Finite Group Databasebeta

← C3×#63005 #10681612

Subgroups — C3×#63005 #10681612

Order 768.

7024 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3524C214yesmaximal, complemented
2C3×#3524C214yesmaximal, complemented
3C3×#3522C214yesmaximal, complemented
4C3×#3518C214yesmaximal, complemented
5C3×#3516C214yesmaximal, complemented
6C3×#3516C214yesmaximal, complemented
7C3×#3510C216yesmaximal, complemented
8C3×#3502C211yesmaximal, characteristic, complemented
9C3×#3495C216yesmaximal, complemented
10C3×#3494C216yesmaximal, complemented
11C3×#3487C211yesmaximal, characteristic, complemented
12C3×#3486C211yesmaximal, characteristic, complemented
13C3×#3482C214yesmaximal, complemented
14C3×#3480C214yesmaximal, complemented
15C3×#3475C216yesmaximal, complemented
16C2×C3×#548C211yesmaximal, characteristic, complemented
17C3×C4×2−1+4C211yesmaximal, characteristic, complemented
18C3×#3428C211yesmaximal, characteristic, complemented
19C2×C3×#519C211yesmaximal, characteristic, complemented
20#63005C311yesmaximal, characteristic, direct product factor, Sylow
21C2×C3×2−1+4C2211yescharacteristic
22C22×C3×#41C2211yescharacteristic
23C23×C3×Q8C2211yescharacteristic
24C3×#559C22112yescomplemented
25C3×#559C22112yescomplemented
26C3×Q82C2214yescomplemented
27C3×#557C2214yescomplemented
28C3×#557C2214yescomplemented
29C3×#557C2214yescomplemented
30C3×#556C2216yescomplemented
31C3×#556C22112yescomplemented
32C3×#556C22112yescomplemented
33C3×#556C22112yescomplemented
34C3×#555C2216yescomplemented
35C3×#555C22112yescomplemented
36C3×#554C2216yescomplemented
37C3×#554C22112yescomplemented
38C3×#553C2216yescomplemented
39C3×#553C2216yescomplemented
40C3×#553C22112yescomplemented
41C3×#553C22112yescomplemented
42C3×#552C22112yes—
43C3×#552C2216yescomplemented
44C3×#552C2216yescomplemented
45C3×#552C22112yescomplemented
46C3×#552C22112yescomplemented
47C3×#551C2214yes—
48C3×#551C22112yes—
49C3×#551C22124yes—
50C3×#550C2214yescomplemented
51C3×#550C2214yescomplemented
52C3×D4×Q8C2214yescomplemented
53C3×D4×Q8C2214yescomplemented
54C3×#548C2214yes—
55C3×#548C2214yes—
56C3×#548C2214yes—
57C3×#548C2214yes—
58C3×#548C2214yescomplemented
59C3×#548C2214yescomplemented
60C3×#548C2214yescomplemented
61C3×#548C2214yescomplemented
62C3×#547C2216yescomplemented
63C3×#547C22112yescomplemented
64C3×#546C22112yes—
65C3×#544C2216yes—
66C3×#542C22112yescomplemented
67C3×#542C22112yescomplemented
68C3×#542C22112yescomplemented
69C3×#542C22112yescomplemented
70C3×#541C22112yescomplemented
71C3×#540C22112yescomplemented
72C3×#536C2216yes—
73C3×#535C2216yes—
74C3×#533C2216yes—
75C3×#533C22112yescomplemented
76C3×#532C22112yescomplemented
77C3×#529C22112yescomplemented
78C3×#529C22112yescomplemented
79C3×#529C22112yescomplemented
80C3×#529C22112yescomplemented
81C3×#529C22112yescomplemented
82C3×#529C22112yescomplemented
83C3×#529C22112yescomplemented
84C2×C3×#124C2213yes—
85C3×#525C2216yes—
86C3×#525C2216yes—
87C2×C3×C22⋊Q8C2213yes—
88C2×C3×#121C2213yes—
89C3×#520C2216yes—
90C3×#520C2214yescomplemented
91C3×#520C2214yescomplemented
92C3×#520C2214yescomplemented
93C3×#519C2211yescharacteristic
94C3×#519C2211yescharacteristic
95C3×#519C2216yes—
96C3×#519C2211yescharacteristic
97C3×#519C2214yescomplemented
98C3×#519C2214yescomplemented
99C3×#519C2214yescomplemented
100C3×#518C2216yes—
101C3×C4×#41C2216yes—
102C3×C4×#41C2214yescomplemented
103C3×C4×#41C2214yescomplemented
104C3×C4×#41C2214yescomplemented
105C3×C4×#41C22112yescomplemented
106C2×C3×C4×Q8C2211yescharacteristic
107C2×C3×C4×Q8C2214yescomplemented
108C2×C3×C4×Q8C2214yescomplemented
109C2×C3×C4×Q8C2214yescomplemented
110C2×C3×C4×D4C2213yes—
111C2×C3×#117C2216yes—
112C2×C3×#117C2216yes—
113#3524C2×C314yescomplemented
114#3524C2×C314yescomplemented
115#3522C2×C314yescomplemented
116#3518C2×C314yescomplemented
117#3516C2×C314yescomplemented
118#3516C2×C314yescomplemented
119#3510C2×C316yescomplemented
120#3502C2×C311yescharacteristic, complemented
121#3495C2×C316yescomplemented
122#3494C2×C316yescomplemented
123#3487C2×C311yescharacteristic, complemented
124#3486C2×C311yescharacteristic, complemented
125#3482C2×C314yescomplemented
126#3480C2×C314yescomplemented
127#3475C2×C316yescomplemented
128C2×#548C2×C311yescharacteristic, complemented
129C4×2−1+4C2×C311yescharacteristic, complemented
130#3428C2×C311yescharacteristic, complemented
131C2×#519C2×C311yescharacteristic, complemented
132C3×2−1+4—28no—
133C2×C3×#41—28no—
134C2×C3×#41C2314yes—
135C2×C3×#41C2314yes—
136C2×C3×#41C2316yes—
137C2×C3×#41C2314yes—
138C2×C3×#41C23112yes—
139C22×C3×Q8—28no—
140C22×C3×Q8C2314yes—
141C22×C3×Q8C2313yes—
142C22×C3×Q8C2314yes—
143C22×C3×Q8C2314yes—
144C22×C3×Q8C2311yescharacteristic
145C22×C3×D4C2313yes—
146C22×C3×D4C2313yes—
147C23×C3×C4C2313yes—
148C23×C3×C4C2313yes—
149C3×C4⋊Q8C2316yes—
150C3×C4⋊Q8C23112yes—
151C3×C4⋊Q8C23112yes—
152C3×C4⋊Q8C2316yes—
153C3×C4⋊Q8C23112yes—
154C3×#127C23112yes—
155C3×#126C2314yes—
156C3×#126C23112yes—
157C3×#126C2314yes—
158C3×#126C23112yes—
159C3×#126C23124yes—
160C3×#126C23124yes—
161C3×#126C23112yes—
162C3×#126C23112yes—
163C3×#125C2316yes—
164C3×#125C2316yes—
165C3×#125C23112yes—
166C3×#125C23112yes—
167C3×#125C23112yes—
168C3×#125C23112yes—
169C3×#125C23112yes—
170C3×#124C23112yes—
171C3×#124C23112yes—
172C3×#124C23112yes—
173C3×#124C23112yes—
174C3×#124C23124yes—
175C3×#124C2314yes—
176C3×#124C23112yes—
177C3×#124C23112yes—
178C3×#123C23112yes—
179C3×#123C23112yes—
180C3×#123C23124yes—
181C3×#123C23124yes—
182C3×#123C2314yes—
183C3×#123C23112yes—
184C3×#123C23112yes—
185C3×#123C2314yes—
186C3×#123C2314yes—
187C3×#123C23112yes—
188C3×C22⋊Q8C23112yes—
189C3×C22⋊Q8C23112yes—
190C3×C22⋊Q8C2316yes—
191C3×C22⋊Q8C2316yes—
192C3×C22⋊Q8C2316yes—
193C3×C22⋊Q8C2316yes—
194C3×C22⋊Q8C2314yes—
195C3×C22⋊Q8C23112yes—
196C3×C22⋊Q8C23112yes—
197C3×C22⋊Q8C23112yes—
198C3×C22⋊Q8C23112yes—
199C3×C22⋊Q8C2314yes—
200C3×C22⋊Q8C23112yes—
201C3×C22⋊Q8C23124yes—
202C3×#121C23112yes—
203C3×#121C23112yes—
204C3×#121C2316yes—
205C3×#121C2316yes—
206C3×#121C2316yes—
207C3×#121C2316yes—
208C3×#121C23112yes—
209C3×#121C23112yes—
210C3×#121C23112yes—
211C3×#121C23112yes—
212C3×#121C23112yes—
213C3×#120C2314yes—
214C3×#120C23112yes—
215C3×C4×Q8C23112yes—
216C3×C4×Q8C2314yes—
217C3×C4×Q8C2314yes—
218C3×C4×Q8C2314yes—
219C3×C4×Q8C23112yes—
220C3×C4×Q8C23112yes—
221C3×C4×Q8C23112yes—
222C3×C4×Q8C2314yes—
223C3×C4×Q8C2316yes—
224C3×C4×Q8C2314yes—
225C3×C4×Q8C2314yes—
226C3×C4×Q8C23112yes—
227C3×C4×Q8C23112yes—
228C3×C4×Q8C2314yes—
229C3×C4×Q8C23112yes—
230C3×C4×Q8C2316yes—
231C3×C4×Q8C2314yes—
232C3×C4×Q8C23112yes—
233C3×C4×D4C2316yes—
234C3×C4×D4C2316yes—
235C3×C4×D4C23112yes—
236C3×C4×D4C23112yes—
237C3×C4×D4C23112yes—
238C3×C4×D4C23124yes—
239C3×C4×D4C2316yes—
240C3×C4×D4C2316yes—
241C3×C4×D4C2316yes—
242C3×C4×D4C2316yes—
243C3×C4×D4C2314yes—
244C3×C4×D4C23112yes—
245C3×C4×D4C2314yes—
246C3×C4×D4C23112yes—
247C3×C4×D4C23112yes—
248C3×C4×D4C23112yes—
249C3×C4×D4C23112yes—
250C3×C4×D4C23112yes—
251C3×C4×D4C23112yes—
252C3×C4×D4C23112yes—
253C3×C4×D4C23112yes—
254C3×#117C2314yes—
255C3×#117C2316yes—
256C3×#117C2316yes—
257C3×#117C2316yes—
258C3×#117C2316yes—
259C3×#117C2316yes—
260C3×#117C23112yes—
261C3×#117C23112yes—
262C3×#117C2316yes—
263C3×#117C2316yes—
264C3×#117C23112yes—
265C3×#117C23112yes—
266C3×#117C2314yes—
267C3×#117C23112yes—
268C3×#117C23112yes—
269C3×#117C23112yes—
270C3×#117C23124yes—
271C2×C3×C4⋊C4C2316yes—
272C2×C3×C4⋊C4C2316yes—
273C2×C3×C4⋊C4C2316yes—
274C2×C3×C4⋊C4C2316yes—
275C2×C3×C4⋊C4C2313yes—
276C2×C3×C4⋊C4C2313yes—
277C2×C3×C4⋊C4C23112yes—
278C2×C3×C22⋊C4C2314yes—
279C2×C3×C22⋊C4C23112yes—
280C2×C3×C22⋊C4C2311yescharacteristic
281C2×C3×C22⋊C4C2313yes—
282C2×C3×C22⋊C4C2316yes—
283C2×C3×C42C23112yes—
284C2×C3×C42C23112yes—
285C2×C3×C42C2313yes—
286C2×C3×C42C23112yes—
287C2×2−1+4C22×C311yescharacteristic
288C22×#41C22×C311yescharacteristic
289C23×Q8C22×C311yescharacteristic
290#559C22×C3112yescomplemented
291#559C22×C3112yescomplemented
292Q82C22×C314yescomplemented
293#557C22×C314yescomplemented
294#557C22×C314yescomplemented
295#557C22×C314yescomplemented
296#556C22×C316yescomplemented
297#556C22×C3112yescomplemented
298#556C22×C3112yescomplemented
299#556C22×C3112yescomplemented
300#555C22×C316yescomplemented
301#555C22×C3112yescomplemented
302#554C22×C316yescomplemented
303#554C22×C3112yescomplemented
304#553C22×C316yescomplemented
305#553C22×C316yescomplemented
306#553C22×C3112yescomplemented
307#553C22×C3112yescomplemented
308#552C22×C3112yes—
309#552C22×C316yescomplemented
310#552C22×C316yescomplemented
311#552C22×C3112yescomplemented
312#552C22×C3112yescomplemented
313#551C22×C314yes—
314#551C22×C3112yes—
315#551C22×C3124yes—
316#550C22×C314yescomplemented
317#550C22×C314yescomplemented
318D4×Q8C22×C314yescomplemented
319D4×Q8C22×C314yescomplemented
320#548C22×C314yes—
321#548C22×C314yes—
322#548C22×C314yes—
323#548C22×C314yes—
324#548C22×C314yescomplemented
325#548C22×C314yescomplemented
326#548C22×C314yescomplemented
327#548C22×C314yescomplemented
328#547C22×C316yescomplemented
329#547C22×C3112yescomplemented
330#546C22×C3112yes—
331#544C22×C316yes—
332#542C22×C3112yescomplemented
333#542C22×C3112yescomplemented
334#542C22×C3112yescomplemented
335#542C22×C3112yescomplemented
336#541C22×C3112yescomplemented
337#540C22×C3112yescomplemented
338#536C22×C316yes—
339#535C22×C316yes—
340#533C22×C316yes—
341#533C22×C3112yescomplemented
342#532C22×C3112yescomplemented
343#529C22×C3112yescomplemented
344#529C22×C3112yescomplemented
345#529C22×C3112yescomplemented
346#529C22×C3112yescomplemented
347#529C22×C3112yescomplemented
348#529C22×C3112yescomplemented
349#529C22×C3112yescomplemented
350C2×#124C22×C313yes—
351#525C22×C316yes—
352#525C22×C316yes—
353C2×C22⋊Q8C22×C313yes—
354C2×#121C22×C313yes—
355#520C22×C316yes—
356#520C22×C314yescomplemented
357#520C22×C314yescomplemented
358#520C22×C314yescomplemented
359#519C22×C311yescharacteristic
360#519C22×C311yescharacteristic
361#519C22×C316yes—
362#519C22×C311yescharacteristic
363#519C22×C314yescomplemented
364#519C22×C314yescomplemented
365#519C22×C314yescomplemented
366#518C22×C316yes—
367C4×#41C22×C316yes—
368C4×#41C22×C314yescomplemented
369C4×#41C22×C314yescomplemented
370C4×#41C22×C314yescomplemented
371C4×#41C22×C3112yescomplemented
372C2×C4×Q8C22×C311yescharacteristic
373C2×C4×Q8C22×C314yescomplemented
374C2×C4×Q8C22×C314yescomplemented
375C2×C4×Q8C22×C314yescomplemented
376C2×C4×D4C22×C313yes—
377C2×#117C22×C316yes—
378C2×#117C22×C316yes—
379C24×C3C2411yescharacteristic
380C24×C3C2413yes—
381C3×#41—216no—
382C3×#41—216no—
383C3×#41—216no—
384C3×#41—224no—
385C3×#41—424no—
386C2×C3×Q8—216no—
387C2×C3×Q8—216no—
388C2×C3×Q8—216no—
389C2×C3×Q8—212no—
390C2×C3×Q8#4118yescomplemented
391C2×C3×Q8C24112yes—
392C2×C3×Q8C2416yes—
393C2×C3×Q8C2414yes—
394C2×C3×Q8C24112yes—
395C2×C3×Q8C2414yes—
396C2×C3×D4—212no—
397C2×C3×D4—46no—
398C2×C3×D4C2414yes—
399C2×C3×D4C2414yes—
400C2×C3×D4C2416yes—
401C2×C3×D4C24112yes—
402C2×C3×D4C2416yes—
403C2×C3×D4C2414yes—
404C2×C3×D4C24112yes—
405C2×C3×D4C24112yes—
406C2×C3×D4C2416yes—
407C22×C3×C4—212no—
408C22×C3×C4—212no—
409C22×C3×C4C2414yes—
410C22×C3×C4C2416yes—
411C22×C3×C4C2416yes—
412C22×C3×C4C24112yes—
413C22×C3×C4C2413yes—
414C22×C3×C4C2411yescharacteristic
415C22×C3×C4C2416yes—
416C22×C3×C4C2416yes—
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2414yes—
419C22×C3×C4C2414yes—
420C22×C3×C4C2413yes—
421C22×C3×C4C24112yes—
422C22×C3×C4C24112yes—
423C22×C3×C4C24112yes—
424C22×C3×C4C2413yes—
425C3×C4⋊C4C2416yes—
426C3×C4⋊C4C2414yes—
427C3×C4⋊C4C2414yes—
428C3×C4⋊C4C2416yes—
429C3×C4⋊C4C24112yes—
430C3×C4⋊C4C24112yes—
431C3×C4⋊C4C2416yes—
432C3×C4⋊C4C2416yes—
433C3×C4⋊C4C2416yes—
434C3×C4⋊C4C2416yes—
435C3×C4⋊C4C2416yes—
436C3×C4⋊C4C24112yes—
437C3×C4⋊C4C24112yes—
438C3×C4⋊C4C2416yes—
439C3×C4⋊C4C2414yes—
440C3×C4⋊C4C2414yes—
441C3×C4⋊C4C24112yes—
442C3×C4⋊C4C24112yes—
443C3×C4⋊C4C2414yes—
444C3×C4⋊C4C2414yes—
445C3×C4⋊C4C24112yes—
446C3×C4⋊C4C24112yes—
447C3×C4⋊C4C2414yes—
448C3×C4⋊C4C24112yes—
449C3×C4⋊C4C2414yes—
450C3×C22⋊C4C2414yes—
451C3×C22⋊C4C2414yes—
452C3×C22⋊C4C2414yes—
453C3×C22⋊C4C2414yes—
454C3×C22⋊C4C2414yes—
455C3×C22⋊C4C2411yescharacteristic
456C3×C22⋊C4C24112yes—
457C3×C22⋊C4C24112yes—
458C3×C22⋊C4C2416yes—
459C3×C22⋊C4C24124yes—
460C3×C22⋊C4C2411yescharacteristic
461C3×C22⋊C4C2411yescharacteristic
462C3×C22⋊C4C2411yescharacteristic
463C3×C22⋊C4C2416yes—
464C3×C22⋊C4C2414yes—
465C3×C22⋊C4C24112yes—
466C3×C22⋊C4C2414yes—
467C3×C22⋊C4C24112yes—
468C3×C22⋊C4C2414yes—
469C3×C22⋊C4C24112yes—
470C3×C22⋊C4C24112yes—
471C3×C22⋊C4C2414yes—
472C3×C22⋊C4C2414yes—
473C3×C22⋊C4C24112yes—
474C3×C42C2414yes—
475C3×C42C24112yes—
476C3×C42C2414yes—
477C3×C42C2414yes—
478C3×C42C2416yes—
479C3×C42C24112yes—
480C3×C42C24112yes—
481C3×C42C24112yes—
482C3×C42C24112yes—
483C3×C42C2416yes—
484C3×C42C24112yes—
4852−1+4—28no—
486C2×#41—28no—
487C2×#41C23×C316yes—
488C2×#41C23×C314yes—
489C2×#41C23×C314yes—
490C2×#41C23×C314yes—
491C2×#41C23×C3112yes—
492C22×Q8—28no—
493C22×Q8C23×C314yes—
494C22×Q8C23×C314yes—
495C22×Q8C23×C313yes—
496C22×Q8C23×C314yes—
497C22×Q8C23×C311yescharacteristic
498C22×D4C23×C313yes—
499C22×D4C23×C313yes—
500C23×C4C23×C313yes—
501C23×C4C23×C313yes—
502C4⋊Q8C23×C3112yes—
503C4⋊Q8C23×C316yes—
504C4⋊Q8C23×C316yes—
505C4⋊Q8C23×C3112yes—
506C4⋊Q8C23×C3112yes—
507#127C23×C3112yes—
508#126C23×C314yes—
509#126C23×C3112yes—
510#126C23×C314yes—
511#126C23×C3112yes—
512#126C23×C3124yes—
513#126C23×C3124yes—
514#126C23×C3112yes—
515#126C23×C3112yes—
516#125C23×C316yes—
517#125C23×C316yes—
518#125C23×C3112yes—
519#125C23×C3112yes—
520#125C23×C3112yes—
521#125C23×C3112yes—
522#125C23×C3112yes—
523#124C23×C3112yes—
524#124C23×C3112yes—
525#124C23×C314yes—
526#124C23×C3112yes—
527#124C23×C3112yes—
528#124C23×C3112yes—
529#124C23×C3112yes—
530#124C23×C3124yes—
531#123C23×C314yes—
532#123C23×C3112yes—
533#123C23×C3112yes—
534#123C23×C314yes—
535#123C23×C314yes—
536#123C23×C3112yes—
537#123C23×C3124yes—
538#123C23×C3124yes—
539#123C23×C3112yes—
540#123C23×C3112yes—
541C22⋊Q8C23×C3112yes—
542C22⋊Q8C23×C3112yes—
543C22⋊Q8C23×C316yes—
544C22⋊Q8C23×C316yes—
545C22⋊Q8C23×C316yes—
546C22⋊Q8C23×C316yes—
547C22⋊Q8C23×C314yes—
548C22⋊Q8C23×C3112yes—
549C22⋊Q8C23×C3112yes—
550C22⋊Q8C23×C3112yes—
551C22⋊Q8C23×C3112yes—
552C22⋊Q8C23×C314yes—
553C22⋊Q8C23×C3112yes—
554C22⋊Q8C23×C3124yes—
555#121C23×C3112yes—
556#121C23×C3112yes—
557#121C23×C316yes—
558#121C23×C316yes—
559#121C23×C316yes—
560#121C23×C316yes—
561#121C23×C3112yes—
562#121C23×C3112yes—
563#121C23×C3112yes—
564#121C23×C3112yes—
565#121C23×C3112yes—
566#120C23×C314yes—
567#120C23×C3112yes—
568C4×Q8C23×C314yes—
569C4×Q8C23×C314yes—
570C4×Q8C23×C316yes—
571C4×Q8C23×C314yes—
572C4×Q8C23×C314yes—
573C4×Q8C23×C3112yes—
574C4×Q8C23×C3112yes—
575C4×Q8C23×C314yes—
576C4×Q8C23×C314yes—
577C4×Q8C23×C3112yes—
578C4×Q8C23×C3112yes—
579C4×Q8C23×C3112yes—
580C4×Q8C23×C316yes—
581C4×Q8C23×C314yes—
582C4×Q8C23×C314yes—
583C4×Q8C23×C3112yes—
584C4×Q8C23×C3112yes—
585C4×Q8C23×C3112yes—
586C4×D4C23×C316yes—
587C4×D4C23×C316yes—
588C4×D4C23×C316yes—
589C4×D4C23×C316yes—
590C4×D4C23×C314yes—
591C4×D4C23×C316yes—
592C4×D4C23×C3112yes—
593C4×D4C23×C316yes—
594C4×D4C23×C314yes—
595C4×D4C23×C3112yes—
596C4×D4C23×C3112yes—
597C4×D4C23×C3112yes—
598C4×D4C23×C3112yes—
599C4×D4C23×C3112yes—
600C4×D4C23×C3112yes—
601C4×D4C23×C3112yes—
602C4×D4C23×C3112yes—
603C4×D4C23×C3112yes—
604C4×D4C23×C3112yes—
605C4×D4C23×C3112yes—
606C4×D4C23×C3124yes—
607#117C23×C314yes—
608#117C23×C316yes—
609#117C23×C316yes—
610#117C23×C316yes—
611#117C23×C316yes—
612#117C23×C316yes—
613#117C23×C3112yes—
614#117C23×C3112yes—
615#117C23×C316yes—
616#117C23×C316yes—
617#117C23×C3112yes—
618#117C23×C3112yes—
619#117C23×C314yes—
620#117C23×C3112yes—
621#117C23×C3112yes—
622#117C23×C3112yes—
623#117C23×C3124yes—
624C2×C4⋊C4C23×C316yes—
625C2×C4⋊C4C23×C316yes—
626C2×C4⋊C4C23×C316yes—
627C2×C4⋊C4C23×C316yes—
628C2×C4⋊C4C23×C313yes—
629C2×C4⋊C4C23×C313yes—
630C2×C4⋊C4C23×C3112yes—
631C2×C22⋊C4C23×C314yes—
632C2×C22⋊C4C23×C3112yes—
633C2×C22⋊C4C23×C311yescharacteristic
634C2×C22⋊C4C23×C313yes—
635C2×C22⋊C4C23×C316yes—
636C2×C42C23×C3112yes—
637C2×C42C23×C3112yes—
638C2×C42C23×C313yes—
639C2×C42C23×C3112yes—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—26no—
643C23×C3—41no—
644C23×C3—43no—
645C23×C3—43no—
646C23×C3C2511yescharacteristic
647C23×C3C2516yes—
648C23×C3C2514yes—
649C23×C3C2511yescharacteristic
650C23×C3C2511yescharacteristic
651C3×Q8—224no—
652C3×Q8—212no—
653C3×Q8—44no—
654C3×Q8—412no—
655C3×Q8C2×#41116yes—
656C3×D4—28no—
657C3×D4—212no—
658C3×D4—28no—
659C3×D4—224no—
660C3×D4—212no—
661C3×D4—46no—
662C3×D4—44no—
663C3×D4—412no—
664C3×D4—412no—
665C2×C3×C4—22no—
666C2×C3×C4—26no—
667C2×C3×C4—28no—
668C2×C3×C4—212no—
669C2×C3×C4—212no—
670C2×C3×C4—212no—
671C2×C3×C4—212no—
672C2×C3×C4—224no—
673C2×C3×C4—44no—
674C2×C3×C4—412no—
675C2×C3×C4—44no—
676C2×C3×C4—41no—
677C2×C3×C4—43no—
678C2×C3×C4—412no—
679C2×C3×C4—412no—
680C2×C3×C4C2×#41112yes—
681C2×C3×C4C2514yes—
682C2×C3×C4C2511yescharacteristic
683C2×C3×C4C2511yescharacteristic
684C2×C3×C4C2514yes—
685C2×C3×C4C2511yescharacteristic
686C2×C3×C4C2514yes—
687C2×C3×C4C2514yes—
688C2×C3×C4C2516yes—
689C2×C3×C4C2514yes—
690C2×C3×C4C2514yes—
691C2×C3×C4C2514yes—
692C2×C3×C4C2516yes—
693C2×C3×C4C2511yescharacteristic
694C2×C3×C4C2516yes—
695C24C24×C311yescharacteristic
696C24C24×C313yes—
697#41—216no—
698#41—216no—
699#41—216no—
700#41—224no—
701#41—424no—
702C2×Q8—216no—
703C2×Q8—216no—
704C2×Q8—216no—
705C2×Q8—212no—
706C2×Q8C3×#4118yescomplemented
707C2×Q8C24×C3112yes—
708C2×Q8C24×C316yes—
709C2×Q8C24×C314yes—
710C2×Q8C24×C3112yes—
711C2×Q8C24×C314yes—
712C2×D4—212no—
713C2×D4—46no—
714C2×D4C24×C314yes—
715C2×D4C24×C314yes—
716C2×D4C24×C316yes—
717C2×D4C24×C3112yes—
718C2×D4C24×C316yes—
719C2×D4C24×C314yes—
720C2×D4C24×C3112yes—
721C2×D4C24×C3112yes—
722C2×D4C24×C316yes—
723C22×C4—212no—
724C22×C4—212no—
725C22×C4C24×C314yes—
726C22×C4C24×C316yes—
727C22×C4C24×C316yes—
728C22×C4C24×C3112yes—
729C22×C4C24×C313yes—
730C22×C4C24×C311yescharacteristic
731C22×C4C24×C316yes—
732C22×C4C24×C316yes—
733C22×C4C24×C311yescharacteristic
734C22×C4C24×C314yes—
735C22×C4C24×C314yes—
736C22×C4C24×C313yes—
737C22×C4C24×C3112yes—
738C22×C4C24×C3112yes—
739C22×C4C24×C3112yes—
740C22×C4C24×C313yes—
741C4⋊C4C24×C316yes—
742C4⋊C4C24×C314yes—
743C4⋊C4C24×C314yes—
744C4⋊C4C24×C316yes—
745C4⋊C4C24×C3112yes—
746C4⋊C4C24×C3112yes—
747C4⋊C4C24×C316yes—
748C4⋊C4C24×C316yes—
749C4⋊C4C24×C316yes—
750C4⋊C4C24×C316yes—
751C4⋊C4C24×C316yes—
752C4⋊C4C24×C3112yes—
753C4⋊C4C24×C3112yes—
754C4⋊C4C24×C316yes—
755C4⋊C4C24×C314yes—
756C4⋊C4C24×C314yes—
757C4⋊C4C24×C3112yes—
758C4⋊C4C24×C3112yes—
759C4⋊C4C24×C314yes—
760C4⋊C4C24×C314yes—
761C4⋊C4C24×C3112yes—
762C4⋊C4C24×C3112yes—
763C4⋊C4C24×C314yes—
764C4⋊C4C24×C3112yes—
765C4⋊C4C24×C314yes—
766C22⋊C4C24×C314yes—
767C22⋊C4C24×C314yes—
768C22⋊C4C24×C314yes—
769C22⋊C4C24×C314yes—
770C22⋊C4C24×C314yes—
771C22⋊C4C24×C311yescharacteristic
772C22⋊C4C24×C3112yes—
773C22⋊C4C24×C3112yes—
774C22⋊C4C24×C316yes—
775C22⋊C4C24×C3124yes—
776C22⋊C4C24×C311yescharacteristic
777C22⋊C4C24×C311yescharacteristic
778C22⋊C4C24×C311yescharacteristic
779C22⋊C4C24×C316yes—
780C22⋊C4C24×C314yes—
781C22⋊C4C24×C3112yes—
782C22⋊C4C24×C314yes—
783C22⋊C4C24×C3112yes—
784C22⋊C4C24×C314yes—
785C22⋊C4C24×C3112yes—
786C22⋊C4C24×C3112yes—
787C22⋊C4C24×C314yes—
788C22⋊C4C24×C314yes—
789C22⋊C4C24×C3112yes—
790C42C24×C314yes—
791C42C24×C3112yes—
792C42C24×C314yes—
793C42C24×C314yes—
794C42C24×C316yes—
795C42C24×C3112yes—
796C42C24×C3112yes—
797C42C24×C3112yes—
798C42C24×C3112yes—
799C42C24×C316yes—
800C42C24×C3112yes—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—24no—
807C22×C3—26no—
808C22×C3—24no—
809C22×C3—26no—
810C22×C3—21no—
811C22×C3—26no—
812C22×C3—24no—
813C22×C3—21no—
814C22×C3—44no—
815C22×C3—86no—
816C22×C3C22×#4112yes—
817C22×C3#58512yes—
818C22×C3C2611yescharacteristic
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—24no—
822C3×C4—26no—
823C3×C4—24no—
824C3×C4—24no—
825C3×C4—26no—
826C3×C4—24no—
827C3×C4—21no—
828C3×C4—24no—
829C3×C4—24no—
830C3×C4—24no—
831C3×C4—21no—
832C3×C4C22×#41112yes—
833C23—22no—
834C23—22no—
835C23—26no—
836C23—41no—
837C23—43no—
838C23—43no—
839C23C25×C311yescharacteristic
840C23C25×C316yes—
841C23C25×C314yes—
842C23C25×C311yescharacteristic
843C23C25×C311yescharacteristic
844Q8—224no—
845Q8—212no—
846Q8—412no—
847Q8—44no—
848Q8C2×C3×#41116yes—
849D4—28no—
850D4—212no—
851D4—28no—
852D4—224no—
853D4—212no—
854D4—46no—
855D4—412no—
856D4—44no—
857D4—412no—
858C2×C4—22no—
859C2×C4—26no—
860C2×C4—28no—
861C2×C4—212no—
862C2×C4—212no—
863C2×C4—212no—
864C2×C4—212no—
865C2×C4—224no—
866C2×C4—43no—
867C2×C4—412no—
868C2×C4—412no—
869C2×C4—44no—
870C2×C4—412no—
871C2×C4—44no—
872C2×C4—41no—
873C2×C4C2×C3×#41112yes—
874C2×C4C25×C314yes—
875C2×C4C25×C311yescharacteristic
876C2×C4C25×C311yescharacteristic
877C2×C4C25×C314yes—
878C2×C4C25×C311yescharacteristic
879C2×C4C25×C314yes—
880C2×C4C25×C314yes—
881C2×C4C25×C316yes—
882C2×C4C25×C314yes—
883C2×C4C25×C314yes—
884C2×C4C25×C314yes—
885C2×C4C25×C316yes—
886C2×C4C25×C311yescharacteristic
887C2×C4C25×C316yes—
888C2×C3—22no—
889C2×C3—22no—
890C2×C3—44no—
891C2×C3—41no—
892C2×C3—46no—
893C2×C3C23×#4111yescharacteristic
894C2×C3C2×#58511yescharacteristic
895C2×C32−1+611yescharacteristic
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—24no—
902C22—26no—
903C22—24no—
904C22—26no—
905C22—21no—
906C22—26no—
907C22—24no—
908C22—21no—
909C22—44no—
910C22—86no—
911C22C22×C3×#4112yes—
912C22C3×#58512yes—
913C22C26×C311yescharacteristic
914C4—21no—
915C4—21no—
916C4—24no—
917C4—26no—
918C4—24no—
919C4—24no—
920C4—26no—
921C4—24no—
922C4—21no—
923C4—24no—
924C4—24no—
925C4—24no—
926C4—21no—
927C4C22×C3×#41112yes—
928C3#6300511yescharacteristic, direct product factor, Sylow
929C2—22no—
930C2—22no—
931C2—41no—
932C2—46no—
933C2—44no—
934C2C23×C3×#4111yescharacteristic
935C2C2×C3×#58511yescharacteristic
936C2C3×2−1+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×#3524C2semidirect
2. C3×#3524C2semidirect
3. C3×#3522C2semidirect
4. C3×#3518C2semidirect
5. C3×#3516C2semidirect
6. C3×#3516C2semidirect
7. C3×#3510C2semidirect
8. C3×#3502C2semidirect
9. C3×#3495C2semidirect
10. C3×#3494C2semidirect
11. C3×#3487C2semidirect
12. C3×#3486C2semidirect
13. C3×#3482C2semidirect
14. C3×#3480C2semidirect
15. C3×#3475C2semidirect
16. C2×C3×#548C2semidirect
17. C3×C4×2−1+4C2semidirect
18. C3×#3428C2semidirect
19. C2×C3×#519C2semidirect
20. #63005C3direct (N × H)
24. C3×#559C22semidirect
25. C3×#559C22semidirect
26. C3×Q82C22semidirect
27. C3×#557C22semidirect
28. C3×#557C22semidirect
29. C3×#557C22semidirect
30. C3×#556C22semidirect
31. C3×#556C22semidirect
32. C3×#556C22semidirect
33. C3×#556C22semidirect
34. C3×#555C22semidirect
35. C3×#555C22semidirect
36. C3×#554C22semidirect
37. C3×#554C22semidirect
38. C3×#553C22semidirect
39. C3×#553C22semidirect
40. C3×#553C22semidirect
41. C3×#553C22semidirect
43. C3×#552C22semidirect
44. C3×#552C22semidirect
45. C3×#552C22semidirect
46. C3×#552C22semidirect
50. C3×#550C22semidirect
51. C3×#550C22semidirect
52. C3×D4×Q8C22semidirect
53. C3×D4×Q8C22semidirect
58. C3×#548C22semidirect
59. C3×#548C22semidirect
60. C3×#548C22semidirect
61. C3×#548C22semidirect
62. C3×#547C22semidirect
63. C3×#547C22semidirect
66. C3×#542C22semidirect
67. C3×#542C22semidirect
68. C3×#542C22semidirect
69. C3×#542C22semidirect
70. C3×#541C22semidirect
71. C3×#540C22semidirect
75. C3×#533C22semidirect
76. C3×#532C22semidirect
77. C3×#529C22semidirect
78. C3×#529C22semidirect
79. C3×#529C22semidirect
80. C3×#529C22semidirect
81. C3×#529C22semidirect
82. C3×#529C22semidirect
83. C3×#529C22semidirect
90. C3×#520C22semidirect
91. C3×#520C22semidirect
92. C3×#520C22semidirect
97. C3×#519C22semidirect
98. C3×#519C22semidirect
99. C3×#519C22semidirect
102. C3×C4×#41C22semidirect
103. C3×C4×#41C22semidirect
104. C3×C4×#41C22semidirect
105. C3×C4×#41C22semidirect
107. C2×C3×C4×Q8C22semidirect
108. C2×C3×C4×Q8C22semidirect
109. C2×C3×C4×Q8C22semidirect
113. #3524C2×C3semidirect
114. #3524C2×C3semidirect
115. #3522C2×C3semidirect
116. #3518C2×C3semidirect
117. #3516C2×C3semidirect
118. #3516C2×C3semidirect
119. #3510C2×C3semidirect
120. #3502C2×C3semidirect
121. #3495C2×C3semidirect
122. #3494C2×C3semidirect
123. #3487C2×C3semidirect
124. #3486C2×C3semidirect
125. #3482C2×C3semidirect
126. #3480C2×C3semidirect
127. #3475C2×C3semidirect
128. C2×#548C2×C3semidirect
129. C4×2−1+4C2×C3semidirect
130. #3428C2×C3semidirect
131. C2×#519C2×C3semidirect
290. #559C22×C3semidirect
291. #559C22×C3semidirect
292. Q82C22×C3semidirect
293. #557C22×C3semidirect
294. #557C22×C3semidirect
295. #557C22×C3semidirect
296. #556C22×C3semidirect
297. #556C22×C3semidirect
298. #556C22×C3semidirect
299. #556C22×C3semidirect
300. #555C22×C3semidirect
301. #555C22×C3semidirect
302. #554C22×C3semidirect
303. #554C22×C3semidirect
304. #553C22×C3semidirect
305. #553C22×C3semidirect
306. #553C22×C3semidirect
307. #553C22×C3semidirect
309. #552C22×C3semidirect
310. #552C22×C3semidirect
311. #552C22×C3semidirect
312. #552C22×C3semidirect
316. #550C22×C3semidirect
317. #550C22×C3semidirect
318. D4×Q8C22×C3semidirect
319. D4×Q8C22×C3semidirect
324. #548C22×C3semidirect
325. #548C22×C3semidirect
326. #548C22×C3semidirect
327. #548C22×C3semidirect
328. #547C22×C3semidirect
329. #547C22×C3semidirect
332. #542C22×C3semidirect
333. #542C22×C3semidirect
334. #542C22×C3semidirect
335. #542C22×C3semidirect
336. #541C22×C3semidirect
337. #540C22×C3semidirect
341. #533C22×C3semidirect
342. #532C22×C3semidirect
343. #529C22×C3semidirect
344. #529C22×C3semidirect
345. #529C22×C3semidirect
346. #529C22×C3semidirect
347. #529C22×C3semidirect
348. #529C22×C3semidirect
349. #529C22×C3semidirect
356. #520C22×C3semidirect
357. #520C22×C3semidirect
358. #520C22×C3semidirect
363. #519C22×C3semidirect
364. #519C22×C3semidirect
365. #519C22×C3semidirect
368. C4×#41C22×C3semidirect
369. C4×#41C22×C3semidirect
370. C4×#41C22×C3semidirect
371. C4×#41C22×C3semidirect
373. C2×C4×Q8C22×C3semidirect
374. C2×C4×Q8C22×C3semidirect
375. C2×C4×Q8C22×C3semidirect
390. C2×C3×Q8#41semidirect
706. C2×Q8C3×#41semidirect
928. C3#63005direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35242
C3×#35222
C3×#35182
C3×#35162
C3×#35102
C3×#35022
C3×#34952
C3×#34942
C3×#34872
C3×#34862
C3×#34822
C3×#34802
C3×#34752
C2×C3×#5482
C3×C4×2−1+42
C3×#34282
C2×C3×#5192
#630053