Finite Group Databasebeta

← C3×#63047 #10681654

Subgroups — C3×#63047 #10681654

Order 768.

6492 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3567C216yesmaximal, complemented
2C3×#3563C213yesmaximal, complemented
3C3×#3559C213yesmaximal, complemented
4C3×#3559C216yesmaximal, complemented
5C3×#3553C216yesmaximal, complemented
6C3×#3548C213yesmaximal, complemented
7C3×#3539C216yesmaximal, complemented
8C3×#3539C2112yesmaximal, complemented
9C3×#3529C212yesmaximal, complemented
10C3×#3529C211yesmaximal, characteristic, complemented
11C3×#3517C213yesmaximal, complemented
12C3×#3515C213yesmaximal, complemented
13C3×#3512C213yesmaximal, complemented
14C3×#3492C216yesmaximal, complemented
15#63047C311yesmaximal, characteristic, direct product factor, Sylow
16C3×#564C2216yescomplemented
17C3×#563C2213yes—
18C3×#563C2216yes—
19C3×#563C2216yescomplemented
20C3×#562C2216yes—
21C3×#562C2213yes—
22C3×#562C2216yes—
23C3×#562C2213yes—
24C3×#562C2216yescomplemented
25C3×H(3,𝔽4)C2211yescharacteristic
26C3×#560C2216yes—
27C3×#560C22112yes—
28C3×#560C22112yescomplemented
29C3×#557C2211yescharacteristic, complemented
30C3×#557C2213yescomplemented
31C3×#554C2213yes—
32C3×#554C2216yescomplemented
33C3×#554C22112yescomplemented
34C3×#554C2213yescomplemented
35C3×#554C2216yescomplemented
36C3×#553C2216yes—
37C3×#553C22112yes—
38C3×#553C2216yes—
39C3×#553C22112yes—
40C3×#553C2216yescomplemented
41C3×#553C2216yescomplemented
42C3×#553C22112yescomplemented
43C3×#553C22112yescomplemented
44C3×#553C22112yescomplemented
45C3×#553C22112yescomplemented
46C3×#552C2216yes—
47C3×#552C2216yescomplemented
48C3×#552C22112yescomplemented
49C3×#552C2216yescomplemented
50C3×#552C22112yescomplemented
51C3×#552C2216yescomplemented
52C3×#552C22112yescomplemented
53C3×#550C2216yes—
54C3×#550C2213yes—
55C3×#550C2216yes—
56C3×#550C2211yescharacteristic, complemented
57C3×#550C2216yescomplemented
58C3×#547C2213yes—
59C3×#547C22112yes—
60C3×#547C2213yes—
61C3×#547C2216yescomplemented
62C3×#547C2216yescomplemented
63C3×#547C2216yescomplemented
64C3×#547C22112yescomplemented
65C3×#544C2216yescomplemented
66C3×#544C2216yescomplemented
67C3×#541C2216yescomplemented
68C3×#541C2216yescomplemented
69C3×#541C22112yescomplemented
70C3×#540C2216yes—
71C3×#540C22112yes—
72C3×#540C22112yes—
73C3×#540C2216yescomplemented
74C3×#540C22112yescomplemented
75C3×#540C22112yescomplemented
76C3×#539C22112yes—
77C3×#539C2216yes—
78C3×#539C22112yescomplemented
79C3×#539C22112yescomplemented
80C3×#539C22112yescomplemented
81C3×#539C22112yescomplemented
82C3×#539C22112yescomplemented
83C3×#539C2216yescomplemented
84C3×#537C2216yes—
85C3×#537C2213yes—
86C3×#537C2216yes—
87C3×#537C2213yescomplemented
88C3×#537C22112yescomplemented
89C3×#533C2213yescomplemented
90C3×#532C2213yes—
91C3×#532C2216yes—
92C3×#532C2213yescomplemented
93C3×#529C2216yes—
94C3×#529C2213yes—
95C3×#529C2216yes—
96C3×#529C2213yes—
97C3×#529C2216yescomplemented
98C3×#529C2216yescomplemented
99C2×C3×#125C2213yescomplemented
100C2×C3×#125C2216yescomplemented
101C3×#525C2216yes—
102C3×#525C22112yes—
103C3×#525C2216yescomplemented
104C3×#525C22112yescomplemented
105C3×#520C2213yes—
106C3×#520C2216yescomplemented
107C3×#520C2211yescharacteristic, complemented
108C3×C4×#41C2213yescomplemented
109C22×C3×C4⋊C4C2212yescomplemented
110#3567C2×C316yescomplemented
111#3563C2×C313yescomplemented
112#3559C2×C313yescomplemented
113#3559C2×C316yescomplemented
114#3553C2×C316yescomplemented
115#3548C2×C313yescomplemented
116#3539C2×C316yescomplemented
117#3539C2×C3112yescomplemented
118#3529C2×C312yescomplemented
119#3529C2×C311yescharacteristic, complemented
120#3517C2×C313yescomplemented
121#3515C2×C313yescomplemented
122#3512C2×C313yescomplemented
123#3492C2×C316yescomplemented
124C2×C3×#41C2313yes—
125C2×C3×#41C2313yes—
126C2×C3×#41C2316yes—
127C2×C3×#41C2311yescharacteristic
128C2×C3×#41C2316yes—
129C2×C3×#41C23112yes—
130C2×C3×#41C2312yes—
131C2×C3×#41C2316yes—
132C23×C3×C4C2312yes—
133C23×C3×C4C2314yes—
134C3×C4⋊Q8C2313yes—
135C3×C4⋊Q8C2316yes—
136C3×C4⋊Q8C23112yes—
137C3×C4⋊Q8C2313yes—
138C3×C4⋊Q8C2313yes—
139C3×C4⋊Q8C2313yes—
140C3×#127C2316yes—
141C3×#127C2313yes—
142C3×#127C23112yes—
143C3×#127C2313yes—
144C3×#126C2316yes—
145C3×#126C23112yes—
146C3×#126C23112yes—
147C3×#126C2316yes—
148C3×#126C23112yes—
149C3×#126C23112yes—
150C3×#126C23112yes—
151C3×#126C23112yes—
152C3×#126C23112yes—
153C3×#126C23112yes—
154C3×#125C2316yes—
155C3×#125C2313yes—
156C3×#125C2316yes—
157C3×#125C2313yes—
158C3×#125C23112yes—
159C3×#125C23112yes—
160C3×#125C23112yes—
161C3×#125C23112yes—
162C3×#125C23112yes—
163C3×#125C23112yes—
164C3×#125C23112yes—
165C3×#125C2316yes—
166C3×#125C23112yes—
167C3×#125C2316yes—
168C3×#125C2316yes—
169C3×#125C2316yes—
170C3×#125C2316yes—
171C3×#124C2313yes—
172C3×#124C2313yes—
173C3×#124C2313yes—
174C3×#124C2313yes—
175C3×#124C2316yes—
176C3×#123C2316yes—
177C3×#123C23112yes—
178C3×#123C23112yes—
179C3×#123C2316yes—
180C3×#123C2316yes—
181C3×#123C23112yes—
182C3×#123C23112yes—
183C3×#123C23112yes—
184C3×#123C23112yes—
185C3×#123C2316yes—
186C3×#123C23112yes—
187C3×#123C23112yes—
188C3×#123C23112yes—
189C3×#123C23112yes—
190C3×#123C23112yes—
191C3×#123C23112yes—
192C3×#123C23112yes—
193C3×#123C23112yes—
194C3×#123C23112yes—
195C3×C22⋊Q8C2316yes—
196C3×C22⋊Q8C2313yes—
197C3×C22⋊Q8C2316yes—
198C3×C22⋊Q8C2313yes—
199C3×C22⋊Q8C23112yes—
200C3×C22⋊Q8C2316yes—
201C3×C22⋊Q8C2316yes—
202C3×C22⋊Q8C23112yes—
203C3×C22⋊Q8C23112yes—
204C3×C22⋊Q8C23112yes—
205C3×C22⋊Q8C23112yes—
206C3×C22⋊Q8C23112yes—
207C3×C22⋊Q8C23112yes—
208C3×C22⋊Q8C2316yes—
209C3×C22⋊Q8C2316yes—
210C3×C22⋊Q8C23112yes—
211C3×C22⋊Q8C2316yes—
212C3×C22⋊Q8C2316yes—
213C3×C22⋊Q8C2316yes—
214C3×C22⋊Q8C2316yes—
215C3×#121C2313yes—
216C3×#121C2316yes—
217C3×#121C2313yes—
218C3×#121C2316yes—
219C3×#121C23112yes—
220C3×#121C23112yes—
221C3×#121C2316yes—
222C3×#121C2316yes—
223C3×#121C2316yes—
224C3×#121C23112yes—
225C3×#121C23112yes—
226C3×#121C2316yes—
227C3×#121C23112yes—
228C3×#121C23112yes—
229C3×#121C23112yes—
230C3×#121C23112yes—
231C3×#121C23112yes—
232C3×#121C23112yes—
233C3×#121C23112yes—
234C3×#121C23112yes—
235C3×#121C23112yes—
236C3×#121C2316yes—
237C3×#121C2316yes—
238C3×#121C23112yes—
239C3×#121C2316yes—
240C3×#121C2316yes—
241C3×#121C2316yes—
242C3×#121C2316yes—
243C3×#120C2316yes—
244C3×#120C2316yes—
245C3×#120C23112yes—
246C3×C4×Q8C2313yes—
247C3×C4×Q8C2313yes—
248C3×C4×Q8C2316yes—
249C3×C4×Q8C2312yes—
250C3×C4×Q8C2316yes—
251C3×C4×Q8C2311yescharacteristic
252C3×C4×Q8C2312yes—
253C3×C4×Q8C2311yescharacteristic
254C3×C4×Q8C2316yes—
255C3×C4×Q8C2316yes—
256C3×C4×D4C2313yes—
257C3×C4×D4C2316yes—
258C3×C4×D4C2313yes—
259C3×C4×D4C2316yes—
260C3×C4×D4C2316yes—
261C3×C4×D4C23112yes—
262C3×C4×D4C23112yes—
263C3×C4×D4C23112yes—
264C3×C4×D4C2316yes—
265C3×C4×D4C2316yes—
266C3×C4×D4C2313yes—
267C3×C4×D4C2313yes—
268C3×C4×D4C2316yes—
269C3×C4×D4C2316yes—
270C3×C4×D4C2316yes—
271C3×C4×D4C23112yes—
272C3×C4×D4C23112yes—
273C3×C4×D4C23112yes—
274C3×C4×D4C23112yes—
275C3×C4×D4C23112yes—
276C3×C4×D4C2316yes—
277C3×C4×D4C23112yes—
278C3×C4×D4C23112yes—
279C3×C4×D4C2316yes—
280C3×#117C2313yes—
281C3×#117C2316yes—
282C3×#117C2316yes—
283C3×#117C2316yes—
284C3×#117C23112yes—
285C3×#117C23112yes—
286C3×#117C23112yes—
287C3×#117C23112yes—
288C3×#117C2316yes—
289C2×C3×C4⋊C4C2316yes—
290C2×C3×C4⋊C4C2316yes—
291C2×C3×C4⋊C4C23112yes—
292C2×C3×C4⋊C4C2313yes—
293C2×C3×C4⋊C4C2313yes—
294C2×C3×C4⋊C4C23112yes—
295C2×C3×C4⋊C4C2316yes—
296C2×C3×C4⋊C4C23112yes—
297C2×C3×C4⋊C4C2316yes—
298C2×C3×C4⋊C4C2316yes—
299C2×C3×C4⋊C4C2316yes—
300C2×C3×C42C2316yes—
301C2×C3×C42C2313yes—
302#564C22×C316yescomplemented
303#563C22×C313yes—
304#563C22×C316yes—
305#563C22×C316yescomplemented
306#562C22×C316yes—
307#562C22×C313yes—
308#562C22×C316yes—
309#562C22×C313yes—
310#562C22×C316yescomplemented
311H(3,𝔽4)C22×C311yescharacteristic
312#560C22×C3112yes—
313#560C22×C316yes—
314#560C22×C3112yescomplemented
315#557C22×C311yescharacteristic, complemented
316#557C22×C313yescomplemented
317#554C22×C313yes—
318#554C22×C316yescomplemented
319#554C22×C3112yescomplemented
320#554C22×C313yescomplemented
321#554C22×C316yescomplemented
322#553C22×C316yes—
323#553C22×C3112yes—
324#553C22×C316yes—
325#553C22×C3112yes—
326#553C22×C316yescomplemented
327#553C22×C316yescomplemented
328#553C22×C3112yescomplemented
329#553C22×C3112yescomplemented
330#553C22×C3112yescomplemented
331#553C22×C3112yescomplemented
332#552C22×C316yes—
333#552C22×C316yescomplemented
334#552C22×C3112yescomplemented
335#552C22×C316yescomplemented
336#552C22×C3112yescomplemented
337#552C22×C316yescomplemented
338#552C22×C3112yescomplemented
339#550C22×C316yes—
340#550C22×C313yes—
341#550C22×C316yes—
342#550C22×C311yescharacteristic, complemented
343#550C22×C316yescomplemented
344#547C22×C313yes—
345#547C22×C3112yes—
346#547C22×C313yes—
347#547C22×C316yescomplemented
348#547C22×C316yescomplemented
349#547C22×C316yescomplemented
350#547C22×C3112yescomplemented
351#544C22×C316yescomplemented
352#544C22×C316yescomplemented
353#541C22×C316yescomplemented
354#541C22×C316yescomplemented
355#541C22×C3112yescomplemented
356#540C22×C316yes—
357#540C22×C3112yes—
358#540C22×C3112yes—
359#540C22×C316yescomplemented
360#540C22×C3112yescomplemented
361#540C22×C3112yescomplemented
362#539C22×C3112yes—
363#539C22×C316yes—
364#539C22×C3112yescomplemented
365#539C22×C3112yescomplemented
366#539C22×C3112yescomplemented
367#539C22×C3112yescomplemented
368#539C22×C3112yescomplemented
369#539C22×C316yescomplemented
370#537C22×C316yes—
371#537C22×C313yes—
372#537C22×C316yes—
373#537C22×C313yescomplemented
374#537C22×C3112yescomplemented
375#533C22×C313yescomplemented
376#532C22×C313yes—
377#532C22×C316yes—
378#532C22×C313yescomplemented
379#529C22×C316yes—
380#529C22×C313yes—
381#529C22×C316yes—
382#529C22×C313yes—
383#529C22×C316yescomplemented
384#529C22×C316yescomplemented
385C2×#125C22×C313yescomplemented
386C2×#125C22×C316yescomplemented
387#525C22×C316yes—
388#525C22×C3112yes—
389#525C22×C316yescomplemented
390#525C22×C3112yescomplemented
391#520C22×C313yes—
392#520C22×C316yescomplemented
393#520C22×C311yescharacteristic, complemented
394C4×#41C22×C313yescomplemented
395C22×C4⋊C4C22×C312yescomplemented
396C24×C3C2412yes—
397C3×#41—46no—
398C3×#41—42no—
399C3×#41—412no—
400C3×#41—46no—
401C3×#41—86no—
402C3×#41—812no—
403C3×#41—82no—
404C3×#41—86no—
405C2×C3×Q8C2413yes—
406C2×C3×Q8C2411yescharacteristic
407C2×C3×Q8C2413yes—
408C2×C3×Q8C2411yescharacteristic
409C2×C3×Q8C2416yes—
410C2×C3×Q8C2416yes—
411C2×C3×Q8C2411yescharacteristic
412C2×C3×D4C2413yes—
413C2×C3×D4C2413yes—
414C2×C3×D4C24112yes—
415C2×C3×D4C2416yes—
416C2×C3×D4C2416yes—
417C2×C3×D4C2413yes—
418C2×C3×D4C2416yes—
419C2×C3×D4C24112yes—
420C2×C3×D4C2413yes—
421C2×C3×D4C2416yes—
422C2×C3×D4C2413yes—
423C2×C3×D4C2416yes—
424C2×C3×D4C24112yes—
425C2×C3×D4C24112yes—
426C2×C3×D4C2416yes—
427C22×C3×C4—44no—
428C22×C3×C4—84no—
429C22×C3×C4C2413yes—
430C22×C3×C4C2416yes—
431C22×C3×C4C2413yes—
432C22×C3×C4C2416yes—
433C22×C3×C4C2416yes—
434C22×C3×C4C2416yes—
435C22×C3×C4C2413yes—
436C22×C3×C4C2416yes—
437C22×C3×C4C24112yes—
438C22×C3×C4C2416yes—
439C22×C3×C4C24112yes—
440C22×C3×C4C24112yes—
441C22×C3×C4C24112yes—
442C22×C3×C4C2416yes—
443C3×C4⋊C4C2411yescharacteristic
444C3×C4⋊C4C2416yes—
445C3×C4⋊C4C24112yes—
446C3×C4⋊C4C24112yes—
447C3×C4⋊C4C2413yes—
448C3×C4⋊C4C2416yes—
449C3×C4⋊C4C2416yes—
450C3×C4⋊C4C2416yes—
451C3×C4⋊C4C24112yes—
452C3×C4⋊C4C2413yes—
453C3×C4⋊C4C2416yes—
454C3×C4⋊C4C2413yes—
455C3×C4⋊C4C24112yes—
456C3×C4⋊C4C24112yes—
457C3×C4⋊C4C24112yes—
458C3×C4⋊C4C24112yes—
459C3×C4⋊C4C2416yes—
460C3×C4⋊C4C24112yes—
461C3×C4⋊C4C24112yes—
462C3×C4⋊C4C2416yes—
463C3×C4⋊C4C24112yes—
464C3×C4⋊C4C2416yes—
465C3×C4⋊C4C2416yes—
466C3×C4⋊C4C2416yes—
467C3×C4⋊C4C2416yes—
468C3×C4⋊C4C2416yes—
469C3×C4⋊C4C2416yes—
470C3×C4⋊C4C2413yes—
471C3×C4⋊C4C2413yes—
472C3×C22⋊C4C2416yes—
473C3×C22⋊C4C2416yes—
474C3×C22⋊C4C24112yes—
475C3×C22⋊C4C2416yes—
476C3×C22⋊C4C24112yes—
477C3×C22⋊C4C2416yes—
478C3×C22⋊C4C2416yes—
479C3×C22⋊C4C2416yes—
480C3×C22⋊C4C24112yes—
481C3×C22⋊C4C2416yes—
482C3×C22⋊C4C2416yes—
483C3×C22⋊C4C24112yes—
484C3×C22⋊C4C24112yes—
485C3×C22⋊C4C2416yes—
486C3×C22⋊C4C2416yes—
487C3×C22⋊C4C24112yes—
488C3×C22⋊C4C24112yes—
489C3×C22⋊C4C24112yes—
490C3×C22⋊C4C2416yes—
491C3×C42C2413yes—
492C3×C42C2416yes—
493C3×C42C2416yes—
494C3×C42C2413yes—
495C3×C42C2413yes—
496C3×C42C2413yes—
497C3×C42C2416yes—
498C3×C42C24112yes—
499C3×C42C24112yes—
500C2×#41C23×C313yes—
501C2×#41C23×C313yes—
502C2×#41C23×C316yes—
503C2×#41C23×C311yescharacteristic
504C2×#41C23×C316yes—
505C2×#41C23×C3112yes—
506C2×#41C23×C312yes—
507C2×#41C23×C316yes—
508C23×C4C23×C312yes—
509C23×C4C23×C314yes—
510C4⋊Q8C23×C313yes—
511C4⋊Q8C23×C316yes—
512C4⋊Q8C23×C313yes—
513C4⋊Q8C23×C313yes—
514C4⋊Q8C23×C313yes—
515C4⋊Q8C23×C3112yes—
516#127C23×C316yes—
517#127C23×C313yes—
518#127C23×C313yes—
519#127C23×C3112yes—
520#126C23×C316yes—
521#126C23×C3112yes—
522#126C23×C3112yes—
523#126C23×C316yes—
524#126C23×C3112yes—
525#126C23×C3112yes—
526#126C23×C3112yes—
527#126C23×C3112yes—
528#126C23×C3112yes—
529#126C23×C3112yes—
530#125C23×C313yes—
531#125C23×C316yes—
532#125C23×C316yes—
533#125C23×C3112yes—
534#125C23×C316yes—
535#125C23×C3112yes—
536#125C23×C316yes—
537#125C23×C316yes—
538#125C23×C316yes—
539#125C23×C316yes—
540#125C23×C313yes—
541#125C23×C3112yes—
542#125C23×C3112yes—
543#125C23×C3112yes—
544#125C23×C3112yes—
545#125C23×C3112yes—
546#125C23×C3112yes—
547#124C23×C313yes—
548#124C23×C313yes—
549#124C23×C313yes—
550#124C23×C313yes—
551#124C23×C316yes—
552#123C23×C316yes—
553#123C23×C3112yes—
554#123C23×C316yes—
555#123C23×C3112yes—
556#123C23×C3112yes—
557#123C23×C3112yes—
558#123C23×C3112yes—
559#123C23×C316yes—
560#123C23×C3112yes—
561#123C23×C3112yes—
562#123C23×C316yes—
563#123C23×C3112yes—
564#123C23×C3112yes—
565#123C23×C3112yes—
566#123C23×C3112yes—
567#123C23×C3112yes—
568#123C23×C3112yes—
569#123C23×C3112yes—
570#123C23×C3112yes—
571C22⋊Q8C23×C3112yes—
572C22⋊Q8C23×C316yes—
573C22⋊Q8C23×C316yes—
574C22⋊Q8C23×C3112yes—
575C22⋊Q8C23×C3112yes—
576C22⋊Q8C23×C316yes—
577C22⋊Q8C23×C316yes—
578C22⋊Q8C23×C3112yes—
579C22⋊Q8C23×C316yes—
580C22⋊Q8C23×C313yes—
581C22⋊Q8C23×C316yes—
582C22⋊Q8C23×C313yes—
583C22⋊Q8C23×C316yes—
584C22⋊Q8C23×C316yes—
585C22⋊Q8C23×C316yes—
586C22⋊Q8C23×C316yes—
587C22⋊Q8C23×C3112yes—
588C22⋊Q8C23×C3112yes—
589C22⋊Q8C23×C3112yes—
590C22⋊Q8C23×C3112yes—
591#121C23×C3112yes—
592#121C23×C3112yes—
593#121C23×C316yes—
594#121C23×C316yes—
595#121C23×C3112yes—
596#121C23×C316yes—
597#121C23×C316yes—
598#121C23×C3112yes—
599#121C23×C313yes—
600#121C23×C316yes—
601#121C23×C313yes—
602#121C23×C316yes—
603#121C23×C316yes—
604#121C23×C316yes—
605#121C23×C316yes—
606#121C23×C3112yes—
607#121C23×C3112yes—
608#121C23×C316yes—
609#121C23×C316yes—
610#121C23×C316yes—
611#121C23×C3112yes—
612#121C23×C3112yes—
613#121C23×C3112yes—
614#121C23×C3112yes—
615#121C23×C3112yes—
616#121C23×C3112yes—
617#121C23×C3112yes—
618#121C23×C3112yes—
619#120C23×C316yes—
620#120C23×C316yes—
621#120C23×C3112yes—
622C4×Q8C23×C313yes—
623C4×Q8C23×C313yes—
624C4×Q8C23×C316yes—
625C4×Q8C23×C312yes—
626C4×Q8C23×C316yes—
627C4×Q8C23×C311yescharacteristic
628C4×Q8C23×C312yes—
629C4×Q8C23×C311yescharacteristic
630C4×Q8C23×C316yes—
631C4×Q8C23×C316yes—
632C4×D4C23×C313yes—
633C4×D4C23×C316yes—
634C4×D4C23×C313yes—
635C4×D4C23×C316yes—
636C4×D4C23×C316yes—
637C4×D4C23×C3112yes—
638C4×D4C23×C3112yes—
639C4×D4C23×C3112yes—
640C4×D4C23×C316yes—
641C4×D4C23×C316yes—
642C4×D4C23×C313yes—
643C4×D4C23×C313yes—
644C4×D4C23×C316yes—
645C4×D4C23×C316yes—
646C4×D4C23×C316yes—
647C4×D4C23×C3112yes—
648C4×D4C23×C3112yes—
649C4×D4C23×C3112yes—
650C4×D4C23×C3112yes—
651C4×D4C23×C3112yes—
652C4×D4C23×C316yes—
653C4×D4C23×C3112yes—
654C4×D4C23×C3112yes—
655C4×D4C23×C316yes—
656#117C23×C313yes—
657#117C23×C316yes—
658#117C23×C316yes—
659#117C23×C316yes—
660#117C23×C3112yes—
661#117C23×C3112yes—
662#117C23×C3112yes—
663#117C23×C3112yes—
664#117C23×C316yes—
665C2×C4⋊C4C23×C316yes—
666C2×C4⋊C4C23×C316yes—
667C2×C4⋊C4C23×C3112yes—
668C2×C4⋊C4C23×C313yes—
669C2×C4⋊C4C23×C313yes—
670C2×C4⋊C4C23×C3112yes—
671C2×C4⋊C4C23×C316yes—
672C2×C4⋊C4C23×C3112yes—
673C2×C4⋊C4C23×C316yes—
674C2×C4⋊C4C23×C316yes—
675C2×C4⋊C4C23×C316yes—
676C2×C42C23×C316yes—
677C2×C42C23×C313yes—
678C23×C3—42no—
679C23×C3—42no—
680C23×C3—42no—
681C23×C3C2516yes—
682C23×C3C2513yes—
683C23×C3C2516yes—
684C3×Q8—26no—
685C3×Q8—41no—
686C3×Q8—43no—
687C3×Q8—41no—
688C3×Q8—46no—
689C3×Q8—46no—
690C3×Q8—41no—
691C3×D4—26no—
692C3×D4—412no—
693C3×D4—43no—
694C3×D4—46no—
695C3×D4—46no—
696C3×D4—46no—
697C3×D4—43no—
698C3×D4—43no—
699C3×D4—412no—
700C3×D4—46no—
701C3×D4—412no—
702C3×D4—46no—
703C3×D4—412no—
704C3×D4—43no—
705C3×D4—46no—
706C2×C3×C4—212no—
707C2×C3×C4—26no—
708C2×C3×C4—46no—
709C2×C3×C4—412no—
710C2×C3×C4—412no—
711C2×C3×C4—46no—
712C2×C3×C4—46no—
713C2×C3×C4—43no—
714C2×C3×C4—412no—
715C2×C3×C4—46no—
716C2×C3×C4—46no—
717C2×C3×C4—46no—
718C2×C3×C4—412no—
719C2×C3×C4—43no—
720C2×C3×C4C2513yes—
721C2×C3×C4C2512yes—
722C2×C3×C4C2513yes—
723C2×C3×C4C2516yes—
724C2×C3×C4C2513yes—
725C2×C3×C4C2516yes—
726C2×C3×C4C2513yes—
727C2×C3×C4C2516yes—
728C2×C3×C4C2513yes—
729C2×C3×C4C25112yes—
730C2×C3×C4C2511yescharacteristic
731C24C24×C312yes—
732#41—46no—
733#41—42no—
734#41—412no—
735#41—46no—
736#41—86no—
737#41—812no—
738#41—82no—
739#41—86no—
740C2×Q8C24×C313yes—
741C2×Q8C24×C311yescharacteristic
742C2×Q8C24×C313yes—
743C2×Q8C24×C311yescharacteristic
744C2×Q8C24×C316yes—
745C2×Q8C24×C316yes—
746C2×Q8C24×C311yescharacteristic
747C2×D4C24×C313yes—
748C2×D4C24×C313yes—
749C2×D4C24×C3112yes—
750C2×D4C24×C316yes—
751C2×D4C24×C316yes—
752C2×D4C24×C313yes—
753C2×D4C24×C316yes—
754C2×D4C24×C3112yes—
755C2×D4C24×C313yes—
756C2×D4C24×C316yes—
757C2×D4C24×C313yes—
758C2×D4C24×C316yes—
759C2×D4C24×C3112yes—
760C2×D4C24×C3112yes—
761C2×D4C24×C316yes—
762C22×C4—44no—
763C22×C4—84no—
764C22×C4C24×C313yes—
765C22×C4C24×C316yes—
766C22×C4C24×C313yes—
767C22×C4C24×C316yes—
768C22×C4C24×C316yes—
769C22×C4C24×C316yes—
770C22×C4C24×C313yes—
771C22×C4C24×C316yes—
772C22×C4C24×C3112yes—
773C22×C4C24×C316yes—
774C22×C4C24×C3112yes—
775C22×C4C24×C3112yes—
776C22×C4C24×C3112yes—
777C22×C4C24×C316yes—
778C4⋊C4C24×C311yescharacteristic
779C4⋊C4C24×C316yes—
780C4⋊C4C24×C3112yes—
781C4⋊C4C24×C3112yes—
782C4⋊C4C24×C313yes—
783C4⋊C4C24×C316yes—
784C4⋊C4C24×C316yes—
785C4⋊C4C24×C316yes—
786C4⋊C4C24×C3112yes—
787C4⋊C4C24×C313yes—
788C4⋊C4C24×C316yes—
789C4⋊C4C24×C313yes—
790C4⋊C4C24×C3112yes—
791C4⋊C4C24×C3112yes—
792C4⋊C4C24×C3112yes—
793C4⋊C4C24×C3112yes—
794C4⋊C4C24×C316yes—
795C4⋊C4C24×C3112yes—
796C4⋊C4C24×C3112yes—
797C4⋊C4C24×C316yes—
798C4⋊C4C24×C3112yes—
799C4⋊C4C24×C316yes—
800C4⋊C4C24×C316yes—
801C4⋊C4C24×C316yes—
802C4⋊C4C24×C316yes—
803C4⋊C4C24×C316yes—
804C4⋊C4C24×C316yes—
805C4⋊C4C24×C313yes—
806C4⋊C4C24×C313yes—
807C22⋊C4C24×C316yes—
808C22⋊C4C24×C316yes—
809C22⋊C4C24×C3112yes—
810C22⋊C4C24×C316yes—
811C22⋊C4C24×C3112yes—
812C22⋊C4C24×C316yes—
813C22⋊C4C24×C316yes—
814C22⋊C4C24×C316yes—
815C22⋊C4C24×C3112yes—
816C22⋊C4C24×C316yes—
817C22⋊C4C24×C316yes—
818C22⋊C4C24×C3112yes—
819C22⋊C4C24×C3112yes—
820C22⋊C4C24×C316yes—
821C22⋊C4C24×C316yes—
822C22⋊C4C24×C3112yes—
823C22⋊C4C24×C3112yes—
824C22⋊C4C24×C3112yes—
825C22⋊C4C24×C316yes—
826C42C24×C313yes—
827C42C24×C316yes—
828C42C24×C316yes—
829C42C24×C313yes—
830C42C24×C313yes—
831C42C24×C313yes—
832C42C24×C316yes—
833C42C24×C3112yes—
834C42C24×C3112yes—
835C22×C3—26no—
836C22×C3—23no—
837C22×C3—26no—
838C22×C3—26no—
839C22×C3—23no—
840C22×C3—26no—
841C22×C3—23no—
842C22×C3—26no—
843C22×C3—26no—
844C22×C3—48no—
845C22×C3C2611yescharacteristic
846C3×C4—26no—
847C3×C4—23no—
848C3×C4—26no—
849C3×C4—22no—
850C3×C4—212no—
851C3×C4—23no—
852C3×C4—23no—
853C3×C4—26no—
854C3×C4—23no—
855C3×C4—23no—
856C3×C4#58512yes—
857C23—42no—
858C23—42no—
859C23—42no—
860C23C25×C316yes—
861C23C25×C313yes—
862C23C25×C316yes—
863Q8—26no—
864Q8—43no—
865Q8—41no—
866Q8—46no—
867Q8—46no—
868Q8—41no—
869Q8—41no—
870D4—26no—
871D4—46no—
872D4—43no—
873D4—43no—
874D4—412no—
875D4—46no—
876D4—412no—
877D4—46no—
878D4—412no—
879D4—43no—
880D4—46no—
881D4—412no—
882D4—43no—
883D4—46no—
884D4—46no—
885C2×C4—212no—
886C2×C4—26no—
887C2×C4—46no—
888C2×C4—412no—
889C2×C4—412no—
890C2×C4—412no—
891C2×C4—46no—
892C2×C4—46no—
893C2×C4—46no—
894C2×C4—412no—
895C2×C4—43no—
896C2×C4—46no—
897C2×C4—46no—
898C2×C4—43no—
899C2×C4C25×C313yes—
900C2×C4C25×C312yes—
901C2×C4C25×C313yes—
902C2×C4C25×C316yes—
903C2×C4C25×C313yes—
904C2×C4C25×C316yes—
905C2×C4C25×C313yes—
906C2×C4C25×C316yes—
907C2×C4C25×C313yes—
908C2×C4C25×C3112yes—
909C2×C4C25×C311yescharacteristic
910C2×C3—43no—
911C2×C3—46no—
912C2×C3—46no—
913C2×C3C2×#58511yescharacteristic
914C2×C3H(7,𝔽2)11yescharacteristic
915C2×C32−1+611yescharacteristic
916C22—26no—
917C22—23no—
918C22—26no—
919C22—26no—
920C22—23no—
921C22—26no—
922C22—23no—
923C22—26no—
924C22—26no—
925C22—48no—
926C22C26×C311yescharacteristic
927C4—26no—
928C4—23no—
929C4—26no—
930C4—22no—
931C4—212no—
932C4—23no—
933C4—23no—
934C4—26no—
935C4—23no—
936C4—23no—
937C4C3×#58512yes—
938C3#6304711yescharacteristic, direct product factor, Sylow
939C2—46no—
940C2—43no—
941C2—46no—
942C2C2×C3×#58511yescharacteristic
943C2C3×H(7,𝔽2)11yescharacteristic
944C2C3×2−1+611yescharacteristic
subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3567C2semidirect
2. C3×#3563C2semidirect
3. C3×#3559C2semidirect
4. C3×#3559C2semidirect
5. C3×#3553C2semidirect
6. C3×#3548C2semidirect
7. C3×#3539C2semidirect
8. C3×#3539C2semidirect
9. C3×#3529C2semidirect
10. C3×#3529C2semidirect
11. C3×#3517C2semidirect
12. C3×#3515C2semidirect
13. C3×#3512C2semidirect
14. C3×#3492C2semidirect
15. #63047C3direct (N × H)
16. C3×#564C22semidirect
19. C3×#563C22semidirect
24. C3×#562C22semidirect
28. C3×#560C22semidirect
29. C3×#557C22semidirect
30. C3×#557C22semidirect
32. C3×#554C22semidirect
33. C3×#554C22semidirect
34. C3×#554C22semidirect
35. C3×#554C22semidirect
40. C3×#553C22semidirect
41. C3×#553C22semidirect
42. C3×#553C22semidirect
43. C3×#553C22semidirect
44. C3×#553C22semidirect
45. C3×#553C22semidirect
47. C3×#552C22semidirect
48. C3×#552C22semidirect
49. C3×#552C22semidirect
50. C3×#552C22semidirect
51. C3×#552C22semidirect
52. C3×#552C22semidirect
56. C3×#550C22semidirect
57. C3×#550C22semidirect
61. C3×#547C22semidirect
62. C3×#547C22semidirect
63. C3×#547C22semidirect
64. C3×#547C22semidirect
65. C3×#544C22semidirect
66. C3×#544C22semidirect
67. C3×#541C22semidirect
68. C3×#541C22semidirect
69. C3×#541C22semidirect
73. C3×#540C22semidirect
74. C3×#540C22semidirect
75. C3×#540C22semidirect
78. C3×#539C22semidirect
79. C3×#539C22semidirect
80. C3×#539C22semidirect
81. C3×#539C22semidirect
82. C3×#539C22semidirect
83. C3×#539C22semidirect
87. C3×#537C22semidirect
88. C3×#537C22semidirect
89. C3×#533C22semidirect
92. C3×#532C22semidirect
97. C3×#529C22semidirect
98. C3×#529C22semidirect
99. C2×C3×#125C22semidirect
100. C2×C3×#125C22semidirect
103. C3×#525C22semidirect
104. C3×#525C22semidirect
106. C3×#520C22semidirect
107. C3×#520C22semidirect
108. C3×C4×#41C22semidirect
109. C22×C3×C4⋊C4C22semidirect
110. #3567C2×C3semidirect
111. #3563C2×C3semidirect
112. #3559C2×C3semidirect
113. #3559C2×C3semidirect
114. #3553C2×C3semidirect
115. #3548C2×C3semidirect
116. #3539C2×C3semidirect
117. #3539C2×C3semidirect
118. #3529C2×C3semidirect
119. #3529C2×C3semidirect
120. #3517C2×C3semidirect
121. #3515C2×C3semidirect
122. #3512C2×C3semidirect
123. #3492C2×C3semidirect
302. #564C22×C3semidirect
305. #563C22×C3semidirect
310. #562C22×C3semidirect
314. #560C22×C3semidirect
315. #557C22×C3semidirect
316. #557C22×C3semidirect
318. #554C22×C3semidirect
319. #554C22×C3semidirect
320. #554C22×C3semidirect
321. #554C22×C3semidirect
326. #553C22×C3semidirect
327. #553C22×C3semidirect
328. #553C22×C3semidirect
329. #553C22×C3semidirect
330. #553C22×C3semidirect
331. #553C22×C3semidirect
333. #552C22×C3semidirect
334. #552C22×C3semidirect
335. #552C22×C3semidirect
336. #552C22×C3semidirect
337. #552C22×C3semidirect
338. #552C22×C3semidirect
342. #550C22×C3semidirect
343. #550C22×C3semidirect
347. #547C22×C3semidirect
348. #547C22×C3semidirect
349. #547C22×C3semidirect
350. #547C22×C3semidirect
351. #544C22×C3semidirect
352. #544C22×C3semidirect
353. #541C22×C3semidirect
354. #541C22×C3semidirect
355. #541C22×C3semidirect
359. #540C22×C3semidirect
360. #540C22×C3semidirect
361. #540C22×C3semidirect
364. #539C22×C3semidirect
365. #539C22×C3semidirect
366. #539C22×C3semidirect
367. #539C22×C3semidirect
368. #539C22×C3semidirect
369. #539C22×C3semidirect
373. #537C22×C3semidirect
374. #537C22×C3semidirect
375. #533C22×C3semidirect
378. #532C22×C3semidirect
383. #529C22×C3semidirect
384. #529C22×C3semidirect
385. C2×#125C22×C3semidirect
386. C2×#125C22×C3semidirect
389. #525C22×C3semidirect
390. #525C22×C3semidirect
392. #520C22×C3semidirect
393. #520C22×C3semidirect
394. C4×#41C22×C3semidirect
395. C22×C4⋊C4C22×C3semidirect
938. C3#63047direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35672
C3×#35632
C3×#35592
C3×#35532
C3×#35482
C3×#35392
C3×#35292
C3×#35172
C3×#35152
C3×#35122
C3×#34922
#630473