Finite Group Databasebeta

← C3×#69689 #11792580

Subgroups — C3×#69689 #11792580

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#216C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×C3×#875C211yesmaximal, characteristic
4C32×#391C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic
7C3×#4524C211yesmaximal, characteristic, complemented
8C3×#2015—31nomaximal
9#69689C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C3×#216—22no—
16C2×C3×#216—22no—
17C2×C3×#216—22no—
18C2×C3×#215—22no—
19C2×C3×#215—22no—
20C2×C3×#215—22no—
21C2×C3×(C2×D3)⋊C4—22no—
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#875—22no—
25C3×#875—22no—
26C32×#95—22no—
27C3×#810—22no—
28C3×#809—22no—
29C22×C3×Q16—31no—
30C22×C3×SD16—31no—
31C2×C3×#124—31no—
32C22×#216C2×C311yescharacteristic, complemented
33C22×#215C2×C311yescharacteristic
34C2×#875C2×C311yescharacteristic
35C2×C3×#103—31no—
36C2×C3×#102—31no—
37C3×#391—21no—
38C3×#391D311yescharacteristic, complemented
39C3×#391C2×C311yescharacteristic, complemented
40C2×#810C2×C311yescharacteristic, complemented
41C2×#809C2×C311yescharacteristic
42C3×#336—31no—
43#4524C2×C311yescharacteristic, complemented
44C23×C3×D3—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8D412yes—
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4D412yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12D412yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—21no—
70C32×C42—21no—
71C32×C42—21no—
72C3×#216—28no—
73C3×#215—28no—
74C3×(C2×D3)⋊C4—28no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D412yes—
80C2×C3×C3⋊C8D412yes—
81#2015—31noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—31no—
84C22×C3×Q8C2×D311yescharacteristic
85C22×C3×Q8C22×C311yescharacteristic
86C22×C3×D4—31no—
87C22×D12C22×C311yescharacteristic
88C22×Dic6C22×C311yescharacteristic
89C2×C3×Q16—62no—
90C2×C3×Q16—62no—
91C2×C3×Q16—62no—
92C2×C3×SD16—62no—
93C2×C3×SD16—62no—
94C2×C3×SD16—62no—
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C3×#124—62no—
98C3×#124—62no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C22×C311yescharacteristic
102C2×C3×C22⋊C4—62no—
103C2×C3×C42—21no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C22×C311yescharacteristic
106C2×#216—22no—
107C2×#216—22no—
108C2×#216—22no—
109C2×#215—22no—
110C2×#215—22no—
111C2×#215—22no—
112C2×(C2×D3)⋊C4—22no—
113C22×C3⋊C8C22×C311yescharacteristic
114C22×C3⋊C8C22×C311yescharacteristic
115#875—22no—
116#875—22no—
117C3×#103—62no—
118C3×#102—62no—
119C3×#95—24no—
120C3×#95—22no—
121C3×#95—22no—
122#810—22no—
123#809—22no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—42no—
129C22×C3×D3—42no—
130C32×Q8—22no—
131C32×Q8—22no—
132C32×Q8—41no—
133C32×Q8—41no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C3×Dic3—22no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—41no—
158C3×Dic6—41no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—22no—
161C22×Q16—31no—
162C22×SD16—31no—
163C2×#124—31no—
164C2×#103—31no—
165C2×#102—31no—
166#391C3×D311yescharacteristic, complemented
167#336—31no—
168C24×C3—61no—
169C23×D3—21no—
170C2×C3×Q8—22no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—22no—
182C2×C3×Q8—32no—
183C2×C3×Q8—41no—
184C2×C3×Q8—41no—
185C2×C3×Q8—41no—
186C2×C3×Q8—41no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8D1212yes—
193C2×C3×Q8C3×D412yes—
194C2×C3×D4—32no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—61no—
209C22×C3×C4#6712yes—
210C22×C3×C4C3×D412yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C23×C311yescharacteristic
213C22×Dic3—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12C3×D412yes—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6C3×D412yes—
226C3×Q16—68no—
227C3×SD16—68no—
228C2×C3×C8—32no—
229C2×C3×C8—32no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—41no—
240C3×C22⋊C4—68no—
241C3×C42—21no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42—41no—
246C3×C42—41no—
247#216—28no—
248#215—28no—
249(C2×D3)⋊C4—28no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8C3×D412yes—
255C2×C3⋊C8C3×D412yes—
256C22×C32#12011yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32#12711yescharacteristic
259C22×C32#13512yes—
260C22×C32#13712yes—
261C2×C3×D3—42no—
262C2×C3×D3—44no—
263C2×C3×D3—82no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C32×C4—42no—
267C32×C4—42no—
268C32×C4—81no—
269C32×C4#12011yescharacteristic
270C32×C4#12011yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×Q8C2×C3×D311yescharacteristic
276C22×D4—31no—
277C2×Q16—62no—
278C2×Q16—62no—
279C2×Q16—62no—
280C2×SD16—62no—
281C2×SD16—62no—
282C2×SD16—62no—
283C22×C8—31no—
284C22×C8—31no—
285#124—62no—
286#124—62no—
287C2×C4⋊C4C2×C3×D311yescharacteristic
288C2×C22⋊C4—62no—
289C2×C42C2×C3×D311yescharacteristic
290#103—62no—
291#102—62no—
292#95—22no—
293C23×C3—21no—
294C23×C3—62no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—122no—
298C23×C3—122no—
299C23×C3C2×#6711yescharacteristic
300C23×C3C2×C3×D411yescharacteristic
301C22×D3—22no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—42no—
305C22×D3—42no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—22no—
309C3×Q8—22no—
310C3×Q8—42no—
311C3×Q8—42no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—41no—
315C3×Q8—41no—
316C3×Q8—41no—
317C3×Q8—41no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—121no—
321C3×Q8—121no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—42no—
351C2×C3×C4—44no—
352C2×C3×C4—41no—
353C2×C3×C4—42no—
354C2×C3×C4—41no—
355C2×C3×C4—42no—
356C2×C3×C4—62no—
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×C4D3×D411yescharacteristic
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
371C2×Dic3—22no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374D12—22no—
375D12—22no—
376D12—41no—
377D12—41no—
378Dic6—22no—
379Dic6—22no—
380Dic6—41no—
381Dic6—41no—
382C3×C8—62no—
383C3×C8—62no—
384C3⋊C8—22no—
385C3⋊C8—22no—
386C2×C32#39211yescharacteristic
387C2×C32#45212yes—
388C2×C32#46412yes—
389C2×C32#49511yescharacteristic
390C2×C32#49711yescharacteristic
391C3×D3—82no—
392C24—61no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—32no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8C3×D1212yes—
405C2×D4—32no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—61no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—61no—
414C22×C4C3×#6712yes—
415C22×C4C22×C3×D311yescharacteristic
416Q16—68no—
417SD16—68no—
418C2×C8—32no—
419C2×C8—32no—
420C2×C8—61no—
421C2×C8—61no—
422C2×C8—61no—
423C2×C8—61no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C22⋊C4—68no—
427C42—21no—
428C42—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—122no—
435C22×C3—124no—
436C22×C3—242no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3#93011yescharacteristic
440C22×C3#93711yescharacteristic
441C22×C3#94011yescharacteristic
442C22×C3#94212yes—
443C22×C3#95012yes—
444C22×C3C3×#12011yescharacteristic
445C22×C3C3×#12111yescharacteristic
446C22×C3C3×#12711yescharacteristic
447C22×C3C3×#13512yes—
448C22×C3C3×#13712yes—
449C2×D3—42no—
450C2×D3—44no—
451C2×D3—82no—
452C2×D3—81no—
453C2×D3—81no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—44no—
459C3×C4—44no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—82no—
465C3×C4—81no—
466C3×C4—81no—
467C3×C4—122no—
468C3×C4#88211yescharacteristic
469C3×C4#88211yescharacteristic
470C3×C4#88411yescharacteristic
471C3×C4#88411yescharacteristic
472C3×C4C3×#12011yescharacteristic
473C3×C4C3×#12011yescharacteristic
474C3×C4C3×#12111yescharacteristic
475C3×C4C3×#12111yescharacteristic
476Dic3—42no—
477C32#201511yescharacteristic, complemented, Sylow
478C23—62no—
479C23—121no—
480C23—121no—
481C23—122no—
482C23—122no—
483C23C2×C3×#6711yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—41no—
487Q8—41no—
488Q8—62no—
489Q8—62no—
490Q8—121no—
491Q8—121no—
492D4—62no—
493D4—62no—
494D4—121no—
495D4—121no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—62no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4C2×C3×D1211yescharacteristic
508C2×C4C3×#23511yescharacteristic
509C2×C4C3×D3×D411yescharacteristic
510C2×C4C3×D3×D411yescharacteristic
511C2×C4C3×D3×D411yescharacteristic
512C2×C4C3×D3×D411yescharacteristic
513C8—62no—
514C8—62no—
515C2×C3—21no—
516C2×C3—22no—
517C2×C3—22no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—242no—
521C2×C3#496011yescharacteristic
522C2×C3#502812yes—
523C2×C3#504712yes—
524C2×C3#505911yescharacteristic
525C2×C3#508611yescharacteristic
526C2×C3C3×#39211yescharacteristic
527C2×C3C3×#45212yes—
528C2×C3C3×#46412yes—
529C2×C3C3×#49511yescharacteristic
530C2×C3C3×#49711yescharacteristic
531D3—82no—
532C22—122no—
533C22—124no—
534C22—242no—
535C22—241no—
536C22—241no—
537C22C3×#93011yescharacteristic
538C22C3×#93711yescharacteristic
539C22C3×#94011yescharacteristic
540C22C3×#94212yes—
541C22C3×#95012yes—
542C4—42no—
543C4—42no—
544C4—81no—
545C4—122no—
546C4C3×#88211yescharacteristic
547C4C3×#88211yescharacteristic
548C4C3×#88411yescharacteristic
549C4C3×#88411yescharacteristic
550C3—21no—
551C3#6968911yescharacteristic, direct product factor
552C3C3×#201511yescharacteristic, complemented
553C2—242no—
554C2C3×#496011yescharacteristic
555C2C3×#502812yes—
556C2C3×#504712yes—
557C2C3×#505911yescharacteristic
558C2C3×#508611yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#391C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC3×#391D3
hypocenterC3C3×#2015
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#391

Complements

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

NH ≅ G/Ntype
1. C22×C3×#216C2semidirect
4. C32×#391C2semidirect
5. C2×C3×#810C2semidirect
7. C3×#4524C2semidirect
9. #69689C3direct (N × H)
32. C22×#216C2×C3semidirect
38. C3×#391D3semidirect
39. C3×#391C2×C3semidirect
40. C2×#810C2×C3semidirect
43. #4524C2×C3semidirect
166. #391C3×D3semidirect
477. C32#2015semidirect
551. C3#69689direct (N × H)
552. C3C3×#2015semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2162
C22×C3×#2152
C2×C3×#8752
C32×#3912
C2×C3×#8102
C2×C3×#8092
C3×#45242
C3×#20153
#696893