Finite Group Databasebeta

← C3×#70346 #11792191

Subgroups — C3×#70346 #11792191

Order 1152.

799 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3C3×#5526C211yesmaximal, characteristic
4C32×#419C211yesmaximal, characteristic, complemented
5C2×C3×#825C211yesmaximal, characteristic
6C2×C3×#824C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#2005—31nomaximal
9#70346C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C3×#944—22no—
16C3×#944—22no—
17C2×C3×#216—21no—
18C3×#942—22no—
19C3×#942—22no—
20C2×C3×#215—21no—
21C2×C3×Dic3⋊C4—22no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C3×#897—22no—
25C3×#886—22no—
26C3×#875—21no—
27C3×#869—21no—
28C32×#103—22no—
29C3×#825—22no—
30C3×#824—22no—
31C2×C3×#137—31no—
32C3×#536—31no—
33C2×C3×C4⋊Q8—31no—
34C2×#944C2×C311yescharacteristic, complemented
35C2×#942C2×C311yescharacteristic
36#5526C2×C311yescharacteristic
37C2×C3×#104—31no—
38C3×#419—21no—
39C3×#419D311yescharacteristic, complemented
40C3×#419C2×C311yescharacteristic, complemented
41C2×C3×#101—31no—
42C2×#825C2×C311yescharacteristic
43C2×#824C2×C311yescharacteristic, complemented
44C3×#339—31no—
45#4532C2×C311yescharacteristic, complemented
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8D412yes—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D412yes—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6D411yescharacteristic
70C32×M16—21no—
71C32×M16—21no—
72C2×C32×C8—21no—
73C32×C4⋊C4D412yes—
74C32×C22⋊C4—21no—
75C32×C42—21no—
76C3×#216—24no—
77C3×#215—24no—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3—24no—
80C3×Dic3⋊C4—28no—
81C3×C4×Dic3—21no—
82C3×C4×Dic3D412yes—
83C3×#208—21no—
84C3×#208D412yes—
85C2×C3×C3⋊C8—21no—
86#2005—31noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—21no—
89C22×C3×Q8—31no—
90C22×C3×Q8C2×D311yescharacteristic
91C22×C3×Q8C22×C311yescharacteristic
92C2×#235C22×C311yescharacteristic
93C22×Dic6C22×C311yescharacteristic
94C3×#137—62no—
95C3×#137—62no—
96C2×C3×Q16—61no—
97C2×C3×SD16—61no—
98C2×C3×M16—21no—
99C2×C3×M16—31no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C22×C311yescharacteristic
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×C4⋊Q8—62no—
105C3×#124—61no—
106C3×#123—62no—
107C3×C22⋊Q8—62no—
108C3×#117—21no—
109C3×#117C2×D311yescharacteristic
110C3×#117C22×C311yescharacteristic
111C2×C3×C4⋊C4—62no—
112C2×C3×C42—31no—
113#944—22no—
114#944—22no—
115C2×#216—21no—
116#942—22no—
117#942—22no—
118C2×#215—21no—
119C2×Dic3⋊C4—22no—
120C2×C4×Dic3C22×C311yescharacteristic
121C2×#208C22×C311yescharacteristic
122#897—22no—
123#886—22no—
124#875—21no—
125#869—21no—
126C3×#104—62no—
127C3×#103—24no—
128C3×#103—22no—
129C3×#103—22no—
130C3×#101—62no—
131#825—22no—
132#824—22no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C32×Q8—22no—
136C32×Q8—22no—
137C32×Q8—41no—
138C32×Q8—41no—
139C2×C32×C4—22no—
140C2×C32×C4—22no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C3×#67—41no—
150C3×#67—41no—
151C2×C3×Dic3—24no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—21no—
162C3×Dic6—21no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C32×C8—41no—
168C3×C3⋊C8—22no—
169C2×#137—31no—
170#536—31no—
171C2×C4⋊Q8—31no—
172C2×#104—31no—
173#419C3×D311yescharacteristic, complemented
174C2×#101—31no—
175#339—31no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—21no—
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—22no—
193C2×C3×Q8—31no—
194C2×C3×Q8—41no—
195C2×C3×Q8—41no—
196C2×C3×Q8—41no—
197C2×C3×Q8—61no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×Q8D1212yes—
204C2×C3×Q8C3×D412yes—
205C2×C3×D4—31no—
206C2×C3×D4—61no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—32no—
211C22×C3×C4—41no—
212C22×C3×C4—61no—
213C22×C3×C4—61no—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C23×C311yescharacteristic
216C2×#67—21no—
217C22×Dic3—21no—
218C22×Dic3C3×D412yes—
219#235—21no—
220#235—21no—
221#235—21no—
222#235—21no—
223C2×D12C3×D411yescharacteristic
224C2×C4×D3—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6—21no—
231C2×Dic6C3×D411yescharacteristic
232C3×Q16—64no—
233C3×SD16—64no—
234C3×M16—21no—
235C3×M16—21no—
236C3×M16—21no—
237C3×M16—21no—
238C3×M16—32no—
239C3×M16—41no—
240C3×M16—41no—
241C3×M16—61no—
242C2×C3×C8—22no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—61no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—68no—
248C3×C4⋊C4—64no—
249C3×C4⋊C4#6712yes—
250C3×C4⋊C4C3×D412yes—
251C3×C22⋊C4—21no—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—41no—
254C3×C22⋊C4—64no—
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—32no—
258C3×C42—41no—
259C3×C42—61no—
260#216—24no—
261#215—24no—
262(C2×D3)⋊C4—24no—
263C4⋊Dic3—24no—
264Dic3⋊C4—28no—
265C4×Dic3—21no—
266C4×Dic3C3×D412yes—
267#208—21no—
268#208C3×D412yes—
269C2×C3⋊C8—21no—
270C22×C32—22no—
271C22×C32#12011yescharacteristic
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C2×C3×D3—41no—
275C2×C3×D3—42no—
276C32×C4—42no—
277C32×C4—42no—
278C32×C4#12011yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12711yescharacteristic
282C3×Dic3—24no—
283C3×Dic3—41no—
284C3×Dic3—42no—
285C2×#41—31no—
286C22×Q8—31no—
287C22×Q8C2×C3×D311yescharacteristic
288#137—62no—
289#137—62no—
290C2×Q16—61no—
291C2×SD16—61no—
292C2×M16—31no—
293C2×M16C2×C3×D311yescharacteristic
294C4⋊Q8—61no—
295C4⋊Q8—62no—
296C4⋊Q8—62no—
297#124—61no—
298#123—62no—
299C22⋊Q8—62no—
300#117C2×C3×D311yescharacteristic
301C2×C4⋊C4—62no—
302C2×C42—31no—
303#104—62no—
304#103—22no—
305#101—62no—
306C23×C3—21no—
307C23×C3—61no—
308C23×C3D3×D411yescharacteristic
309C23×C3C2×C3×D411yescharacteristic
310C22×D3—21no—
311C3×Q8—24no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—42no—
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—41no—
320C3×Q8—41no—
321C3×Q8—41no—
322C3×Q8—41no—
323C3×Q8—61no—
324C3×Q8—61no—
325C3×Q8—121no—
326C3×Q8—121no—
327C3×Q8—121no—
328C3×Q8—121no—
329C3×D4—61no—
330C3×D4—61no—
331C3×D4—121no—
332C3×D4—121no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—64no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—121no—
358C2×C3×C4—121no—
359C2×C3×C4C2×D1211yescharacteristic
360C2×C3×C4#23511yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C3×#4111yescharacteristic
371#67—41no—
372#67—41no—
373C2×Dic3—24no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379D12—21no—
380D12—21no—
381C4×D3—41no—
382C4×D3—41no—
383Dic6—21no—
384Dic6—21no—
385Dic6—41no—
386Dic6—41no—
387Dic6—41no—
388Dic6—41no—
389C3×C8—42no—
390C3×C8—41no—
391C3×C8—41no—
392C3×C8—62no—
393C3⋊C8—22no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32#39211yescharacteristic
397C2×C32#45612yes—
398C3×D3—81no—
399#41—61no—
400#41—61no—
401#41—61no—
402#41—61no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—31no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8C3×D1212yes—
416C2×D4—31no—
417C2×D4—61no—
418C22×C4—21no—
419C22×C4—32no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4C22×C3×D311yescharacteristic
423Q16—64no—
424SD16—64no—
425M16—21no—
426M16—21no—
427M16—32no—
428M16—61no—
429C2×C8—21no—
430C2×C8—61no—
431C4⋊C4—68no—
432C4⋊C4—64no—
433C4⋊C4C3×#6712yes—
434C22⋊C4—21no—
435C22⋊C4—64no—
436C42—21no—
437C42—32no—
438C42—61no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—42no—
445C22×C3—122no—
446C22×C3—121no—
447C22×C3#88211yescharacteristic
448C22×C3#88411yescharacteristic
449C22×C3#93711yescharacteristic
450C22×C3C3×#12011yescharacteristic
451C22×C3C3×#12011yescharacteristic
452C22×C3C3×#12111yescharacteristic
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—44no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—64no—
465C3×C4—82no—
466C3×C4—122no—
467C3×C4—121no—
468C3×C4#88211yescharacteristic
469C3×C4#88411yescharacteristic
470C3×C4#93011yescharacteristic
471C3×C4#94011yescharacteristic
472C3×C4C3×#12011yescharacteristic
473C3×C4C3×#12111yescharacteristic
474C3×C4C3×#12111yescharacteristic
475C3×C4C3×#12711yescharacteristic
476Dic3—24no—
477Dic3—41no—
478Dic3—42no—
479C32#200511yescharacteristic, complemented, Sylow
480C23—61no—
481C23C3×D3×D411yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—61no—
487Q8—61no—
488Q8—121no—
489Q8—121no—
490Q8—121no—
491Q8—121no—
492D4—61no—
493D4—61no—
494D4—121no—
495D4—121no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—64no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4C2×C3×D1211yescharacteristic
509C2×C4C3×#23511yescharacteristic
510C2×C4C3×D3×D411yescharacteristic
511C2×C4C3×D3×D411yescharacteristic
512C2×C4C3×D3×D411yescharacteristic
513C2×C4C2×C3×#6711yescharacteristic
514C8—41no—
515C8—62no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—241no—
525C2×C3#496011yescharacteristic
526C2×C3#520512yes—
527C2×C3C3×#39211yescharacteristic
528C2×C3C3×#45612yes—
529D3—81no—
530C22—22no—
531C22—122no—
532C22—121no—
533C22C3×#88211yescharacteristic
534C22C3×#88411yescharacteristic
535C22C3×#93711yescharacteristic
536C4—42no—
537C4—42no—
538C4—64no—
539C4—122no—
540C4—121no—
541C4C3×#88211yescharacteristic
542C4C3×#88411yescharacteristic
543C4C3×#93011yescharacteristic
544C4C3×#94011yescharacteristic
545C3—21no—
546C3#7034611yescharacteristic, direct product factor
547C3C3×#200511yescharacteristic, complemented
548C2—21no—
549C2—21no—
550C2—241no—
551C2C3×#496011yescharacteristic
552C2C3×#520512yes—
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#419C2
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC3×#419D3
hypocenterC3C3×#2005
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
1. C2×C3×#944C2semidirect
4. C32×#419C2semidirect
6. C2×C3×#824C2semidirect
7. C3×#4532C2semidirect
9. #70346C3direct (N × H)
34. C2×#944C2×C3semidirect
39. C3×#419D3semidirect
40. C3×#419C2×C3semidirect
43. C2×#824C2×C3semidirect
45. #4532C2×C3semidirect
173. #419C3×D3semidirect
479. C32#2005semidirect
546. C3#70346direct (N × H)
547. C3C3×#2005semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9442
C2×C3×#9422
C3×#55262
C32×#4192
C2×C3×#8252
C2×C3×#8242
C3×#45322
C3×#20053
#703463