Finite Group Databasebeta

← C3×#10930 #10629537

Subgroups — C3×#10930 #10629537

Order 768.

970 conjugacy classes of subgroups.

The subgroup lattice has 606 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
4C22×C3×#97C211yesmaximal, characteristic, complemented
5C2×C3×#341C211yesmaximal, characteristic, complemented
6C2×C3×#339C211yesmaximal, characteristic, complemented
7C3×#1729C211yesmaximal, characteristic, complemented
8#10930C311yesmaximal, 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—22no—
26C2×C3×#97—22no—
27C2×C3×#97—22no—
28C2×C3×#97—22no—
29C3×#341—22no—
30C3×#339—22no—
31C3×#336—22no—
32C22×#104C2×C311yescharacteristic
33C2×#416C2×C311yescharacteristic
34C2×#408C2×C311yescharacteristic
35C22×#97C2×C311yescharacteristic, complemented
36C2×#341C2×C311yescharacteristic, complemented
37C2×#339C2×C311yescharacteristic, complemented
38#1729C2×C311yescharacteristic, complemented
39C2×C3×#41—21no—
40C2×C3×#41—21no—
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×#41C2×C412yes—
50C2×C3×#41C2×C412yes—
51C22×C3×Q8C2×C411yescharacteristic
52C22×C3×D4—21no—
53C22×C3×D4C2×C411yescharacteristic
54C23×C3×C4—21no—
55C23×C3×C4—21no—
56C23×C3×C4C2311yescharacteristic
57C2×C3×M16—21no—
58C2×C3×M16—21no—
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—
69C22×C3×C8—21no—
70C22×C3×C8—21no—
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×C8C2×C412yes—
80C22×C3×C8C2×C412yes—
81C22×C3×C8D412yes—
82C22×C3×C8D412yes—
83C22×C3×C8D412yes—
84C22×C3×C8D412yes—
85C3×#117—21no—
86C3×#117—21no—
87C3×#117—21no—
88C3×#117—21no—
89C2×C3×C4⋊C4C2×C412yes—
90C2×C3×C22⋊C4—21no—
91C2×C3×C42—21no—
92C2×C3×C42—21no—
93C2×C3×C42—21no—
94C2×C3×C42—21no—
95C2×C3×C42C2×C412yes—
96C2×C3×C42D412yes—
97C2×C3×C42D412yes—
98C3×#104—28no—
99C3×#103—24no—
100C3×#102—24no—
101C3×C22⋊C8—28no—
102C3×#97—28no—
103C22×#41C22×C311yescharacteristic
104C22×M16C22×C311yescharacteristic
105C22×M16C22×C311yescharacteristic
106C23×C8C22×C311yescharacteristic
107C23×C8C22×C311yescharacteristic
108C2×#117C22×C311yescharacteristic
109C22×C42C22×C311yescharacteristic
110C2×#104—22no—
111C2×#104—22no—
112C2×#104C3×C414yescomplemented
113#416—22no—
114#416—22no—
115C2×#103C3×C412yescomplemented
116C2×#102C3×C412yescomplemented
117#408—22no—
118#408C3×C414yescomplemented
119C2×C22⋊C8—22no—
120C2×#97—22no—
121C2×#97—22no—
122C2×#97—22no—
123#341—22no—
124#339—22no—
125#336—22no—
126C24×C3—21no—
127C24×C3#4111yescharacteristic
128C3×#41—22no—
129C3×#41—22no—
130C3×#41—22no—
131C3×#41—22no—
132C3×#41—22no—
133C3×#41—22no—
134C3×#41—22no—
135C3×#41—22no—
136C3×#41—41no—
137C3×#41—41no—
138C3×#41—41no—
139C3×#41—41no—
140C3×#41—41no—
141C3×#41—41no—
142C3×#41—41no—
143C3×#41—41no—
144C2×C3×Q8—21no—
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×Q8—21no—
148C2×C3×Q8—21no—
149C2×C3×Q8C4212yes—
150C2×C3×D4—22no—
151C2×C3×D4—22no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—41no—
158C2×C3×D4—41no—
159C2×C3×D4—41no—
160C2×C3×D4—41no—
161C2×C3×D4C4212yes—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—44no—
170C22×C3×C4—41no—
171C22×C3×C4—41no—
172C22×C3×C4—41no—
173C22×C3×C4—41no—
174C22×C3×C4C22×C411yescharacteristic
175C22×C3×C4C22×C411yescharacteristic
176C22×C3×C4C22×C411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2×D411yescharacteristic
182C22×C3×C4C2×D411yescharacteristic
183C22×C3×C4#4111yescharacteristic
184C22×C3×C4#4111yescharacteristic
185C22×C3×C4#4111yescharacteristic
186C22×C3×C4#4111yescharacteristic
187C22×C3×C4#4111yescharacteristic
188C3×M16—22no—
189C3×M16—22no—
190C3×M16—22no—
191C3×M16—22no—
192C3×M16—41no—
193C3×M16—41no—
194C3×M16—41no—
195C3×M16—41no—
196C2×C3×C8—22no—
197C2×C3×C8—22no—
198C2×C3×C8—22no—
199C2×C3×C8—22no—
200C2×C3×C8—22no—
201C2×C3×C8—22no—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8—22no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—22no—
208C2×C3×C8—22no—
209C2×C3×C8—22no—
210C2×C3×C8—41no—
211C2×C3×C8—41no—
212C2×C3×C8—41no—
213C2×C3×C8—41no—
214C2×C3×C8C22⋊C414yes—
215C2×C3×C8C22⋊C414yes—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—22no—
218C3×C22⋊C4—41no—
219C3×C22⋊C4—41no—
220C3×C42—22no—
221C3×C42—22no—
222C3×C42—22no—
223C3×C42—41no—
224C3×C42—41no—
225C3×C42C22⋊C414yes—
226C2×#41—21no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C2×#41—21no—
232C2×#41—21no—
233C2×#41—21no—
234C2×#41—21no—
235C2×#41—21no—
236C2×#41C2×C3×C412yes—
237C2×#41C2×C3×C412yes—
238C22×Q8C2×C3×C411yescharacteristic
239C22×D4—21no—
240C22×D4C2×C3×C411yescharacteristic
241C23×C4—21no—
242C23×C4—21no—
243C23×C4C23×C311yescharacteristic
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16C2×C3×C412yes—
255C2×M16C2×C3×C412yes—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8C2×C3×C412yes—
267C22×C8C2×C3×C412yes—
268C22×C8C3×D412yes—
269C22×C8C3×D412yes—
270C22×C8C3×D412yes—
271C22×C8C3×D412yes—
272#117—21no—
273#117—21no—
274#117—21no—
275#117—21no—
276C2×C4⋊C4C2×C3×C412yes—
277C2×C22⋊C4—21no—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42C2×C3×C412yes—
283C2×C42C3×D412yes—
284C2×C42C3×D412yes—
285#104—28no—
286#103—24no—
287#102—24no—
288C22⋊C8—28no—
289#97—28no—
290C23×C3—24no—
291C23×C3—22no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—44no—
295C23×C3#11711yescharacteristic
296C23×C3C4×D411yescharacteristic
297C23×C3C4×D411yescharacteristic
298C23×C3#12111yescharacteristic
299C23×C3#12311yescharacteristic
300C23×C3#12411yescharacteristic
301C23×C3#12611yescharacteristic
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—41no—
305C3×Q8—41no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—42no—
309C3×D4—42no—
310C3×D4—42no—
311C3×D4—42no—
312C3×D4—41no—
313C3×D4—41no—
314C2×C3×C4—22no—
315C2×C3×C4—24no—
316C2×C3×C4—44no—
317C2×C3×C4—44no—
318C2×C3×C4—44no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—44no—
327C2×C3×C4C2×C4211yescharacteristic
328C2×C3×C4C2×C22⋊C411yescharacteristic
329C2×C3×C4C2×C22⋊C411yescharacteristic
330C2×C3×C4C2×C22⋊C411yescharacteristic
331C2×C3×C4#11711yescharacteristic
332C2×C3×C4#11711yescharacteristic
333C2×C3×C4C4×D411yescharacteristic
334C2×C3×C4C4×D411yescharacteristic
335C2×C3×C4C4×D411yescharacteristic
336C2×C3×C4C4×D411yescharacteristic
337C2×C3×C4C4×D411yescharacteristic
338C2×C3×C4C4×D411yescharacteristic
339C2×C3×C4C4×D411yescharacteristic
340C2×C3×C4C4×D411yescharacteristic
341C2×C3×C4C4×D411yescharacteristic
342C2×C3×C4C4×D411yescharacteristic
343C2×C3×C4#12011yescharacteristic
344C2×C3×C4#12111yescharacteristic
345C2×C3×C4#12111yescharacteristic
346C2×C3×C4#12111yescharacteristic
347C2×C3×C4#12111yescharacteristic
348C2×C3×C4#12111yescharacteristic
349C2×C3×C4#12311yescharacteristic
350C2×C3×C4#12311yescharacteristic
351C2×C3×C4#12411yescharacteristic
352C2×C3×C4#12411yescharacteristic
353C2×C3×C4#12611yescharacteristic
354C2×C3×C4#12711yescharacteristic
355C3×C8—24no—
356C3×C8—24no—
357C3×C8—42no—
358C3×C8—42no—
359C24—21no—
360C24C3×#4111yescharacteristic
361#41—22no—
362#41—22no—
363#41—22no—
364#41—22no—
365#41—22no—
366#41—22no—
367#41—22no—
368#41—22no—
369#41—41no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41—41no—
374#41—41no—
375#41—41no—
376#41—41no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8C3×C4212yes—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4C3×C4212yes—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—44no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4C22×C3×C411yescharacteristic
408C22×C4C22×C3×C411yescharacteristic
409C22×C4C22×C3×C411yescharacteristic
410C22×C4C2×C3×D411yescharacteristic
411C22×C4C2×C3×D411yescharacteristic
412C22×C4C2×C3×D411yescharacteristic
413C22×C4C2×C3×D411yescharacteristic
414C22×C4C2×C3×D411yescharacteristic
415C22×C4C2×C3×D411yescharacteristic
416C22×C4C3×#4111yescharacteristic
417C22×C4C3×#4111yescharacteristic
418C22×C4C3×#4111yescharacteristic
419C22×C4C3×#4111yescharacteristic
420C22×C4C3×#4111yescharacteristic
421M16—22no—
422M16—22no—
423M16—22no—
424M16—22no—
425M16—41no—
426M16—41no—
427M16—41no—
428M16—41no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—41no—
444C2×C8—41no—
445C2×C8—41no—
446C2×C8—41no—
447C2×C8C3×C22⋊C414yes—
448C2×C8C3×C22⋊C414yes—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C42—22no—
454C42—22no—
455C42—22no—
456C42—41no—
457C42—41no—
458C42C3×C22⋊C414yes—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—42no—
466C22×C3—44no—
467C22×C3—82no—
468C22×C3—82no—
469C22×C3C4×C22⋊C411yescharacteristic
470C22×C3#38611yescharacteristic
471C22×C3#38811yescharacteristic
472C22×C3#38811yescharacteristic
473C22×C3#38811yescharacteristic
474C22×C3#38811yescharacteristic
475C22×C3#39011yescharacteristic
476C22×C3#44414yes—
477C3×C4—44no—
478C3×C4—42no—
479C3×C4—82no—
480C3×C4C4×C22⋊C411yescharacteristic
481C3×C4C4×C22⋊C411yescharacteristic
482C3×C4#38611yescharacteristic
483C3×C4#38611yescharacteristic
484C3×C4#38811yescharacteristic
485C3×C4#38811yescharacteristic
486C3×C4#39011yescharacteristic
487C3×C4#39011yescharacteristic
488C23—24no—
489C23—22no—
490C23—41no—
491C23—41no—
492C23—44no—
493C23C3×#11711yescharacteristic
494C23C3×C4×D411yescharacteristic
495C23C3×C4×D411yescharacteristic
496C23C3×#12111yescharacteristic
497C23C3×#12311yescharacteristic
498C23C3×#12411yescharacteristic
499C23C3×#12611yescharacteristic
500Q8—22no—
501Q8—22no—
502Q8—41no—
503Q8—41no—
504D4—22no—
505D4—22no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—42no—
510D4—41no—
511D4—41no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4C2×C3×C4211yescharacteristic
526C2×C4C2×C3×C22⋊C411yescharacteristic
527C2×C4C2×C3×C22⋊C411yescharacteristic
528C2×C4C2×C3×C22⋊C411yescharacteristic
529C2×C4C3×#11711yescharacteristic
530C2×C4C3×#11711yescharacteristic
531C2×C4C3×C4×D411yescharacteristic
532C2×C4C3×C4×D411yescharacteristic
533C2×C4C3×C4×D411yescharacteristic
534C2×C4C3×C4×D411yescharacteristic
535C2×C4C3×C4×D411yescharacteristic
536C2×C4C3×C4×D411yescharacteristic
537C2×C4C3×C4×D411yescharacteristic
538C2×C4C3×C4×D411yescharacteristic
539C2×C4C3×C4×D411yescharacteristic
540C2×C4C3×C4×D411yescharacteristic
541C2×C4C3×#12011yescharacteristic
542C2×C4C3×#12111yescharacteristic
543C2×C4C3×#12111yescharacteristic
544C2×C4C3×#12111yescharacteristic
545C2×C4C3×#12111yescharacteristic
546C2×C4C3×#12111yescharacteristic
547C2×C4C3×#12311yescharacteristic
548C2×C4C3×#12311yescharacteristic
549C2×C4C3×#12411yescharacteristic
550C2×C4C3×#12411yescharacteristic
551C2×C4C3×#12611yescharacteristic
552C2×C4C3×#12711yescharacteristic
553C8—24no—
554C8—24no—
555C8—42no—
556C8—42no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—82no—
562C2×C3#143711yescharacteristic
563C2×C3#176512yes—
564C2×C3#193812yes—
565C2×C3#197512yes—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—82no—
576C22C3×C4×C22⋊C411yescharacteristic
577C22C3×#38611yescharacteristic
578C22C3×#38811yescharacteristic
579C22C3×#38811yescharacteristic
580C22C3×#38811yescharacteristic
581C22C3×#38811yescharacteristic
582C22C3×#39011yescharacteristic
583C22C3×#44414yes—
584C4—44no—
585C4—42no—
586C4—82no—
587C4C3×C4×C22⋊C411yescharacteristic
588C4C3×C4×C22⋊C411yescharacteristic
589C4C3×#38611yescharacteristic
590C4C3×#38611yescharacteristic
591C4C3×#38811yescharacteristic
592C4C3×#38811yescharacteristic
593C4C3×#39011yescharacteristic
594C4C3×#39011yescharacteristic
595C3#1093011yescharacteristic, direct product factor, Sylow
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—82no—
601C2C3×#143711yescharacteristic
602C2C3×#176512yes—
603C2C3×#193812yes—
604C2C3×#197512yes—
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. C22×C3×#97C2semidirect
5. C2×C3×#341C2semidirect
6. C2×C3×#339C2semidirect
7. C3×#1729C2semidirect
8. #10930C3direct (N × H)
18. C2×C3×#104C4semidirect
21. C2×C3×#103C4semidirect
22. C2×C3×#102C4semidirect
24. C3×#408C4semidirect
35. C22×#97C2×C3semidirect
36. C2×#341C2×C3semidirect
37. C2×#339C2×C3semidirect
38. #1729C2×C3semidirect
112. C2×#104C3×C4semidirect
115. C2×#103C3×C4semidirect
116. C2×#102C3×C4semidirect
118. #408C3×C4semidirect
595. C3#10930direct (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
C22×C3×#972
C2×C3×#3412
C2×C3×#3392
C3×#17292
#109303