Finite Group Databasebeta

← C3×#11067 #10629674

Subgroups — C3×#11067 #10629674

Order 768.

1066 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#103C211yesmaximal, characteristic
2C22×C3×#103C211yesmaximal, characteristic
3C2×C3×#391C211yesmaximal, characteristic
4C2×C3×#389C211yesmaximal, characteristic
5C2×C3×#340C211yesmaximal, characteristic
6C2×C3×#340C211yesmaximal, characteristic
7C2×C3×#336C211yesmaximal, characteristic
8#11067C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×Q8C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×C3×C4⋊C4—21no—
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C42C2211yescharacteristic
17C2×C3×#103—22no—
18C2×C3×#103—22no—
19C2×C3×#103—22no—
20C2×C3×#103—22no—
21C2×C3×#103—22no—
22C2×C3×#103C414yescomplemented
23C3×#391—22no—
24C3×#391—22no—
25C3×#389—22no—
26C3×#389—22no—
27C2×C3×#95—21no—
28C2×C3×#95—21no—
29C2×C3×#95—21no—
30C3×#340—22no—
31C3×#340—22no—
32C3×#336—22no—
33C22×#103C2×C311yescharacteristic
34C22×#103C2×C311yescharacteristic
35C2×#391C2×C311yescharacteristic
36C2×#389C2×C311yescharacteristic
37C2×#340C2×C311yescharacteristic
38C2×#340C2×C311yescharacteristic
39C2×#336C2×C311yescharacteristic
40C22×C3×Q8—21no—
41C22×C3×Q8—21no—
42C22×C3×Q8—21no—
43C22×C3×Q8—21no—
44C22×C3×Q8—21no—
45C22×C3×Q8—21no—
46C22×C3×Q8—21no—
47C22×C3×Q8—21no—
48C22×C3×Q8—21no—
49C22×C3×Q8—21no—
50C22×C3×Q8—21no—
51C22×C3×Q8C2×C412yes—
52C22×C3×Q8D412yes—
53C22×C3×Q8Q812yes—
54C23×C3×C4—21no—
55C23×C3×C4—21no—
56C23×C3×C4—21no—
57C23×C3×C4—21no—
58C23×C3×C4D411yescharacteristic
59C23×C3×C4D411yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C22×C3×C8—21no—
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C22×C3×C8—21no—
66C22×C3×C8—21no—
67C22×C3×C8—21no—
68C22×C3×C8—21no—
69C22×C3×C8—21no—
70C22×C3×C8—21no—
71C22×C3×C8—21no—
72C22×C3×C8—21no—
73C22×C3×C8C2×C412yes—
74C22×C3×C8D412yes—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—42no—
90C2×C3×C4⋊C4—42no—
91C2×C3×C4⋊C4C2×C412yes—
92C2×C3×C4⋊C4D412yes—
93C2×C3×C4⋊C4D412yes—
94C2×C3×C4⋊C4D412yes—
95C2×C3×C4⋊C4D412yes—
96C2×C3×C42—21no—
97C2×C3×C42—21no—
98C2×C3×C42—21no—
99C2×C3×C42—21no—
100C2×C3×C42—21no—
101C2×C3×C42—21no—
102C3×#103—28no—
103C3×#103—28no—
104C3×#95—24no—
105C3×#95—24no—
106C3×#95—24no—
107C23×Q8C22×C311yescharacteristic
108C23×C8C22×C311yescharacteristic
109C23×C8C22×C311yescharacteristic
110C22×C4⋊C4—21no—
111C22×C4⋊C4C22×C311yescharacteristic
112C22×C4⋊C4C22×C311yescharacteristic
113C22×C4⋊C4C22×C311yescharacteristic
114C22×C42C22×C311yescharacteristic
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103C3×C414yescomplemented
121#391—22no—
122#391—22no—
123#389—22no—
124#389—22no—
125C2×#95—21no—
126C2×#95—21no—
127C2×#95—21no—
128#340—22no—
129#340—22no—
130#336—22no—
131C24×C3C2×D411yescharacteristic
132C2×C3×Q8—22no—
133C2×C3×Q8—22no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8—22no—
138C2×C3×Q8—22no—
139C2×C3×Q8—22no—
140C2×C3×Q8—22no—
141C2×C3×Q8—22no—
142C2×C3×Q8—22no—
143C2×C3×Q8—22no—
144C2×C3×Q8—22no—
145C2×C3×Q8—22no—
146C2×C3×Q8—22no—
147C2×C3×Q8—41no—
148C2×C3×Q8—41no—
149C2×C3×Q8—41no—
150C2×C3×Q8—41no—
151C2×C3×Q8—41no—
152C2×C3×Q8—41no—
153C2×C3×Q8—41no—
154C2×C3×Q8—41no—
155C2×C3×Q8—41no—
156C2×C3×Q8—41no—
157C2×C3×Q8—41no—
158C2×C3×Q8—41no—
159C2×C3×Q8C4⋊C414yescomplemented
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—41no—
181C22×C3×C4—41no—
182C22×C3×C4—41no—
183C22×C3×C4—41no—
184C22×C3×C4—41no—
185C22×C3×C4—41no—
186C22×C3×C4—41no—
187C22×C3×C4—41no—
188C22×C3×C4—41no—
189C22×C3×C4—41no—
190C22×C3×C4—41no—
191C22×C3×C4—41no—
192C22×C3×C4—41no—
193C22×C3×C4—41no—
194C22×C3×C4—41no—
195C22×C3×C4—41no—
196C22×C3×C4—41no—
197C22×C3×C4—41no—
198C22×C3×C4—41no—
199C22×C3×C4—41no—
200C22×C3×C4SD1612yes—
201C22×C3×C4Q1612yes—
202C22×C3×C4C22×C411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×Q811yescharacteristic
210C22×C3×C4#4111yescharacteristic
211C22×C3×C4#4111yescharacteristic
212C22×C3×C4#4111yescharacteristic
213C22×C3×C4#4111yescharacteristic
214C22×C3×C4#4111yescharacteristic
215C22×C3×C4#4111yescharacteristic
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—22no—
219C2×C3×C8—22no—
220C2×C3×C8—22no—
221C2×C3×C8—22no—
222C2×C3×C8—41no—
223C2×C3×C8—41no—
224C2×C3×C8—41no—
225C2×C3×C8—41no—
226C2×C3×C8—41no—
227C2×C3×C8—41no—
228C2×C3×C8—41no—
229C2×C3×C8—41no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—48no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4C22⋊C414yes—
243C3×C42—41no—
244C3×C42—41no—
245C3×C42—41no—
246C3×C42—41no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8—21no—
258C22×Q8C2×C3×C412yes—
259C22×Q8C3×D412yes—
260C22×Q8C3×Q812yes—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4C3×D411yescharacteristic
266C23×C4C3×D411yescharacteristic
267C23×C4C23×C311yescharacteristic
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×C8—21no—
280C22×C8C2×C3×C412yes—
281C22×C8C3×D412yes—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C2×C3×C412yes—
299C2×C4⋊C4C3×D412yes—
300C2×C4⋊C4C3×D412yes—
301C2×C4⋊C4C3×D412yes—
302C2×C4⋊C4C3×D412yes—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309#103—28no—
310#103—28no—
311#95—24no—
312#95—24no—
313#95—24no—
314C23×C3C4×D411yescharacteristic
315C23×C3#12011yescharacteristic
316C23×C3#12011yescharacteristic
317C23×C3#12111yescharacteristic
318C23×C3#12111yescharacteristic
319C23×C3C22⋊Q811yescharacteristic
320C23×C3#12411yescharacteristic
321C23×C3C2×SD1611yescharacteristic
322C23×C3C2×Q1611yescharacteristic
323C23×C3#13511yescharacteristic
324C23×C3#13511yescharacteristic
325C23×C3AGL(1,ℤ/8)11yescharacteristic
326C23×C3#13711yescharacteristic
327C23×C3#13711yescharacteristic
328C23×C3#13711yescharacteristic
329C3×Q8—24no—
330C3×Q8—24no—
331C3×Q8—42no—
332C3×Q8—42no—
333C3×Q8—42no—
334C3×Q8—42no—
335C3×Q8—42no—
336C3×Q8—42no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—41no—
356C2×C3×C4—42no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—81no—
372C2×C3×C4—81no—
373C2×C3×C4—81no—
374C2×C3×C4—81no—
375C2×C3×C4—81no—
376C2×C3×C4—81no—
377C2×C3×C4—81no—
378C2×C3×C4—81no—
379C2×C3×C4C2×C22⋊C411yescharacteristic
380C2×C3×C4C2×C4⋊C411yescharacteristic
381C2×C3×C4#11711yescharacteristic
382C2×C3×C4C4×D411yescharacteristic
383C2×C3×C4C4×D411yescharacteristic
384C2×C3×C4C4×D411yescharacteristic
385C2×C3×C4#12011yescharacteristic
386C2×C3×C4#12111yescharacteristic
387C2×C3×C4#12111yescharacteristic
388C2×C3×C4#12111yescharacteristic
389C2×C3×C4#12111yescharacteristic
390C2×C3×C4#12111yescharacteristic
391C2×C3×C4#12111yescharacteristic
392C2×C3×C4C22⋊Q811yescharacteristic
393C2×C3×C4C22⋊Q811yescharacteristic
394C2×C3×C4C22⋊Q811yescharacteristic
395C2×C3×C4C22⋊Q811yescharacteristic
396C2×C3×C4C22⋊Q811yescharacteristic
397C2×C3×C4#12311yescharacteristic
398C2×C3×C4#12311yescharacteristic
399C2×C3×C4#12311yescharacteristic
400C2×C3×C4#12311yescharacteristic
401C2×C3×C4#12311yescharacteristic
402C2×C3×C4#12411yescharacteristic
403C2×C3×C4#12411yescharacteristic
404C2×C3×C4#12611yescharacteristic
405C2×C3×C4#12611yescharacteristic
406C2×C3×C4#12711yescharacteristic
407C3×C8—42no—
408C3×C8—42no—
409C24C2×C3×D411yescharacteristic
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8C3×C4⋊C414yescomplemented
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4C3×SD1612yes—
479C22×C4C3×Q1612yes—
480C22×C4C22×C3×C411yescharacteristic
481C22×C4C2×C3×D411yescharacteristic
482C22×C4C2×C3×D411yescharacteristic
483C22×C4C2×C3×D411yescharacteristic
484C22×C4C2×C3×D411yescharacteristic
485C22×C4C2×C3×D411yescharacteristic
486C22×C4C2×C3×D411yescharacteristic
487C22×C4C2×C3×Q811yescharacteristic
488C22×C4C3×#4111yescharacteristic
489C22×C4C3×#4111yescharacteristic
490C22×C4C3×#4111yescharacteristic
491C22×C4C3×#4111yescharacteristic
492C22×C4C3×#4111yescharacteristic
493C22×C4C3×#4111yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—48no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4C3×C22⋊C414yes—
521C42—41no—
522C42—41no—
523C42—41no—
524C42—41no—
525C22×C3#38511yescharacteristic
526C22×C3#38611yescharacteristic
527C22×C3#38811yescharacteristic
528C22×C3#39211yescharacteristic
529C22×C3#39311yescharacteristic
530C22×C3#39411yescharacteristic
531C22×C3#39611yescharacteristic
532C22×C3C4×SD1611yescharacteristic
533C22×C3C4×Q1611yescharacteristic
534C22×C3#44011yescharacteristic
535C22×C3#44111yescharacteristic
536C22×C3#44811yescharacteristic
537C22×C3#44911yescharacteristic
538C22×C3#45011yescharacteristic
539C22×C3#45111yescharacteristic
540C22×C3#45111yescharacteristic
541C22×C3#45211yescharacteristic
542C22×C3#45211yescharacteristic
543C22×C3#45211yescharacteristic
544C22×C3#46111yescharacteristic
545C22×C3#46211yescharacteristic
546C22×C3#46311yescharacteristic
547C22×C3#46411yescharacteristic
548C22×C3#46511yescharacteristic
549C22×C3#46711yescharacteristic
550C22×C3#46811yescharacteristic
551C22×C3#47011yescharacteristic
552C22×C3#47511yescharacteristic
553C22×C3#47711yescharacteristic
554C22×C3#47911yescharacteristic
555C22×C3#47911yescharacteristic
556C22×C3#48711yescharacteristic
557C22×C3#48811yescharacteristic
558C22×C3#48911yescharacteristic
559C22×C3#49111yescharacteristic
560C3×C4—44no—
561C3×C4—44no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4—82no—
565C3×C4—82no—
566C3×C4#38011yescharacteristic
567C3×C4#38511yescharacteristic
568C3×C4#38811yescharacteristic
569C3×C4#39011yescharacteristic
570C3×C4#39411yescharacteristic
571C3×C4#39611yescharacteristic
572C3×C4#39711yescharacteristic
573C3×C4#39911yescharacteristic
574C23C3×C4×D411yescharacteristic
575C23C3×#12011yescharacteristic
576C23C3×#12011yescharacteristic
577C23C3×#12111yescharacteristic
578C23C3×#12111yescharacteristic
579C23C3×C22⋊Q811yescharacteristic
580C23C3×#12411yescharacteristic
581C23C2×C3×SD1611yescharacteristic
582C23C2×C3×Q1611yescharacteristic
583C23C3×#13511yescharacteristic
584C23C3×#13511yescharacteristic
585C23C3×AGL(1,ℤ/8)11yescharacteristic
586C23C3×#13711yescharacteristic
587C23C3×#13711yescharacteristic
588C23C3×#13711yescharacteristic
589Q8—24no—
590Q8—24no—
591Q8—42no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—42no—
596Q8—42no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4C2×C3×C22⋊C411yescharacteristic
640C2×C4C2×C3×C4⋊C411yescharacteristic
641C2×C4C3×#11711yescharacteristic
642C2×C4C3×C4×D411yescharacteristic
643C2×C4C3×C4×D411yescharacteristic
644C2×C4C3×C4×D411yescharacteristic
645C2×C4C3×#12011yescharacteristic
646C2×C4C3×#12111yescharacteristic
647C2×C4C3×#12111yescharacteristic
648C2×C4C3×#12111yescharacteristic
649C2×C4C3×#12111yescharacteristic
650C2×C4C3×#12111yescharacteristic
651C2×C4C3×#12111yescharacteristic
652C2×C4C3×C22⋊Q811yescharacteristic
653C2×C4C3×C22⋊Q811yescharacteristic
654C2×C4C3×C22⋊Q811yescharacteristic
655C2×C4C3×C22⋊Q811yescharacteristic
656C2×C4C3×C22⋊Q811yescharacteristic
657C2×C4C3×#12311yescharacteristic
658C2×C4C3×#12311yescharacteristic
659C2×C4C3×#12311yescharacteristic
660C2×C4C3×#12311yescharacteristic
661C2×C4C3×#12311yescharacteristic
662C2×C4C3×#12411yescharacteristic
663C2×C4C3×#12411yescharacteristic
664C2×C4C3×#12611yescharacteristic
665C2×C4C3×#12611yescharacteristic
666C2×C4C3×#12711yescharacteristic
667C8—42no—
668C8—42no—
669C2×C3#143911yescharacteristic
670C2×C3#186311yescharacteristic
671C2×C3#186511yescharacteristic
672C2×C3#187711yescharacteristic
673C2×C3#187811yescharacteristic
674C2×C3#193311yescharacteristic
675C2×C3#193511yescharacteristic
676C2×C3#200011yescharacteristic
677C2×C3#200111yescharacteristic
678C2×C3#202411yescharacteristic
679C2×C3#202611yescharacteristic
680C2×C3#204211yescharacteristic
681C2×C3#204311yescharacteristic
682C2×C3#206611yescharacteristic
683C2×C3#206811yescharacteristic
684C22C3×#38511yescharacteristic
685C22C3×#38611yescharacteristic
686C22C3×#38811yescharacteristic
687C22C3×#39211yescharacteristic
688C22C3×#39311yescharacteristic
689C22C3×#39411yescharacteristic
690C22C3×#39611yescharacteristic
691C22C3×C4×SD1611yescharacteristic
692C22C3×C4×Q1611yescharacteristic
693C22C3×#44011yescharacteristic
694C22C3×#44111yescharacteristic
695C22C3×#44811yescharacteristic
696C22C3×#44911yescharacteristic
697C22C3×#45011yescharacteristic
698C22C3×#45111yescharacteristic
699C22C3×#45111yescharacteristic
700C22C3×#45211yescharacteristic
701C22C3×#45211yescharacteristic
702C22C3×#45211yescharacteristic
703C22C3×#46111yescharacteristic
704C22C3×#46211yescharacteristic
705C22C3×#46311yescharacteristic
706C22C3×#46411yescharacteristic
707C22C3×#46511yescharacteristic
708C22C3×#46711yescharacteristic
709C22C3×#46811yescharacteristic
710C22C3×#47011yescharacteristic
711C22C3×#47511yescharacteristic
712C22C3×#47711yescharacteristic
713C22C3×#47911yescharacteristic
714C22C3×#47911yescharacteristic
715C22C3×#48711yescharacteristic
716C22C3×#48811yescharacteristic
717C22C3×#48911yescharacteristic
718C22C3×#49111yescharacteristic
719C4—42no—
720C4—42no—
721C4—44no—
722C4—44no—
723C4—82no—
724C4—82no—
725C4C3×#38011yescharacteristic
726C4C3×#38511yescharacteristic
727C4C3×#38811yescharacteristic
728C4C3×#39011yescharacteristic
729C4C3×#39411yescharacteristic
730C4C3×#39611yescharacteristic
731C4C3×#39711yescharacteristic
732C4C3×#39911yescharacteristic
733C3#1106711yescharacteristic, direct product factor, Sylow
734C2C3×#143911yescharacteristic
735C2C3×#186311yescharacteristic
736C2C3×#186511yescharacteristic
737C2C3×#187711yescharacteristic
738C2C3×#187811yescharacteristic
739C2C3×#193311yescharacteristic
740C2C3×#193511yescharacteristic
741C2C3×#200011yescharacteristic
742C2C3×#200111yescharacteristic
743C2C3×#202411yescharacteristic
744C2C3×#202611yescharacteristic
745C2C3×#204211yescharacteristic
746C2C3×#204311yescharacteristic
747C2C3×#206611yescharacteristic
748C2C3×#206811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C2×D4
commutatorC22×C4C22×C3×C4
Frattini, cosocleC23×C4C23×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
8. #11067C3direct (N × H)
22. C2×C3×#103C4semidirect
120. C2×#103C3×C4semidirect
159. C2×C3×Q8C4⋊C4semidirect
437. C2×Q8C3×C4⋊C4semidirect
733. C3#11067direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1032
C2×C3×#3912
C2×C3×#3892
C2×C3×#3402
C2×C3×#3362
#110673