Finite Group Databasebeta

← C3×#70389 #11792185

Subgroups — C3×#70389 #11792185

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5825C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×C32×#104C211yesmaximal, characteristic
5C2×C3×#824C211yesmaximal, characteristic, complemented
6C3×#5120C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#2005—31nomaximal
9#70389C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C3×#951—22no—
16C3×#951—22no—
17C3×#944—21no—
18C2×C3×#216—21no—
19C3×#936—21no—
20C3×#935—22no—
21C2×C3×#214—21no—
22C3×#926C2211yescharacteristic
23C2×C3×C4⋊Dic3—22no—
24C3×#924—22no—
25C2×C3×#208C2211yescharacteristic
26C3×#869—22no—
27C3×#869—22no—
28C32×#104—22no—
29C3×#824—22no—
30C3×#816—22no—
31C2×C3×#137—31no—
32C3×#536—31no—
33C2×C3×C4⋊Q8—31no—
34#5825C2×C311yescharacteristic
35C2×#951C2×C311yescharacteristic
36C2×#869C2×C311yescharacteristic, complemented
37C2×C3×#104—21no—
38C2×C3×#104D311yescharacteristic
39C2×C3×#104C2×C311yescharacteristic
40C3×#419—31no—
41C2×C3×#101—31no—
42C2×#824C2×C311yescharacteristic, complemented
43#5120C2×C311yescharacteristic, complemented
44C3×#339—31no—
45#4523C2×C311yescharacteristic, complemented
46C32×#41—21no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41—21no—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3D412yes—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—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×Dic6D412yes—
70C32×M16—21no—
71C32×M16—21no—
72C2×C32×C8—21no—
73C32×C42—21no—
74C32×C42D412yes—
75C3×#217—24no—
76C3×#217—21no—
77C3×#216—24no—
78C3×#214—24no—
79C3×C4⋊Dic3—28no—
80C3×C4⋊Dic3D412yes—
81C3×Dic3⋊C4—24no—
82C3×C4×Dic3—21no—
83C3×#208—21no—
84C3×#208D412yes—
85C2×C3×C3⋊C8—21no—
86#2005—31noSylow
87C2×C3×#41—21no—
88C2×C3×#41C2×D311yescharacteristic
89C2×C3×#41C22×C311yescharacteristic
90C22×C3×Q8—31no—
91C22×C3×Q8—31no—
92C22×Dic6C22×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—62no—
103C3×C4⋊Q8—61no—
104C3×C4⋊Q8—62no—
105C3×#124—61no—
106C3×#123—62no—
107C3×C22⋊Q8—62no—
108C3×#117—31no—
109C2×C3×C4⋊C4—62no—
110C2×C3×C42—21no—
111C2×C3×C42C2×D311yescharacteristic
112C2×C3×C42C22×C311yescharacteristic
113#951—22no—
114#951—22no—
115#944—21no—
116C2×#216—21no—
117#936—21no—
118#935—22no—
119C2×#214—21no—
120#926C22×C311yescharacteristic
121C2×C4⋊Dic3—22no—
122#924—22no—
123C2×#208C22×C311yescharacteristic
124#869—22no—
125#869—22no—
126C3×#104—24no—
127C3×#104—22no—
128C3×#104—22no—
129C3×#103—62no—
130C3×#101—62no—
131#824—22no—
132#816—22no—
133C23×C32—21no—
134C23×C32C2×D411yescharacteristic
135C32×Q8—21no—
136C32×Q8—21no—
137C32×D4—21no—
138C32×D4—21no—
139C32×D4—41no—
140C32×D4—41no—
141C2×C32×C4—24no—
142C2×C32×C4—22no—
143C2×C32×C4—21no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—41no—
162C3×Dic6—41no—
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×#104C3×D311yescharacteristic
173#419—31no—
174C2×#101—31no—
175#339—31no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—21no—
186C3×#41—41no—
187C3×#41—41no—
188C2×C3×Q8—21no—
189C2×C3×Q8—32no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8—61no—
193C2×C3×Q8—61no—
194C2×C3×Q8—61no—
195C2×C3×Q8—61no—
196C2×C3×Q8—61no—
197C2×C3×Q8—61no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8D1211yescharacteristic
202C2×C3×Q8C3×D411yescharacteristic
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—41no—
207C2×C3×D4D1211yescharacteristic
208C2×C3×D4C3×D411yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—41no—
216C22×C3×C4—41no—
217C22×C3×C4—61no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C23×C311yescharacteristic
220C22×Dic3—21no—
221C22×Dic3C3×D412yes—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6C3×D412yes—
234C3×Q16—64no—
235C3×SD16—64no—
236C3×M16—22no—
237C3×M16—21no—
238C3×M16—21no—
239C3×M16—21no—
240C3×M16—21no—
241C3×M16—32no—
242C3×M16—41no—
243C3×M16—61no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—41no—
247C2×C3×C8—61no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—64no—
250C3×C4⋊C4—68no—
251C3×C22⋊C4—64no—
252C3×C22⋊C4—61no—
253C3×C42—21no—
254C3×C42—21no—
255C3×C42—22no—
256C3×C42—41no—
257C3×C42—61no—
258C3×C42#6712yes—
259C3×C42C3×D412yes—
260#217—24no—
261#217—21no—
262#216—24no—
263#214—24no—
264C4⋊Dic3—28no—
265C4⋊Dic3C3×D412yes—
266Dic3⋊C4—24no—
267C4×Dic3—21no—
268#208—21no—
269#208C3×D412yes—
270C2×C3⋊C8—21no—
271C22×C32—22no—
272C22×C32—41no—
273C22×C32—42no—
274C22×C32#12011yescharacteristic
275C22×C32#12011yescharacteristic
276C22×C32#12111yescharacteristic
277C32×C4—24no—
278C32×C4—41no—
279C32×C4#12011yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4#12711yescharacteristic
283C3×Dic3—42no—
284C3×Dic3—42no—
285C3×Dic3—42no—
286C2×#41C2×C3×D311yescharacteristic
287C22×Q8—31no—
288C22×Q8—31no—
289#137—62no—
290#137—62no—
291C2×Q16—61no—
292C2×SD16—61no—
293C2×M16—31no—
294C2×M16C2×C3×D311yescharacteristic
295C4⋊Q8—62no—
296C4⋊Q8—61no—
297C4⋊Q8—62no—
298#124—61no—
299#123—62no—
300C22⋊Q8—62no—
301#117—31no—
302C2×C4⋊C4—62no—
303C2×C42C2×C3×D311yescharacteristic
304#104—22no—
305#103—62no—
306#101—62no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—41no—
311C23×C3D3×D411yescharacteristic
312C23×C3C2×C3×D411yescharacteristic
313C3×Q8—22no—
314C3×Q8—21no—
315C3×Q8—21no—
316C3×Q8—21no—
317C3×Q8—21no—
318C3×Q8—41no—
319C3×Q8—62no—
320C3×Q8—62no—
321C3×Q8—121no—
322C3×Q8—121no—
323C3×Q8—121no—
324C3×Q8—121no—
325C3×Q8—121no—
326C3×Q8—121no—
327C3×D4—22no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—41no—
333C3×D4—42no—
334C3×D4—42no—
335C3×D4—41no—
336C3×D4—41no—
337C3×D4—41no—
338C3×D4—41no—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—42no—
352C2×C3×C4—41no—
353C2×C3×C4—44no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C2×C3×D411yescharacteristic
375C2×C3×C4C2×C3×D411yescharacteristic
376C2×C3×C4C2×C3×D411yescharacteristic
377C2×C3×C4C2×C3×D411yescharacteristic
378C2×C3×C4C3×#4111yescharacteristic
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—41no—
385C2×Dic3—41no—
386Dic6—22no—
387Dic6—22no—
388Dic6—41no—
389Dic6—41no—
390Dic6—41no—
391Dic6—41no—
392Dic6—41no—
393Dic6—41no—
394C3×C8—42no—
395C3×C8—41no—
396C3×C8—41no—
397C3×C8—62no—
398C3⋊C8—22no—
399C2×C32—21no—
400C2×C32—21no—
401C2×C32—81no—
402C2×C32#39211yescharacteristic
403C2×C32#45612yes—
404#41—21no—
405#41—21no—
406#41—21no—
407#41—21no—
408C2×Q8—32no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8—61no—
416C2×Q8—61no—
417C2×Q8—61no—
418C2×Q8—61no—
419C2×Q8—61no—
420C2×Q8C3×D1211yescharacteristic
421C2×D4—21no—
422C2×D4C3×D1211yescharacteristic
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—32no—
426C22×C4—61no—
427C22×C4C22×C3×D311yescharacteristic
428Q16—64no—
429SD16—64no—
430M16—21no—
431M16—21no—
432M16—32no—
433M16—61no—
434C2×C8—21no—
435C2×C8—61no—
436C4⋊C4—32no—
437C4⋊C4—68no—
438C4⋊C4—64no—
439C22⋊C4—64no—
440C22⋊C4—61no—
441C42—21no—
442C42—61no—
443C42C3×#6712yes—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—82no—
456C22×C3#88211yescharacteristic
457C22×C3#88411yescharacteristic
458C22×C3#93711yescharacteristic
459C22×C3C3×#12011yescharacteristic
460C22×C3C3×#12011yescharacteristic
461C22×C3C3×#12111yescharacteristic
462C3×C4—24no—
463C3×C4—24no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—44no—
469C3×C4—42no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—122no—
473C3×C4—122no—
474C3×C4—122no—
475C3×C4#88211yescharacteristic
476C3×C4#88411yescharacteristic
477C3×C4#93011yescharacteristic
478C3×C4#94011yescharacteristic
479C3×C4C3×#12011yescharacteristic
480C3×C4C3×#12111yescharacteristic
481C3×C4C3×#12111yescharacteristic
482C3×C4C3×#12711yescharacteristic
483Dic3—42no—
484Dic3—42no—
485Dic3—42no—
486C32#200511yescharacteristic, complemented, Sylow
487C23—21no—
488C23C3×D3×D411yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—62no—
492Q8—62no—
493Q8—121no—
494Q8—121no—
495Q8—121no—
496Q8—121no—
497Q8—121no—
498Q8—121no—
499D4—21no—
500D4—21no—
501D4—41no—
502D4—41no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—121no—
514C2×C4—121no—
515C2×C4C2×C3×D1211yescharacteristic
516C2×C4C3×#23511yescharacteristic
517C2×C4C3×D3×D411yescharacteristic
518C2×C4C3×D3×D411yescharacteristic
519C2×C4C3×D3×D411yescharacteristic
520C2×C4C2×C3×#6711yescharacteristic
521C8—41no—
522C8—62no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—22no—
529C2×C3—41no—
530C2×C3—41no—
531C2×C3—82no—
532C2×C3—81no—
533C2×C3—81no—
534C2×C3#482612yes—
535C2×C3#496011yescharacteristic
536C2×C3C3×#39211yescharacteristic
537C2×C3C3×#45612yes—
538C22—22no—
539C22—41no—
540C22—42no—
541C22C3×#88211yescharacteristic
542C22C3×#88411yescharacteristic
543C22C3×#93711yescharacteristic
544C4—24no—
545C4—41no—
546C4—122no—
547C4—122no—
548C4—122no—
549C4C3×#88211yescharacteristic
550C4C3×#88411yescharacteristic
551C4C3×#93011yescharacteristic
552C4C3×#94011yescharacteristic
553C3—21no—
554C3#7038911yescharacteristic, direct product factor
555C3C3×#200511yescharacteristic, complemented
556C2—21no—
557C2—21no—
558C2—81no—
559C2C3×#482612yes—
560C2C3×#496011yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32#120
prime radicalC2×C32×#41C22
hypercenterC2×C3×#104D3
hypocenterC3C3×#2005
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
3. C2×C3×#869C2semidirect
5. C2×C3×#824C2semidirect
6. C3×#5120C2semidirect
7. C3×#4523C2semidirect
9. #70389C3direct (N × H)
36. C2×#869C2×C3semidirect
42. C2×#824C2×C3semidirect
43. #5120C2×C3semidirect
45. #4523C2×C3semidirect
486. C32#2005semidirect
554. C3#70389direct (N × H)
555. C3C3×#2005semidirect

Maximal subgroups

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

subgroupindex
C3×#58252
C2×C3×#9512
C2×C3×#8692
C2×C32×#1042
C2×C3×#8242
C3×#51202
C3×#45232
C3×#20053
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