Finite Group Databasebeta

← C3×#10934 #10629541

Subgroups — C3×#10934 #10629541

Order 768.

982 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#104C211yesmaximal, characteristic
2C2×C3×#416C211yesmaximal, characteristic
3C2×C3×#408C211yesmaximal, characteristic
4C2×C3×#405C211yesmaximal, characteristic, complemented
5C2×C3×#341C211yesmaximal, characteristic, complemented
6C2×C3×#339C211yesmaximal, characteristic, complemented
7C2×C3×#336C211yesmaximal, characteristic, complemented
8#10934C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C23×C3×C8C2211yescharacteristic
13C23×C3×C8C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C22×C3×C42C2211yescharacteristic
16C2×C3×#104—22no—
17C2×C3×#104—22no—
18C2×C3×#104C414yescomplemented
19C3×#416—22no—
20C3×#416—22no—
21C2×C3×#103C412yescomplemented
22C2×C3×#102C412yescomplemented
23C3×#408—22no—
24C3×#408C414yescomplemented
25C2×C3×C22⋊C8—21no—
26C2×C3×C22⋊C8—21no—
27C3×#405—22no—
28C3×#405—22no—
29C2×C3×#97—21no—
30C2×C3×C4×C8—21no—
31C3×#341—22no—
32C3×#339—22no—
33C3×#336—22no—
34C22×#104C2×C311yescharacteristic
35C2×#416C2×C311yescharacteristic
36C2×#408C2×C311yescharacteristic
37C2×#405C2×C311yescharacteristic, complemented
38C2×#341C2×C311yescharacteristic, complemented
39C2×#339C2×C311yescharacteristic, complemented
40C2×#336C2×C311yescharacteristic, complemented
41C2×C3×#41—21no—
42C2×C3×#41—21no—
43C2×C3×#41—21no—
44C2×C3×#41—21no—
45C2×C3×#41—21no—
46C2×C3×#41—21no—
47C2×C3×#41—21no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41—21no—
51C2×C3×#41C2×C412yes—
52C2×C3×#41C2×C412yes—
53C22×C3×Q8C2×C411yescharacteristic
54C22×C3×D4—21no—
55C22×C3×D4C2×C411yescharacteristic
56C23×C3×C4—21no—
57C23×C3×C4—21no—
58C23×C3×C4C2311yescharacteristic
59C2×C3×M16—21no—
60C2×C3×M16—21no—
61C2×C3×M16—21no—
62C2×C3×M16—21no—
63C2×C3×M16—21no—
64C2×C3×M16—21no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16C2×C412yes—
68C2×C3×M16C2×C412yes—
69C2×C3×M16D412yes—
70C2×C3×M16D412yes—
71C22×C3×C8—21no—
72C22×C3×C8—21no—
73C22×C3×C8—21no—
74C22×C3×C8—21no—
75C22×C3×C8—21no—
76C22×C3×C8—21no—
77C22×C3×C8—21no—
78C22×C3×C8—21no—
79C22×C3×C8—21no—
80C22×C3×C8—21no—
81C22×C3×C8—21no—
82C22×C3×C8—21no—
83C22×C3×C8C2×C412yes—
84C22×C3×C8C2×C412yes—
85C22×C3×C8D412yes—
86C22×C3×C8D411yescharacteristic
87C22×C3×C8D411yescharacteristic
88C3×#117—21no—
89C3×#117—21no—
90C3×#117D412yes—
91C3×#117D412yes—
92C2×C3×C4⋊C4C2×C412yes—
93C2×C3×C22⋊C4—21no—
94C2×C3×C42—21no—
95C2×C3×C42—21no—
96C2×C3×C42—21no—
97C2×C3×C42—21no—
98C2×C3×C42—21no—
99C2×C3×C42—21no—
100C2×C3×C42C2×C412yes—
101C3×#104—28no—
102C3×#103—24no—
103C3×#102—24no—
104C3×C22⋊C8—24no—
105C3×C22⋊C8—24no—
106C3×#97—24no—
107C3×C4×C8—24no—
108C22×#41C22×C311yescharacteristic
109C22×M16C22×C311yescharacteristic
110C22×M16C22×C311yescharacteristic
111C23×C8C22×C311yescharacteristic
112C23×C8C22×C311yescharacteristic
113C2×#117C22×C311yescharacteristic
114C22×C42C22×C311yescharacteristic
115C2×#104—22no—
116C2×#104—22no—
117C2×#104C3×C414yescomplemented
118#416—22no—
119#416—22no—
120C2×#103C3×C412yescomplemented
121C2×#102C3×C412yescomplemented
122#408—22no—
123#408C3×C414yescomplemented
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126#405—22no—
127#405—22no—
128C2×#97—21no—
129C2×C4×C8—21no—
130#341—22no—
131#339—22no—
132#336—22no—
133C24×C3—21no—
134C24×C3#4111yescharacteristic
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—22no—
138C3×#41—22no—
139C3×#41—22no—
140C3×#41—22no—
141C3×#41—22no—
142C3×#41—22no—
143C3×#41—41no—
144C3×#41—41no—
145C3×#41—41no—
146C3×#41—41no—
147C3×#41—41no—
148C3×#41—41no—
149C3×#41—41no—
150C3×#41—41no—
151C2×C3×Q8—21no—
152C2×C3×Q8—21no—
153C2×C3×Q8—21no—
154C2×C3×Q8—21no—
155C2×C3×Q8—21no—
156C2×C3×Q8C4212yes—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—41no—
165C2×C3×D4—41no—
166C2×C3×D4—41no—
167C2×C3×D4—41no—
168C2×C3×D4C4212yes—
169C22×C3×C4—24no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—21no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—42no—
176C22×C3×C4—41no—
177C22×C3×C4—41no—
178C22×C3×C4—41no—
179C22×C3×C4—41no—
180C22×C3×C4—41no—
181C22×C3×C4—41no—
182C22×C3×C4C22×C411yescharacteristic
183C22×C3×C4C22×C411yescharacteristic
184C22×C3×C4C22×C411yescharacteristic
185C22×C3×C4C2×D411yescharacteristic
186C22×C3×C4C2×D411yescharacteristic
187C22×C3×C4C2×D411yescharacteristic
188C22×C3×C4C2×D411yescharacteristic
189C22×C3×C4C2×D411yescharacteristic
190C22×C3×C4C2×D411yescharacteristic
191C22×C3×C4#4111yescharacteristic
192C22×C3×C4#4111yescharacteristic
193C22×C3×C4#4111yescharacteristic
194C22×C3×C4#4111yescharacteristic
195C22×C3×C4#4111yescharacteristic
196C3×M16—22no—
197C3×M16—22no—
198C3×M16—22no—
199C3×M16—22no—
200C3×M16—22no—
201C3×M16—41no—
202C3×M16—41no—
203C3×M16C22⋊C414yes—
204C2×C3×C8—22no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—21no—
208C2×C3×C8—22no—
209C2×C3×C8—21no—
210C2×C3×C8—22no—
211C2×C3×C8—22no—
212C2×C3×C8—22no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—22no—
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—22no—
219C2×C3×C8—41no—
220C2×C3×C8—41no—
221C2×C3×C8—41no—
222C2×C3×C8—41no—
223C2×C3×C8—41no—
224C2×C3×C8—41no—
225C2×C3×C8C22⋊C412yes—
226C2×C3×C8C22⋊C412yes—
227C3×C4⋊C4—22no—
228C3×C4⋊C4C22⋊C414yes—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—22no—
231C3×C42—22no—
232C3×C42—22no—
233C3×C42—22no—
234C3×C42—22no—
235C3×C42—41no—
236C3×C42—41no—
237C2×#41—21no—
238C2×#41—21no—
239C2×#41—21no—
240C2×#41—21no—
241C2×#41—21no—
242C2×#41—21no—
243C2×#41—21no—
244C2×#41—21no—
245C2×#41—21no—
246C2×#41—21no—
247C2×#41C2×C3×C412yes—
248C2×#41C2×C3×C412yes—
249C22×Q8C2×C3×C411yescharacteristic
250C22×D4—21no—
251C22×D4C2×C3×C411yescharacteristic
252C23×C4—21no—
253C23×C4—21no—
254C23×C4C23×C311yescharacteristic
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16C2×C3×C412yes—
264C2×M16C2×C3×C412yes—
265C2×M16C3×D412yes—
266C2×M16C3×D412yes—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8C2×C3×C412yes—
280C22×C8C2×C3×C412yes—
281C22×C8C3×D412yes—
282C22×C8C3×D411yescharacteristic
283C22×C8C3×D411yescharacteristic
284#117—21no—
285#117—21no—
286#117C3×D412yes—
287#117C3×D412yes—
288C2×C4⋊C4C2×C3×C412yes—
289C2×C22⋊C4—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42C2×C3×C412yes—
297#104—28no—
298#103—24no—
299#102—24no—
300C22⋊C8—24no—
301C22⋊C8—24no—
302#97—24no—
303C4×C8—24no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3#11711yescharacteristic
312C23×C3C4×D411yescharacteristic
313C23×C3C4×D411yescharacteristic
314C23×C3#12111yescharacteristic
315C23×C3#12311yescharacteristic
316C23×C3#12411yescharacteristic
317C23×C3#12611yescharacteristic
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—41no—
321C3×Q8—41no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—42no—
325C3×D4—42no—
326C3×D4—42no—
327C3×D4—42no—
328C3×D4—41no—
329C3×D4—41no—
330C2×C3×C4—24no—
331C2×C3×C4—22no—
332C2×C3×C4—24no—
333C2×C3×C4—44no—
334C2×C3×C4—44no—
335C2×C3×C4—42no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4C2×C4211yescharacteristic
346C2×C3×C4C2×C22⋊C411yescharacteristic
347C2×C3×C4C2×C22⋊C411yescharacteristic
348C2×C3×C4C2×C22⋊C411yescharacteristic
349C2×C3×C4#11711yescharacteristic
350C2×C3×C4#11711yescharacteristic
351C2×C3×C4C4×D411yescharacteristic
352C2×C3×C4C4×D411yescharacteristic
353C2×C3×C4C4×D411yescharacteristic
354C2×C3×C4C4×D411yescharacteristic
355C2×C3×C4C4×D411yescharacteristic
356C2×C3×C4C4×D411yescharacteristic
357C2×C3×C4C4×D411yescharacteristic
358C2×C3×C4C4×D411yescharacteristic
359C2×C3×C4C4×D411yescharacteristic
360C2×C3×C4C4×D411yescharacteristic
361C2×C3×C4#12011yescharacteristic
362C2×C3×C4#12111yescharacteristic
363C2×C3×C4#12111yescharacteristic
364C2×C3×C4#12111yescharacteristic
365C2×C3×C4#12111yescharacteristic
366C2×C3×C4#12111yescharacteristic
367C2×C3×C4#12311yescharacteristic
368C2×C3×C4#12311yescharacteristic
369C2×C3×C4#12411yescharacteristic
370C2×C3×C4#12411yescharacteristic
371C2×C3×C4#12611yescharacteristic
372C2×C3×C4#12711yescharacteristic
373C3×C8—22no—
374C3×C8—22no—
375C3×C8—24no—
376C3×C8—42no—
377C3×C8—42no—
378C24—21no—
379C24C3×#4111yescharacteristic
380#41—22no—
381#41—22no—
382#41—22no—
383#41—22no—
384#41—22no—
385#41—22no—
386#41—22no—
387#41—22no—
388#41—41no—
389#41—41no—
390#41—41no—
391#41—41no—
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8C3×C4212yes—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4C3×C4212yes—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—42no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4C22×C3×C411yescharacteristic
428C22×C4C22×C3×C411yescharacteristic
429C22×C4C22×C3×C411yescharacteristic
430C22×C4C2×C3×D411yescharacteristic
431C22×C4C2×C3×D411yescharacteristic
432C22×C4C2×C3×D411yescharacteristic
433C22×C4C2×C3×D411yescharacteristic
434C22×C4C2×C3×D411yescharacteristic
435C22×C4C2×C3×D411yescharacteristic
436C22×C4C3×#4111yescharacteristic
437C22×C4C3×#4111yescharacteristic
438C22×C4C3×#4111yescharacteristic
439C22×C4C3×#4111yescharacteristic
440C22×C4C3×#4111yescharacteristic
441M16—22no—
442M16—22no—
443M16—22no—
444M16—22no—
445M16—22no—
446M16—41no—
447M16—41no—
448M16C3×C22⋊C414yes—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8C3×C22⋊C412yes—
471C2×C8C3×C22⋊C412yes—
472C4⋊C4—22no—
473C4⋊C4C3×C22⋊C414yes—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42—41no—
481C42—41no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—82no—
494C22×C3—82no—
495C22×C3C4×C22⋊C411yescharacteristic
496C22×C3#38611yescharacteristic
497C22×C3#38811yescharacteristic
498C22×C3#38811yescharacteristic
499C22×C3#38811yescharacteristic
500C22×C3#38811yescharacteristic
501C22×C3#39011yescharacteristic
502C22×C3#44312yes—
503C22×C3#44412yes—
504C3×C4—44no—
505C3×C4—44no—
506C3×C4—42no—
507C3×C4C4×C22⋊C411yescharacteristic
508C3×C4C4×C22⋊C411yescharacteristic
509C3×C4#38611yescharacteristic
510C3×C4#38611yescharacteristic
511C3×C4#38811yescharacteristic
512C3×C4#38811yescharacteristic
513C3×C4#39011yescharacteristic
514C3×C4#39011yescharacteristic
515C23—22no—
516C23—22no—
517C23—22no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23C3×#11711yescharacteristic
523C23C3×C4×D411yescharacteristic
524C23C3×C4×D411yescharacteristic
525C23C3×#12111yescharacteristic
526C23C3×#12311yescharacteristic
527C23C3×#12411yescharacteristic
528C23C3×#12611yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—41no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4C2×C3×C4211yescharacteristic
557C2×C4C2×C3×C22⋊C411yescharacteristic
558C2×C4C2×C3×C22⋊C411yescharacteristic
559C2×C4C2×C3×C22⋊C411yescharacteristic
560C2×C4C3×#11711yescharacteristic
561C2×C4C3×#11711yescharacteristic
562C2×C4C3×C4×D411yescharacteristic
563C2×C4C3×C4×D411yescharacteristic
564C2×C4C3×C4×D411yescharacteristic
565C2×C4C3×C4×D411yescharacteristic
566C2×C4C3×C4×D411yescharacteristic
567C2×C4C3×C4×D411yescharacteristic
568C2×C4C3×C4×D411yescharacteristic
569C2×C4C3×C4×D411yescharacteristic
570C2×C4C3×C4×D411yescharacteristic
571C2×C4C3×C4×D411yescharacteristic
572C2×C4C3×#12011yescharacteristic
573C2×C4C3×#12111yescharacteristic
574C2×C4C3×#12111yescharacteristic
575C2×C4C3×#12111yescharacteristic
576C2×C4C3×#12111yescharacteristic
577C2×C4C3×#12111yescharacteristic
578C2×C4C3×#12311yescharacteristic
579C2×C4C3×#12311yescharacteristic
580C2×C4C3×#12411yescharacteristic
581C2×C4C3×#12411yescharacteristic
582C2×C4C3×#12611yescharacteristic
583C2×C4C3×#12711yescharacteristic
584C8—22no—
585C8—22no—
586C8—24no—
587C8—42no—
588C8—42no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—82no—
594C2×C3#143711yescharacteristic
595C2×C3#176411yescharacteristic
596C2×C3#176511yescharacteristic
597C2×C3#187612yes—
598C2×C3#192912yes—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—82no—
611C22—82no—
612C22C3×C4×C22⋊C411yescharacteristic
613C22C3×#38611yescharacteristic
614C22C3×#38811yescharacteristic
615C22C3×#38811yescharacteristic
616C22C3×#38811yescharacteristic
617C22C3×#38811yescharacteristic
618C22C3×#39011yescharacteristic
619C22C3×#44312yes—
620C22C3×#44412yes—
621C4—44no—
622C4—44no—
623C4—42no—
624C4C3×C4×C22⋊C411yescharacteristic
625C4C3×C4×C22⋊C411yescharacteristic
626C4C3×#38611yescharacteristic
627C4C3×#38611yescharacteristic
628C4C3×#38811yescharacteristic
629C4C3×#38811yescharacteristic
630C4C3×#39011yescharacteristic
631C4C3×#39011yescharacteristic
632C3#1093411yescharacteristic, direct product factor, Sylow
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—82no—
638C2C3×#143711yescharacteristic
639C2C3×#176411yescharacteristic
640C2C3×#176511yescharacteristic
641C2C3×#187612yes—
642C2C3×#192912yes—
subgroupG/H
centerC22×C3×C4C2×D4
commutatorC2×C4C2×C3×C42
Frattini, cosocleC23×C4C23×C3
socleC23×C3C4×D4
prime radicalC22×C3×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C4 ◁ C23×C3×C8 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C3×#405C2semidirect
5. C2×C3×#341C2semidirect
6. C2×C3×#339C2semidirect
7. C2×C3×#336C2semidirect
8. #10934C3direct (N × H)
18. C2×C3×#104C4semidirect
21. C2×C3×#103C4semidirect
22. C2×C3×#102C4semidirect
24. C3×#408C4semidirect
37. C2×#405C2×C3semidirect
38. C2×#341C2×C3semidirect
39. C2×#339C2×C3semidirect
40. C2×#336C2×C3semidirect
117. C2×#104C3×C4semidirect
120. C2×#103C3×C4semidirect
121. C2×#102C3×C4semidirect
123. #408C3×C4semidirect
632. C3#10934direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1042
C2×C3×#4162
C2×C3×#4082
C2×C3×#4052
C2×C3×#3412
C2×C3×#3392
C2×C3×#3362
#109343