Finite Group Databasebeta

← C3×#63032 #10681639

Subgroups — C3×#63032 #10681639

Order 768.

6420 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3563C2112yesmaximal, complemented
2C3×#3556C213yesmaximal, complemented
3C3×#3555C216yesmaximal, complemented
4C3×#3552C216yesmaximal, complemented
5C3×#3523C212yesmaximal, complemented
6C3×#3523C216yesmaximal, complemented
7C3×#3516C214yesmaximal, complemented
8C3×#3515C216yesmaximal, complemented
9C3×#3509C213yesmaximal, complemented
10C3×#3503C211yesmaximal, characteristic, complemented
11C3×#3503C213yesmaximal, complemented
12C3×#3502C212yesmaximal, complemented
13C3×#3482C213yesmaximal, complemented
14C3×#3482C211yesmaximal, characteristic, complemented
15C3×#3482C211yesmaximal, characteristic, complemented
16C3×Q8×#41C212yesmaximal, complemented
17C2×C3×#557C212yesmaximal, complemented
18#63032C311yesmaximal, characteristic, direct product factor, Sylow
19C3×#564C22112yes—
20C3×#563C22124yes—
21C3×Q82C2212yes—
22C3×Q82C2216yes—
23C3×#557C2211yescharacteristic
24C3×#557C2214yes—
25C3×#557C2212yes—
26C3×#557C2216yes—
27C3×#557C2216yes—
28C3×#557C22112yes—
29C3×#557C2216yes—
30C3×#557C2211yescharacteristic
31C3×#557C2213yes—
32C3×#557C2216yes—
33C3×#557C22112yes—
34C3×#557C2216yes—
35C3×#557C2216yes—
36C3×#556C2213yes—
37C3×#556C2213yes—
38C3×#556C2216yes—
39C3×#556C2213yes—
40C3×#556C2216yes—
41C3×#556C22112yes—
42C3×#554C2216yes—
43C3×#554C22112yes—
44C3×#554C2216yes—
45C3×#554C22112yes—
46C3×#553C22112yes—
47C3×#552C2216yes—
48C3×#552C22112yes—
49C3×#552C2216yes—
50C3×#552C2216yes—
51C3×#552C22112yes—
52C3×#552C22112yes—
53C3×#552C22124yes—
54C3×#552C22112yes—
55C3×D4×Q8C2211yescharacteristic
56C3×D4×Q8C2214yes—
57C3×D4×Q8C2213yes—
58C3×D4×Q8C2211yescharacteristic
59C3×D4×Q8C2216yes—
60C3×D4×Q8C22112yes—
61C3×#548C2212yes—
62C3×#548C2212yes—
63C3×#548C2216yes—
64C3×#547C2211yescharacteristic
65C3×#547C2213yes—
66C3×#547C2216yes—
67C3×#547C2213yes—
68C3×#544C22112yes—
69C3×#544C2216yes—
70C3×#544C22112yes—
71C3×#544C2216yes—
72C3×#542C22112yes—
73C3×#541C22112yes—
74C3×#541C22112yes—
75C3×#541C22112yes—
76C3×#541C22112yes—
77C3×#541C22112yes—
78C3×#541C22124yes—
79C3×#539C22124yes—
80C3×#536C2216yes—
81C3×#533C2216yes—
82C3×#533C22112yes—
83C3×#533C2216yes—
84C3×#533C2213yes—
85C3×#533C2213yes—
86C3×#533C2213yes—
87C3×#533C2216yes—
88C3×#533C2216yes—
89C2×C3×C4⋊Q8C2216yes—
90C2×C3×C4⋊Q8C2213yes—
91C3×#529C2216yes—
92C3×#529C22112yes—
93C3×#529C2216yes—
94C3×#529C2216yes—
95C3×#529C22112yes—
96C2×C3×#125C22112yes—
97C3×#520C2216yes—
98C3×#520C2212yes—
99C3×#519C2214yes—
100C3×#519C2216yes—
101C3×C4×#41C2216yes—
102C3×C4×#41C2213yes—
103C3×C4×#41C2211yescharacteristic
104C3×C4×#41C2213yes—
105C2×C3×C4×Q8C2214yes—
106C2×C3×C4×Q8C2216yes—
107C2×C3×C4×Q8C2212yes—
108C2×C3×C4×Q8C2212yes—
109#3563C2×C3112yescomplemented
110#3556C2×C313yescomplemented
111#3555C2×C316yescomplemented
112#3552C2×C316yescomplemented
113#3523C2×C312yescomplemented
114#3523C2×C316yescomplemented
115#3516C2×C314yescomplemented
116#3515C2×C316yescomplemented
117#3509C2×C313yescomplemented
118#3503C2×C313yescomplemented
119#3503C2×C311yescharacteristic, complemented
120#3502C2×C312yescomplemented
121#3482C2×C313yescomplemented
122#3482C2×C311yescharacteristic, complemented
123#3482C2×C311yescharacteristic, complemented
124Q8×#41C2×C312yescomplemented
125C2×#557C2×C312yescomplemented
126C2×C3×#41C2312yes—
127C2×C3×#41C2313yes—
128C2×C3×#41C2311yescharacteristic
129C2×C3×#41C2313yes—
130C22×C3×Q8C2312yes—
131C22×C3×Q8C2312yes—
132C22×C3×Q8C2316yes—
133C22×C3×Q8C2316yes—
134C3×C4⋊Q8C2316yes—
135C3×C4⋊Q8C2316yes—
136C3×C4⋊Q8C23124yes—
137C3×C4⋊Q8C23112yes—
138C3×C4⋊Q8C23112yes—
139C3×C4⋊Q8C23112yes—
140C3×C4⋊Q8C2313yes—
141C3×C4⋊Q8C2316yes—
142C3×C4⋊Q8C2313yes—
143C3×C4⋊Q8C23112yes—
144C3×C4⋊Q8C2316yes—
145C3×C4⋊Q8C2313yes—
146C3×C4⋊Q8C2311yescharacteristic
147C3×C4⋊Q8C2313yes—
148C3×C4⋊Q8C2313yes—
149C3×C4⋊Q8C2316yes—
150C3×C4⋊Q8C23112yes—
151C3×#126C23112yes—
152C3×#126C23112yes—
153C3×#126C23124yes—
154C3×#126C23124yes—
155C3×#126C23124yes—
156C3×#126C23112yes—
157C3×#126C23112yes—
158C3×#126C23112yes—
159C3×#125C23124yes—
160C3×#125C23124yes—
161C3×#125C23112yes—
162C3×#125C2316yes—
163C3×#125C2316yes—
164C3×#125C2316yes—
165C3×#125C23124yes—
166C3×#125C23124yes—
167C3×#125C23124yes—
168C3×#125C2316yes—
169C3×#125C23112yes—
170C3×#125C23124yes—
171C3×#125C23112yes—
172C3×#125C23112yes—
173C3×#125C2316yes—
174C3×#125C2316yes—
175C3×#125C23112yes—
176C3×#125C23112yes—
177C3×#125C23112yes—
178C3×#124C23112yes—
179C3×#124C2316yes—
180C3×#124C2316yes—
181C3×#124C2316yes—
182C3×#123C23112yes—
183C3×#123C23124yes—
184C3×#123C23112yes—
185C3×#123C2314yes—
186C3×#123C23112yes—
187C3×#123C23112yes—
188C3×C22⋊Q8C23112yes—
189C3×C22⋊Q8C23112yes—
190C3×C22⋊Q8C23124yes—
191C3×C22⋊Q8C23124yes—
192C3×C22⋊Q8C2316yes—
193C3×C22⋊Q8C2316yes—
194C3×C22⋊Q8C23112yes—
195C3×C22⋊Q8C2316yes—
196C3×C22⋊Q8C23112yes—
197C3×C22⋊Q8C2316yes—
198C3×C22⋊Q8C2312yes—
199C3×C22⋊Q8C23112yes—
200C3×C22⋊Q8C23124yes—
201C3×C22⋊Q8C2316yes—
202C3×C22⋊Q8C2316yes—
203C3×C22⋊Q8C2316yes—
204C3×C22⋊Q8C2316yes—
205C3×C22⋊Q8C2316yes—
206C3×C22⋊Q8C2316yes—
207C3×C22⋊Q8C23112yes—
208C3×#121C2312yes—
209C3×#121C2316yes—
210C3×#121C23112yes—
211C3×#121C2316yes—
212C3×C4×Q8C2311yescharacteristic
213C3×C4×Q8C2313yes—
214C3×C4×Q8C2314yes—
215C3×C4×Q8C2316yes—
216C3×C4×Q8C2316yes—
217C3×C4×Q8C23112yes—
218C3×C4×Q8C23112yes—
219C3×C4×Q8C2312yes—
220C3×C4×Q8C2311yescharacteristic
221C3×C4×Q8C2313yes—
222C3×C4×Q8C2312yes—
223C3×C4×Q8C2316yes—
224C3×C4×Q8C2316yes—
225C3×C4×Q8C2316yes—
226C3×C4×Q8C23112yes—
227C3×C4×Q8C23112yes—
228C3×C4×Q8C2316yes—
229C3×C4×Q8C2316yes—
230C3×C4×Q8C23112yes—
231C3×C4×Q8C2316yes—
232C3×C4×Q8C23112yes—
233C3×C4×Q8C2313yes—
234C3×C4×Q8C2313yes—
235C3×C4×Q8C2316yes—
236C3×C4×Q8C23112yes—
237C3×C4×Q8C23112yes—
238C3×C4×Q8C23112yes—
239C3×C4×Q8C23112yes—
240C3×C4×D4C2311yescharacteristic
241C3×C4×D4C2313yes—
242C3×C4×D4C2311yescharacteristic
243C3×C4×D4C2316yes—
244C3×C4×D4C2313yes—
245C3×C4×D4C2313yes—
246C3×C4×D4C2316yes—
247C3×C4×D4C2313yes—
248C3×C4×D4C2316yes—
249C3×C4×D4C2316yes—
250C3×C4×D4C2316yes—
251C3×C4×D4C23112yes—
252C3×C4×D4C23112yes—
253C3×C4×D4C23124yes—
254C3×C4×D4C23112yes—
255C3×#117C2313yes—
256C3×#117C23112yes—
257C3×#117C2316yes—
258C3×#117C2316yes—
259C3×#117C2313yes—
260C3×#117C2316yes—
261C3×#117C2313yes—
262C3×#117C2316yes—
263C3×#117C23112yes—
264C3×#117C23124yes—
265C3×#117C23112yes—
266C3×#117C2316yes—
267C3×#117C2316yes—
268C3×#117C23112yes—
269C2×C3×C4⋊C4C2312yes—
270C2×C3×C4⋊C4C2316yes—
271C2×C3×C4⋊C4C23112yes—
272C2×C3×C4⋊C4C23112yes—
273C2×C3×C4⋊C4C2316yes—
274C2×C3×C4⋊C4C23112yes—
275C2×C3×C4⋊C4C2316yes—
276C2×C3×C4⋊C4C2316yes—
277C2×C3×C42C23112yes—
278C2×C3×C42C2316yes—
279C2×C3×C42C2316yes—
280C2×C3×C42C2313yes—
281#564C22×C3112yes—
282#563C22×C3124yes—
283Q82C22×C312yes—
284Q82C22×C316yes—
285#557C22×C311yescharacteristic
286#557C22×C314yes—
287#557C22×C312yes—
288#557C22×C316yes—
289#557C22×C316yes—
290#557C22×C3112yes—
291#557C22×C316yes—
292#557C22×C311yescharacteristic
293#557C22×C313yes—
294#557C22×C316yes—
295#557C22×C3112yes—
296#557C22×C316yes—
297#557C22×C316yes—
298#556C22×C313yes—
299#556C22×C313yes—
300#556C22×C316yes—
301#556C22×C313yes—
302#556C22×C316yes—
303#556C22×C3112yes—
304#554C22×C316yes—
305#554C22×C3112yes—
306#554C22×C316yes—
307#554C22×C3112yes—
308#553C22×C3112yes—
309#552C22×C316yes—
310#552C22×C3112yes—
311#552C22×C316yes—
312#552C22×C316yes—
313#552C22×C3112yes—
314#552C22×C3112yes—
315#552C22×C3124yes—
316#552C22×C3112yes—
317D4×Q8C22×C311yescharacteristic
318D4×Q8C22×C314yes—
319D4×Q8C22×C313yes—
320D4×Q8C22×C311yescharacteristic
321D4×Q8C22×C316yes—
322D4×Q8C22×C3112yes—
323#548C22×C312yes—
324#548C22×C312yes—
325#548C22×C316yes—
326#547C22×C311yescharacteristic
327#547C22×C313yes—
328#547C22×C316yes—
329#547C22×C313yes—
330#544C22×C3112yes—
331#544C22×C316yes—
332#544C22×C3112yes—
333#544C22×C316yes—
334#542C22×C3112yes—
335#541C22×C3112yes—
336#541C22×C3112yes—
337#541C22×C3112yes—
338#541C22×C3112yes—
339#541C22×C3112yes—
340#541C22×C3124yes—
341#539C22×C3124yes—
342#536C22×C316yes—
343#533C22×C316yes—
344#533C22×C3112yes—
345#533C22×C316yes—
346#533C22×C313yes—
347#533C22×C313yes—
348#533C22×C313yes—
349#533C22×C316yes—
350#533C22×C316yes—
351C2×C4⋊Q8C22×C316yes—
352C2×C4⋊Q8C22×C313yes—
353#529C22×C316yes—
354#529C22×C3112yes—
355#529C22×C316yes—
356#529C22×C316yes—
357#529C22×C3112yes—
358C2×#125C22×C3112yes—
359#520C22×C316yes—
360#520C22×C312yes—
361#519C22×C314yes—
362#519C22×C316yes—
363C4×#41C22×C316yes—
364C4×#41C22×C313yes—
365C4×#41C22×C311yescharacteristic
366C4×#41C22×C313yes—
367C2×C4×Q8C22×C314yes—
368C2×C4×Q8C22×C316yes—
369C2×C4×Q8C22×C312yes—
370C2×C4×Q8C22×C312yes—
371C3×#41—24no—
372C3×#41—28no—
373C3×#41—212no—
374C3×#41—46no—
375C2×C3×Q8—28no—
376C2×C3×Q8—28no—
377C2×C3×Q8—412no—
378C2×C3×Q8—412no—
379C2×C3×Q8C2416yes—
380C2×C3×Q8C2416yes—
381C2×C3×Q8C2413yes—
382C2×C3×Q8C2412yes—
383C2×C3×Q8C2416yes—
384C2×C3×Q8C2413yes—
385C2×C3×Q8C24112yes—
386C2×C3×Q8C24112yes—
387C2×C3×Q8C2411yescharacteristic
388C2×C3×D4C2416yes—
389C2×C3×D4C2414yes—
390C2×C3×D4C2413yes—
391C2×C3×D4C2411yescharacteristic
392C2×C3×D4C2416yes—
393C2×C3×D4C2411yescharacteristic
394C22×C3×C4C2414yes—
395C22×C3×C4C2416yes—
396C22×C3×C4C2412yes—
397C22×C3×C4C2412yes—
398C22×C3×C4C2416yes—
399C22×C3×C4C2413yes—
400C22×C3×C4C2413yes—
401C22×C3×C4C2416yes—
402C22×C3×C4C2413yes—
403C22×C3×C4C24112yes—
404C22×C3×C4C2416yes—
405C22×C3×C4C24112yes—
406C3×C4⋊C4C2416yes—
407C3×C4⋊C4C2411yescharacteristic
408C3×C4⋊C4C2413yes—
409C3×C4⋊C4C24112yes—
410C3×C4⋊C4C2413yes—
411C3×C4⋊C4C2416yes—
412C3×C4⋊C4C2416yes—
413C3×C4⋊C4C24112yes—
414C3×C4⋊C4C2416yes—
415C3×C4⋊C4C2416yes—
416C3×C4⋊C4C2416yes—
417C3×C4⋊C4C24112yes—
418C3×C4⋊C4C24124yes—
419C3×C4⋊C4C2412yes—
420C3×C4⋊C4C2414yes—
421C3×C4⋊C4C24112yes—
422C3×C4⋊C4C24112yes—
423C3×C4⋊C4C24124yes—
424C3×C4⋊C4C24112yes—
425C3×C4⋊C4C24112yes—
426C3×C4⋊C4C2413yes—
427C3×C4⋊C4C2411yescharacteristic
428C3×C4⋊C4C2416yes—
429C3×C4⋊C4C2412yes—
430C3×C4⋊C4C2413yes—
431C3×C4⋊C4C2416yes—
432C3×C4⋊C4C24112yes—
433C3×C4⋊C4C2416yes—
434C3×C4⋊C4C2416yes—
435C3×C4⋊C4C24112yes—
436C3×C4⋊C4C2416yes—
437C3×C4⋊C4C24124yes—
438C3×C4⋊C4C24112yes—
439C3×C4⋊C4C2416yes—
440C3×C4⋊C4C24112yes—
441C3×C22⋊C4C2416yes—
442C3×C22⋊C4C2416yes—
443C3×C22⋊C4C24112yes—
444C3×C22⋊C4C2412yes—
445C3×C22⋊C4C2412yes—
446C3×C22⋊C4C24112yes—
447C3×C22⋊C4C2414yes—
448C3×C22⋊C4C24112yes—
449C3×C22⋊C4C24112yes—
450C3×C22⋊C4C24112yes—
451C3×C22⋊C4C2416yes—
452C3×C22⋊C4C24112yes—
453C3×C22⋊C4C2416yes—
454C3×C22⋊C4C2416yes—
455C3×C42C2413yes—
456C3×C42C2411yescharacteristic
457C3×C42C2413yes—
458C3×C42C2416yes—
459C3×C42C2413yes—
460C3×C42C24112yes—
461C3×C42C2416yes—
462C3×C42C2416yes—
463C3×C42C24112yes—
464C3×C42C2416yes—
465C3×C42C2416yes—
466C3×C42C2416yes—
467C3×C42C24112yes—
468C3×C42C24124yes—
469C2×#41C23×C312yes—
470C2×#41C23×C313yes—
471C2×#41C23×C311yescharacteristic
472C2×#41C23×C313yes—
473C22×Q8C23×C312yes—
474C22×Q8C23×C312yes—
475C22×Q8C23×C316yes—
476C22×Q8C23×C316yes—
477C4⋊Q8C23×C313yes—
478C4⋊Q8C23×C316yes—
479C4⋊Q8C23×C313yes—
480C4⋊Q8C23×C316yes—
481C4⋊Q8C23×C3112yes—
482C4⋊Q8C23×C316yes—
483C4⋊Q8C23×C3112yes—
484C4⋊Q8C23×C3112yes—
485C4⋊Q8C23×C313yes—
486C4⋊Q8C23×C311yescharacteristic
487C4⋊Q8C23×C313yes—
488C4⋊Q8C23×C313yes—
489C4⋊Q8C23×C316yes—
490C4⋊Q8C23×C3112yes—
491C4⋊Q8C23×C3112yes—
492C4⋊Q8C23×C316yes—
493C4⋊Q8C23×C3124yes—
494#126C23×C3124yes—
495#126C23×C3112yes—
496#126C23×C3112yes—
497#126C23×C3112yes—
498#126C23×C3112yes—
499#126C23×C3112yes—
500#126C23×C3124yes—
501#126C23×C3124yes—
502#125C23×C316yes—
503#125C23×C3112yes—
504#125C23×C3124yes—
505#125C23×C3124yes—
506#125C23×C3112yes—
507#125C23×C3112yes—
508#125C23×C316yes—
509#125C23×C3112yes—
510#125C23×C316yes—
511#125C23×C3112yes—
512#125C23×C3112yes—
513#125C23×C316yes—
514#125C23×C3124yes—
515#125C23×C3112yes—
516#125C23×C316yes—
517#125C23×C316yes—
518#125C23×C3124yes—
519#125C23×C3124yes—
520#125C23×C3124yes—
521#124C23×C316yes—
522#124C23×C316yes—
523#124C23×C316yes—
524#124C23×C3112yes—
525#123C23×C3112yes—
526#123C23×C314yes—
527#123C23×C3112yes—
528#123C23×C3112yes—
529#123C23×C3112yes—
530#123C23×C3124yes—
531C22⋊Q8C23×C316yes—
532C22⋊Q8C23×C316yes—
533C22⋊Q8C23×C3112yes—
534C22⋊Q8C23×C316yes—
535C22⋊Q8C23×C3112yes—
536C22⋊Q8C23×C316yes—
537C22⋊Q8C23×C312yes—
538C22⋊Q8C23×C3112yes—
539C22⋊Q8C23×C3112yes—
540C22⋊Q8C23×C3124yes—
541C22⋊Q8C23×C316yes—
542C22⋊Q8C23×C316yes—
543C22⋊Q8C23×C316yes—
544C22⋊Q8C23×C316yes—
545C22⋊Q8C23×C316yes—
546C22⋊Q8C23×C316yes—
547C22⋊Q8C23×C3112yes—
548C22⋊Q8C23×C3112yes—
549C22⋊Q8C23×C3124yes—
550C22⋊Q8C23×C3124yes—
551#121C23×C312yes—
552#121C23×C316yes—
553#121C23×C3112yes—
554#121C23×C316yes—
555C4×Q8C23×C312yes—
556C4×Q8C23×C311yescharacteristic
557C4×Q8C23×C311yescharacteristic
558C4×Q8C23×C313yes—
559C4×Q8C23×C312yes—
560C4×Q8C23×C316yes—
561C4×Q8C23×C314yes—
562C4×Q8C23×C316yes—
563C4×Q8C23×C316yes—
564C4×Q8C23×C316yes—
565C4×Q8C23×C3112yes—
566C4×Q8C23×C3112yes—
567C4×Q8C23×C316yes—
568C4×Q8C23×C316yes—
569C4×Q8C23×C3112yes—
570C4×Q8C23×C316yes—
571C4×Q8C23×C3112yes—
572C4×Q8C23×C313yes—
573C4×Q8C23×C316yes—
574C4×Q8C23×C313yes—
575C4×Q8C23×C313yes—
576C4×Q8C23×C316yes—
577C4×Q8C23×C3112yes—
578C4×Q8C23×C3112yes—
579C4×Q8C23×C3112yes—
580C4×Q8C23×C3112yes—
581C4×Q8C23×C3112yes—
582C4×Q8C23×C3112yes—
583C4×D4C23×C311yescharacteristic
584C4×D4C23×C313yes—
585C4×D4C23×C311yescharacteristic
586C4×D4C23×C316yes—
587C4×D4C23×C313yes—
588C4×D4C23×C313yes—
589C4×D4C23×C316yes—
590C4×D4C23×C313yes—
591C4×D4C23×C316yes—
592C4×D4C23×C316yes—
593C4×D4C23×C316yes—
594C4×D4C23×C3112yes—
595C4×D4C23×C3112yes—
596C4×D4C23×C3124yes—
597C4×D4C23×C3112yes—
598#117C23×C313yes—
599#117C23×C3112yes—
600#117C23×C316yes—
601#117C23×C316yes—
602#117C23×C313yes—
603#117C23×C316yes—
604#117C23×C313yes—
605#117C23×C316yes—
606#117C23×C3112yes—
607#117C23×C3124yes—
608#117C23×C3112yes—
609#117C23×C316yes—
610#117C23×C316yes—
611#117C23×C3112yes—
612C2×C4⋊C4C23×C312yes—
613C2×C4⋊C4C23×C316yes—
614C2×C4⋊C4C23×C3112yes—
615C2×C4⋊C4C23×C3112yes—
616C2×C4⋊C4C23×C316yes—
617C2×C4⋊C4C23×C3112yes—
618C2×C4⋊C4C23×C316yes—
619C2×C4⋊C4C23×C316yes—
620C2×C42C23×C3112yes—
621C2×C42C23×C316yes—
622C2×C42C23×C316yes—
623C2×C42C23×C313yes—
624C23×C3C2512yes—
625C23×C3C2513yes—
626C23×C3C2512yes—
627C3×Q8—212no—
628C3×Q8—212no—
629C3×Q8—26no—
630C3×Q8—24no—
631C3×Q8—212no—
632C3×Q8—26no—
633C3×Q8—412no—
634C3×Q8—412no—
635C3×Q82−1+414yes—
636C3×D4—212no—
637C3×D4—28no—
638C3×D4—26no—
639C3×D4—22no—
640C3×D4—46no—
641C3×D42−1+414yes—
642C2×C3×C4—28no—
643C2×C3×C4—212no—
644C2×C3×C4—212no—
645C2×C3×C4—212no—
646C2×C3×C4—26no—
647C2×C3×C4—24no—
648C2×C3×C4—26no—
649C2×C3×C4—24no—
650C2×C3×C4—26no—
651C2×C3×C4—412no—
652C2×C3×C4—412no—
653C2×C3×C4—46no—
654C2×C3×C4C2512yes—
655C2×C3×C4C2516yes—
656C2×C3×C4C2516yes—
657C2×C3×C4C2512yes—
658C2×C3×C4C2514yes—
659C2×C3×C4C2516yes—
660C2×C3×C4C2511yescharacteristic
661C2×C3×C4C2513yes—
662C2×C3×C4C2513yes—
663C2×C3×C4C25112yes—
664C2×C3×C4C2516yes—
665C2×C3×C4C2513yes—
666C2×C3×C4C2511yescharacteristic
667C2×C3×C4C2511yescharacteristic
668#41—24no—
669#41—28no—
670#41—212no—
671#41—46no—
672C2×Q8—28no—
673C2×Q8—28no—
674C2×Q8—412no—
675C2×Q8—412no—
676C2×Q8C24×C316yes—
677C2×Q8C24×C316yes—
678C2×Q8C24×C312yes—
679C2×Q8C24×C313yes—
680C2×Q8C24×C316yes—
681C2×Q8C24×C313yes—
682C2×Q8C24×C3112yes—
683C2×Q8C24×C3112yes—
684C2×Q8C24×C311yescharacteristic
685C2×D4C24×C316yes—
686C2×D4C24×C314yes—
687C2×D4C24×C313yes—
688C2×D4C24×C311yescharacteristic
689C2×D4C24×C316yes—
690C2×D4C24×C311yescharacteristic
691C22×C4C24×C314yes—
692C22×C4C24×C316yes—
693C22×C4C24×C312yes—
694C22×C4C24×C312yes—
695C22×C4C24×C316yes—
696C22×C4C24×C313yes—
697C22×C4C24×C313yes—
698C22×C4C24×C316yes—
699C22×C4C24×C313yes—
700C22×C4C24×C3112yes—
701C22×C4C24×C316yes—
702C22×C4C24×C3112yes—
703C4⋊C4C24×C316yes—
704C4⋊C4C24×C311yescharacteristic
705C4⋊C4C24×C313yes—
706C4⋊C4C24×C3112yes—
707C4⋊C4C24×C313yes—
708C4⋊C4C24×C316yes—
709C4⋊C4C24×C316yes—
710C4⋊C4C24×C3112yes—
711C4⋊C4C24×C316yes—
712C4⋊C4C24×C316yes—
713C4⋊C4C24×C316yes—
714C4⋊C4C24×C3112yes—
715C4⋊C4C24×C3124yes—
716C4⋊C4C24×C312yes—
717C4⋊C4C24×C314yes—
718C4⋊C4C24×C3112yes—
719C4⋊C4C24×C3112yes—
720C4⋊C4C24×C3124yes—
721C4⋊C4C24×C3112yes—
722C4⋊C4C24×C3112yes—
723C4⋊C4C24×C313yes—
724C4⋊C4C24×C311yescharacteristic
725C4⋊C4C24×C316yes—
726C4⋊C4C24×C312yes—
727C4⋊C4C24×C313yes—
728C4⋊C4C24×C316yes—
729C4⋊C4C24×C3112yes—
730C4⋊C4C24×C316yes—
731C4⋊C4C24×C316yes—
732C4⋊C4C24×C3112yes—
733C4⋊C4C24×C316yes—
734C4⋊C4C24×C3124yes—
735C4⋊C4C24×C3112yes—
736C4⋊C4C24×C316yes—
737C4⋊C4C24×C3112yes—
738C22⋊C4C24×C316yes—
739C22⋊C4C24×C316yes—
740C22⋊C4C24×C3112yes—
741C22⋊C4C24×C312yes—
742C22⋊C4C24×C312yes—
743C22⋊C4C24×C3112yes—
744C22⋊C4C24×C314yes—
745C22⋊C4C24×C3112yes—
746C22⋊C4C24×C3112yes—
747C22⋊C4C24×C3112yes—
748C22⋊C4C24×C316yes—
749C22⋊C4C24×C3112yes—
750C22⋊C4C24×C316yes—
751C22⋊C4C24×C316yes—
752C42C24×C313yes—
753C42C24×C311yescharacteristic
754C42C24×C313yes—
755C42C24×C316yes—
756C42C24×C313yes—
757C42C24×C3112yes—
758C42C24×C316yes—
759C42C24×C316yes—
760C42C24×C3112yes—
761C42C24×C316yes—
762C42C24×C316yes—
763C42C24×C316yes—
764C42C24×C3112yes—
765C42C24×C3124yes—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—23no—
771C22×C3—23no—
772C22×C3—23no—
773C22×C3—22no—
774C22×C3C2×2−1+414yes—
775C22×C3C2611yescharacteristic
776C3×C4—22no—
777C3×C4—23no—
778C3×C4—21no—
779C3×C4—24no—
780C3×C4—26no—
781C3×C4—26no—
782C3×C4—26no—
783C3×C4—23no—
784C3×C4—22no—
785C3×C4—26no—
786C3×C4—212no—
787C3×C4C2×2−1+416yes—
788C3×C4C2×2−1+412yes—
789C3×C4#58512yes—
790C23C25×C312yes—
791C23C25×C313yes—
792C23C25×C312yes—
793Q8—212no—
794Q8—212no—
795Q8—24no—
796Q8—26no—
797Q8—212no—
798Q8—26no—
799Q8—412no—
800Q8—412no—
801Q8C3×2−1+414yes—
802D4—212no—
803D4—28no—
804D4—26no—
805D4—22no—
806D4—46no—
807D4C3×2−1+414yes—
808C2×C4—28no—
809C2×C4—212no—
810C2×C4—212no—
811C2×C4—212no—
812C2×C4—26no—
813C2×C4—24no—
814C2×C4—26no—
815C2×C4—24no—
816C2×C4—26no—
817C2×C4—412no—
818C2×C4—412no—
819C2×C4—46no—
820C2×C4C25×C312yes—
821C2×C4C25×C316yes—
822C2×C4C25×C316yes—
823C2×C4C25×C312yes—
824C2×C4C25×C314yes—
825C2×C4C25×C316yes—
826C2×C4C25×C311yescharacteristic
827C2×C4C25×C313yes—
828C2×C4C25×C313yes—
829C2×C4C25×C3112yes—
830C2×C4C25×C316yes—
831C2×C4C25×C313yes—
832C2×C4C25×C311yescharacteristic
833C2×C4C25×C311yescharacteristic
834C2×C3—24no—
835C2×C3—42no—
836C2×C3—43no—
837C2×C3C22×2−1+411yescharacteristic
838C2×C3C22×2−1+411yescharacteristic
839C2×C3C2×#58511yescharacteristic
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—23no—
845C22—23no—
846C22—23no—
847C22—22no—
848C22C2×C3×2−1+414yes—
849C22C26×C311yescharacteristic
850C4—22no—
851C4—23no—
852C4—21no—
853C4—24no—
854C4—26no—
855C4—26no—
856C4—26no—
857C4—23no—
858C4—22no—
859C4—26no—
860C4—212no—
861C4C2×C3×2−1+416yes—
862C4C2×C3×2−1+412yes—
863C4C3×#58512yes—
864C3#6303211yescharacteristic, direct product factor, Sylow
865C2—24no—
866C2—42no—
867C2—43no—
868C2C22×C3×2−1+411yescharacteristic
869C2C22×C3×2−1+411yescharacteristic
870C2C2×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×#3563C2semidirect
2. C3×#3556C2semidirect
3. C3×#3555C2semidirect
4. C3×#3552C2semidirect
5. C3×#3523C2semidirect
6. C3×#3523C2semidirect
7. C3×#3516C2semidirect
8. C3×#3515C2semidirect
9. C3×#3509C2semidirect
10. C3×#3503C2semidirect
11. C3×#3503C2semidirect
12. C3×#3502C2semidirect
13. C3×#3482C2semidirect
14. C3×#3482C2semidirect
15. C3×#3482C2semidirect
16. C3×Q8×#41C2semidirect
17. C2×C3×#557C2semidirect
18. #63032C3direct (N × H)
109. #3563C2×C3semidirect
110. #3556C2×C3semidirect
111. #3555C2×C3semidirect
112. #3552C2×C3semidirect
113. #3523C2×C3semidirect
114. #3523C2×C3semidirect
115. #3516C2×C3semidirect
116. #3515C2×C3semidirect
117. #3509C2×C3semidirect
118. #3503C2×C3semidirect
119. #3503C2×C3semidirect
120. #3502C2×C3semidirect
121. #3482C2×C3semidirect
122. #3482C2×C3semidirect
123. #3482C2×C3semidirect
124. Q8×#41C2×C3semidirect
125. C2×#557C2×C3semidirect
864. C3#63032direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35632
C3×#35562
C3×#35552
C3×#35522
C3×#35232
C3×#35162
C3×#35152
C3×#35092
C3×#35032
C3×#35022
C3×#34822
C3×Q8×#412
C2×C3×#5572
#630323