Finite Group Databasebeta

← C3×#71795 #11792188

Subgroups — C3×#71795 #11792188

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×#5816C211yesmaximal, characteristic
3C2×C3×#942C211yesmaximal, characteristic
4C2×C3×#836C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6C2×C3×#805C211yesmaximal, characteristic
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#2005—31nomaximal
9#71795C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C32×C4⋊Q8—22no—
14C32×C4⋊Q8—22no—
15C2×C32×C4⋊C4—22no—
16C2×C32×C42C2211yescharacteristic
17C3×#947—21no—
18C3×#946—22no—
19C3×#944—21no—
20C2×C3×#216—21no—
21C3×#942—22no—
22C3×#942—22no—
23C2×C3×#215—21no—
24C3×#929—22no—
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C3×#836—22no—
29C3×#835—22no—
30C3×#805—22no—
31C2×C3×#137—31no—
32C3×#536—31no—
33C2×C3×C4⋊Q8—21no—
34C2×C3×C4⋊Q8D311yescharacteristic, complemented
35C2×C3×C4⋊Q8C2×C311yescharacteristic, complemented
36#5816C2×C311yescharacteristic
37C2×#942C2×C311yescharacteristic
38C2×C3×#104—31no—
39C3×#419—31no—
40C2×C3×#101—31no—
41C2×#836C2×C311yescharacteristic, complemented
42#5225C2×C311yescharacteristic, complemented
43C2×#805C2×C311yescharacteristic
44C3×#339—31no—
45#4523C2×C311yescharacteristic, complemented
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—21no—
57C2×C32×Q8D412yes—
58C22×C32×C4—21no—
59C22×C32×C4—21no—
60C22×C32×C4D412yes—
61C22×C32×C4C2311yescharacteristic
62C2×C3×#67—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235—21no—
67C2×C3×D12D411yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6D411yescharacteristic
70C32×C4⋊C4—28no—
71C32×C42—21no—
72C32×C42D412yes—
73C3×#217—21no—
74C3×#216—24no—
75C3×#215—24no—
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3D412yes—
78C3×Dic3⋊C4—24no—
79C3×C4×Dic3—21no—
80C3×#208—21no—
81C3×#208—21no—
82C3×#208—21no—
83C3×#208D412yes—
84C2×C3×C3⋊C8—21no—
85C2×C3×C3⋊C8—21no—
86#2005—31noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—21no—
89C22×C3×Q8—21no—
90C22×C3×Q8C2×D311yescharacteristic
91C22×C3×Q8C2×D311yescharacteristic
92C22×C3×Q8C22×C311yescharacteristic
93C22×C3×Q8C22×C311yescharacteristic
94C2×#235C22×C311yescharacteristic
95C3×#137—62no—
96C3×#137—62no—
97C2×C3×Q16—61no—
98C2×C3×SD16—61no—
99C2×C3×M16—31no—
100C2×C3×M16—31no—
101C3×C4⋊Q8—24no—
102C3×C4⋊Q8—24no—
103C3×C4⋊Q8—22no—
104C3×C4⋊Q8—22no—
105C3×C4⋊Q8—22no—
106C3×C4⋊Q8—22no—
107C3×C4⋊Q8—61no—
108C3×#124—61no—
109C3×#123—62no—
110C3×C22⋊Q8—62no—
111C3×#117—31no—
112C2×C3×C4⋊C4—24no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C42—21no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C22×C311yescharacteristic
118#947—21no—
119#946—22no—
120#944—21no—
121C2×#216—21no—
122#942—22no—
123#942—22no—
124C2×#215—21no—
125#929—22no—
126#926C22×C311yescharacteristic
127C2×#208C22×C311yescharacteristic
128C2×#208C22×C311yescharacteristic
129C3×#104—62no—
130C3×#103—62no—
131C3×#101—62no—
132#836—22no—
133#835—22no—
134#805—22no—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—21no—
137C32×Q8—22no—
138C32×Q8—22no—
139C32×Q8—41no—
140C32×Q8—41no—
141C32×Q8—41no—
142C32×Q8—41no—
143C32×Q8—41no—
144C32×Q8—41no—
145C2×C32×C4—24no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—41no—
152C2×C32×C4—41no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4#4111yescharacteristic
159C3×#67—41no—
160C3×#67—41no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C3×D12—21no—
164C3×D12—21no—
165C3×C4×D3—41no—
166C3×C4×D3—41no—
167C3×Dic6—21no—
168C3×Dic6—21no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—41no—
171C2×#137—31no—
172#536—31no—
173C2×C4⋊Q8C3×D311yescharacteristic, complemented
174C2×#104—31no—
175#419—31no—
176C2×#101—31no—
177#339—31no—
178C3×#41—61no—
179C3×#41—61no—
180C3×#41—61no—
181C3×#41—61no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—22no—
208C2×C3×Q8—31no—
209C2×C3×Q8—41no—
210C2×C3×Q8—41no—
211C2×C3×Q8—41no—
212C2×C3×Q8—41no—
213C2×C3×Q8—41no—
214C2×C3×Q8—41no—
215C2×C3×Q8—41no—
216C2×C3×Q8—41no—
217C2×C3×Q8#6712yes—
218C2×C3×Q8C3×D412yes—
219C2×C3×D4—31no—
220C2×C3×D4—61no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—61no—
230C22×C3×C4#6712yes—
231C22×C3×C4C3×D412yes—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C23×C311yescharacteristic
234C2×#67—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238#235—21no—
239C2×D12C3×D411yescharacteristic
240C2×C4×D3—21no—
241C2×Dic6C3×D411yescharacteristic
242C3×Q16—64no—
243C3×SD16—64no—
244C3×M16—32no—
245C3×M16—61no—
246C3×M16—61no—
247C3×M16—61no—
248C2×C3×C8—61no—
249C2×C3×C8—61no—
250C3×C4⋊C4—216no—
251C3×C4⋊C4—28no—
252C3×C4⋊C4—28no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—64no—
255C3×C22⋊C4—64no—
256C3×C22⋊C4—61no—
257C3×C42—22no—
258C3×C42—21no—
259C3×C42—21no—
260C3×C42—22no—
261C3×C42—61no—
262C3×C42#6712yes—
263C3×C42C3×D412yes—
264#217—21no—
265#216—24no—
266#215—24no—
267(C2×D3)⋊C4—24no—
268C4⋊Dic3C3×D412yes—
269Dic3⋊C4—24no—
270C4×Dic3—21no—
271#208—21no—
272#208—21no—
273#208—21no—
274#208C3×D412yes—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—21no—
277C22×C32—22no—
278C22×C32#12011yescharacteristic
279C22×C32#12011yescharacteristic
280C22×C32#12111yescharacteristic
281C2×C3×D3—41no—
282C2×C3×D3—42no—
283C32×C4—24no—
284C32×C4—42no—
285C32×C4—42no—
286C32×C4#12011yescharacteristic
287C32×C4#12111yescharacteristic
288C32×C4#12111yescharacteristic
289C32×C4#12711yescharacteristic
290C3×Dic3—41no—
291C3×Dic3—42no—
292C2×#41—31no—
293C22×Q8C2×C3×D311yescharacteristic
294C22×Q8C2×C3×D311yescharacteristic
295#137—62no—
296#137—62no—
297C2×Q16—61no—
298C2×SD16—61no—
299C2×M16—31no—
300C2×M16—31no—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—61no—
304#124—61no—
305#123—62no—
306C22⋊Q8—62no—
307#117—31no—
308C2×C4⋊C4—22no—
309C2×C42C2×C3×D311yescharacteristic
310#104—62no—
311#103—62no—
312#101—62no—
313C23×C3—21no—
314C23×C3—61no—
315C23×C3C2×#6711yescharacteristic
316C23×C3C2×C3×D411yescharacteristic
317C22×D3—21no—
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—42no—
323C3×Q8—42no—
324C3×Q8—42no—
325C3×Q8—42no—
326C3×Q8—42no—
327C3×Q8—42no—
328C3×Q8—42no—
329C3×Q8—42no—
330C3×Q8—41no—
331C3×Q8—41no—
332C3×Q8—41no—
333C3×Q8—41no—
334C3×Q8—41no—
335C3×Q8—41no—
336C3×Q8—41no—
337C3×Q8—41no—
338C3×Q8—41no—
339C3×Q8—41no—
340C3×Q8—41no—
341C3×Q8—41no—
342C3×Q8—61no—
343C3×Q8—61no—
344C3×D4—61no—
345C3×D4—61no—
346C3×D4—121no—
347C3×D4—121no—
348C2×C3×C4—24no—
349C2×C3×C4—28no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4—121no—
381C2×C3×C4—121no—
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23711yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C2×C3×D411yescharacteristic
389C2×C3×C4C2×C3×D411yescharacteristic
390C2×C3×C4C2×C3×D411yescharacteristic
391C2×C3×C4C2×C3×D411yescharacteristic
392C2×C3×C4C2×C3×D411yescharacteristic
393C2×C3×C4C3×#4111yescharacteristic
394#67—41no—
395#67—41no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398D12—21no—
399D12—21no—
400C4×D3—41no—
401C4×D3—41no—
402Dic6—21no—
403Dic6—21no—
404C3×C8—62no—
405C3×C8—121no—
406C3⋊C8—22no—
407C3⋊C8—41no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32#39211yescharacteristic
411C2×C32#45612yes—
412C3×D3—81no—
413#41—61no—
414#41—61no—
415#41—61no—
416#41—61no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—31no—
429C2×Q8C3×#6712yes—
430C2×D4—31no—
431C2×D4—61no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—61no—
435C22×C4C3×#6712yes—
436C22×C4C22×C3×D311yescharacteristic
437Q16—64no—
438SD16—64no—
439M16—32no—
440M16—61no—
441M16—61no—
442M16—61no—
443C2×C8—61no—
444C2×C8—61no—
445C4⋊C4—28no—
446C4⋊C4—32no—
447C4⋊C4—64no—
448C22⋊C4—64no—
449C22⋊C4—61no—
450C42—21no—
451C42—61no—
452C42C3×#6712yes—
453C22×C3—24no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—121no—
460C22×C3—122no—
461C22×C3#93711yescharacteristic
462C22×C3#93911yescharacteristic
463C22×C3#95311yescharacteristic
464C22×C3C3×#12011yescharacteristic
465C22×C3C3×#12011yescharacteristic
466C22×C3C3×#12111yescharacteristic
467C2×D3—41no—
468C2×D3—42no—
469C3×C4—28no—
470C3×C4—24no—
471C3×C4—24no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—44no—
477C3×C4—44no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—42no—
481C3×C4—42no—
482C3×C4—121no—
483C3×C4—122no—
484C3×C4#93711yescharacteristic
485C3×C4#93811yescharacteristic
486C3×C4#93911yescharacteristic
487C3×C4#94011yescharacteristic
488C3×C4C3×#12011yescharacteristic
489C3×C4C3×#12111yescharacteristic
490C3×C4C3×#12111yescharacteristic
491C3×C4C3×#12711yescharacteristic
492Dic3—41no—
493Dic3—42no—
494C32#200511yescharacteristic, complemented, Sylow
495C23—61no—
496C23C2×C3×#6711yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—61no—
506Q8—61no—
507D4—61no—
508D4—61no—
509D4—121no—
510D4—121no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—62no—
520C2×C4—61no—
521C2×C4—121no—
522C2×C4—121no—
523C2×C4C3×D3×D411yescharacteristic
524C2×C4C3×D3×D411yescharacteristic
525C2×C4C3×D3×D411yescharacteristic
526C2×C4C3×#23711yescharacteristic
527C2×C4C2×C3×#6711yescharacteristic
528C2×C4C2×C3×#6711yescharacteristic
529C8—62no—
530C8—121no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—22no—
539C2×C3—241no—
540C2×C3#509512yes—
541C2×C3#522311yescharacteristic
542C2×C3C3×#39211yescharacteristic
543C2×C3C3×#45612yes—
544D3—81no—
545C22—22no—
546C22—121no—
547C22—122no—
548C22C3×#93711yescharacteristic
549C22C3×#93911yescharacteristic
550C22C3×#95311yescharacteristic
551C4—24no—
552C4—42no—
553C4—42no—
554C4—121no—
555C4—122no—
556C4C3×#93711yescharacteristic
557C4C3×#93811yescharacteristic
558C4C3×#93911yescharacteristic
559C4C3×#94011yescharacteristic
560C3—21no—
561C3#7179511yescharacteristic, direct product factor
562C3C3×#200511yescharacteristic, complemented
563C2—21no—
564C2—21no—
565C2—241no—
566C2C3×#509512yes—
567C2C3×#522311yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4⋊Q8C2
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C3×#2005
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4⋊Q8C2semidirect
4. C2×C3×#836C2semidirect
5. C3×#5225C2semidirect
7. C3×#4523C2semidirect
9. #71795C3direct (N × H)
34. C2×C3×C4⋊Q8D3semidirect
35. C2×C3×C4⋊Q8C2×C3semidirect
41. C2×#836C2×C3semidirect
42. #5225C2×C3semidirect
45. #4523C2×C3semidirect
173. C2×C4⋊Q8C3×D3semidirect
494. C32#2005semidirect
561. C3#71795direct (N × H)
562. C3C3×#2005semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Q82
C3×#58162
C2×C3×#9422
C2×C3×#8362
C3×#52252
C2×C3×#8052
C3×#45232
C3×#20053
#717953