4—31no—
382C4⋊C4—31no—
383C4⋊C4—32no—
384C4⋊C4—31no—
385C4⋊C4—91no—
386C4⋊C4—91no—
387C4⋊C4—91no—
388C4⋊C4—91no—
389C4⋊C4—91no—
390C4⋊C4—91no—
391C4⋊C4—92no—
392C4⋊C4—91no—
393C22⋊C4—31no—
394C22⋊C4—31no—
395C22⋊C4—91no—
396C22⋊C4—91no—
397C22⋊C4—92no—
398C22⋊C4—91no—
399C22⋊C4—91no—
400C42—31no—
401C42—31no—
402C42—31no—
403C42—31no—
404C42—31no—
405C42—91no—
406C42—91no—
407C42—91no—
408C42—91no—
409C42—92no—
410C42—92no—
411C42—91no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—81no—
417C22×C3—81no—
418C22×C3—82no—
419C22×C3—82no—
420C22×C3—82no—
421C22×C3—81no—
422C22×C3—122no—
423C22×C3—241no—
424C22×C3—241no—
425C22×C3C2×C4×A412yes—
426C22×C3C23×A411yescharacteristic
427C2×D3—21no—
428C2×D3—21no—
429C2×D3—32no—
430C2×D3—61no—
431C2×D3—61no—
432C2×D3C2×C4×A412yes—
433C3×C4—21no—
434C3×C4—31no—
435C3×C4—32no—
436C3×C4—31no—
437C3×C4—42no—
438C3×C4—61no—
439C3×C4—61no—
440C3×C4—81no—
441C3×C4—82no—
442C3×C4—82no—
443C3×C4—122no—
444C3×C4—241no—
445C3×C4—241no—
446C3×C42−1+4⋊C312yescomplemented
447Dic3—21no—
448Dic3—21no—
449Dic3—32no—
450Dic3—61no—
451Dic3—61no—
452Dic3C2×C4×A412yes—
453C32—41noSylow
454C23—31no—
455C23—91no—
456C23C2×D3×A411yescharacteristic
457Q8—32no—
458Q8—31no—
459Q8—32no—
460Q8—94no—
461Q8—92no—
462Q8—92no—
463Q8C2×C3×C4×D311yescharacteristic
464D4—34no—
465D4—94no—
466D4—92no—
467D4—92no—
468D4—94no—
469C2×C4—22no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—31no—
473C2×C4—31no—
474C2×C4—31no—
475C2×C4—31no—
476C2×C4—31no—
477C2×C4—31no—
478C2×C4—31no—
479C2×C4—62no—
480C2×C4—92no—
481C2×C4—92no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—98no—
485C2×C4—91no—
486C2×C4—91no—
487C2×C4—91no—
488C2×C4—121no—
489C2×C4—182no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4—362no—
493C2×C4C2×D3×A411yescharacteristic
494C2×C4C2×D3×A411yescharacteristic
495C2×C3—22no—
496C2×C3—41no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3—82no—
500C2×C3—84no—
501C2×C3—81no—
502C2×C3—81no—
503C2×C3—81no—
504C2×C3—242no—
505C2×C3C22×C4×A411yescharacteristic
506C2×C3C2×2−1+4⋊C311yescharacteristic
507C2×C3#594511yescharacteristic
508D3—22no—
509D3—62no—
510C22—21no—
511C22—21no—
512C22—32no—
513C22—61no—
514C22—61no—
515C22—92no—
516C22—181no—
517C22—181no—
518C22C4×D3×A412yes—
519C22C22×D3×A411yescharacteristic
520C4—21no—
521C4—31no—
522C4—32no—
523C4—31no—
524C4—32no—
525C4—61no—
526C4—61no—
527C4—61no—
528C4—61no—
529C4—92no—
530C4—181no—
531C4—181no—
532C4#1007⋊C312yesdirect product factor
533C3—41no—
534C3—81no—
535C3C4×2−1+4⋊C311yescharacteristic, complemented
536C2—22no—
537C2—62no—
538C2—182no—
539C2C2×C4×D3×A411yescharacteristic
540C2C2×#1007⋊C311yescharacteristic
541C2#5964⋊C311yescharacteristic
subgroupG/H
centerC2×C4C2×D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FrattiniC22C22×D3×A4
FittingC2×C3×C4×Q8C2×C3
socleC22×C3C23×A4
prime radicalC2×#1007⋊C3C2
cosocleC2×C3×Q8C23×C3
hypercenterC22×C4D3×A4
LCSG ▷ C3×Q8
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×SL(2,𝔽3)C2semidirect
3. #5812⋊C3C2semidirect
4. #5572⋊C3C2semidirect
5. C4×D3×SL(2,𝔽3)C2semidirect
6. #5574⋊C3C2semidirect
7. C4×C3⋊(#41⋊C3)C2semidirect
8. C4×#1007C3semidirect
11. #1007⋊C3C4direct (N × H)
21. C2×C3×C4×Q8C2×C3semidirect
22. #5812C2×C3semidirect
24. #5574C2×C3semidirect
26. C4×#239C2×C3semidirect
28. #5572C2×C3semidirect
30. C4×D3×Q8C2×C3semidirect
41. C2×C4×SL(2,𝔽3)D3semidirect
45. C2×C3×SL(2,𝔽3)C2×C4semidirect
47. D3×SL(2,𝔽3)C2×C4semidirect
48. C3⋊(#41⋊C3)C2×C4semidirect
56. #1007C3×C4semidirect
143. C2×C4×Q8C3×D3semidirect
146. C2×C3×Q8C2×C3×C4semidirect
160. #239C2×C3×C4semidirect
164. D3×Q8C2×C3×C4semidirect
185. C2×SL(2,𝔽3)C4×D3semidirect
364. C2×Q8C3×C4×D3semidirect
446. C3×C42−1+4⋊C3semidirect
532. C4#1007⋊C3direct (N × H)
535. C3C4×2−1+4⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#1007⋊C32
C2×C3×C4×SL(2,𝔽3)2
#5812⋊C32
#5572⋊C32
C4×D3×SL(2,𝔽3)2
#5574⋊C32
C4×C3⋊(#41⋊C3)2
C4×#10073
C4×2−1+4⋊C33
C3×C4×#674