Finite Group Databasebeta

← C3×#61660 #10680267

Subgroups — C3×#61660 #10680267

Order 768.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3547C211yesmaximal, characteristic, complemented
2C3×#3497C211yesmaximal, characteristic, complemented
3C3×#3333C211yesmaximal, characteristic, complemented
4C3×#3329C211yesmaximal, characteristic, complemented
5C3×#3327C212yesmaximal, complemented
6C3×#3305C211yesmaximal, characteristic, complemented
7C3×#3300C212yesmaximal, complemented
8C3×#3299C211yesmaximal, characteristic, complemented
9C3×D4×Q16C211yesmaximal, characteristic, complemented
10C3×#3285C212yesmaximal, complemented
11C3×#3284C211yesmaximal, characteristic, complemented
12C3×#3278C211yesmaximal, characteristic, complemented
13C3×#3277C212yesmaximal, complemented
14C3×#3276C211yesmaximal, characteristic, complemented
15C3×#3212C211yesmaximal, characteristic, complemented
16C3×#3210C211yesmaximal, characteristic, complemented
17C3×#3203C212yesmaximal, complemented
18C3×#3201C212yesmaximal, complemented
19C3×#3108C211yesmaximal, characteristic, complemented
20C3×#3104C211yesmaximal, characteristic, complemented
21C3×#3013C212yesmaximal, complemented
22C3×#3011C212yesmaximal, complemented
23C3×#2979C211yesmaximal, characteristic, complemented
24#61660C311yesmaximal, characteristic, direct product factor, Sylow
25C2×C3×2−1+4C2212yes—
26C2×C3×#137C2212yes—
27C2×C3×#137C2212yes—
28C2×C3×#135C2212yes—
29C22×C3×Q16C2212yes—
30C3×#562—22no—
31C3×#555—21no—
32C3×#555C2211yescharacteristic
33C3×#554C2211yescharacteristic
34C3×#553—21no—
35C3×#552C2212yes—
36C3×#550—21no—
37C3×#550C2211yescharacteristic
38C3×#550C2211yescharacteristic
39C3×D4×Q8—21no—
40C3×D4×Q8C2211yescharacteristic
41C3×D4×Q8C2211yescharacteristic
42C3×D4×Q8C2211yescharacteristic
43C3×#548—22no—
44C3×#548C2212yes—
45C3×#548C2212yes—
46C3×#548C2212yes—
47C3×#547C2211yescharacteristic
48C3×#544—21no—
49C3×#542—22no—
50C3×#540—21no—
51C3×#537—22no—
52C3×#537C2212yes—
53C3×#537C2212yes—
54C3×#536C2212yes—
55C3×#533C2211yescharacteristic
56C3×#532—21no—
57C3×#532—21no—
58C3×#532C2211yescharacteristic
59C3×#532C2211yescharacteristic
60C3×#529C2211yescharacteristic
61C2×C3×C4×Q8C2211yescharacteristic
62C3×#495C2212yes—
63C3×#494C2211yescharacteristic
64C3×#492C2211yescharacteristic
65C3×#488C2212yes—
66C3×#487C2211yescharacteristic
67C3×#486C2211yescharacteristic
68C3×#485C2212yes—
69C3×#484C2212yes—
70C3×#484C2212yes—
71C3×#483C2211yescharacteristic
72C3×#482C2212yes—
73C3×#480C2211yescharacteristic
74C3×#480C2212yes—
75C3×#479C2211yescharacteristic
76C3×#479C2211yescharacteristic
77C3×#477C2211yescharacteristic
78C3×#477C2211yescharacteristic
79C3×#470C2212yes—
80C3×#468C2212yes—
81C3×#468C2212yes—
82C3×#468C2212yes—
83C3×#467C2212yes—
84C3×#467C2212yes—
85C3×#466C2212yes—
86C3×#465C2212yes—
87C3×#464C2212yes—
88C3×#464C2212yes—
89C3×#464C2211yescharacteristic
90C3×#464C2211yescharacteristic
91C3×#462C2211yescharacteristic
92C3×#462C2211yescharacteristic
93C3×#462C2211yescharacteristic
94C3×#461C2211yescharacteristic
95C3×#460C2211yescharacteristic
96C3×#459C2211yescharacteristic
97C3×#452C2212yes—
98C3×#452C2212yes—
99C3×#452C2212yes—
100C3×#452C2212yes—
101C3×#452C2212yes—
102C3×#452C2212yes—
103C3×#452C2212yes—
104C3×#451C2212yes—
105C3×#451C2211yescharacteristic
106C3×#451C2212yes—
107C3×#451C2212yes—
108C3×#451C2212yes—
109C3×#451C2212yes—
110C3×#449C2212yes—
111C3×#449C2212yes—
112C3×#449C2212yes—
113C3×#448C2212yes—
114C3×#448C2211yescharacteristic
115C3×#448C2212yes—
116C3×C4×Q16C2212yes—
117C3×C4×Q16C2211yescharacteristic
118C3×C4×Q16C2212yes—
119C3×C4×Q16C2211yescharacteristic
120C3×C4×SD16C2211yescharacteristic
121C3×C4×SD16C2211yescharacteristic
122C3×#436C2211yescharacteristic
123C3×#436C2212yes—
124C3×#436C2211yescharacteristic
125C3×C8×D4C2211yescharacteristic
126C3×C8×D4C2212yes—
127C3×C8×D4C2211yescharacteristic
128C3×#431C2211yescharacteristic
129C3×#431C2211yescharacteristic
130C3×#419C2212yes—
131C3×#417C2212yes—
132C3×#416C2212yes—
133C2×C3×#103C2212yes—
134C3×#408C2212yes—
135C3×#408C2212yes—
136#3547C2×C311yescharacteristic, complemented
137#3497C2×C311yescharacteristic, complemented
138#3333C2×C311yescharacteristic, complemented
139#3329C2×C311yescharacteristic, complemented
140#3327C2×C312yescomplemented
141#3305C2×C311yescharacteristic, complemented
142#3300C2×C312yescomplemented
143#3299C2×C311yescharacteristic, complemented
144D4×Q16C2×C311yescharacteristic, complemented
145#3285C2×C312yescomplemented
146#3284C2×C311yescharacteristic, complemented
147#3278C2×C311yescharacteristic, complemented
148#3277C2×C312yescomplemented
149#3276C2×C311yescharacteristic, complemented
150#3212C2×C311yescharacteristic, complemented
151#3210C2×C311yescharacteristic, complemented
152#3203C2×C312yescomplemented
153#3201C2×C312yescomplemented
154#3108C2×C311yescharacteristic, complemented
155#3104C2×C311yescharacteristic, complemented
156#3013C2×C312yescomplemented
157#3011C2×C312yescomplemented
158#2979C2×C311yescharacteristic, complemented
159C3×2−1+4—44no—
160C3×2−1+4—44no—
161C2×C3×#41—22no—
162C2×C3×#41—22no—
163C2×C3×#41—22no—
164C2×C3×#41C2312yes—
165C2×C3×#41C2312yes—
166C2×C3×#41C2312yes—
167C2×C3×#41C2312yes—
168C2×C3×#41C2312yes—
169C22×C3×Q8—22no—
170C22×C3×Q8C2311yescharacteristic
171C22×C3×Q8C2312yes—
172C22×C3×Q8C2312yes—
173C22×C3×Q8C2312yes—
174C3×#137—44no—
175C3×#137—44no—
176C3×#135—44no—
177C2×C3×Q16—44no—
178C2×C3×Q16C2311yescharacteristic
179C2×C3×Q16C2312yes—
180C2×C3×Q16C2311yescharacteristic
181C2×C3×Q16C2312yes—
182C2×C3×Q16C2312yes—
183C2×C3×Q16C2312yes—
184C2×C3×Q16C2312yes—
185C2×C3×SD16C2311yescharacteristic
186C2×C3×SD16C2311yescharacteristic
187C2×C3×SD16C2312yes—
188C2×C3×SD16C2312yes—
189C2×C3×SD16C2312yes—
190C2×C3×SD16C2312yes—
191C2×C3×D8C2312yes—
192C2×C3×M16C2312yes—
193C2×C3×M16C2312yes—
194C22×C3×C8C2312yes—
195C22×C3×C8C2312yes—
196C3×C4⋊Q8—22no—
197C3×C4⋊Q8—21no—
198C3×C4⋊Q8—21no—
199C3×C4⋊Q8—21no—
200C3×C4⋊Q8D411yescharacteristic
201C3×C4⋊Q8C2311yescharacteristic
202C3×C4⋊Q8C2311yescharacteristic
203C3×C4⋊Q8C2311yescharacteristic
204C3×#127—21no—
205C3×#127—21no—
206C3×#127D411yescharacteristic
207C3×#127C2311yescharacteristic
208C3×#126—22no—
209C3×#126—21no—
210C3×#125—22no—
211C3×#125—21no—
212C3×#125—21no—
213C3×#125C2311yescharacteristic
214C3×#124—22no—
215C3×#124—22no—
216C3×#124—22no—
217C3×#124—22no—
218C3×#124—22no—
219C3×#124D412yes—
220C3×#124C2311yescharacteristic
221C3×#124C2312yes—
222C3×#123—22no—
223C3×#123—22no—
224C3×#123—22no—
225C3×#123—21no—
226C3×#123—22no—
227C3×C22⋊Q8—22no—
228C3×C22⋊Q8—22no—
229C3×C22⋊Q8—21no—
230C3×C22⋊Q8—22no—
231C3×C22⋊Q8—22no—
232C3×C22⋊Q8—22no—
233C3×C22⋊Q8—22no—
234C3×C22⋊Q8—22no—
235C3×C22⋊Q8—22no—
236C3×C22⋊Q8—22no—
237C3×C22⋊Q8C2311yescharacteristic
238C3×C22⋊Q8C2312yes—
239C3×C22⋊Q8C2312yes—
240C3×C22⋊Q8C2312yes—
241C3×C22⋊Q8C2312yes—
242C3×C22⋊Q8C2312yes—
243C3×C22⋊Q8C2312yes—
244C3×#121—22no—
245C3×#121—22no—
246C3×#121—22no—
247C3×#121—22no—
248C3×#121—22no—
249C3×#121—22no—
250C3×#121—22no—
251C3×#121—22no—
252C3×#121—22no—
253C3×#121—21no—
254C3×#121—21no—
255C3×#121—21no—
256C3×#121—21no—
257C3×#121—22no—
258C3×#121—22no—
259C3×#121D412yes—
260C3×#121D411yescharacteristic
261C3×#121D411yescharacteristic
262C3×#121C2311yescharacteristic
263C3×#121C2312yes—
264C3×#121C2312yes—
265C3×#121C2312yes—
266C3×C4×Q8—21no—
267C3×C4×Q8—21no—
268C3×C4×Q8—21no—
269C3×C4×Q8C2311yescharacteristic
270C3×C4×Q8C2311yescharacteristic
271C3×C4×Q8C2311yescharacteristic
272C3×C4×Q8C2311yescharacteristic
273C3×C4×Q8C2311yescharacteristic
274C3×C4×Q8C2312yes—
275C3×C4×D4—21no—
276C3×C4×D4—21no—
277C3×C4×D4—21no—
278C3×C4×D4—21no—
279C3×C4×D4—21no—
280C3×C4×D4—21no—
281C3×C4×D4—21no—
282C3×C4×D4—22no—
283C3×C4×D4—22no—
284C3×C4×D4—22no—
285C3×C4×D4—21no—
286C3×C4×D4—21no—
287C3×C4×D4C2311yescharacteristic
288C3×C4×D4C2311yescharacteristic
289C3×C4×D4C2312yes—
290C3×C4×D4C2311yescharacteristic
291C3×#117—21no—
292C3×#117—21no—
293C3×#117—22no—
294C3×#117—21no—
295C3×#117C2312yes—
296C2×C3×C4⋊C4—21no—
297C2×C3×C4⋊C4—21no—
298C2×C3×C4⋊C4C2312yes—
299C2×C3×C4⋊C4C2311yescharacteristic
300C2×C3×C42—21no—
301C2×C3×C42C2311yescharacteristic
302C3×#107C2312yes—
303C3×#107C2311yescharacteristic
304C3×#107C2312yes—
305C3×#107C2311yescharacteristic
306C3×#106C2311yescharacteristic
307C3×#106C2311yescharacteristic
308C3×C4⋊C8C2311yescharacteristic
309C3×C4⋊C8C2311yescharacteristic
310C3×C4⋊C8C2311yescharacteristic
311C3×C4⋊C8C2311yescharacteristic
312C3×#103C2311yescharacteristic
313C3×#103C2312yes—
314C3×#103C2312yes—
315C3×#103C2312yes—
316C3×#103C2311yescharacteristic
317C3×#103C2311yescharacteristic
318C3×#103C2312yes—
319C3×#103C2311yescharacteristic
320C3×#103C2312yes—
321C3×#103C2312yes—
322C3×#103C2311yescharacteristic
323C3×#103C2312yes—
324C3×#103C2312yes—
325C3×#103C2311yescharacteristic
326C3×#102C2312yes—
327C3×#102C2312yes—
328C3×#102C2312yes—
329C3×#102C2312yes—
330C3×#102C2311yescharacteristic
331C3×#102C2311yescharacteristic
332C3×C22⋊C8C2311yescharacteristic
333C3×C22⋊C8C2312yes—
334C3×C22⋊C8C2311yescharacteristic
335C3×C22⋊C8C2312yes—
336C3×C22⋊C8C2312yes—
337C3×C22⋊C8C2312yes—
338C3×C22⋊C8C2312yes—
339C3×C4×C8C2311yescharacteristic
340C3×C4×C8C2311yescharacteristic
341C3×C4×C8C2312yes—
342C2×2−1+4C22×C312yes—
343C2×#137C22×C312yes—
344C2×#137C22×C312yes—
345C2×#135C22×C312yes—
346C22×Q16C22×C312yes—
347#562—22no—
348#555—21no—
349#555C22×C311yescharacteristic
350#554C22×C311yescharacteristic
351#553—21no—
352#552C22×C312yes—
353#550—21no—
354#550C22×C311yescharacteristic
355#550C22×C311yescharacteristic
356D4×Q8—21no—
357D4×Q8C22×C311yescharacteristic
358D4×Q8C22×C311yescharacteristic
359D4×Q8C22×C311yescharacteristic
360#548—22no—
361#548C22×C312yes—
362#548C22×C312yes—
363#548C22×C312yes—
364#547C22×C311yescharacteristic
365#544—21no—
366#542—22no—
367#540—21no—
368#537—22no—
369#537C22×C312yes—
370#537C22×C312yes—
371#536C22×C312yes—
372#533C22×C311yescharacteristic
373#532—21no—
374#532—21no—
375#532C22×C311yescharacteristic
376#532C22×C311yescharacteristic
377#529C22×C311yescharacteristic
378C2×C4×Q8C22×C311yescharacteristic
379#495C22×C312yes—
380#494C22×C311yescharacteristic
381#492C22×C311yescharacteristic
382#488C22×C312yes—
383#487C22×C311yescharacteristic
384#486C22×C311yescharacteristic
385#485C22×C312yes—
386#484C22×C312yes—
387#484C22×C312yes—
388#483C22×C311yescharacteristic
389#482C22×C312yes—
390#480C22×C312yes—
391#480C22×C311yescharacteristic
392#479C22×C311yescharacteristic
393#479C22×C311yescharacteristic
394#477C22×C311yescharacteristic
395#477C22×C311yescharacteristic
396#470C22×C312yes—
397#468C22×C312yes—
398#468C22×C312yes—
399#468C22×C312yes—
400#467C22×C312yes—
401#467C22×C312yes—
402#466C22×C312yes—
403#465C22×C312yes—
404#464C22×C311yescharacteristic
405#464C22×C311yescharacteristic
406#464C22×C312yes—
407#464C22×C312yes—
408#462C22×C311yescharacteristic
409#462C22×C311yescharacteristic
410#462C22×C311yescharacteristic
411#461C22×C311yescharacteristic
412#460C22×C311yescharacteristic
413#459C22×C311yescharacteristic
414#452C22×C312yes—
415#452C22×C312yes—
416#452C22×C312yes—
417#452C22×C312yes—
418#452C22×C312yes—
419#452C22×C312yes—
420#452C22×C312yes—
421#451C22×C312yes—
422#451C22×C311yescharacteristic
423#451C22×C312yes—
424#451C22×C312yes—
425#451C22×C312yes—
426#451C22×C312yes—
427#449C22×C312yes—
428#449C22×C312yes—
429#449C22×C312yes—
430#448C22×C312yes—
431#448C22×C311yescharacteristic
432#448C22×C312yes—
433C4×Q16C22×C311yescharacteristic
434C4×Q16C22×C312yes—
435C4×Q16C22×C312yes—
436C4×Q16C22×C311yescharacteristic
437C4×SD16C22×C311yescharacteristic
438C4×SD16C22×C311yescharacteristic
439#436C22×C311yescharacteristic
440#436C22×C311yescharacteristic
441#436C22×C312yes—
442C8×D4C22×C311yescharacteristic
443C8×D4C22×C312yes—
444C8×D4C22×C311yescharacteristic
445#431C22×C311yescharacteristic
446#431C22×C311yescharacteristic
447#419C22×C312yes—
448#417C22×C312yes—
449#416C22×C312yes—
450C2×#103C22×C312yes—
451#408C22×C312yes—
452#408C22×C312yes—
453C3×#41—24no—
454C3×#41—24no—
455C3×#41—42no—
456C3×#41—42no—
457C3×#41—42no—
458C3×#41—42no—
459C3×#41—42no—
460C3×#41—42no—
461C3×#41—48no—
462C3×#41—48no—
463C3×#41—42no—
464C3×#41—42no—
465C3×#41—48no—
466C2×C3×Q8—22no—
467C2×C3×Q8—22no—
468C2×C3×Q8—21no—
469C2×C3×Q8—22no—
470C2×C3×Q8—22no—
471C2×C3×Q8—21no—
472C2×C3×Q8—22no—
473C2×C3×Q8—24no—
474C2×C3×Q8—24no—
475C2×C3×Q8—42no—
476C2×C3×Q8—42no—
477C2×C3×Q8—42no—
478C2×C3×Q8—42no—
479C2×C3×Q8—48no—
480C2×C3×Q8C2×D412yes—
481C2×C3×Q8C2412yes—
482C2×C3×Q8C2411yescharacteristic
483C2×C3×Q8C2412yes—
484C2×C3×Q8C2411yescharacteristic
485C2×C3×Q8C2411yescharacteristic
486C2×C3×D4—22no—
487C2×C3×D4—22no—
488C2×C3×D4—22no—
489C2×C3×D4—21no—
490C2×C3×D4—22no—
491C2×C3×D4—22no—
492C2×C3×D4—22no—
493C2×C3×D4—22no—
494C2×C3×D4—21no—
495C2×C3×D4—21no—
496C2×C3×D4C2×D411yescharacteristic
497C2×C3×D4C2×D411yescharacteristic
498C2×C3×D4C2×D412yes—
499C2×C3×D4C2×D412yes—
500C2×C3×D4C2×D412yes—
501C2×C3×D4C2×D412yes—
502C2×C3×D4C2412yes—
503C2×C3×D4C2411yescharacteristic
504C22×C3×C4—21no—
505C22×C3×C4—22no—
506C22×C3×C4—22no—
507C22×C3×C4—21no—
508C22×C3×C4—22no—
509C22×C3×C4—22no—
510C22×C3×C4—21no—
511C22×C3×C4—22no—
512C22×C3×C4—22no—
513C22×C3×C4—22no—
514C22×C3×C4—22no—
515C22×C3×C4C2×D411yescharacteristic
516C22×C3×C4C2×D411yescharacteristic
517C22×C3×C4C2411yescharacteristic
518C22×C3×C4C2412yes—
519C22×C3×C4C2412yes—
520C3×Q16—22no—
521C3×Q16—24no—
522C3×Q16—22no—
523C3×Q16—24no—
524C3×Q16—42no—
525C3×Q16—42no—
526C3×Q16—42no—
527C3×SD16—22no—
528C3×SD16—22no—
529C3×SD16—42no—
530C3×SD16—42no—
531C3×SD16—42no—
532C3×SD16—42no—
533C3×D8—42no—
534C3×M16—42no—
535C3×M16—42no—
536C2×C3×C8—42no—
537C2×C3×C8—42no—
538C2×C3×C8C2411yescharacteristic
539C2×C3×C8C2411yescharacteristic
540C2×C3×C8C2412yes—
541C2×C3×C8C2411yescharacteristic
542C2×C3×C8C2412yes—
543C2×C3×C8C2411yescharacteristic
544C3×C4⋊C4—21no—
545C3×C4⋊C4—21no—
546C3×C4⋊C4—21no—
547C3×C4⋊C4—21no—
548C3×C4⋊C4—21no—
549C3×C4⋊C4—22no—
550C3×C4⋊C4—21no—
551C3×C4⋊C4—22no—
552C3×C4⋊C4—21no—
553C3×C4⋊C4—21no—
554C3×C4⋊C4—22no—
555C3×C4⋊C4—21no—
556C3×C4⋊C4—21no—
557C3×C4⋊C4—21no—
558C3×C4⋊C4—21no—
559C3×C4⋊C4—22no—
560C3×C4⋊C4—22no—
561C3×C4⋊C4—22no—
562C3×C4⋊C4—22no—
563C3×C4⋊C4—21no—
564C3×C4⋊C4—22no—
565C3×C4⋊C4—21no—
566C3×C4⋊C4C2×D411yescharacteristic
567C3×C4⋊C4C2×D411yescharacteristic
568C3×C4⋊C4C2×D412yes—
569C3×C4⋊C4C2411yescharacteristic
570C3×C4⋊C4C2411yescharacteristic
571C3×C4⋊C4C2412yes—
572C3×C4⋊C4C2411yescharacteristic
573C3×C4⋊C4C2411yescharacteristic
574C3×C22⋊C4—22no—
575C3×C22⋊C4—22no—
576C3×C22⋊C4—22no—
577C3×C22⋊C4—22no—
578C3×C22⋊C4—22no—
579C3×C22⋊C4—22no—
580C3×C22⋊C4—22no—
581C3×C22⋊C4—21no—
582C3×C22⋊C4—21no—
583C3×C22⋊C4—21no—
584C3×C22⋊C4—22no—
585C3×C22⋊C4—22no—
586C3×C22⋊C4—21no—
587C3×C22⋊C4—22no—
588C3×C22⋊C4—22no—
589C3×C22⋊C4—22no—
590C3×C22⋊C4—21no—
591C3×C22⋊C4C2×D412yes—
592C3×C22⋊C4C2×D412yes—
593C3×C22⋊C4C2×D412yes—
594C3×C22⋊C4C2×D412yes—
595C3×C42—21no—
596C3×C42—21no—
597C3×C42—21no—
598C3×C42—21no—
599C3×C42—22no—
600C3×C42—22no—
601C3×C42—21no—
602C3×C42C2×D411yescharacteristic
603C3×C42C2×D411yescharacteristic
604C3×C42C2411yescharacteristic
605C3×C42C2411yescharacteristic
6062−1+4—44no—
6072−1+4—44no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—22no—
611C2×#41C23×C312yes—
612C2×#41C23×C312yes—
613C2×#41C23×C312yes—
614C2×#41C23×C312yes—
615C2×#41C23×C312yes—
616C22×Q8—22no—
617C22×Q8C23×C311yescharacteristic
618C22×Q8C23×C312yes—
619C22×Q8C23×C312yes—
620C22×Q8C23×C312yes—
621#137—44no—
622#137—44no—
623#135—44no—
624C2×Q16—44no—
625C2×Q16C23×C311yescharacteristic
626C2×Q16C23×C312yes—
627C2×Q16C23×C311yescharacteristic
628C2×Q16C23×C312yes—
629C2×Q16C23×C312yes—
630C2×Q16C23×C312yes—
631C2×Q16C23×C312yes—
632C2×SD16C23×C311yescharacteristic
633C2×SD16C23×C311yescharacteristic
634C2×SD16C23×C312yes—
635C2×SD16C23×C312yes—
636C2×SD16C23×C312yes—
637C2×SD16C23×C312yes—
638C2×D8C23×C312yes—
639C2×M16C23×C312yes—
640C2×M16C23×C312yes—
641C22×C8C23×C312yes—
642C22×C8C23×C312yes—
643C4⋊Q8—22no—
644C4⋊Q8—21no—
645C4⋊Q8—21no—
646C4⋊Q8—21no—
647C4⋊Q8C3×D411yescharacteristic
648C4⋊Q8C23×C311yescharacteristic
649C4⋊Q8C23×C311yescharacteristic
650C4⋊Q8C23×C311yescharacteristic
651#127—21no—
652#127—21no—
653#127C3×D411yescharacteristic
654#127C23×C311yescharacteristic
655#126—22no—
656#126—21no—
657#125—22no—
658#125—21no—
659#125—21no—
660#125C23×C311yescharacteristic
661#124—22no—
662#124—22no—
663#124—22no—
664#124—22no—
665#124—22no—
666#124C3×D412yes—
667#124C23×C311yescharacteristic
668#124C23×C312yes—
669#123—22no—
670#123—22no—
671#123—22no—
672#123—21no—
673#123—22no—
674C22⋊Q8—22no—
675C22⋊Q8—22no—
676C22⋊Q8—21no—
677C22⋊Q8—22no—
678C22⋊Q8—22no—
679C22⋊Q8—22no—
680C22⋊Q8—22no—
681C22⋊Q8—22no—
682C22⋊Q8—22no—
683C22⋊Q8—22no—
684C22⋊Q8C23×C311yescharacteristic
685C22⋊Q8C23×C312yes—
686C22⋊Q8C23×C312yes—
687C22⋊Q8C23×C312yes—
688C22⋊Q8C23×C312yes—
689C22⋊Q8C23×C312yes—
690C22⋊Q8C23×C312yes—
691#121—22no—
692#121—22no—
693#121—22no—
694#121—22no—
695#121—22no—
696#121—22no—
697#121—22no—
698#121—22no—
699#121—21no—
700#121—22no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—22no—
705#121—22no—
706#121C3×D411yescharacteristic
707#121C3×D411yescharacteristic
708#121C3×D412yes—
709#121C23×C311yescharacteristic
710#121C23×C312yes—
711#121C23×C312yes—
712#121C23×C312yes—
713C4×Q8—21no—
714C4×Q8—21no—
715C4×Q8—21no—
716C4×Q8C23×C311yescharacteristic
717C4×Q8C23×C311yescharacteristic
718C4×Q8C23×C311yescharacteristic
719C4×Q8C23×C311yescharacteristic
720C4×Q8C23×C311yescharacteristic
721C4×Q8C23×C312yes—
722C4×D4—21no—
723C4×D4—21no—
724C4×D4—21no—
725C4×D4—21no—
726C4×D4—21no—
727C4×D4—21no—
728C4×D4—21no—
729C4×D4—22no—
730C4×D4—22no—
731C4×D4—22no—
732C4×D4—21no—
733C4×D4—21no—
734C4×D4C23×C311yescharacteristic
735C4×D4C23×C311yescharacteristic
736C4×D4C23×C312yes—
737C4×D4C23×C311yescharacteristic
738#117—21no—
739#117—21no—
740#117—22no—
741#117—21no—
742#117C23×C312yes—
743C2×C4⋊C4—21no—
744C2×C4⋊C4—21no—
745C2×C4⋊C4C23×C311yescharacteristic
746C2×C4⋊C4C23×C312yes—
747C2×C42—21no—
748C2×C42C23×C311yescharacteristic
749#107C23×C312yes—
750#107C23×C311yescharacteristic
751#107C23×C312yes—
752#107C23×C311yescharacteristic
753#106C23×C311yescharacteristic
754#106C23×C311yescharacteristic
755C4⋊C8C23×C311yescharacteristic
756C4⋊C8C23×C311yescharacteristic
757C4⋊C8C23×C311yescharacteristic
758C4⋊C8C23×C311yescharacteristic
759#103C23×C311yescharacteristic
760#103C23×C312yes—
761#103C23×C312yes—
762#103C23×C312yes—
763#103C23×C311yescharacteristic
764#103C23×C311yescharacteristic
765#103C23×C312yes—
766#103C23×C311yescharacteristic
767#103C23×C312yes—
768#103C23×C312yes—
769#103C23×C311yescharacteristic
770#103C23×C312yes—
771#103C23×C312yes—
772#103C23×C311yescharacteristic
773#102C23×C312yes—
774#102C23×C312yes—
775#102C23×C312yes—
776#102C23×C312yes—
777#102C23×C311yescharacteristic
778#102C23×C311yescharacteristic
779C22⋊C8C23×C311yescharacteristic
780C22⋊C8C23×C312yes—
781C22⋊C8C23×C311yescharacteristic
782C22⋊C8C23×C312yes—
783C22⋊C8C23×C312yes—
784C22⋊C8C23×C312yes—
785C22⋊C8C23×C312yes—
786C4×C8C23×C311yescharacteristic
787C4×C8C23×C311yescharacteristic
788C4×C8C23×C312yes—
789C23×C3—21no—
790C23×C3—22no—
791C23×C3C22×D412yes—
792C23×C3C22×D412yes—
793C23×C3C22×D411yescharacteristic
794C3×Q8—24no—
795C3×Q8—21no—
796C3×Q8—21no—
797C3×Q8—21no—
798C3×Q8—22no—
799C3×Q8—22no—
800C3×Q8—22no—
801C3×Q8—21no—
802C3×Q8—22no—
803C3×Q8—42no—
804C3×Q8—44no—
805C3×Q8—44no—
806C3×Q8—81no—
807C3×Q8—82no—
808C3×Q8H(5,𝔽2)12yes—
809C3×Q8H(5,𝔽2)12yes—
810C3×D4—22no—
811C3×D4—22no—
812C3×D4—21no—
813C3×D4—22no—
814C3×D4—21no—
815C3×D4—22no—
816C3×D4—42no—
817C3×D4—42no—
818C3×D4—42no—
819C3×D4—42no—
820C3×D4—44no—
821C3×D4—44no—
822C3×D4—44no—
823C3×D4—42no—
824C3×D4—81no—
825C3×D4—81no—
826C3×D4—82no—
827C3×D4—82no—
828C3×D4—82no—
829C3×D4—82no—
830C2×C3×C4—24no—
831C2×C3×C4—21no—
832C2×C3×C4—21no—
833C2×C3×C4—22no—
834C2×C3×C4—22no—
835C2×C3×C4—22no—
836C2×C3×C4—22no—
837C2×C3×C4—22no—
838C2×C3×C4—21no—
839C2×C3×C4—21no—
840C2×C3×C4—21no—
841C2×C3×C4—21no—
842C2×C3×C4—21no—
843C2×C3×C4—22no—
844C2×C3×C4—21no—
845C2×C3×C4—21no—
846C2×C3×C4—22no—
847C2×C3×C4—22no—
848C2×C3×C4—41no—
849C2×C3×C4—44no—
850C2×C3×C4—44no—
851C2×C3×C4—44no—
852C2×C3×C4—44no—
853C2×C3×C4—44no—
854C2×C3×C4—42no—
855C2×C3×C4—82no—
856C2×C3×C4—82no—
857C2×C3×C4—81no—
858C2×C3×C4—82no—
859C2×C3×C4C22×D411yescharacteristic
860C2×C3×C4C22×D412yes—
861C2×C3×C4C22×D411yescharacteristic
862C2×C3×C4C22×D411yescharacteristic
863C2×C3×C4C22×D411yescharacteristic
864C2×C3×C4C22×D412yes—
865C2×C3×C4C22×D411yescharacteristic
866C2×C3×C4C2511yescharacteristic
867C3×C8—22no—
868C3×C8—21no—
869C3×C8—21no—
870C3×C8—21no—
871C3×C8—21no—
872C3×C8—22no—
873#41—24no—
874#41—24no—
875#41—42no—
876#41—42no—
877#41—42no—
878#41—42no—
879#41—42no—
880#41—42no—
881#41—48no—
882#41—48no—
883#41—42no—
884#41—42no—
885#41—48no—
886C2×Q8—22no—
887C2×Q8—22no—
888C2×Q8—21no—
889C2×Q8—22no—
890C2×Q8—22no—
891C2×Q8—21no—
892C2×Q8—22no—
893C2×Q8—24no—
894C2×Q8—24no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—48no—
900C2×Q8C2×C3×D412yes—
901C2×Q8C24×C312yes—
902C2×Q8C24×C311yescharacteristic
903C2×Q8C24×C312yes—
904C2×Q8C24×C311yescharacteristic
905C2×Q8C24×C311yescharacteristic
906C2×D4—22no—
907C2×D4—22no—
908C2×D4—22no—
909C2×D4—21no—
910C2×D4—22no—
911C2×D4—22no—
912C2×D4—22no—
913C2×D4—22no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4C2×C3×D411yescharacteristic
917C2×D4C2×C3×D411yescharacteristic
918C2×D4C2×C3×D412yes—
919C2×D4C2×C3×D412yes—
920C2×D4C2×C3×D412yes—
921C2×D4C2×C3×D412yes—
922C2×D4C24×C312yes—
923C2×D4C24×C311yescharacteristic
924C22×C4—21no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—21no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—21no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4C2×C3×D411yescharacteristic
936C22×C4C2×C3×D411yescharacteristic
937C22×C4C24×C311yescharacteristic
938C22×C4C24×C312yes—
939C22×C4C24×C312yes—
940Q16—22no—
941Q16—24no—
942Q16—22no—
943Q16—24no—
944Q16—42no—
945Q16—42no—
946Q16—42no—
947SD16—22no—
948SD16—22no—
949SD16—42no—
950SD16—42no—
951SD16—42no—
952SD16—42no—
953D8—42no—
954M16—42no—
955M16—42no—
956C2×C8—42no—
957C2×C8—42no—
958C2×C8C24×C311yescharacteristic
959C2×C8C24×C311yescharacteristic
960C2×C8C24×C312yes—
961C2×C8C24×C311yescharacteristic
962C2×C8C24×C312yes—
963C2×C8C24×C311yescharacteristic
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—22no—
970C4⋊C4—21no—
971C4⋊C4—22no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—22no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—21no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4C2×C3×D411yescharacteristic
987C4⋊C4C2×C3×D411yescharacteristic
988C4⋊C4C2×C3×D412yes—
989C4⋊C4C24×C311yescharacteristic
990C4⋊C4C24×C311yescharacteristic
991C4⋊C4C24×C312yes—
992C4⋊C4C24×C311yescharacteristic
993C4⋊C4C24×C311yescharacteristic
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—21no—
1002C22⋊C4—21no—
1003C22⋊C4—21no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—21no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—21no—
1011C22⋊C4C2×C3×D412yes—
1012C22⋊C4C2×C3×D412yes—
1013C22⋊C4C2×C3×D412yes—
1014C22⋊C4C2×C3×D412yes—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—22no—
1020C42—22no—
1021C42—21no—
1022C42C2×C3×D411yescharacteristic
1023C42C2×C3×D411yescharacteristic
1024C42C24×C311yescharacteristic
1025C42C24×C311yescharacteristic
1026C22×C3—21no—
1027C22×C3—22no—
1028C22×C3—22no—
1029C22×C3—21no—
1030C22×C3—22no—
1031C22×C3—22no—
1032C22×C3—21no—
1033C22×C3—22no—
1034C22×C3—22no—
1035C22×C3—42no—
1036C22×C3—41no—
1037C22×C3—42no—
1038C22×C3—41no—
1039C22×C3—41no—
1040C22×C3—42no—
1041C22×C3C23×D411yescharacteristic
1042C3×C4—21no—
1043C3×C4—21no—
1044C3×C4—22no—
1045C3×C4—22no—
1046C3×C4—21no—
1047C3×C4—22no—
1048C3×C4—22no—
1049C3×C4—21no—
1050C3×C4—41no—
1051C3×C4—41no—
1052C3×C4—41no—
1053C3×C4—42no—
1054C3×C4—42no—
1055C3×C4—42no—
1056C3×C4—41no—
1057C3×C4—41no—
1058C3×C4#57812yes—
1059C3×C4C2×H(5,𝔽2)11yescharacteristic
1060C3×C4C2×H(5,𝔽2)11yescharacteristic
1061C23—21no—
1062C23—22no—
1063C23C22×C3×D412yes—
1064C23C22×C3×D412yes—
1065C23C22×C3×D411yescharacteristic
1066Q8—24no—
1067Q8—21no—
1068Q8—21no—
1069Q8—21no—
1070Q8—22no—
1071Q8—22no—
1072Q8—22no—
1073Q8—21no—
1074Q8—22no—
1075Q8—42no—
1076Q8—44no—
1077Q8—44no—
1078Q8—82no—
1079Q8—81no—
1080Q8C3×H(5,𝔽2)12yes—
1081Q8C3×H(5,𝔽2)12yes—
1082D4—22no—
1083D4—22no—
1084D4—21no—
1085D4—22no—
1086D4—21no—
1087D4—22no—
1088D4—42no—
1089D4—42no—
1090D4—42no—
1091D4—42no—
1092D4—44no—
1093D4—44no—
1094D4—44no—
1095D4—42no—
1096D4—81no—
1097D4—82no—
1098D4—81no—
1099D4—82no—
1100D4—82no—
1101D4—82no—
1102C2×C4—24no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—41no—
1121C2×C4—44no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—44no—
1125C2×C4—44no—
1126C2×C4—42no—
1127C2×C4—82no—
1128C2×C4—82no—
1129C2×C4—82no—
1130C2×C4—81no—
1131C2×C4C22×C3×D411yescharacteristic
1132C2×C4C22×C3×D412yes—
1133C2×C4C22×C3×D411yescharacteristic
1134C2×C4C22×C3×D411yescharacteristic
1135C2×C4C22×C3×D411yescharacteristic
1136C2×C4C22×C3×D412yes—
1137C2×C4C22×C3×D411yescharacteristic
1138C2×C4C25×C311yescharacteristic
1139C8—22no—
1140C8—21no—
1141C8—21no—
1142C8—21no—
1143C8—21no—
1144C8—22no—
1145C2×C3—41no—
1146C2×C3—42no—
1147C2×C3—42no—
1148C2×C3—82no—
1149C2×C3—81no—
1150C2×C3#348411yescharacteristic
1151C2×C3C2×#57811yescharacteristic
1152C2×C3#358411yescharacteristic
1153C22—21no—
1154C22—22no—
1155C22—22no—
1156C22—21no—
1157C22—22no—
1158C22—22no—
1159C22—21no—
1160C22—22no—
1161C22—22no—
1162C22—42no—
1163C22—41no—
1164C22—41no—
1165C22—42no—
1166C22—42no—
1167C22—41no—
1168C22C23×C3×D411yescharacteristic
1169C4—22no—
1170C4—22no—
1171C4—21no—
1172C4—22no—
1173C4—22no—
1174C4—21no—
1175C4—21no—
1176C4—21no—
1177C4—42no—
1178C4—42no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—42no—
1185C4C3×#57812yes—
1186C4C2×C3×H(5,𝔽2)11yescharacteristic
1187C4C2×C3×H(5,𝔽2)11yescharacteristic
1188C3#6166011yescharacteristic, direct product factor, Sylow
1189C2—41no—
1190C2—42no—
1191C2—42no—
1192C2—82no—
1193C2—81no—
1194C2C3×#348411yescharacteristic
1195C2C2×C3×#57811yescharacteristic
1196C2C3×#358411yescharacteristic
subgroupG/H
center, socleC22×C3C23×D4
commutator, Frattini, cosocleC2×C4C25×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3547C2semidirect
2. C3×#3497C2semidirect
3. C3×#3333C2semidirect
4. C3×#3329C2semidirect
5. C3×#3327C2semidirect
6. C3×#3305C2semidirect
7. C3×#3300C2semidirect
8. C3×#3299C2semidirect
9. C3×D4×Q16C2semidirect
10. C3×#3285C2semidirect
11. C3×#3284C2semidirect
12. C3×#3278C2semidirect
13. C3×#3277C2semidirect
14. C3×#3276C2semidirect
15. C3×#3212C2semidirect
16. C3×#3210C2semidirect
17. C3×#3203C2semidirect
18. C3×#3201C2semidirect
19. C3×#3108C2semidirect
20. C3×#3104C2semidirect
21. C3×#3013C2semidirect
22. C3×#3011C2semidirect
23. C3×#2979C2semidirect
24. #61660C3direct (N × H)
136. #3547C2×C3semidirect
137. #3497C2×C3semidirect
138. #3333C2×C3semidirect
139. #3329C2×C3semidirect
140. #3327C2×C3semidirect
141. #3305C2×C3semidirect
142. #3300C2×C3semidirect
143. #3299C2×C3semidirect
144. D4×Q16C2×C3semidirect
145. #3285C2×C3semidirect
146. #3284C2×C3semidirect
147. #3278C2×C3semidirect
148. #3277C2×C3semidirect
149. #3276C2×C3semidirect
150. #3212C2×C3semidirect
151. #3210C2×C3semidirect
152. #3203C2×C3semidirect
153. #3201C2×C3semidirect
154. #3108C2×C3semidirect
155. #3104C2×C3semidirect
156. #3013C2×C3semidirect
157. #3011C2×C3semidirect
158. #2979C2×C3semidirect
1188. C3#61660direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35472
C3×#34972
C3×#33332
C3×#33292
C3×#33272
C3×#33052
C3×#33002
C3×#32992
C3×D4×Q162
C3×#32852
C3×#32842
C3×#32782
C3×#32772
C3×#32762
C3×#32122
C3×#32102
C3×#32032
C3×#32012
C3×#31082
C3×#31042
C3×#30132
C3×#30112
C3×#29792
#616603