Finite Group Databasebeta

← C3×#62904 #10681511

Subgroups — C3×#62904 #10681511

Order 768.

6370 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3564C2112yesmaximal, complemented
2C3×#3563C2112yesmaximal, complemented
3C3×#3563C216yesmaximal, complemented
4C3×#3538C216yesmaximal, complemented
5C3×#3523C216yesmaximal, complemented
6C3×#3501C213yesmaximal, complemented
7C3×#3495C216yesmaximal, complemented
8C3×#3491C216yesmaximal, complemented
9C2×C3×#552C213yesmaximal, complemented
10C3×#3459C211yesmaximal, characteristic
11C3×#3458C212yesmaximal, complemented
12#62904C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#564C22112yescomplemented
14C3×#563C22124yescomplemented
15C3×#563C22112yescomplemented
16C3×#557C2212yescomplemented
17C3×#557C2216yescomplemented
18C3×#557C22112yescomplemented
19C3×#556C2216yescomplemented
20C3×#556C22112yescomplemented
21C3×#554C22112yescomplemented
22C3×#554C22124yescomplemented
23C3×#552C22112yescomplemented
24C3×#552C22112yescomplemented
25C3×#552C22124yescomplemented
26C3×#552C22124yescomplemented
27C3×#552C22124yescomplemented
28C3×#552C22112yescomplemented
29C3×#552C22124yescomplemented
30C3×#551C22124yescomplemented
31C3×#551C22124yescomplemented
32C3×D4×Q8C22112yescomplemented
33C3×D4×Q8C2216yescomplemented
34C3×#544C22112yescomplemented
35C3×#544C22112yescomplemented
36C3×#544C2216yescomplemented
37C3×#544C2216yescomplemented
38C3×#544C22112yescomplemented
39C3×#543C2211yescharacteristic
40C3×#543C2216yes—
41C3×#543C2216yescomplemented
42C3×#542C22112yescomplemented
43C3×#541C22112yescomplemented
44C3×#541C22112yescomplemented
45C3×#541C22124yescomplemented
46C3×#541C22124yescomplemented
47C3×#539C2216yes—
48C3×#539C22112yes—
49C3×#539C22112yes—
50C3×#539C22112yescomplemented
51C3×#538C2216yes—
52C3×#536C2216yescomplemented
53C3×#534C2213yes—
54C3×#533C22112yescomplemented
55C3×#533C22112yescomplemented
56C3×#533C2216yescomplemented
57C3×#529C2216yes—
58C3×#529C22112yes—
59C3×#529C22112yes—
60C2×C3×#126C2216yescomplemented
61C2×C3×#125C2216yescomplemented
62C2×C3×#125C2213yescomplemented
63C3×#525C2216yes—
64C2×C3×#123C2216yes—
65C2×C3×C22⋊Q8C2213yes—
66C2×C3×C22⋊Q8C2213yescomplemented
67C2×C3×C22⋊Q8C2216yescomplemented
68C3×#520C2212yescomplemented
69C3×#519C2216yescomplemented
70C3×#518C2216yes—
71C2×C3×C4×Q8C2213yescomplemented
72C2×C3×C4×D4C2213yes—
73C2×C3×#117C2216yes—
74C2×C3×#117C2213yescomplemented
75C22×C3×C4⋊C4C2211yescharacteristic
76#3564C2×C3112yescomplemented
77#3563C2×C316yescomplemented
78#3563C2×C3112yescomplemented
79#3538C2×C316yescomplemented
80#3523C2×C316yescomplemented
81#3501C2×C313yescomplemented
82#3495C2×C316yescomplemented
83#3491C2×C316yescomplemented
84C2×#552C2×C313yescomplemented
85#3459C2×C311yescharacteristic
86#3458C2×C312yescomplemented
87C2×C3×#41C2312yes—
88C22×C3×Q8C2313yes—
89C22×C3×Q8C2316yes—
90C22×C3×D4C2313yes—
91C23×C3×C4C2312yes—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2313yes—
94C3×C4⋊Q8C23112yes—
95C3×C4⋊Q8C23112yes—
96C3×C4⋊Q8C23124yes—
97C3×C4⋊Q8C23112yes—
98C3×C4⋊Q8C23112yes—
99C3×C4⋊Q8C2316yes—
100C3×C4⋊Q8C2316yes—
101C3×#126C23124yes—
102C3×#126C23124yes—
103C3×#126C23124yes—
104C3×#126C23124yes—
105C3×#126C23124yes—
106C3×#126C23112yes—
107C3×#126C23124yes—
108C3×#125C23112yes—
109C3×#125C23124yes—
110C3×#125C23112yes—
111C3×#125C23124yes—
112C3×#125C2316yes—
113C3×#125C23112yes—
114C3×#125C23124yes—
115C3×#125C23124yes—
116C3×#125C23124yes—
117C3×#125C23124yes—
118C3×#125C23112yes—
119C3×#125C23112yes—
120C3×#125C23124yes—
121C3×#124C23112yes—
122C3×#124C2316yes—
123C3×#124C23112yes—
124C3×#123C23112yes—
125C3×#123C23124yes—
126C3×#123C23124yes—
127C3×#123C23124yes—
128C3×#123C23124yes—
129C3×#123C23112yes—
130C3×C22⋊Q8C23112yes—
131C3×C22⋊Q8C23112yes—
132C3×C22⋊Q8C23124yes—
133C3×C22⋊Q8C23124yes—
134C3×C22⋊Q8C23124yes—
135C3×C22⋊Q8C23124yes—
136C3×C22⋊Q8C23112yes—
137C3×C22⋊Q8C23112yes—
138C3×C22⋊Q8C23112yes—
139C3×C22⋊Q8C23112yes—
140C3×C22⋊Q8C23112yes—
141C3×C22⋊Q8C2316yes—
142C3×C22⋊Q8C2316yes—
143C3×C22⋊Q8C2316yes—
144C3×C22⋊Q8C23112yes—
145C3×C22⋊Q8C23124yes—
146C3×C22⋊Q8C23124yes—
147C3×#121C2316yes—
148C3×#121C2316yes—
149C3×#121C2316yes—
150C3×#120C23112yes—
151C3×C4×Q8C2316yes—
152C3×C4×Q8C2316yes—
153C3×C4×Q8C23112yes—
154C3×C4×Q8C23112yes—
155C3×C4×Q8C23112yes—
156C3×C4×Q8C23112yes—
157C3×C4×Q8C2314yes—
158C3×C4×Q8C2312yes—
159C3×C4×Q8C23112yes—
160C3×C4×Q8C23112yes—
161C3×C4×Q8C2314yes—
162C3×C4×Q8C23112yes—
163C3×C4×D4C23112yes—
164C3×C4×D4C23112yes—
165C3×C4×D4C23124yes—
166C3×C4×D4C23124yes—
167C3×C4×D4C23112yes—
168C3×C4×D4C2316yes—
169C3×C4×D4C23112yes—
170C3×#117C23124yes—
171C3×#117C23124yes—
172C3×#117C2316yes—
173C3×#117C2316yes—
174C3×#117C23112yes—
175C3×#117C23112yes—
176C3×#117C2316yes—
177C3×#117C23124yes—
178C3×#117C23124yes—
179C2×C3×C4⋊C4C2313yes—
180C2×C3×C4⋊C4C2313yes—
181C2×C3×C4⋊C4C2316yes—
182C2×C3×C4⋊C4C2316yes—
183C2×C3×C4⋊C4C2316yes—
184C2×C3×C4⋊C4C2313yes—
185C2×C3×C4⋊C4C2313yes—
186C2×C3×C4⋊C4C2316yes—
187C2×C3×C4⋊C4C2316yes—
188C2×C3×C4⋊C4C2316yes—
189C2×C3×C4⋊C4C23112yes—
190C2×C3×C4⋊C4C2316yes—
191C2×C3×C22⋊C4C2313yes—
192C2×C3×C22⋊C4C2316yes—
193C2×C3×C22⋊C4C2316yes—
194C2×C3×C22⋊C4C2313yes—
195C2×C3×C22⋊C4C23112yes—
196C2×C3×C22⋊C4C2316yes—
197C2×C3×C42C2316yes—
198C2×C3×C42C2316yes—
199C2×C3×C42C2313yes—
200#564C22×C3112yescomplemented
201#563C22×C3124yescomplemented
202#563C22×C3112yescomplemented
203#557C22×C312yescomplemented
204#557C22×C316yescomplemented
205#557C22×C3112yescomplemented
206#556C22×C316yescomplemented
207#556C22×C3112yescomplemented
208#554C22×C3112yescomplemented
209#554C22×C3124yescomplemented
210#552C22×C3112yescomplemented
211#552C22×C3112yescomplemented
212#552C22×C3124yescomplemented
213#552C22×C3124yescomplemented
214#552C22×C3124yescomplemented
215#552C22×C3112yescomplemented
216#552C22×C3124yescomplemented
217#551C22×C3124yescomplemented
218#551C22×C3124yescomplemented
219D4×Q8C22×C3112yescomplemented
220D4×Q8C22×C316yescomplemented
221#544C22×C3112yescomplemented
222#544C22×C3112yescomplemented
223#544C22×C316yescomplemented
224#544C22×C316yescomplemented
225#544C22×C3112yescomplemented
226#543C22×C311yescharacteristic
227#543C22×C316yes—
228#543C22×C316yescomplemented
229#542C22×C3112yescomplemented
230#541C22×C3112yescomplemented
231#541C22×C3112yescomplemented
232#541C22×C3124yescomplemented
233#541C22×C3124yescomplemented
234#539C22×C316yes—
235#539C22×C3112yes—
236#539C22×C3112yes—
237#539C22×C3112yescomplemented
238#538C22×C316yes—
239#536C22×C316yescomplemented
240#534C22×C313yes—
241#533C22×C3112yescomplemented
242#533C22×C3112yescomplemented
243#533C22×C316yescomplemented
244#529C22×C316yes—
245#529C22×C3112yes—
246#529C22×C3112yes—
247C2×#126C22×C316yescomplemented
248C2×#125C22×C316yescomplemented
249C2×#125C22×C313yescomplemented
250#525C22×C316yes—
251C2×#123C22×C316yes—
252C2×C22⋊Q8C22×C313yes—
253C2×C22⋊Q8C22×C313yescomplemented
254C2×C22⋊Q8C22×C316yescomplemented
255#520C22×C312yescomplemented
256#519C22×C316yescomplemented
257#518C22×C316yes—
258C2×C4×Q8C22×C313yescomplemented
259C2×C4×D4C22×C313yes—
260C2×#117C22×C316yes—
261C2×#117C22×C313yescomplemented
262C22×C4⋊C4C22×C311yescharacteristic
263C24×C3C2413yes—
264C24×C3C2411yescharacteristic
265C3×#41—44no—
266C2×C3×Q8—46no—
267C2×C3×Q8—412no—
268C2×C3×Q8C2416yes—
269C2×C3×Q8C24112yes—
270C2×C3×Q8C2412yes—
271C2×C3×Q8C2416yes—
272C2×C3×Q8C24112yes—
273C2×C3×Q8C2412yes—
274C2×C3×D4—212no—
275C2×C3×D4C24112yes—
276C2×C3×D4C2416yes—
277C2×C3×D4C2416yes—
278C22×C3×C4—28no—
279C22×C3×C4—42no—
280C22×C3×C4—46no—
281C22×C3×C4C2416yes—
282C22×C3×C4C2413yes—
283C22×C3×C4C2413yes—
284C22×C3×C4C2416yes—
285C22×C3×C4C2416yes—
286C22×C3×C4C2413yes—
287C22×C3×C4C2413yes—
288C22×C3×C4C2416yes—
289C22×C3×C4C2416yes—
290C22×C3×C4C2413yes—
291C22×C3×C4C24112yes—
292C22×C3×C4C24112yes—
293C22×C3×C4C2416yes—
294C3×C4⋊C4C2411yescharacteristic
295C3×C4⋊C4C2413yes—
296C3×C4⋊C4C2416yes—
297C3×C4⋊C4C2416yes—
298C3×C4⋊C4C2416yes—
299C3×C4⋊C4C24124yes—
300C3×C4⋊C4C24112yes—
301C3×C4⋊C4C2416yes—
302C3×C4⋊C4C24124yes—
303C3×C4⋊C4C24124yes—
304C3×C4⋊C4C24124yes—
305C3×C4⋊C4C24124yes—
306C3×C4⋊C4C24112yes—
307C3×C4⋊C4C24112yes—
308C3×C4⋊C4C24112yes—
309C3×C4⋊C4C24112yes—
310C3×C4⋊C4C24112yes—
311C3×C4⋊C4C2416yes—
312C3×C4⋊C4C2416yes—
313C3×C4⋊C4C24124yes—
314C3×C4⋊C4C24112yes—
315C3×C4⋊C4C2416yes—
316C3×C4⋊C4C2416yes—
317C3×C22⋊C4C24124yes—
318C3×C22⋊C4C24112yes—
319C3×C22⋊C4C24112yes—
320C3×C22⋊C4C24112yes—
321C3×C22⋊C4C24124yes—
322C3×C22⋊C4C24112yes—
323C3×C22⋊C4C24124yes—
324C3×C22⋊C4C24112yes—
325C3×C22⋊C4C24112yes—
326C3×C42C24112yes—
327C3×C42C24112yes—
328C3×C42C24112yes—
329C3×C42C2416yes—
330C3×C42C24112yes—
331C3×C42C2416yes—
332C3×C42C24124yes—
333C2×#41C23×C312yes—
334C22×Q8C23×C313yes—
335C22×Q8C23×C316yes—
336C22×D4C23×C313yes—
337C23×C4C23×C312yes—
338C23×C4C23×C311yescharacteristic
339C23×C4C23×C313yes—
340C4⋊Q8C23×C3112yes—
341C4⋊Q8C23×C3112yes—
342C4⋊Q8C23×C316yes—
343C4⋊Q8C23×C3112yes—
344C4⋊Q8C23×C316yes—
345C4⋊Q8C23×C3112yes—
346C4⋊Q8C23×C3124yes—
347#126C23×C3124yes—
348#126C23×C3124yes—
349#126C23×C3112yes—
350#126C23×C3124yes—
351#126C23×C3124yes—
352#126C23×C3124yes—
353#126C23×C3124yes—
354#125C23×C3124yes—
355#125C23×C3112yes—
356#125C23×C3112yes—
357#125C23×C3124yes—
358#125C23×C316yes—
359#125C23×C3112yes—
360#125C23×C3112yes—
361#125C23×C3124yes—
362#125C23×C3112yes—
363#125C23×C3124yes—
364#125C23×C3124yes—
365#125C23×C3124yes—
366#125C23×C3124yes—
367#124C23×C3112yes—
368#124C23×C316yes—
369#124C23×C3112yes—
370#123C23×C3124yes—
371#123C23×C3124yes—
372#123C23×C3112yes—
373#123C23×C3112yes—
374#123C23×C3124yes—
375#123C23×C3124yes—
376C22⋊Q8C23×C3112yes—
377C22⋊Q8C23×C3112yes—
378C22⋊Q8C23×C3112yes—
379C22⋊Q8C23×C3112yes—
380C22⋊Q8C23×C3112yes—
381C22⋊Q8C23×C3112yes—
382C22⋊Q8C23×C3112yes—
383C22⋊Q8C23×C316yes—
384C22⋊Q8C23×C316yes—
385C22⋊Q8C23×C316yes—
386C22⋊Q8C23×C3112yes—
387C22⋊Q8C23×C3124yes—
388C22⋊Q8C23×C3124yes—
389C22⋊Q8C23×C3124yes—
390C22⋊Q8C23×C3124yes—
391C22⋊Q8C23×C3124yes—
392C22⋊Q8C23×C3124yes—
393#121C23×C316yes—
394#121C23×C316yes—
395#121C23×C316yes—
396#120C23×C3112yes—
397C4×Q8C23×C316yes—
398C4×Q8C23×C316yes—
399C4×Q8C23×C3112yes—
400C4×Q8C23×C3112yes—
401C4×Q8C23×C3112yes—
402C4×Q8C23×C3112yes—
403C4×Q8C23×C314yes—
404C4×Q8C23×C312yes—
405C4×Q8C23×C3112yes—
406C4×Q8C23×C3112yes—
407C4×Q8C23×C314yes—
408C4×Q8C23×C3112yes—
409C4×D4C23×C3112yes—
410C4×D4C23×C3112yes—
411C4×D4C23×C3124yes—
412C4×D4C23×C3124yes—
413C4×D4C23×C3112yes—
414C4×D4C23×C316yes—
415C4×D4C23×C3112yes—
416#117C23×C3124yes—
417#117C23×C3124yes—
418#117C23×C316yes—
419#117C23×C316yes—
420#117C23×C3112yes—
421#117C23×C3112yes—
422#117C23×C316yes—
423#117C23×C3124yes—
424#117C23×C3124yes—
425C2×C4⋊C4C23×C313yes—
426C2×C4⋊C4C23×C313yes—
427C2×C4⋊C4C23×C316yes—
428C2×C4⋊C4C23×C316yes—
429C2×C4⋊C4C23×C316yes—
430C2×C4⋊C4C23×C313yes—
431C2×C4⋊C4C23×C313yes—
432C2×C4⋊C4C23×C316yes—
433C2×C4⋊C4C23×C316yes—
434C2×C4⋊C4C23×C316yes—
435C2×C4⋊C4C23×C3112yes—
436C2×C4⋊C4C23×C316yes—
437C2×C22⋊C4C23×C313yes—
438C2×C22⋊C4C23×C316yes—
439C2×C22⋊C4C23×C316yes—
440C2×C22⋊C4C23×C313yes—
441C2×C22⋊C4C23×C3112yes—
442C2×C22⋊C4C23×C316yes—
443C2×C42C23×C316yes—
444C2×C42C23×C316yes—
445C2×C42C23×C313yes—
446C23×C3—26no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—43no—
450C23×C3—43no—
451C23×C32−1+414yes—
452C23×C3C2516yes—
453C23×C3C2513yes—
454C3×Q8—212no—
455C3×Q8—46no—
456C3×Q8—412no—
457C3×Q8—412no—
458C3×Q8—42no—
459C3×Q8—42no—
460C3×D4—224no—
461C3×D4—46no—
462C3×D4—46no—
463C2×C3×C4—212no—
464C2×C3×C4—212no—
465C2×C3×C4—26no—
466C2×C3×C4—26no—
467C2×C3×C4—212no—
468C2×C3×C4—43no—
469C2×C3×C4—46no—
470C2×C3×C4—43no—
471C2×C3×C4—46no—
472C2×C3×C4—412no—
473C2×C3×C4—43no—
474C2×C3×C4—46no—
475C2×C3×C4—412no—
476C2×C3×C4C2512yes—
477C2×C3×C4C2516yes—
478C2×C3×C4C2516yes—
479C2×C3×C4C2516yes—
480C2×C3×C4C25112yes—
481C2×C3×C4C25112yes—
482C2×C3×C4C2516yes—
483C2×C3×C4C2513yes—
484C2×C3×C4C2511yescharacteristic
485C24C24×C313yes—
486C24C24×C311yescharacteristic
487#41—44no—
488C2×Q8—46no—
489C2×Q8—412no—
490C2×Q8C24×C316yes—
491C2×Q8C24×C3112yes—
492C2×Q8C24×C312yes—
493C2×Q8C24×C316yes—
494C2×Q8C24×C3112yes—
495C2×Q8C24×C312yes—
496C2×D4—212no—
497C2×D4C24×C3112yes—
498C2×D4C24×C316yes—
499C2×D4C24×C316yes—
500C22×C4—28no—
501C22×C4—42no—
502C22×C4—46no—
503C22×C4C24×C316yes—
504C22×C4C24×C313yes—
505C22×C4C24×C313yes—
506C22×C4C24×C316yes—
507C22×C4C24×C316yes—
508C22×C4C24×C313yes—
509C22×C4C24×C313yes—
510C22×C4C24×C316yes—
511C22×C4C24×C316yes—
512C22×C4C24×C313yes—
513C22×C4C24×C3112yes—
514C22×C4C24×C3112yes—
515C22×C4C24×C316yes—
516C4⋊C4C24×C311yescharacteristic
517C4⋊C4C24×C313yes—
518C4⋊C4C24×C316yes—
519C4⋊C4C24×C316yes—
520C4⋊C4C24×C316yes—
521C4⋊C4C24×C3124yes—
522C4⋊C4C24×C3112yes—
523C4⋊C4C24×C316yes—
524C4⋊C4C24×C3124yes—
525C4⋊C4C24×C3124yes—
526C4⋊C4C24×C3124yes—
527C4⋊C4C24×C3124yes—
528C4⋊C4C24×C3112yes—
529C4⋊C4C24×C3112yes—
530C4⋊C4C24×C3112yes—
531C4⋊C4C24×C3112yes—
532C4⋊C4C24×C3112yes—
533C4⋊C4C24×C316yes—
534C4⋊C4C24×C316yes—
535C4⋊C4C24×C3124yes—
536C4⋊C4C24×C3112yes—
537C4⋊C4C24×C316yes—
538C4⋊C4C24×C316yes—
539C22⋊C4C24×C3124yes—
540C22⋊C4C24×C3112yes—
541C22⋊C4C24×C3112yes—
542C22⋊C4C24×C3112yes—
543C22⋊C4C24×C3124yes—
544C22⋊C4C24×C3112yes—
545C22⋊C4C24×C3124yes—
546C22⋊C4C24×C3112yes—
547C22⋊C4C24×C3112yes—
548C42C24×C3112yes—
549C42C24×C3112yes—
550C42C24×C3112yes—
551C42C24×C316yes—
552C42C24×C3112yes—
553C42C24×C316yes—
554C42C24×C3124yes—
555C22×C3—23no—
556C22×C3—23no—
557C22×C3—26no—
558C22×C3—26no—
559C22×C3—26no—
560C22×C3—44no—
561C22×C3—86no—
562C22×C3C2×2−1+416yes—
563C22×C3C2611yescharacteristic
564C3×C4—22no—
565C3×C4—26no—
566C3×C4—26no—
567C3×C4—23no—
568C3×C4—26no—
569C3×C4—212no—
570C3×C4—212no—
571C3×C4—26no—
572C3×C4#58512yes—
573C23—26no—
574C23—41no—
575C23—41no—
576C23—43no—
577C23—43no—
578C23C3×2−1+414yes—
579C23C25×C316yes—
580C23C25×C313yes—
581Q8—212no—
582Q8—46no—
583Q8—412no—
584Q8—42no—
585Q8—412no—
586Q8—42no—
587D4—224no—
588D4—46no—
589D4—46no—
590C2×C4—212no—
591C2×C4—212no—
592C2×C4—26no—
593C2×C4—26no—
594C2×C4—212no—
595C2×C4—43no—
596C2×C4—46no—
597C2×C4—43no—
598C2×C4—46no—
599C2×C4—412no—
600C2×C4—46no—
601C2×C4—412no—
602C2×C4—43no—
603C2×C4C25×C312yes—
604C2×C4C25×C316yes—
605C2×C4C25×C316yes—
606C2×C4C25×C316yes—
607C2×C4C25×C3112yes—
608C2×C4C25×C3112yes—
609C2×C4C25×C316yes—
610C2×C4C25×C313yes—
611C2×C4C25×C311yescharacteristic
612C2×C3—26no—
613C2×C3—46no—
614C2×C3C22×2−1+411yescharacteristic
615C2×C3C2×#58511yescharacteristic
616C2×C32−1+611yescharacteristic
617C22—23no—
618C22—23no—
619C22—26no—
620C22—26no—
621C22—26no—
622C22—44no—
623C22—86no—
624C22C2×C3×2−1+416yes—
625C22C26×C311yescharacteristic
626C4—22no—
627C4—26no—
628C4—26no—
629C4—23no—
630C4—26no—
631C4—212no—
632C4—212no—
633C4—26no—
634C4C3×#58512yes—
635C3#6290411yescharacteristic, direct product factor, Sylow
636C2—26no—
637C2—46no—
638C2C22×C3×2−1+411yescharacteristic
639C2C2×C3×#58511yescharacteristic
640C2C3×2−1+611yescharacteristic
subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
prime radicalC3×#3459C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3564C2semidirect
2. C3×#3563C2semidirect
3. C3×#3563C2semidirect
4. C3×#3538C2semidirect
5. C3×#3523C2semidirect
6. C3×#3501C2semidirect
7. C3×#3495C2semidirect
8. C3×#3491C2semidirect
9. C2×C3×#552C2semidirect
11. C3×#3458C2semidirect
12. #62904C3direct (N × H)
13. C3×#564C22semidirect
14. C3×#563C22semidirect
15. C3×#563C22semidirect
16. C3×#557C22semidirect
17. C3×#557C22semidirect
18. C3×#557C22semidirect
19. C3×#556C22semidirect
20. C3×#556C22semidirect
21. C3×#554C22semidirect
22. C3×#554C22semidirect
23. C3×#552C22semidirect
24. C3×#552C22semidirect
25. C3×#552C22semidirect
26. C3×#552C22semidirect
27. C3×#552C22semidirect
28. C3×#552C22semidirect
29. C3×#552C22semidirect
30. C3×#551C22semidirect
31. C3×#551C22semidirect
32. C3×D4×Q8C22semidirect
33. C3×D4×Q8C22semidirect
34. C3×#544C22semidirect
35. C3×#544C22semidirect
36. C3×#544C22semidirect
37. C3×#544C22semidirect
38. C3×#544C22semidirect
41. C3×#543C22semidirect
42. C3×#542C22semidirect
43. C3×#541C22semidirect
44. C3×#541C22semidirect
45. C3×#541C22semidirect
46. C3×#541C22semidirect
50. C3×#539C22semidirect
52. C3×#536C22semidirect
54. C3×#533C22semidirect
55. C3×#533C22semidirect
56. C3×#533C22semidirect
60. C2×C3×#126C22semidirect
61. C2×C3×#125C22semidirect
62. C2×C3×#125C22semidirect
66. C2×C3×C22⋊Q8C22semidirect
67. C2×C3×C22⋊Q8C22semidirect
68. C3×#520C22semidirect
69. C3×#519C22semidirect
71. C2×C3×C4×Q8C22semidirect
74. C2×C3×#117C22semidirect
76. #3564C2×C3semidirect
77. #3563C2×C3semidirect
78. #3563C2×C3semidirect
79. #3538C2×C3semidirect
80. #3523C2×C3semidirect
81. #3501C2×C3semidirect
82. #3495C2×C3semidirect
83. #3491C2×C3semidirect
84. C2×#552C2×C3semidirect
86. #3458C2×C3semidirect
200. #564C22×C3semidirect
201. #563C22×C3semidirect
202. #563C22×C3semidirect
203. #557C22×C3semidirect
204. #557C22×C3semidirect
205. #557C22×C3semidirect
206. #556C22×C3semidirect
207. #556C22×C3semidirect
208. #554C22×C3semidirect
209. #554C22×C3semidirect
210. #552C22×C3semidirect
211. #552C22×C3semidirect
212. #552C22×C3semidirect
213. #552C22×C3semidirect
214. #552C22×C3semidirect
215. #552C22×C3semidirect
216. #552C22×C3semidirect
217. #551C22×C3semidirect
218. #551C22×C3semidirect
219. D4×Q8C22×C3semidirect
220. D4×Q8C22×C3semidirect
221. #544C22×C3semidirect
222. #544C22×C3semidirect
223. #544C22×C3semidirect
224. #544C22×C3semidirect
225. #544C22×C3semidirect
228. #543C22×C3semidirect
229. #542C22×C3semidirect
230. #541C22×C3semidirect
231. #541C22×C3semidirect
232. #541C22×C3semidirect
233. #541C22×C3semidirect
237. #539C22×C3semidirect
239. #536C22×C3semidirect
241. #533C22×C3semidirect
242. #533C22×C3semidirect
243. #533C22×C3semidirect
247. C2×#126C22×C3semidirect
248. C2×#125C22×C3semidirect
249. C2×#125C22×C3semidirect
253. C2×C22⋊Q8C22×C3semidirect
254. C2×C22⋊Q8C22×C3semidirect
255. #520C22×C3semidirect
256. #519C22×C3semidirect
258. C2×C4×Q8C22×C3semidirect
261. C2×#117C22×C3semidirect
635. C3#62904direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35642
C3×#35632
C3×#35382
C3×#35232
C3×#35012
C3×#34952
C3×#34912
C2×C3×#5522
C3×#34592
C3×#34582
#629043