Finite Group Databasebeta

← C3×#63034 #10681641

Subgroups — C3×#63034 #10681641

Order 768.

6508 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3565C2112yesmaximal, complemented
2C3×#3554C216yesmaximal, complemented
3C3×#3550C213yesmaximal, complemented
4C3×#3547C216yesmaximal, complemented
5C3×#3524C214yesmaximal, complemented
6C3×#3518C212yesmaximal, complemented
7C3×#3518C216yesmaximal, complemented
8C3×#3511C213yesmaximal, complemented
9C3×#3509C213yesmaximal, complemented
10C3×#3507C216yesmaximal, complemented
11C3×#3503C211yesmaximal, characteristic, complemented
12C3×#3502C212yesmaximal, complemented
13C3×#3483C211yesmaximal, characteristic, complemented
14C3×#3482C213yesmaximal, complemented
15C3×#3482C211yesmaximal, characteristic, complemented
16C3×#3480C212yesmaximal, complemented
17C3×Q8×#41C212yesmaximal, complemented
18#63034C311yesmaximal, characteristic, direct product factor, Sylow
19C3×#563C22112yes—
20C3×#562C22124yes—
21C3×#559C2216yes—
22C3×#559C22112yes—
23C3×Q82C2212yes—
24C3×Q82C2211yescharacteristic
25C3×Q82C2216yes—
26C3×#557C2211yescharacteristic
27C3×#557C2214yes—
28C3×#557C2212yes—
29C3×#557C2213yes—
30C3×#557C22112yes—
31C3×#557C2216yes—
32C3×#556C2216yes—
33C3×#556C2211yescharacteristic
34C3×#556C2213yes—
35C3×#556C2216yes—
36C3×#556C2216yes—
37C3×#556C22124yes—
38C3×#556C2216yes—
39C3×#556C22112yes—
40C3×#555C2213yes—
41C3×#555C2216yes—
42C3×#555C2216yes—
43C3×#555C22112yes—
44C3×#554C2216yes—
45C3×#554C22112yes—
46C3×#554C2216yes—
47C3×#553C22112yes—
48C3×#553C22112yes—
49C3×#552C2216yes—
50C3×#552C22112yes—
51C3×#552C2216yes—
52C3×#552C22112yes—
53C3×#552C22112yes—
54C3×#550C2211yescharacteristic
55C3×#550C2212yes—
56C3×#550C2213yes—
57C3×D4×Q8C2216yes—
58C3×D4×Q8C2211yescharacteristic
59C3×D4×Q8C2213yes—
60C3×D4×Q8C2216yes—
61C3×#548C2214yes—
62C3×#548C2212yes—
63C3×#548C2216yes—
64C3×#548C22112yes—
65C3×#547C2213yes—
66C3×#547C2213yes—
67C3×#547C2216yes—
68C3×#544C22112yes—
69C3×#544C2216yes—
70C3×#542C22112yes—
71C3×#542C22124yes—
72C3×#542C22112yes—
73C3×#542C22112yes—
74C3×#542C22112yes—
75C3×#541C22112yes—
76C3×#540C22112yes—
77C3×#539C22124yes—
78C3×#537C2216yes—
79C3×#536C22112yes—
80C3×#536C2216yes—
81C3×#533C2216yes—
82C3×#533C22112yes—
83C3×#533C2216yes—
84C3×#533C2213yes—
85C3×#533C2213yes—
86C3×#533C2216yes—
87C3×#533C2216yes—
88C3×#532C2216yes—
89C3×#532C2216yes—
90C3×#532C2213yes—
91C2×C3×C4⋊Q8C2213yes—
92C3×#529C22112yes—
93C3×#529C2216yes—
94C3×#529C2216yes—
95C3×#529C22112yes—
96C3×#529C22112yes—
97C3×#520C2212yes—
98C3×#520C2216yes—
99C3×#519C2214yes—
100C3×#519C2216yes—
101C3×C4×#41C2214yes—
102C3×C4×#41C2212yes—
103C3×C4×#41C2216yes—
104C3×C4×#41C2213yes—
105C3×C4×#41C2211yescharacteristic
106C3×C4×#41C2213yes—
107C2×C3×C4×Q8C2216yes—
108C2×C3×C4×Q8C2212yes—
109#3565C2×C3112yescomplemented
110#3554C2×C316yescomplemented
111#3550C2×C313yescomplemented
112#3547C2×C316yescomplemented
113#3524C2×C314yescomplemented
114#3518C2×C312yescomplemented
115#3518C2×C316yescomplemented
116#3511C2×C313yescomplemented
117#3509C2×C313yescomplemented
118#3507C2×C316yescomplemented
119#3503C2×C311yescharacteristic, complemented
120#3502C2×C312yescomplemented
121#3483C2×C311yescharacteristic, complemented
122#3482C2×C313yescomplemented
123#3482C2×C311yescharacteristic, complemented
124#3480C2×C312yescomplemented
125Q8×#41C2×C312yescomplemented
126C2×C3×#41C2312yes—
127C2×C3×#41C2311yescharacteristic
128C2×C3×#41C2316yes—
129C2×C3×#41C2313yes—
130C2×C3×#41C2313yes—
131C2×C3×#41C2316yes—
132C22×C3×Q8C2312yes—
133C22×C3×Q8C2316yes—
134C22×C3×Q8C2316yes—
135C3×C4⋊Q8C2313yes—
136C3×C4⋊Q8C2316yes—
137C3×C4⋊Q8C23124yes—
138C3×C4⋊Q8C2316yes—
139C3×C4⋊Q8C2316yes—
140C3×C4⋊Q8C23112yes—
141C3×C4⋊Q8C23112yes—
142C3×C4⋊Q8C2313yes—
143C3×C4⋊Q8C2316yes—
144C3×C4⋊Q8C2316yes—
145C3×C4⋊Q8C2313yes—
146C3×C4⋊Q8C2311yescharacteristic
147C3×C4⋊Q8C2313yes—
148C3×C4⋊Q8C2316yes—
149C3×#127C2313yes—
150C3×#127C2316yes—
151C3×#126C23124yes—
152C3×#126C23124yes—
153C3×#126C2314yes—
154C3×#126C23112yes—
155C3×#126C23112yes—
156C3×#126C23124yes—
157C3×#126C23112yes—
158C3×#125C23124yes—
159C3×#125C2316yes—
160C3×#125C2316yes—
161C3×#125C2316yes—
162C3×#125C2316yes—
163C3×#125C23112yes—
164C3×#125C23112yes—
165C3×#125C23112yes—
166C3×#125C23112yes—
167C3×#125C23112yes—
168C3×#124C2316yes—
169C3×#124C23112yes—
170C3×#124C23124yes—
171C3×#124C23112yes—
172C3×#124C23124yes—
173C3×#124C2316yes—
174C3×#124C2312yes—
175C3×#124C23112yes—
176C3×#124C23112yes—
177C3×#123C23112yes—
178C3×#123C23124yes—
179C3×#123C23124yes—
180C3×#123C23112yes—
181C3×#123C23112yes—
182C3×#123C23124yes—
183C3×#123C23112yes—
184C3×C22⋊Q8C23112yes—
185C3×C22⋊Q8C23112yes—
186C3×C22⋊Q8C23124yes—
187C3×C22⋊Q8C23124yes—
188C3×C22⋊Q8C23112yes—
189C3×C22⋊Q8C23112yes—
190C3×C22⋊Q8C2316yes—
191C3×C22⋊Q8C2316yes—
192C3×C22⋊Q8C2312yes—
193C3×C22⋊Q8C2316yes—
194C3×C22⋊Q8C2316yes—
195C3×C22⋊Q8C2316yes—
196C3×C22⋊Q8C23112yes—
197C3×C22⋊Q8C23112yes—
198C3×C22⋊Q8C23112yes—
199C3×C22⋊Q8C23124yes—
200C3×C22⋊Q8C2316yes—
201C3×C22⋊Q8C2316yes—
202C3×#121C23112yes—
203C3×#121C23112yes—
204C3×#121C23112yes—
205C3×#121C23124yes—
206C3×#121C2316yes—
207C3×#121C2316yes—
208C3×#121C2316yes—
209C3×#121C2316yes—
210C3×#121C23112yes—
211C3×#121C2316yes—
212C3×#121C2316yes—
213C3×C4×Q8C2311yescharacteristic
214C3×C4×Q8C2316yes—
215C3×C4×Q8C2316yes—
216C3×C4×Q8C2311yescharacteristic
217C3×C4×Q8C2316yes—
218C3×C4×Q8C2312yes—
219C3×C4×Q8C2314yes—
220C3×C4×Q8C2313yes—
221C3×C4×Q8C23112yes—
222C3×C4×Q8C23112yes—
223C3×C4×Q8C23112yes—
224C3×C4×Q8C23112yes—
225C3×C4×Q8C2312yes—
226C3×C4×Q8C2313yes—
227C3×C4×Q8C2312yes—
228C3×C4×Q8C2316yes—
229C3×C4×Q8C2316yes—
230C3×C4×Q8C23112yes—
231C3×C4×Q8C2311yescharacteristic
232C3×C4×Q8C2316yes—
233C3×C4×Q8C2313yes—
234C3×C4×Q8C23112yes—
235C3×C4×Q8C23112yes—
236C3×C4×Q8C23112yes—
237C3×C4×D4C2316yes—
238C3×C4×D4C23112yes—
239C3×C4×D4C23112yes—
240C3×C4×D4C23124yes—
241C3×C4×D4C23112yes—
242C3×C4×D4C2311yescharacteristic
243C3×C4×D4C2313yes—
244C3×C4×D4C2316yes—
245C3×C4×D4C2313yes—
246C3×C4×D4C2316yes—
247C3×C4×D4C23112yes—
248C3×C4×D4C2313yes—
249C3×C4×D4C2316yes—
250C3×C4×D4C2313yes—
251C3×C4×D4C2313yes—
252C3×C4×D4C2316yes—
253C3×C4×D4C2316yes—
254C3×C4×D4C23112yes—
255C3×C4×D4C2316yes—
256C3×C4×D4C23112yes—
257C3×#117C2312yes—
258C3×#117C2313yes—
259C3×#117C2313yes—
260C3×#117C23112yes—
261C3×#117C23112yes—
262C3×#117C2316yes—
263C3×#117C2316yes—
264C3×#117C2316yes—
265C3×#117C2313yes—
266C3×#117C2316yes—
267C3×#117C23112yes—
268C3×#117C23124yes—
269C3×#117C23112yes—
270C3×#117C2316yes—
271C3×#117C23112yes—
272C2×C3×C4⋊C4C2316yes—
273C2×C3×C4⋊C4C23112yes—
274C2×C3×C4⋊C4C2316yes—
275C2×C3×C4⋊C4C2316yes—
276C2×C3×C4⋊C4C2316yes—
277C2×C3×C42C23112yes—
278C2×C3×C42C2316yes—
279C2×C3×C42C2316yes—
280C2×C3×C42C2313yes—
281#563C22×C3112yes—
282#562C22×C3124yes—
283#559C22×C316yes—
284#559C22×C3112yes—
285Q82C22×C312yes—
286Q82C22×C311yescharacteristic
287Q82C22×C316yes—
288#557C22×C311yescharacteristic
289#557C22×C314yes—
290#557C22×C312yes—
291#557C22×C313yes—
292#557C22×C3112yes—
293#557C22×C316yes—
294#556C22×C316yes—
295#556C22×C311yescharacteristic
296#556C22×C313yes—
297#556C22×C316yes—
298#556C22×C316yes—
299#556C22×C3124yes—
300#556C22×C316yes—
301#556C22×C3112yes—
302#555C22×C313yes—
303#555C22×C316yes—
304#555C22×C316yes—
305#555C22×C3112yes—
306#554C22×C316yes—
307#554C22×C3112yes—
308#554C22×C316yes—
309#553C22×C3112yes—
310#553C22×C3112yes—
311#552C22×C316yes—
312#552C22×C3112yes—
313#552C22×C316yes—
314#552C22×C3112yes—
315#552C22×C3112yes—
316#550C22×C311yescharacteristic
317#550C22×C312yes—
318#550C22×C313yes—
319D4×Q8C22×C316yes—
320D4×Q8C22×C311yescharacteristic
321D4×Q8C22×C313yes—
322D4×Q8C22×C316yes—
323#548C22×C314yes—
324#548C22×C312yes—
325#548C22×C316yes—
326#548C22×C3112yes—
327#547C22×C313yes—
328#547C22×C313yes—
329#547C22×C316yes—
330#544C22×C3112yes—
331#544C22×C316yes—
332#542C22×C3112yes—
333#542C22×C3124yes—
334#542C22×C3112yes—
335#542C22×C3112yes—
336#542C22×C3112yes—
337#541C22×C3112yes—
338#540C22×C3112yes—
339#539C22×C3124yes—
340#537C22×C316yes—
341#536C22×C3112yes—
342#536C22×C316yes—
343#533C22×C316yes—
344#533C22×C3112yes—
345#533C22×C316yes—
346#533C22×C313yes—
347#533C22×C313yes—
348#533C22×C316yes—
349#533C22×C316yes—
350#532C22×C316yes—
351#532C22×C316yes—
352#532C22×C313yes—
353C2×C4⋊Q8C22×C313yes—
354#529C22×C3112yes—
355#529C22×C316yes—
356#529C22×C316yes—
357#529C22×C3112yes—
358#529C22×C3112yes—
359#520C22×C312yes—
360#520C22×C316yes—
361#519C22×C314yes—
362#519C22×C316yes—
363C4×#41C22×C314yes—
364C4×#41C22×C312yes—
365C4×#41C22×C316yes—
366C4×#41C22×C313yes—
367C4×#41C22×C311yescharacteristic
368C4×#41C22×C313yes—
369C2×C4×Q8C22×C316yes—
370C2×C4×Q8C22×C312yes—
371C3×#41—28no—
372C3×#41—24no—
373C3×#41—412no—
374C3×#41—46no—
375C3×#41—412no—
376C3×#41—46no—
377C2×C3×Q8—28no—
378C2×C3×Q8—412no—
379C2×C3×Q8—412no—
380C2×C3×Q8C2416yes—
381C2×C3×Q8C2412yes—
382C2×C3×Q8C2413yes—
383C2×C3×Q8C2416yes—
384C2×C3×Q8C2411yescharacteristic
385C2×C3×Q8C24112yes—
386C2×C3×Q8C24112yes—
387C2×C3×Q8C2416yes—
388C2×C3×Q8C2411yescharacteristic
389C2×C3×D4C2416yes—
390C2×C3×D4C2413yes—
391C2×C3×D4C2411yescharacteristic
392C2×C3×D4C2413yes—
393C2×C3×D4C2416yes—
394C2×C3×D4C24112yes—
395C2×C3×D4C2416yes—
396C2×C3×D4C24112yes—
397C2×C3×D4C2416yes—
398C22×C3×C4C2416yes—
399C22×C3×C4C2412yes—
400C22×C3×C4C2413yes—
401C22×C3×C4C2413yes—
402C22×C3×C4C2416yes—
403C22×C3×C4C2416yes—
404C22×C3×C4C2413yes—
405C22×C3×C4C24112yes—
406C22×C3×C4C2416yes—
407C22×C3×C4C2416yes—
408C22×C3×C4C24112yes—
409C22×C3×C4C24112yes—
410C3×C4⋊C4C2411yescharacteristic
411C3×C4⋊C4C2416yes—
412C3×C4⋊C4C2414yes—
413C3×C4⋊C4C2413yes—
414C3×C4⋊C4C2416yes—
415C3×C4⋊C4C2416yes—
416C3×C4⋊C4C2416yes—
417C3×C4⋊C4C24112yes—
418C3×C4⋊C4C24112yes—
419C3×C4⋊C4C24112yes—
420C3×C4⋊C4C24112yes—
421C3×C4⋊C4C24112yes—
422C3×C4⋊C4C24112yes—
423C3×C4⋊C4C2411yescharacteristic
424C3×C4⋊C4C2413yes—
425C3×C4⋊C4C2413yes—
426C3×C4⋊C4C2412yes—
427C3×C4⋊C4C2416yes—
428C3×C4⋊C4C24112yes—
429C3×C4⋊C4C2412yes—
430C3×C4⋊C4C2412yes—
431C3×C4⋊C4C2413yes—
432C3×C4⋊C4C2416yes—
433C3×C4⋊C4C24112yes—
434C3×C4⋊C4C2416yes—
435C3×C4⋊C4C24124yes—
436C3×C4⋊C4C2416yes—
437C3×C4⋊C4C2416yes—
438C3×C4⋊C4C24112yes—
439C3×C4⋊C4C24112yes—
440C3×C22⋊C4C2416yes—
441C3×C22⋊C4C2416yes—
442C3×C22⋊C4C2412yes—
443C3×C22⋊C4C2414yes—
444C3×C22⋊C4C24112yes—
445C3×C22⋊C4C24112yes—
446C3×C22⋊C4C2416yes—
447C3×C22⋊C4C2414yes—
448C3×C22⋊C4C2416yes—
449C3×C22⋊C4C24124yes—
450C3×C22⋊C4C24112yes—
451C3×C22⋊C4C2416yes—
452C3×C22⋊C4C24112yes—
453C3×C22⋊C4C24124yes—
454C3×C22⋊C4C24112yes—
455C3×C22⋊C4C2416yes—
456C3×C42C2414yes—
457C3×C42C2411yescharacteristic
458C3×C42C2413yes—
459C3×C42C2412yes—
460C3×C42C2416yes—
461C3×C42C2413yes—
462C3×C42C2413yes—
463C3×C42C2416yes—
464C3×C42C24112yes—
465C3×C42C2416yes—
466C3×C42C24112yes—
467C3×C42C2416yes—
468C3×C42C2416yes—
469C3×C42C24124yes—
470C2×#41C23×C312yes—
471C2×#41C23×C311yescharacteristic
472C2×#41C23×C316yes—
473C2×#41C23×C313yes—
474C2×#41C23×C313yes—
475C2×#41C23×C316yes—
476C22×Q8C23×C312yes—
477C22×Q8C23×C316yes—
478C22×Q8C23×C316yes—
479C4⋊Q8C23×C313yes—
480C4⋊Q8C23×C316yes—
481C4⋊Q8C23×C316yes—
482C4⋊Q8C23×C316yes—
483C4⋊Q8C23×C313yes—
484C4⋊Q8C23×C316yes—
485C4⋊Q8C23×C313yes—
486C4⋊Q8C23×C311yescharacteristic
487C4⋊Q8C23×C313yes—
488C4⋊Q8C23×C316yes—
489C4⋊Q8C23×C316yes—
490C4⋊Q8C23×C3112yes—
491C4⋊Q8C23×C3112yes—
492C4⋊Q8C23×C3124yes—
493#127C23×C313yes—
494#127C23×C316yes—
495#126C23×C314yes—
496#126C23×C3112yes—
497#126C23×C3112yes—
498#126C23×C3124yes—
499#126C23×C3112yes—
500#126C23×C3124yes—
501#126C23×C3124yes—
502#125C23×C316yes—
503#125C23×C316yes—
504#125C23×C3112yes—
505#125C23×C3112yes—
506#125C23×C3112yes—
507#125C23×C3112yes—
508#125C23×C3112yes—
509#125C23×C316yes—
510#125C23×C316yes—
511#125C23×C3124yes—
512#124C23×C312yes—
513#124C23×C316yes—
514#124C23×C3112yes—
515#124C23×C3112yes—
516#124C23×C3112yes—
517#124C23×C3112yes—
518#124C23×C316yes—
519#124C23×C3124yes—
520#124C23×C3124yes—
521#123C23×C3124yes—
522#123C23×C3124yes—
523#123C23×C3112yes—
524#123C23×C3112yes—
525#123C23×C3112yes—
526#123C23×C3112yes—
527#123C23×C3124yes—
528C22⋊Q8C23×C3112yes—
529C22⋊Q8C23×C316yes—
530C22⋊Q8C23×C316yes—
531C22⋊Q8C23×C3112yes—
532C22⋊Q8C23×C312yes—
533C22⋊Q8C23×C316yes—
534C22⋊Q8C23×C316yes—
535C22⋊Q8C23×C316yes—
536C22⋊Q8C23×C3112yes—
537C22⋊Q8C23×C3112yes—
538C22⋊Q8C23×C3112yes—
539C22⋊Q8C23×C3112yes—
540C22⋊Q8C23×C3124yes—
541C22⋊Q8C23×C316yes—
542C22⋊Q8C23×C316yes—
543C22⋊Q8C23×C3124yes—
544C22⋊Q8C23×C3112yes—
545C22⋊Q8C23×C3124yes—
546#121C23×C316yes—
547#121C23×C316yes—
548#121C23×C316yes—
549#121C23×C316yes—
550#121C23×C3112yes—
551#121C23×C3112yes—
552#121C23×C3112yes—
553#121C23×C3112yes—
554#121C23×C316yes—
555#121C23×C316yes—
556#121C23×C3124yes—
557C4×Q8C23×C312yes—
558C4×Q8C23×C311yescharacteristic
559C4×Q8C23×C313yes—
560C4×Q8C23×C312yes—
561C4×Q8C23×C316yes—
562C4×Q8C23×C316yes—
563C4×Q8C23×C3112yes—
564C4×Q8C23×C316yes—
565C4×Q8C23×C316yes—
566C4×Q8C23×C3112yes—
567C4×Q8C23×C311yescharacteristic
568C4×Q8C23×C311yescharacteristic
569C4×Q8C23×C312yes—
570C4×Q8C23×C316yes—
571C4×Q8C23×C314yes—
572C4×Q8C23×C313yes—
573C4×Q8C23×C316yes—
574C4×Q8C23×C313yes—
575C4×Q8C23×C3112yes—
576C4×Q8C23×C3112yes—
577C4×Q8C23×C3112yes—
578C4×Q8C23×C3112yes—
579C4×Q8C23×C3112yes—
580C4×Q8C23×C3112yes—
581C4×D4C23×C311yescharacteristic
582C4×D4C23×C313yes—
583C4×D4C23×C316yes—
584C4×D4C23×C313yes—
585C4×D4C23×C316yes—
586C4×D4C23×C3112yes—
587C4×D4C23×C313yes—
588C4×D4C23×C316yes—
589C4×D4C23×C3112yes—
590C4×D4C23×C313yes—
591C4×D4C23×C313yes—
592C4×D4C23×C316yes—
593C4×D4C23×C316yes—
594C4×D4C23×C3112yes—
595C4×D4C23×C316yes—
596C4×D4C23×C3112yes—
597C4×D4C23×C316yes—
598C4×D4C23×C3112yes—
599C4×D4C23×C3124yes—
600C4×D4C23×C3112yes—
601#117C23×C312yes—
602#117C23×C313yes—
603#117C23×C313yes—
604#117C23×C3112yes—
605#117C23×C3112yes—
606#117C23×C316yes—
607#117C23×C316yes—
608#117C23×C316yes—
609#117C23×C313yes—
610#117C23×C316yes—
611#117C23×C3112yes—
612#117C23×C3124yes—
613#117C23×C3112yes—
614#117C23×C316yes—
615#117C23×C3112yes—
616C2×C4⋊C4C23×C316yes—
617C2×C4⋊C4C23×C3112yes—
618C2×C4⋊C4C23×C316yes—
619C2×C4⋊C4C23×C316yes—
620C2×C4⋊C4C23×C316yes—
621C2×C42C23×C3112yes—
622C2×C42C23×C316yes—
623C2×C42C23×C316yes—
624C2×C42C23×C313yes—
625C23×C3C2512yes—
626C23×C3C2513yes—
627C23×C3C2516yes—
628C3×Q8—212no—
629C3×Q8—24no—
630C3×Q8—26no—
631C3×Q8—212no—
632C3×Q8—22no—
633C3×Q8—412no—
634C3×Q8—412no—
635C3×Q8—46no—
636C3×Q82−1+414yes—
637C3×D4—212no—
638C3×D4—26no—
639C3×D4—22no—
640C3×D4—26no—
641C3×D4—46no—
642C3×D4—412no—
643C3×D4—46no—
644C3×D4—46no—
645C3×D4—412no—
646C2×C3×C4—212no—
647C2×C3×C4—212no—
648C2×C3×C4—26no—
649C2×C3×C4—26no—
650C2×C3×C4—212no—
651C2×C3×C4—24no—
652C2×C3×C4—26no—
653C2×C3×C4—412no—
654C2×C3×C4—412no—
655C2×C3×C4—412no—
656C2×C3×C4—46no—
657C2×C3×C4—46no—
658C2×C3×C4C2512yes—
659C2×C3×C4C2512yes—
660C2×C3×C4C2516yes—
661C2×C3×C4C2516yes—
662C2×C3×C4C2511yescharacteristic
663C2×C3×C4C2513yes—
664C2×C3×C4C2514yes—
665C2×C3×C4C2516yes—
666C2×C3×C4C25112yes—
667C2×C3×C4C2513yes—
668C2×C3×C4C2512yes—
669C2×C3×C4C2513yes—
670C2×C3×C4C2511yescharacteristic
671C2×C3×C4C2511yescharacteristic
672#41—28no—
673#41—24no—
674#41—412no—
675#41—46no—
676#41—412no—
677#41—46no—
678C2×Q8—28no—
679C2×Q8—412no—
680C2×Q8—412no—
681C2×Q8C24×C316yes—
682C2×Q8C24×C312yes—
683C2×Q8C24×C313yes—
684C2×Q8C24×C316yes—
685C2×Q8C24×C311yescharacteristic
686C2×Q8C24×C3112yes—
687C2×Q8C24×C3112yes—
688C2×Q8C24×C316yes—
689C2×Q8C24×C311yescharacteristic
690C2×D4C24×C313yes—
691C2×D4C24×C316yes—
692C2×D4C24×C311yescharacteristic
693C2×D4C24×C313yes—
694C2×D4C24×C316yes—
695C2×D4C24×C3112yes—
696C2×D4C24×C316yes—
697C2×D4C24×C3112yes—
698C2×D4C24×C316yes—
699C22×C4C24×C316yes—
700C22×C4C24×C312yes—
701C22×C4C24×C313yes—
702C22×C4C24×C313yes—
703C22×C4C24×C316yes—
704C22×C4C24×C316yes—
705C22×C4C24×C313yes—
706C22×C4C24×C3112yes—
707C22×C4C24×C316yes—
708C22×C4C24×C316yes—
709C22×C4C24×C3112yes—
710C22×C4C24×C3112yes—
711C4⋊C4C24×C311yescharacteristic
712C4⋊C4C24×C316yes—
713C4⋊C4C24×C314yes—
714C4⋊C4C24×C313yes—
715C4⋊C4C24×C316yes—
716C4⋊C4C24×C316yes—
717C4⋊C4C24×C316yes—
718C4⋊C4C24×C3112yes—
719C4⋊C4C24×C3112yes—
720C4⋊C4C24×C3112yes—
721C4⋊C4C24×C3112yes—
722C4⋊C4C24×C3112yes—
723C4⋊C4C24×C3112yes—
724C4⋊C4C24×C311yescharacteristic
725C4⋊C4C24×C313yes—
726C4⋊C4C24×C313yes—
727C4⋊C4C24×C312yes—
728C4⋊C4C24×C316yes—
729C4⋊C4C24×C3112yes—
730C4⋊C4C24×C312yes—
731C4⋊C4C24×C312yes—
732C4⋊C4C24×C313yes—
733C4⋊C4C24×C316yes—
734C4⋊C4C24×C3112yes—
735C4⋊C4C24×C316yes—
736C4⋊C4C24×C3124yes—
737C4⋊C4C24×C316yes—
738C4⋊C4C24×C316yes—
739C4⋊C4C24×C3112yes—
740C4⋊C4C24×C3112yes—
741C22⋊C4C24×C316yes—
742C22⋊C4C24×C316yes—
743C22⋊C4C24×C312yes—
744C22⋊C4C24×C314yes—
745C22⋊C4C24×C3112yes—
746C22⋊C4C24×C3112yes—
747C22⋊C4C24×C316yes—
748C22⋊C4C24×C314yes—
749C22⋊C4C24×C316yes—
750C22⋊C4C24×C3124yes—
751C22⋊C4C24×C3112yes—
752C22⋊C4C24×C316yes—
753C22⋊C4C24×C3112yes—
754C22⋊C4C24×C3124yes—
755C22⋊C4C24×C3112yes—
756C22⋊C4C24×C316yes—
757C42C24×C314yes—
758C42C24×C311yescharacteristic
759C42C24×C313yes—
760C42C24×C312yes—
761C42C24×C316yes—
762C42C24×C313yes—
763C42C24×C313yes—
764C42C24×C316yes—
765C42C24×C3112yes—
766C42C24×C316yes—
767C42C24×C3112yes—
768C42C24×C316yes—
769C42C24×C316yes—
770C42C24×C3124yes—
771C22×C3—22no—
772C22×C3—23no—
773C22×C3—26no—
774C22×C3—23no—
775C22×C3—26no—
776C22×C3—22no—
777C22×C3—23no—
778C22×C3—22no—
779C22×C3—26no—
780C22×C3C2611yescharacteristic
781C3×C4—22no—
782C3×C4—21no—
783C3×C4—26no—
784C3×C4—22no—
785C3×C4—23no—
786C3×C4—23no—
787C3×C4—26no—
788C3×C4—22no—
789C3×C4—212no—
790C3×C4—26no—
791C3×C4—24no—
792C3×C4C2×2−1+416yes—
793C3×C4#58512yes—
794C3×C4#58512yes—
795C23C25×C312yes—
796C23C25×C313yes—
797C23C25×C316yes—
798Q8—212no—
799Q8—24no—
800Q8—26no—
801Q8—212no—
802Q8—22no—
803Q8—412no—
804Q8—412no—
805Q8—46no—
806Q8C3×2−1+414yes—
807D4—26no—
808D4—212no—
809D4—22no—
810D4—26no—
811D4—46no—
812D4—412no—
813D4—46no—
814D4—46no—
815D4—412no—
816C2×C4—212no—
817C2×C4—212no—
818C2×C4—26no—
819C2×C4—26no—
820C2×C4—212no—
821C2×C4—24no—
822C2×C4—26no—
823C2×C4—412no—
824C2×C4—412no—
825C2×C4—412no—
826C2×C4—46no—
827C2×C4—46no—
828C2×C4C25×C312yes—
829C2×C4C25×C312yes—
830C2×C4C25×C316yes—
831C2×C4C25×C316yes—
832C2×C4C25×C311yescharacteristic
833C2×C4C25×C313yes—
834C2×C4C25×C314yes—
835C2×C4C25×C316yes—
836C2×C4C25×C3112yes—
837C2×C4C25×C313yes—
838C2×C4C25×C312yes—
839C2×C4C25×C313yes—
840C2×C4C25×C311yescharacteristic
841C2×C4C25×C311yescharacteristic
842C2×C3—42no—
843C2×C3—43no—
844C2×C3—46no—
845C2×C3C22×2−1+411yescharacteristic
846C2×C3C2×#58511yescharacteristic
847C2×C3C2×#58511yescharacteristic
848C22—22no—
849C22—23no—
850C22—26no—
851C22—23no—
852C22—26no—
853C22—22no—
854C22—23no—
855C22—22no—
856C22—26no—
857C22C26×C311yescharacteristic
858C4—22no—
859C4—21no—
860C4—26no—
861C4—22no—
862C4—23no—
863C4—23no—
864C4—26no—
865C4—22no—
866C4—212no—
867C4—26no—
868C4—24no—
869C4C2×C3×2−1+416yes—
870C4C3×#58512yes—
871C4C3×#58512yes—
872C3#6303411yescharacteristic, direct product factor, Sylow
873C2—42no—
874C2—43no—
875C2—46no—
876C2C22×C3×2−1+411yescharacteristic
877C2C2×C3×#58511yescharacteristic
878C2C2×C3×#58511yescharacteristic
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×#3565C2semidirect
2. C3×#3554C2semidirect
3. C3×#3550C2semidirect
4. C3×#3547C2semidirect
5. C3×#3524C2semidirect
6. C3×#3518C2semidirect
7. C3×#3518C2semidirect
8. C3×#3511C2semidirect
9. C3×#3509C2semidirect
10. C3×#3507C2semidirect
11. C3×#3503C2semidirect
12. C3×#3502C2semidirect
13. C3×#3483C2semidirect
14. C3×#3482C2semidirect
15. C3×#3482C2semidirect
16. C3×#3480C2semidirect
17. C3×Q8×#41C2semidirect
18. #63034C3direct (N × H)
109. #3565C2×C3semidirect
110. #3554C2×C3semidirect
111. #3550C2×C3semidirect
112. #3547C2×C3semidirect
113. #3524C2×C3semidirect
114. #3518C2×C3semidirect
115. #3518C2×C3semidirect
116. #3511C2×C3semidirect
117. #3509C2×C3semidirect
118. #3507C2×C3semidirect
119. #3503C2×C3semidirect
120. #3502C2×C3semidirect
121. #3483C2×C3semidirect
122. #3482C2×C3semidirect
123. #3482C2×C3semidirect
124. #3480C2×C3semidirect
125. Q8×#41C2×C3semidirect
872. C3#63034direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35652
C3×#35542
C3×#35502
C3×#35472
C3×#35242
C3×#35182
C3×#35112
C3×#35092
C3×#35072
C3×#35032
C3×#35022
C3×#34832
C3×#34822
C3×#34802
C3×Q8×#412
#630343