Finite Group Databasebeta

← C3×#70355 #11785303

Subgroups — C3×#70355 #11785303

Order 1152.

709 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4C3×#5118C211yesmaximal, characteristic, complemented
5C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1806—31nomaximal
9#70355C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C3×Q8×Dic3C411yescharacteristic, complemented
14C3×Q8×Dic3C411yescharacteristic, complemented
15C3×D4×Dic3—21no—
16C3×D4×Dic3—21no—
17C3×D4×Dic3C411yescharacteristic, complemented
18C3×D4×Dic3C411yescharacteristic, complemented
19C3×#926—21no—
20C3×#926C2211yescharacteristic
21C2×C3×Dic3⋊C4—21no—
22C2×C3×C4×Dic3—21no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C32×#104—22no—
27C3×#837—22no—
28C3×C3⋊#95—21no—
29C3×Dic3⋊C8—21no—
30C3×Dic3⋊C8—21no—
31C3×C4×#41—31no—
32Dic3×#41C2×C311yescharacteristic
33C3×#423—31no—
34C2×C3×#104—21no—
35C2×C3×#104—31no—
36C2×C3×#104D311yescharacteristic
37C2×C3×#104C2×C311yescharacteristic
38C3×C4×C4⋊C4—31no—
39C2×#837C2×C311yescharacteristic
40#5118C2×C311yescharacteristic, complemented
41C4×Dic3⋊C4C2×C311yescharacteristic, complemented
42C3×#339—31no—
43C3×#339—31no—
44#4555C2×C311yescharacteristic, complemented
45#4523C2×C311yescharacteristic, complemented
46C32×#41—21no—
47C32×#41—21no—
48C32×#41D412yes—
49C32×#41Q812yes—
50C2×C32×Q8C2×C411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4C2×C411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C32×M16—21no—
62C32×M16—21no—
63C2×C32×C8—21no—
64C32×C42—21no—
65C32×C42—21no—
66C3×#217—21no—
67C3×#217—21no—
68C3×#217—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2×C411yescharacteristic
72C3×C4⋊Dic3C2×C411yescharacteristic
73C3×Dic3⋊C4—24no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3C2×C411yescharacteristic
80C3×C4×Dic3C2×C411yescharacteristic
81C3×C4×Dic3D411yescharacteristic
82C3×C4×Dic3D411yescharacteristic
83C3×#208—21no—
84C3×#208—21no—
85C2×C3×C3⋊C8—21no—
86#1806—31noSylow
87C2×C3×#41—21no—
88C2×C3×#41C2×D311yescharacteristic
89C2×C3×#41C22×C311yescharacteristic
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C22×C311yescharacteristic
94C3×C4×Q8—31no—
95C3×C4×Q8—31no—
96C3×C4×D4—31no—
97C3×C4×D4—31no—
98C3×C4×D4—61no—
99C3×C4×D4—61no—
100C3×#117—31no—
101C3×#117—61no—
102C2×C3×C4⋊C4—61no—
103C2×C3×C42—21no—
104C2×C3×C42—31no—
105C2×C3×C42—31no—
106C2×C3×C42—61no—
107C2×C3×C42C2×D311yescharacteristic
108C2×C3×C42C22×C311yescharacteristic
109Q8×Dic3C3×C411yescharacteristic, complemented
110Q8×Dic3C3×C411yescharacteristic, complemented
111D4×Dic3—21no—
112D4×Dic3—21no—
113D4×Dic3C3×C411yescharacteristic, complemented
114D4×Dic3C3×C411yescharacteristic, complemented
115#926—21no—
116#926C22×C311yescharacteristic
117C2×Dic3⋊C4—21no—
118C2×C4×Dic3—21no—
119C2×C4×Dic3C22×C311yescharacteristic
120C2×C4×Dic3C22×C311yescharacteristic
121C2×#208C22×C311yescharacteristic
122C3×C4⋊C8—61no—
123C3×C4⋊C8—61no—
124C3×#104—24no—
125C3×#104—22no—
126C3×#104—22no—
127C3×#104—62no—
128C3×#95—61no—
129#837—22no—
130C3⋊#95—21no—
131Dic3⋊C8—21no—
132Dic3⋊C8—21no—
133C23×C32—21no—
134C23×C32C2×D411yescharacteristic
135C32×Q8—21no—
136C32×Q8C4⋊C412yescomplemented
137C32×D4—22no—
138C32×D4—22no—
139C32×D4—21no—
140C32×D4C4⋊C412yescomplemented
141C2×C32×C4—21no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4—22no—
145C2×C32×C4—41no—
146C2×C32×C4—41no—
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×Q811yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—42no—
162C2×C3×Dic3C22⋊C411yescharacteristic
163C2×C3×Dic3C22⋊C411yescharacteristic
164C2×C3×Dic3C22⋊C411yescharacteristic
165C2×C3×Dic3C22⋊C411yescharacteristic
166C32×C8—41no—
167C3×C3⋊C8—41no—
168C4×#41—31no—
169#423—31no—
170C2×#104—31no—
171C2×#104C3×D311yescharacteristic
172C4×C4⋊C4—31no—
173#339—31no—
174#339—31no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—22no—
180C3×#41—22no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41Dic612yes—
184C3×#41#6712yes—
185C3×#41C3×D412yes—
186C3×#41C3×Q812yes—
187C2×C3×Q8—21no—
188C2×C3×Q8C4×D311yescharacteristic
189C2×C3×Q8C2×C3×C411yescharacteristic
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—41no—
194C2×C3×D4C4×D311yescharacteristic
195C2×C3×D4C2×C3×C411yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—41no—
204C22×C3×C4—41no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C23×C311yescharacteristic
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3C3×D411yescharacteristic
214C22×Dic3C3×D411yescharacteristic
215C3×M16—22no—
216C3×M16—21no—
217C3×M16—21no—
218C3×M16—21no—
219C3×M16—21no—
220C3×M16—41no—
221C3×M16—61no—
222C3×M16—61no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—41no—
226C2×C3×C8—61no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—64no—
232C3×C22⋊C4—61no—
233C3×C22⋊C4—61no—
234C3×C22⋊C4—61no—
235C3×C42—22no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—31no—
241C3×C42—31no—
242C3×C42—31no—
243C3×C42—31no—
244C3×C42—41no—
245C3×C42—61no—
246C3×C42—61no—
247C3×C42—61no—
248C3×C42—61no—
249C3×C42—61no—
250#217—21no—
251#217—21no—
252#217—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3C2×C3×C411yescharacteristic
256C4⋊Dic3C2×C3×C411yescharacteristic
257Dic3⋊C4—24no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—21no—
263C4×Dic3C2×C3×C411yescharacteristic
264C4×Dic3C2×C3×C411yescharacteristic
265C4×Dic3C3×D411yescharacteristic
266C4×Dic3C3×D411yescharacteristic
267#208—21no—
268#208—21no—
269C2×C3⋊C8—21no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C2×C22⋊C411yescharacteristic
276C22×C32#12111yescharacteristic
277C22×C32C22⋊Q811yescharacteristic
278C32×C4—22no—
279C32×C4—42no—
280C32×C4C2×C4⋊C411yescharacteristic
281C32×C4#11711yescharacteristic
282C32×C4#12111yescharacteristic
283C32×C4C22⋊Q811yescharacteristic
284C3×Dic3—21no—
285C3×Dic3—21no—
286C3×Dic3—21no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3#10412yescomplemented
291C2×#41C2×C3×D311yescharacteristic
292C2×M16—31no—
293C2×M16C2×C3×D311yescharacteristic
294C4×Q8—31no—
295C4×Q8—31no—
296C4×D4—31no—
297C4×D4—31no—
298C4×D4—61no—
299C4×D4—61no—
300#117—31no—
301#117—61no—
302C2×C4⋊C4—61no—
303C2×C42—31no—
304C2×C42—31no—
305C2×C42—61no—
306C2×C42C2×C3×D311yescharacteristic
307C4⋊C8—61no—
308C4⋊C8—61no—
309#104—22no—
310#104—62no—
311#95—61no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—41no—
316C23×C3D3×D411yescharacteristic
317C23×C3C2×C3×D411yescharacteristic
318C3×Q8—21no—
319C3×Q8—21no—
320C3×Q8—22no—
321C3×Q8—41no—
322C3×Q8Dic3⋊C412yescomplemented
323C3×Q8C3×C4⋊C412yescomplemented
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—22no—
331C3×D4—41no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4Dic3⋊C412yescomplemented
335C3×D4C3×C4⋊C412yescomplemented
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
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—31no—
351C2×C3×C4—31no—
352C2×C3×C4—31no—
353C2×C3×C4—31no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—42no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—122no—
369C2×C3×C4—121no—
370C2×C3×C4—122no—
371C2×C3×C4—121no—
372C2×C3×C4—121no—
373C2×C3×C4C2×Dic611yescharacteristic
374C2×C3×C4C2×C4×D311yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4#23711yescharacteristic
377C2×C3×C4#23711yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C22×C3×C411yescharacteristic
380C2×C3×C4C2×C3×D411yescharacteristic
381C2×C3×C4C2×C3×D411yescharacteristic
382C2×C3×C4C2×C3×Q811yescharacteristic
383C2×C3×C4C3×#4111yescharacteristic
384C2×C3×C4C3×#4111yescharacteristic
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—41no—
390C2×Dic3—42no—
391C2×Dic3—41no—
392C2×Dic3—41no—
393C2×Dic3—42no—
394C2×Dic3C3×C22⋊C411yescharacteristic
395C2×Dic3C3×C22⋊C411yescharacteristic
396C2×Dic3C3×C22⋊C411yescharacteristic
397C2×Dic3C3×C22⋊C411yescharacteristic
398C3×C8—42no—
399C3×C8—41no—
400C3×C8—41no—
401C3×C8—121no—
402C3⋊C8—41no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32—42no—
406C2×C32#38011yescharacteristic
407C2×C32C2×#10411yescharacteristic
408C2×C32#42111yescharacteristic
409#41—21no—
410#41—21no—
411#41C3×Dic612yes—
412#41C3×#6712yes—
413C2×Q8C3×C4×D311yescharacteristic
414C2×D4—21no—
415C2×D4C3×C4×D311yescharacteristic
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4C22×C3×D311yescharacteristic
424M16—21no—
425M16—21no—
426M16—61no—
427M16—61no—
428C2×C8—21no—
429C2×C8—61no—
430C4⋊C4—31no—
431C4⋊C4—31no—
432C4⋊C4—61no—
433C4⋊C4—61no—
434C4⋊C4—64no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C42—21no—
439C42—21no—
440C42—31no—
441C42—31no—
442C42—31no—
443C42—31no—
444C42—61no—
445C42—61no—
446C42—61no—
447C42—61no—
448C42—61no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—42no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—81no—
466C22×C3—81no—
467C22×C3#87811yescharacteristic
468C22×C3D3×C22⋊C411yescharacteristic
469C22×C3#93911yescharacteristic
470C22×C3C2×C3×C22⋊C411yescharacteristic
471C22×C3C3×#12111yescharacteristic
472C22×C3C3×C22⋊Q811yescharacteristic
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—32no—
480C3×C4—42no—
481C3×C4—42no—
482C3×C4—42no—
483C3×C4—44no—
484C3×C4—61no—
485C3×C4—61no—
486C3×C4—61no—
487C3×C4—122no—
488C3×C4—121no—
489C3×C4—121no—
490C3×C4#87711yescharacteristic
491C3×C4#87811yescharacteristic
492C3×C4C2×Dic3⋊C411yescharacteristic
493C3×C4#93911yescharacteristic
494C3×C4C2×C3×C4⋊C411yescharacteristic
495C3×C4C3×#11711yescharacteristic
496C3×C4C3×#12111yescharacteristic
497C3×C4C3×C22⋊Q811yescharacteristic
498Dic3—21no—
499Dic3—21no—
500Dic3—21no—
501Dic3—42no—
502Dic3—41no—
503Dic3—41no—
504Dic3C3×#10412yescomplemented
505C32#180611yescharacteristic, complemented, Sylow
506C23—21no—
507C23C3×D3×D411yescharacteristic
508Q8—21no—
509Q8C3×Dic3⋊C412yescomplemented
510D4—22no—
511D4—22no—
512D4—21no—
513D4C3×Dic3⋊C412yescomplemented
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—31no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—122no—
529C2×C4—121no—
530C2×C4—122no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4C2×C3×Dic611yescharacteristic
534C2×C4C2×C3×C4×D311yescharacteristic
535C2×C4C3×D3×D411yescharacteristic
536C2×C4C3×#23711yescharacteristic
537C2×C4C3×#23711yescharacteristic
538C2×C4C2×C3×#6711yescharacteristic
539C8—41no—
540C8—121no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—41no—
549C2×C3—41no—
550C2×C3—42no—
551C2×C3—42no—
552C2×C3—82no—
553C2×C3D3×#10411yescharacteristic
554C2×C3#482111yescharacteristic
555C2×C3#494211yescharacteristic
556C2×C3C3×#38011yescharacteristic
557C2×C3C2×C3×#10411yescharacteristic
558C2×C3C3×#42111yescharacteristic
559C22—21no—
560C22—21no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22C3×#87811yescharacteristic
565C22C3×D3×C22⋊C411yescharacteristic
566C22C3×#93911yescharacteristic
567C4—22no—
568C4—32no—
569C4—42no—
570C4—61no—
571C4—61no—
572C4—61no—
573C4—122no—
574C4—121no—
575C4—121no—
576C4C3×#87711yescharacteristic
577C4C3×#87811yescharacteristic
578C4C2×C3×Dic3⋊C411yescharacteristic
579C4C3×#93911yescharacteristic
580C3—21no—
581C3#7035511yescharacteristic, direct product factor
582C3C3×#180611yescharacteristic, complemented
583C2—21no—
584C2—21no—
585C2—42no—
586C2C3×D3×#10411yescharacteristic
587C2C3×#482111yescharacteristic
588C2C3×#494211yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#104D3
hypocenterC3C3×#1806
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
4. C3×#5118C2semidirect
5. C3×C4×Dic3⋊C4C2semidirect
6. C3×#4555C2semidirect
7. C3×#4523C2semidirect
9. #70355C3direct (N × H)
13. C3×Q8×Dic3C4semidirect
14. C3×Q8×Dic3C4semidirect
17. C3×D4×Dic3C4semidirect
18. C3×D4×Dic3C4semidirect
40. #5118C2×C3semidirect
41. C4×Dic3⋊C4C2×C3semidirect
44. #4555C2×C3semidirect
45. #4523C2×C3semidirect
109. Q8×Dic3C3×C4semidirect
110. Q8×Dic3C3×C4semidirect
113. D4×Dic3C3×C4semidirect
114. D4×Dic3C3×C4semidirect
136. C32×Q8C4⋊C4semidirect
140. C32×D4C4⋊C4semidirect
290. C3×Dic3#104semidirect
322. C3×Q8Dic3⋊C4semidirect
323. C3×Q8C3×C4⋊C4semidirect
334. C3×D4Dic3⋊C4semidirect
335. C3×D4C3×C4⋊C4semidirect
504. Dic3C3×#104semidirect
505. C32#1806semidirect
509. Q8C3×Dic3⋊C4semidirect
513. D4C3×Dic3⋊C4semidirect
581. C3#70355direct (N × H)
582. C3C3×#1806semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C2×C32×#1042
C2×C3×#8372
C3×#51182
C3×C4×Dic3⋊C42
C3×#45552
C3×#45232
C3×#18063
#703553