Finite Group Databasebeta

← C3×#13997 #10632604

Subgroups — C3×#13997 #10632604

Order 768.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×#391C211yesmaximal, characteristic, complemented
3C2×C3×#391C211yesmaximal, characteristic, complemented
4C2×C3×#389C211yesmaximal, characteristic, complemented
5C2×C3×#380C211yesmaximal, characteristic
6C2×C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
8C3×#1445C212yesmaximal, complemented
9C3×#1439C212yesmaximal
10C3×#1437C212yesmaximal
11C3×C4⋊#95C212yesmaximal, complemented
12#13997C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C2×C3×C22⋊Q8—24no—
16C2×C3×C22⋊Q8—24no—
17C2×C3×C22⋊Q8C418yescomplemented
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C22×C3×C42C2212yes—
29C22×C3×C42C2211yescharacteristic
30C3×#391—24no—
31C3×#391—24no—
32C3×#389—24no—
33C3×#380—24no—
34C3×C4×C4⋊C4—24no—
35C3×C4×C22⋊C4—24no—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C2×C3×#95C2212yes—
43C2×C3×#95C2212yes—
44C2×C3×#95C2212yes—
45C22×C22⋊Q8C2×C311yescharacteristic
46C2×#391C2×C311yescharacteristic, complemented
47C2×#391C2×C311yescharacteristic, complemented
48C2×#389C2×C311yescharacteristic, complemented
49C2×#380C2×C311yescharacteristic
50C2×C4×C4⋊C4C2×C311yescharacteristic, complemented
51C2×C4×C22⋊C4C2×C311yescharacteristic
52#1445C2×C312yescomplemented
53#1439C2×C312yes—
54#1437C2×C312yes—
55C4⋊#95C2×C312yescomplemented
56C25×C3C2311yescharacteristic
57C22×C3×Q8—22no—
58C22×C3×Q8—22no—
59C22×C3×Q8—22no—
60C22×C3×Q8—22no—
61C22×C3×Q8—22no—
62C22×C3×Q8—22no—
63C22×C3×Q8C2×C414yes—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4C2×C414yes—
71C23×C3×C4C2312yes—
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2312yes—
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2312yes—
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C3×C22⋊Q8—232no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—24no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—42no—
92C2×C3×C4⋊C4C2×C418yes—
93C2×C3×C4⋊C4C2×C414yes—
94C2×C3×C4⋊C4D414yes—
95C2×C3×C4⋊C4D414yes—
96C2×C3×C4⋊C4D414yes—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—42no—
107C2×C3×C22⋊C4C2×C418yes—
108C2×C3×C22⋊C4Q814yescomplemented
109C2×C3×C42—22no—
110C2×C3×C42—22no—
111C2×C3×C42—22no—
112C2×C3×C42—24no—
113C2×C3×C42—22no—
114C2×C3×C42—22no—
115C2×C3×C42—24no—
116C2×C3×C42—42no—
117C2×C3×C42D414yes—
118C3×#95—22no—
119C3×#95—22no—
120C3×#95—24no—
121C3×#95—24no—
122C3×#95—24no—
123C3×#95—24no—
124C3×#95—24no—
125C3×#95—24no—
126C3×#95—24no—
127C23×Q8C22×C311yescharacteristic
128C24×C4C22×C311yescharacteristic
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8C3×C418yescomplemented
132C22×C4⋊C4C22×C311yescharacteristic
133C22×C4⋊C4C22×C312yes—
134C22×C4⋊C4C22×C312yes—
135C22×C4⋊C4C22×C311yescharacteristic
136C22×C4⋊C4C22×C311yescharacteristic
137C22×C22⋊C4C22×C311yescharacteristic
138C22×C22⋊C4C22×C312yes—
139C22×C22⋊C4C22×C312yes—
140C22×C22⋊C4C22×C311yescharacteristic
141C22×C42C22×C311yescharacteristic
142C22×C42C22×C312yes—
143C22×C42C22×C311yescharacteristic
144#391—24no—
145#391—24no—
146#389—24no—
147#380—24no—
148C4×C4⋊C4—24no—
149C4×C22⋊C4—24no—
150C2×#95C22×C311yescharacteristic
151C2×#95C22×C312yes—
152C2×#95C22×C312yes—
153C2×#95C22×C312yes—
154C2×#95C22×C312yes—
155C2×#95C22×C312yes—
156C2×#95C22×C312yes—
157C2×#95C22×C312yes—
158C2×#95C22×C311yescharacteristic
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3C22×C412yes—
172C24×C3C2×Q812yes—
173C24×C3#4112yes—
174C24×C3C2411yescharacteristic
175C2×C3×Q8—28no—
176C2×C3×Q8—28no—
177C2×C3×Q8—28no—
178C2×C3×Q8—44no—
179C2×C3×Q8—44no—
180C2×C3×Q8—44no—
181C2×C3×Q8—44no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—28no—
227C22×C3×C4—28no—
228C22×C3×C4—28no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—44no—
237C22×C3×C4—44no—
238C22×C3×C4—44no—
239C22×C3×C4—44no—
240C22×C3×C4C22×C414yes—
241C22×C3×C4C22×C412yes—
242C22×C3×C4C22×C414yes—
243C22×C3×C4C22×C412yes—
244C22×C3×C4C2×D412yes—
245C22×C3×C4C2×D414yes—
246C22×C3×C4C2×D414yes—
247C22×C3×C4C2×D414yes—
248C22×C3×C4C2×D412yes—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4C2×Q812yes—
254C22×C3×C4C2×Q812yes—
255C22×C3×C4#4112yes—
256C22×C3×C4#4112yes—
257C22×C3×C4#4112yes—
258C22×C3×C4#4112yes—
259C3×C4⋊C4—216no—
260C3×C4⋊C4—28no—
261C3×C4⋊C4—48no—
262C3×C4⋊C4—44no—
263C3×C4⋊C4C22⋊C4116yescomplemented
264C3×C22⋊C4—28no—
265C3×C22⋊C4—216no—
266C3×C22⋊C4—28no—
267C3×C22⋊C4—48no—
268C3×C42—28no—
269C3×C42—48no—
270C3×C42—44no—
271C25C23×C311yescharacteristic
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8C2×C3×C414yes—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4C2×C3×C414yes—
286C23×C4C23×C312yes—
287C23×C4C23×C312yes—
288C23×C4C23×C311yescharacteristic
289C23×C4C23×C312yes—
290C23×C4C23×C311yescharacteristic
291C23×C4C23×C311yescharacteristic
292C23×C4C23×C311yescharacteristic
293C23×C4C23×C312yes—
294C23×C4C23×C311yescharacteristic
295C23×C4C23×C311yescharacteristic
296C22⋊Q8—232no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4C2×C3×C418yes—
308C2×C4⋊C4C2×C3×C414yes—
309C2×C4⋊C4C3×D414yes—
310C2×C4⋊C4C3×D414yes—
311C2×C4⋊C4C3×D414yes—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4C2×C3×C418yes—
323C2×C22⋊C4C3×Q814yescomplemented
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—24no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—24no—
331C2×C42—42no—
332C2×C42C3×D414yes—
333#95—22no—
334#95—22no—
335#95—24no—
336#95—24no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95—24no—
341#95—24no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3C4×Q814yes—
377C23×C3C23×C411yescharacteristic
378C23×C3C22×D411yescharacteristic
379C23×C3C22×D411yescharacteristic
380C23×C3C22×D411yescharacteristic
381C23×C3C22×D411yescharacteristic
382C23×C3C22×Q811yescharacteristic
383C23×C3C2×#4111yescharacteristic
384C23×C3C2×#4111yescharacteristic
385C23×C3C2×#4111yescharacteristic
386C23×C3C2×#4111yescharacteristic
387C23×C3C2×#4111yescharacteristic
388C23×C3H(5,𝔽2)11yescharacteristic
389C23×C32−1+411yescharacteristic
390C23×C32−1+411yescharacteristic
391C23×C32−1+411yescharacteristic
392C3×Q8—416no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—22no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—41no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—42no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—42no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—416no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4C2×C22⋊C418yes—
456C2×C3×C4C2×C22⋊C414yes—
457C2×C3×C4C4×D414yes—
458C2×C3×C4C4×D414yes—
459C2×C3×C4#12114yes—
460C2×C3×C4#12114yes—
461C2×C3×C4C22⋊Q814yescomplemented
462C2×C3×C4#12414yes—
463C2×C3×C4#12714yes—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24C22×C3×C412yes—
477C24C2×C3×Q812yes—
478C24C3×#4112yes—
479C24C24×C311yescharacteristic
480C2×Q8—28no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4C22×C3×C414yes—
546C22×C4C22×C3×C412yes—
547C22×C4C22×C3×C414yes—
548C22×C4C22×C3×C412yes—
549C22×C4C2×C3×D412yes—
550C22×C4C2×C3×D414yes—
551C22×C4C2×C3×D414yes—
552C22×C4C2×C3×D414yes—
553C22×C4C2×C3×D412yes—
554C22×C4C2×C3×D412yes—
555C22×C4C2×C3×D412yes—
556C22×C4C2×C3×D412yes—
557C22×C4C2×C3×D412yes—
558C22×C4C2×C3×Q812yes—
559C22×C4C2×C3×Q812yes—
560C22×C4C3×#4112yes—
561C22×C4C3×#4112yes—
562C22×C4C3×#4112yes—
563C22×C4C3×#4112yes—
564C4⋊C4—216no—
565C4⋊C4—28no—
566C4⋊C4—48no—
567C4⋊C4—44no—
568C4⋊C4C3×C22⋊C4116yescomplemented
569C22⋊C4—28no—
570C22⋊C4—216no—
571C22⋊C4—28no—
572C22⋊C4—48no—
573C42—28no—
574C42—48no—
575C42—44no—
576C22×C3—24no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3C22×C22⋊C411yescharacteristic
592C22×C3C2×C4×D411yescharacteristic
593C22×C3C2×C4×D411yescharacteristic
594C22×C3C2×C4×Q811yescharacteristic
595C22×C3C4×#4111yescharacteristic
596C22×C3#51911yescharacteristic
597C22×C3#52011yescharacteristic
598C22×C3C2×#12111yescharacteristic
599C22×C3C2×#12111yescharacteristic
600C22×C3C2×C22⋊Q811yescharacteristic
601C22×C3#52511yescharacteristic
602C22×C3C2×#12411yescharacteristic
603C22×C3#52911yescharacteristic
604C22×C3C2×#12711yescharacteristic
605C22×C3#53311yescharacteristic
606C22×C3#53611yescharacteristic
607C22×C3#53711yescharacteristic
608C22×C3#54111yescharacteristic
609C22×C3#54211yescharacteristic
610C22×C3#54611yescharacteristic
611C22×C3#54611yescharacteristic
612C22×C3#54611yescharacteristic
613C22×C3#54711yescharacteristic
614C22×C3#54711yescharacteristic
615C22×C3#54711yescharacteristic
616C22×C3#54811yescharacteristic
617C22×C3#54811yescharacteristic
618C22×C3#54811yescharacteristic
619C22×C3D4×Q811yescharacteristic
620C22×C3D4×Q811yescharacteristic
621C22×C3D4×Q811yescharacteristic
622C22×C3#55211yescharacteristic
623C22×C3#55211yescharacteristic
624C22×C3#55411yescharacteristic
625C22×C3#55611yescharacteristic
626C3×C4—28no—
627C3×C4—24no—
628C3×C4—42no—
629C3×C4—44no—
630C3×C4—42no—
631C3×C4—42no—
632C3×C4—42no—
633C3×C4—44no—
634C3×C4—82no—
635C3×C4#39018yes—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23C3×C4×Q814yes—
671C23C23×C3×C411yescharacteristic
672C23C22×C3×D411yescharacteristic
673C23C22×C3×D411yescharacteristic
674C23C22×C3×D411yescharacteristic
675C23C22×C3×D411yescharacteristic
676C23C22×C3×Q811yescharacteristic
677C23C2×C3×#4111yescharacteristic
678C23C2×C3×#4111yescharacteristic
679C23C2×C3×#4111yescharacteristic
680C23C2×C3×#4111yescharacteristic
681C23C2×C3×#4111yescharacteristic
682C23C3×H(5,𝔽2)11yescharacteristic
683C23C3×2−1+411yescharacteristic
684C23C3×2−1+411yescharacteristic
685C23C3×2−1+411yescharacteristic
686Q8—416no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—416no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4C2×C3×C22⋊C418yes—
750C2×C4C2×C3×C22⋊C414yes—
751C2×C4C3×C4×D414yes—
752C2×C4C3×C4×D414yes—
753C2×C4C3×#12114yes—
754C2×C4C3×#12114yes—
755C2×C4C3×C22⋊Q814yescomplemented
756C2×C4C3×#12414yes—
757C2×C4C3×#12714yes—
758C2×C3—44no—
759C2×C3C2×#39011yescharacteristic
760C2×C3C4×C22⋊Q811yescharacteristic
761C2×C3#232311yescharacteristic
762C2×C3#233911yescharacteristic
763C2×C3Q8×C22⋊C411yescharacteristic
764C2×C3#236011yescharacteristic
765C2×C3#236211yescharacteristic
766C2×C3#241511yescharacteristic
767C2×C3#241711yescharacteristic
768C2×C3#242711yescharacteristic
769C2×C3#242911yescharacteristic
770C2×C3#248911yescharacteristic
771C2×C3#249211yescharacteristic
772C2×C3#254011yescharacteristic
773C2×C3#254211yescharacteristic
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22C22×C3×C22⋊C411yescharacteristic
790C22C2×C3×C4×D411yescharacteristic
791C22C2×C3×C4×D411yescharacteristic
792C22C2×C3×C4×Q811yescharacteristic
793C22C3×C4×#4111yescharacteristic
794C22C3×#51911yescharacteristic
795C22C3×#52011yescharacteristic
796C22C2×C3×#12111yescharacteristic
797C22C2×C3×#12111yescharacteristic
798C22C2×C3×C22⋊Q811yescharacteristic
799C22C3×#52511yescharacteristic
800C22C2×C3×#12411yescharacteristic
801C22C3×#52911yescharacteristic
802C22C2×C3×#12711yescharacteristic
803C22C3×#53311yescharacteristic
804C22C3×#53611yescharacteristic
805C22C3×#53711yescharacteristic
806C22C3×#54111yescharacteristic
807C22C3×#54211yescharacteristic
808C22C3×#54611yescharacteristic
809C22C3×#54611yescharacteristic
810C22C3×#54611yescharacteristic
811C22C3×#54711yescharacteristic
812C22C3×#54711yescharacteristic
813C22C3×#54711yescharacteristic
814C22C3×#54811yescharacteristic
815C22C3×#54811yescharacteristic
816C22C3×#54811yescharacteristic
817C22C3×D4×Q811yescharacteristic
818C22C3×D4×Q811yescharacteristic
819C22C3×D4×Q811yescharacteristic
820C22C3×#55211yescharacteristic
821C22C3×#55211yescharacteristic
822C22C3×#55411yescharacteristic
823C22C3×#55611yescharacteristic
824C4—24no—
825C4—28no—
826C4—42no—
827C4—44no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—44no—
832C4—82no—
833C4C3×#39018yes—
834C3#1399711yescharacteristic, direct product factor, Sylow
835C2—44no—
836C2C2×C3×#39011yescharacteristic
837C2C3×C4×C22⋊Q811yescharacteristic
838C2C3×#232311yescharacteristic
839C2C3×#233911yescharacteristic
840C2C3×Q8×C22⋊C411yescharacteristic
841C2C3×#236011yescharacteristic
842C2C3×#236211yescharacteristic
843C2C3×#241511yescharacteristic
844C2C3×#241711yescharacteristic
845C2C3×#242711yescharacteristic
846C2C3×#242911yescharacteristic
847C2C3×#248911yescharacteristic
848C2C3×#249211yescharacteristic
849C2C3×#254011yescharacteristic
850C2C3×#254211yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#391C2semidirect
3. C2×C3×#391C2semidirect
4. C2×C3×#389C2semidirect
6. C2×C3×C4×C4⋊C4C2semidirect
8. C3×#1445C2semidirect
11. C3×C4⋊#95C2semidirect
12. #13997C3direct (N × H)
17. C2×C3×C22⋊Q8C4semidirect
46. C2×#391C2×C3semidirect
47. C2×#391C2×C3semidirect
48. C2×#389C2×C3semidirect
50. C2×C4×C4⋊C4C2×C3semidirect
52. #1445C2×C3semidirect
55. C4⋊#95C2×C3semidirect
108. C2×C3×C22⋊C4Q8semidirect
131. C2×C22⋊Q8C3×C4semidirect
263. C3×C4⋊C4C22⋊C4semidirect
323. C2×C22⋊C4C3×Q8semidirect
461. C2×C3×C4C22⋊Q8semidirect
568. C4⋊C4C3×C22⋊C4semidirect
755. C2×C4C3×C22⋊Q8semidirect
834. C3#13997direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×C3×#3912
C2×C3×#3892
C2×C3×#3802
C2×C3×C4×C4⋊C42
C2×C3×C4×C22⋊C42
C3×#14452
C3×#14392
C3×#14372
C3×C4⋊#952
#139973