Finite Group Databasebeta

← C3×#63009 #10681616

Subgroups — C3×#63009 #10681616

Order 768.

7030 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3523C212yesmaximal, complemented
2C3×#3521C2112yesmaximal, complemented
3C3×#3518C214yesmaximal, complemented
4C3×#3514C216yesmaximal, complemented
5C3×#3511C213yesmaximal, complemented
6C3×#3507C213yesmaximal, complemented
7C3×#3503C211yesmaximal, characteristic, complemented
8C3×#3495C216yesmaximal, complemented
9C3×#3493C216yesmaximal, complemented
10C3×#3489C212yesmaximal, complemented
11C3×#3482C216yesmaximal, complemented
12C3×#3480C212yesmaximal, complemented
13C3×#3475C213yesmaximal, complemented
14C2×C3×#556C213yesmaximal, complemented
15C3×D4×#41C211yesmaximal, characteristic, complemented
16C3×C4×2−1+4C211yesmaximal, characteristic, complemented
17C3×#3428C212yesmaximal, complemented
18#63009C311yesmaximal, characteristic, direct product factor, Sylow
19C2×C3×2−1+4C2211yescharacteristic
20C22×C3×#41C2212yes—
21C3×#559C2216yescomplemented
22C3×Q82C2212yescomplemented
23C3×#557C2212yescomplemented
24C3×#557C2216yescomplemented
25C3×#556C2213yes—
26C3×#556C2216yes—
27C3×#556C2216yescomplemented
28C3×#556C22112yescomplemented
29C3×#556C2216yescomplemented
30C3×#556C22112yescomplemented
31C3×#556C22112yescomplemented
32C3×#556C22112yescomplemented
33C3×#555C2211yescharacteristic
34C3×#555C2216yescomplemented
35C3×#555C22112yescomplemented
36C3×#554C2213yescomplemented
37C3×#554C2216yescomplemented
38C3×#554C2216yescomplemented
39C3×#553C2216yescomplemented
40C3×#553C22112yescomplemented
41C3×#553C22112yescomplemented
42C3×#552C2216yescomplemented
43C3×#552C2216yescomplemented
44C3×#552C22124yescomplemented
45C3×#552C22112yescomplemented
46C3×#552C22112yescomplemented
47C3×#551C22112yescomplemented
48C3×#551C22124yescomplemented
49C3×#550C2211yescharacteristic
50C3×D4×Q8C2211yescharacteristic
51C3×D4×Q8C2216yescomplemented
52C3×D4×Q8C2214yescomplemented
53C3×#548C2212yes—
54C3×#548C2214yescomplemented
55C3×#548C22112yescomplemented
56C3×#547C2213yes—
57C3×#547C2213yescomplemented
58C3×#547C22112yescomplemented
59C3×#546C2216yes—
60C3×#546C2216yes—
61C3×#546C22112yescomplemented
62C3×D42C2213yes—
63C3×#544C2216yescomplemented
64C3×#542C22112yescomplemented
65C3×#542C22112yescomplemented
66C3×#541C22112yescomplemented
67C3×#539C22112yescomplemented
68C3×#538C22124yescomplemented
69C3×#537C2216yescomplemented
70C3×#536C2216yescomplemented
71C3×#533C2213yescomplemented
72C3×#533C22112yescomplemented
73C3×#533C2216yescomplemented
74C3×#532C2213yes—
75C3×#532C2216yescomplemented
76C2×C3×C4⋊Q8C2213yescomplemented
77C3×#529C2216yes—
78C3×#529C22112yescomplemented
79C3×#529C22112yescomplemented
80C3×#529C22124yescomplemented
81C3×#529C22112yescomplemented
82C2×C3×#126C22112yescomplemented
83C2×C3×#124C2216yes—
84C3×#525C2216yes—
85C3×#525C2216yescomplemented
86C2×C3×C22⋊Q8C2216yescomplemented
87C3×#520C2211yescharacteristic
88C3×#520C2212yes—
89C3×#520C2216yescomplemented
90C3×#520C2216yescomplemented
91C3×#520C2213yescomplemented
92C3×#520C2216yescomplemented
93C3×#519C2214yescomplemented
94C3×#519C2213yescomplemented
95C3×#519C2212yescomplemented
96C3×#518C22112yescomplemented
97C3×C4×#41C2211yescharacteristic
98C3×C4×#41C2214yescomplemented
99C3×C4×#41C22112yescomplemented
100C3×C4×#41C2213yescomplemented
101C3×C4×#41C2216yescomplemented
102C3×C4×#41C2216yescomplemented
103C2×C3×C4×Q8C2213yescomplemented
104C2×C3×C4×Q8C2212yescomplemented
105C2×C3×C4×Q8C2216yescomplemented
106C2×C3×C4×D4C2213yes—
107C2×C3×#117C2216yescomplemented
108C2×C3×#117C2216yescomplemented
109#3523C2×C312yescomplemented
110#3521C2×C3112yescomplemented
111#3518C2×C314yescomplemented
112#3514C2×C316yescomplemented
113#3511C2×C313yescomplemented
114#3507C2×C313yescomplemented
115#3503C2×C311yescharacteristic, complemented
116#3495C2×C316yescomplemented
117#3493C2×C316yescomplemented
118#3489C2×C312yescomplemented
119#3482C2×C316yescomplemented
120#3480C2×C312yescomplemented
121#3475C2×C313yescomplemented
122C2×#556C2×C313yescomplemented
123D4×#41C2×C311yescharacteristic, complemented
124C4×2−1+4C2×C311yescharacteristic, complemented
125#3428C2×C312yescomplemented
126C3×2−1+4—28no—
127C2×C3×#41—216no—
128C2×C3×#41C2316yes—
129C2×C3×#41C2312yes—
130C2×C3×#41C2316yes—
131C2×C3×#41C2313yes—
132C2×C3×#41C2316yes—
133C2×C3×#41C2316yes—
134C2×C3×#41C2311yescharacteristic
135C22×C3×Q8C2312yes—
136C22×C3×Q8C2313yes—
137C22×C3×Q8C2312yes—
138C22×C3×Q8C2316yes—
139C22×C3×D4C2316yes—
140C22×C3×D4C2313yes—
141C23×C3×C4C2316yes—
142C3×C4⋊Q8C2316yes—
143C3×C4⋊Q8C23112yes—
144C3×C4⋊Q8C2313yes—
145C3×C4⋊Q8C2316yes—
146C3×C4⋊Q8C2316yes—
147C3×C4⋊Q8C2313yes—
148C3×C4⋊Q8C2311yescharacteristic
149C3×C4⋊Q8C23112yes—
150C3×#127C2313yes—
151C3×#126C23112yes—
152C3×#126C23124yes—
153C3×#126C23124yes—
154C3×#126C23124yes—
155C3×#126C23112yes—
156C3×#126C23112yes—
157C3×#126C23124yes—
158C3×#125C2316yes—
159C3×#125C23112yes—
160C3×#125C23124yes—
161C3×#125C23112yes—
162C3×#125C23112yes—
163C3×#125C2316yes—
164C3×#124C23112yes—
165C3×#124C23112yes—
166C3×#124C2316yes—
167C3×#124C23124yes—
168C3×#124C2314yes—
169C3×#124C23124yes—
170C3×#124C2316yes—
171C3×#123C23124yes—
172C3×#123C23112yes—
173C3×#123C23112yes—
174C3×#123C23112yes—
175C3×#123C23124yes—
176C3×#123C23112yes—
177C3×#123C23112yes—
178C3×C22⋊Q8C2316yes—
179C3×C22⋊Q8C23112yes—
180C3×C22⋊Q8C23112yes—
181C3×C22⋊Q8C23112yes—
182C3×C22⋊Q8C2316yes—
183C3×C22⋊Q8C2316yes—
184C3×C22⋊Q8C2316yes—
185C3×C22⋊Q8C2316yes—
186C3×C22⋊Q8C2316yes—
187C3×C22⋊Q8C23124yes—
188C3×C22⋊Q8C23112yes—
189C3×C22⋊Q8C23112yes—
190C3×C22⋊Q8C2316yes—
191C3×C22⋊Q8C23124yes—
192C3×#121C2316yes—
193C3×#121C2316yes—
194C3×#121C2312yes—
195C3×#121C2316yes—
196C3×#121C2312yes—
197C3×#121C2316yes—
198C3×#121C23124yes—
199C3×#121C23112yes—
200C3×#121C2316yes—
201C3×#121C23112yes—
202C3×#121C23112yes—
203C3×#120C23112yes—
204C3×#120C23112yes—
205C3×C4×Q8C2311yescharacteristic
206C3×C4×Q8C2314yes—
207C3×C4×Q8C2316yes—
208C3×C4×Q8C2316yes—
209C3×C4×Q8C2316yes—
210C3×C4×Q8C2311yescharacteristic
211C3×C4×Q8C2316yes—
212C3×C4×Q8C2313yes—
213C3×C4×Q8C2312yes—
214C3×C4×Q8C2316yes—
215C3×C4×Q8C2316yes—
216C3×C4×Q8C2316yes—
217C3×C4×Q8C23112yes—
218C3×C4×Q8C23124yes—
219C3×C4×Q8C2316yes—
220C3×C4×Q8C2313yes—
221C3×C4×Q8C23112yes—
222C3×C4×Q8C23112yes—
223C3×C4×D4C2316yes—
224C3×C4×D4C23112yes—
225C3×C4×D4C2311yescharacteristic
226C3×C4×D4C2313yes—
227C3×C4×D4C2316yes—
228C3×C4×D4C2313yes—
229C3×C4×D4C2316yes—
230C3×C4×D4C2313yes—
231C3×C4×D4C2313yes—
232C3×C4×D4C2313yes—
233C3×C4×D4C2316yes—
234C3×C4×D4C2316yes—
235C3×C4×D4C2311yescharacteristic
236C3×C4×D4C23112yes—
237C3×C4×D4C23124yes—
238C3×C4×D4C23112yes—
239C3×C4×D4C23124yes—
240C3×C4×D4C23112yes—
241C3×C4×D4C2316yes—
242C3×C4×D4C2313yes—
243C3×C4×D4C23112yes—
244C3×C4×D4C23112yes—
245C3×C4×D4C2316yes—
246C3×C4×D4C23112yes—
247C3×C4×D4C23112yes—
248C3×#117C2312yes—
249C3×#117C2316yes—
250C3×#117C2313yes—
251C3×#117C23112yes—
252C3×#117C23112yes—
253C3×#117C23112yes—
254C3×#117C23112yes—
255C3×#117C2316yes—
256C3×#117C23112yes—
257C3×#117C2313yes—
258C3×#117C2312yes—
259C3×#117C2316yes—
260C3×#117C23112yes—
261C3×#117C2316yes—
262C3×#117C23112yes—
263C3×#117C23124yes—
264C3×#117C23112yes—
265C2×C3×C4⋊C4C2313yes—
266C2×C3×C4⋊C4C2316yes—
267C2×C3×C4⋊C4C2316yes—
268C2×C3×C4⋊C4C2316yes—
269C2×C3×C4⋊C4C2313yes—
270C2×C3×C4⋊C4C2316yes—
271C2×C3×C4⋊C4C2316yes—
272C2×C3×C4⋊C4C23112yes—
273C2×C3×C4⋊C4C2316yes—
274C2×C3×C22⋊C4C23112yes—
275C2×C3×C22⋊C4C23112yes—
276C2×C3×C22⋊C4C2316yes—
277C2×C3×C22⋊C4C23112yes—
278C2×C3×C42C23112yes—
279C2×C3×C42C23112yes—
280C2×C3×C42C2313yes—
281C2×C3×C42C2316yes—
282C2×C3×C42C2316yes—
283C2×2−1+4C22×C311yescharacteristic
284C22×#41C22×C312yes—
285#559C22×C316yescomplemented
286Q82C22×C312yescomplemented
287#557C22×C312yescomplemented
288#557C22×C316yescomplemented
289#556C22×C313yes—
290#556C22×C316yes—
291#556C22×C316yescomplemented
292#556C22×C3112yescomplemented
293#556C22×C316yescomplemented
294#556C22×C3112yescomplemented
295#556C22×C3112yescomplemented
296#556C22×C3112yescomplemented
297#555C22×C311yescharacteristic
298#555C22×C316yescomplemented
299#555C22×C3112yescomplemented
300#554C22×C313yescomplemented
301#554C22×C316yescomplemented
302#554C22×C316yescomplemented
303#553C22×C316yescomplemented
304#553C22×C3112yescomplemented
305#553C22×C3112yescomplemented
306#552C22×C316yescomplemented
307#552C22×C316yescomplemented
308#552C22×C3124yescomplemented
309#552C22×C3112yescomplemented
310#552C22×C3112yescomplemented
311#551C22×C3112yescomplemented
312#551C22×C3124yescomplemented
313#550C22×C311yescharacteristic
314D4×Q8C22×C311yescharacteristic
315D4×Q8C22×C316yescomplemented
316D4×Q8C22×C314yescomplemented
317#548C22×C312yes—
318#548C22×C314yescomplemented
319#548C22×C3112yescomplemented
320#547C22×C313yes—
321#547C22×C313yescomplemented
322#547C22×C3112yescomplemented
323#546C22×C316yes—
324#546C22×C316yes—
325#546C22×C3112yescomplemented
326D42C22×C313yes—
327#544C22×C316yescomplemented
328#542C22×C3112yescomplemented
329#542C22×C3112yescomplemented
330#541C22×C3112yescomplemented
331#539C22×C3112yescomplemented
332#538C22×C3124yescomplemented
333#537C22×C316yescomplemented
334#536C22×C316yescomplemented
335#533C22×C313yescomplemented
336#533C22×C3112yescomplemented
337#533C22×C316yescomplemented
338#532C22×C313yes—
339#532C22×C316yescomplemented
340C2×C4⋊Q8C22×C313yescomplemented
341#529C22×C316yes—
342#529C22×C3112yescomplemented
343#529C22×C3112yescomplemented
344#529C22×C3124yescomplemented
345#529C22×C3112yescomplemented
346C2×#126C22×C3112yescomplemented
347C2×#124C22×C316yes—
348#525C22×C316yes—
349#525C22×C316yescomplemented
350C2×C22⋊Q8C22×C316yescomplemented
351#520C22×C311yescharacteristic
352#520C22×C312yes—
353#520C22×C316yescomplemented
354#520C22×C316yescomplemented
355#520C22×C313yescomplemented
356#520C22×C316yescomplemented
357#519C22×C314yescomplemented
358#519C22×C313yescomplemented
359#519C22×C312yescomplemented
360#518C22×C3112yescomplemented
361C4×#41C22×C311yescharacteristic
362C4×#41C22×C314yescomplemented
363C4×#41C22×C3112yescomplemented
364C4×#41C22×C313yescomplemented
365C4×#41C22×C316yescomplemented
366C4×#41C22×C316yescomplemented
367C2×C4×Q8C22×C313yescomplemented
368C2×C4×Q8C22×C312yescomplemented
369C2×C4×Q8C22×C316yescomplemented
370C2×C4×D4C22×C313yes—
371C2×#117C22×C316yescomplemented
372C2×#117C22×C316yescomplemented
373C24×C3C2416yes—
374C3×#41—28no—
375C3×#41—224no—
376C3×#41—224no—
377C3×#41—224no—
378C3×#41—212no—
379C3×#41—412no—
380C3×#41#4118yescomplemented
381C2×C3×Q8—28no—
382C2×C3×Q8—28no—
383C2×C3×Q8—212no—
384C2×C3×Q8—412no—
385C2×C3×Q8C2413yes—
386C2×C3×Q8C2416yes—
387C2×C3×Q8C2416yes—
388C2×C3×Q8C2416yes—
389C2×C3×Q8C2412yes—
390C2×C3×Q8C24112yes—
391C2×C3×Q8C2411yescharacteristic
392C2×C3×D4—224no—
393C2×C3×D4—46no—
394C2×C3×D4C2416yes—
395C2×C3×D4C24112yes—
396C2×C3×D4C2411yescharacteristic
397C2×C3×D4C2416yes—
398C2×C3×D4C2411yescharacteristic
399C2×C3×D4C2413yes—
400C2×C3×D4C2414yes—
401C2×C3×D4C2416yes—
402C2×C3×D4C2416yes—
403C2×C3×D4C24112yes—
404C2×C3×D4C2413yes—
405C22×C3×C4—224no—
406C22×C3×C4C2413yes—
407C22×C3×C4C2412yes—
408C22×C3×C4C2416yes—
409C22×C3×C4C2416yes—
410C22×C3×C4C2416yes—
411C22×C3×C4C2416yes—
412C22×C3×C4C2416yes—
413C22×C3×C4C2412yes—
414C22×C3×C4C2416yes—
415C22×C3×C4C2416yes—
416C22×C3×C4C2413yes—
417C22×C3×C4C24112yes—
418C22×C3×C4C24112yes—
419C22×C3×C4C24112yes—
420C22×C3×C4C2416yes—
421C22×C3×C4C2413yes—
422C3×C4⋊C4C2411yescharacteristic
423C3×C4⋊C4C2413yes—
424C3×C4⋊C4C2412yes—
425C3×C4⋊C4C2416yes—
426C3×C4⋊C4C2411yescharacteristic
427C3×C4⋊C4C2416yes—
428C3×C4⋊C4C2413yes—
429C3×C4⋊C4C24112yes—
430C3×C4⋊C4C2416yes—
431C3×C4⋊C4C24112yes—
432C3×C4⋊C4C2416yes—
433C3×C4⋊C4C24112yes—
434C3×C4⋊C4C24112yes—
435C3×C4⋊C4C24112yes—
436C3×C4⋊C4C24112yes—
437C3×C4⋊C4C2413yes—
438C3×C4⋊C4C2416yes—
439C3×C4⋊C4C24124yes—
440C3×C4⋊C4C2413yes—
441C3×C4⋊C4C2416yes—
442C3×C4⋊C4C2416yes—
443C3×C4⋊C4C24112yes—
444C3×C4⋊C4C24112yes—
445C3×C4⋊C4C2412yes—
446C3×C4⋊C4C24112yes—
447C3×C22⋊C4C2414yes—
448C3×C22⋊C4C24112yes—
449C3×C22⋊C4C2412yes—
450C3×C22⋊C4C2416yes—
451C3×C22⋊C4C24112yes—
452C3×C22⋊C4C24112yes—
453C3×C22⋊C4C2416yes—
454C3×C22⋊C4C24124yes—
455C3×C22⋊C4C24124yes—
456C3×C22⋊C4C2416yes—
457C3×C22⋊C4C2416yes—
458C3×C22⋊C4C2416yes—
459C3×C22⋊C4C2416yes—
460C3×C22⋊C4C2412yes—
461C3×C22⋊C4C24112yes—
462C3×C22⋊C4C24112yes—
463C3×C22⋊C4C2414yes—
464C3×C22⋊C4C24112yes—
465C3×C42C2414yes—
466C3×C42C2416yes—
467C3×C42C24112yes—
468C3×C42C2411yescharacteristic
469C3×C42C2413yes—
470C3×C42C2416yes—
471C3×C42C2416yes—
472C3×C42C24124yes—
473C3×C42C24112yes—
474C3×C42C2413yes—
475C3×C42C24112yes—
476C3×C42C2413yes—
4772−1+4—28no—
478C2×#41—216no—
479C2×#41C23×C316yes—
480C2×#41C23×C312yes—
481C2×#41C23×C313yes—
482C2×#41C23×C316yes—
483C2×#41C23×C316yes—
484C2×#41C23×C316yes—
485C2×#41C23×C311yescharacteristic
486C22×Q8C23×C313yes—
487C22×Q8C23×C312yes—
488C22×Q8C23×C312yes—
489C22×Q8C23×C316yes—
490C22×D4C23×C316yes—
491C22×D4C23×C313yes—
492C23×C4C23×C316yes—
493C4⋊Q8C23×C313yes—
494C4⋊Q8C23×C316yes—
495C4⋊Q8C23×C316yes—
496C4⋊Q8C23×C316yes—
497C4⋊Q8C23×C313yes—
498C4⋊Q8C23×C311yescharacteristic
499C4⋊Q8C23×C3112yes—
500C4⋊Q8C23×C3112yes—
501#127C23×C313yes—
502#126C23×C3112yes—
503#126C23×C3124yes—
504#126C23×C3124yes—
505#126C23×C3124yes—
506#126C23×C3112yes—
507#126C23×C3112yes—
508#126C23×C3124yes—
509#125C23×C316yes—
510#125C23×C3112yes—
511#125C23×C3124yes—
512#125C23×C3112yes—
513#125C23×C3112yes—
514#125C23×C316yes—
515#124C23×C316yes—
516#124C23×C3112yes—
517#124C23×C3124yes—
518#124C23×C314yes—
519#124C23×C3112yes—
520#124C23×C3124yes—
521#124C23×C316yes—
522#123C23×C3112yes—
523#123C23×C3112yes—
524#123C23×C3112yes—
525#123C23×C3124yes—
526#123C23×C3124yes—
527#123C23×C3112yes—
528#123C23×C3112yes—
529C22⋊Q8C23×C316yes—
530C22⋊Q8C23×C3112yes—
531C22⋊Q8C23×C3112yes—
532C22⋊Q8C23×C3112yes—
533C22⋊Q8C23×C316yes—
534C22⋊Q8C23×C316yes—
535C22⋊Q8C23×C316yes—
536C22⋊Q8C23×C316yes—
537C22⋊Q8C23×C316yes—
538C22⋊Q8C23×C3124yes—
539C22⋊Q8C23×C3112yes—
540C22⋊Q8C23×C3112yes—
541C22⋊Q8C23×C316yes—
542C22⋊Q8C23×C3124yes—
543#121C23×C316yes—
544#121C23×C316yes—
545#121C23×C312yes—
546#121C23×C316yes—
547#121C23×C312yes—
548#121C23×C316yes—
549#121C23×C3124yes—
550#121C23×C3112yes—
551#121C23×C316yes—
552#121C23×C3112yes—
553#121C23×C3112yes—
554#120C23×C3112yes—
555#120C23×C3112yes—
556C4×Q8C23×C311yescharacteristic
557C4×Q8C23×C316yes—
558C4×Q8C23×C313yes—
559C4×Q8C23×C316yes—
560C4×Q8C23×C312yes—
561C4×Q8C23×C316yes—
562C4×Q8C23×C316yes—
563C4×Q8C23×C316yes—
564C4×Q8C23×C3112yes—
565C4×Q8C23×C3124yes—
566C4×Q8C23×C311yescharacteristic
567C4×Q8C23×C316yes—
568C4×Q8C23×C313yes—
569C4×Q8C23×C314yes—
570C4×Q8C23×C3112yes—
571C4×Q8C23×C3112yes—
572C4×Q8C23×C316yes—
573C4×Q8C23×C316yes—
574C4×D4C23×C311yescharacteristic
575C4×D4C23×C313yes—
576C4×D4C23×C316yes—
577C4×D4C23×C313yes—
578C4×D4C23×C316yes—
579C4×D4C23×C313yes—
580C4×D4C23×C313yes—
581C4×D4C23×C313yes—
582C4×D4C23×C316yes—
583C4×D4C23×C316yes—
584C4×D4C23×C311yescharacteristic
585C4×D4C23×C3112yes—
586C4×D4C23×C3124yes—
587C4×D4C23×C3112yes—
588C4×D4C23×C3124yes—
589C4×D4C23×C3112yes—
590C4×D4C23×C3112yes—
591C4×D4C23×C316yes—
592C4×D4C23×C313yes—
593C4×D4C23×C3112yes—
594C4×D4C23×C316yes—
595C4×D4C23×C3112yes—
596C4×D4C23×C316yes—
597C4×D4C23×C3112yes—
598C4×D4C23×C3112yes—
599#117C23×C312yes—
600#117C23×C316yes—
601#117C23×C313yes—
602#117C23×C3112yes—
603#117C23×C3112yes—
604#117C23×C3112yes—
605#117C23×C3112yes—
606#117C23×C316yes—
607#117C23×C3112yes—
608#117C23×C313yes—
609#117C23×C312yes—
610#117C23×C316yes—
611#117C23×C3112yes—
612#117C23×C316yes—
613#117C23×C3112yes—
614#117C23×C3124yes—
615#117C23×C3112yes—
616C2×C4⋊C4C23×C313yes—
617C2×C4⋊C4C23×C316yes—
618C2×C4⋊C4C23×C316yes—
619C2×C4⋊C4C23×C316yes—
620C2×C4⋊C4C23×C313yes—
621C2×C4⋊C4C23×C316yes—
622C2×C4⋊C4C23×C316yes—
623C2×C4⋊C4C23×C3112yes—
624C2×C4⋊C4C23×C316yes—
625C2×C22⋊C4C23×C3112yes—
626C2×C22⋊C4C23×C3112yes—
627C2×C22⋊C4C23×C316yes—
628C2×C22⋊C4C23×C3112yes—
629C2×C42C23×C3112yes—
630C2×C42C23×C3112yes—
631C2×C42C23×C313yes—
632C2×C42C23×C316yes—
633C2×C42C23×C316yes—
634C23×C3—212no—
635C23×C3—46no—
636C23×C3—46no—
637C23×C3C2512yes—
638C23×C3C2516yes—
639C23×C3C2512yes—
640C23×C3C2513yes—
641C3×Q8—26no—
642C3×Q8—212no—
643C3×Q8—212no—
644C3×Q8—212no—
645C3×Q8—412no—
646C3×Q8—42no—
647C3×Q8C2×#4114yes—
648C3×D4—224no—
649C3×D4—212no—
650C3×D4—212no—
651C3×D4—22no—
652C3×D4—22no—
653C3×D4—26no—
654C3×D4—46no—
655C3×D4—46no—
656C3×D4—44no—
657C3×D4—412no—
658C3×D4C2×#41112yes—
659C2×C3×C4—212no—
660C2×C3×C4—212no—
661C2×C3×C4—24no—
662C2×C3×C4—212no—
663C2×C3×C4—212no—
664C2×C3×C4—212no—
665C2×C3×C4—212no—
666C2×C3×C4—26no—
667C2×C3×C4—24no—
668C2×C3×C4—46no—
669C2×C3×C4—46no—
670C2×C3×C4—412no—
671C2×C3×C4—43no—
672C2×C3×C4—412no—
673C2×C3×C4—412no—
674C2×C3×C4C2×#41112yes—
675C2×C3×C4C2516yes—
676C2×C3×C4C2512yes—
677C2×C3×C4C2512yes—
678C2×C3×C4C2513yes—
679C2×C3×C4C2511yescharacteristic
680C2×C3×C4C2514yes—
681C2×C3×C4C2516yes—
682C2×C3×C4C25112yes—
683C2×C3×C4C2513yes—
684C2×C3×C4C2516yes—
685C2×C3×C4C2513yes—
686C2×C3×C4C2511yescharacteristic
687C2×C3×C4C2511yescharacteristic
688C24C24×C316yes—
689#41—28no—
690#41—224no—
691#41—224no—
692#41—224no—
693#41—212no—
694#41—412no—
695#41C3×#4118yescomplemented
696C2×Q8—28no—
697C2×Q8—28no—
698C2×Q8—212no—
699C2×Q8—412no—
700C2×Q8C24×C313yes—
701C2×Q8C24×C316yes—
702C2×Q8C24×C316yes—
703C2×Q8C24×C316yes—
704C2×Q8C24×C312yes—
705C2×Q8C24×C3112yes—
706C2×Q8C24×C311yescharacteristic
707C2×D4—224no—
708C2×D4—46no—
709C2×D4C24×C316yes—
710C2×D4C24×C3112yes—
711C2×D4C24×C311yescharacteristic
712C2×D4C24×C316yes—
713C2×D4C24×C311yescharacteristic
714C2×D4C24×C313yes—
715C2×D4C24×C314yes—
716C2×D4C24×C316yes—
717C2×D4C24×C316yes—
718C2×D4C24×C3112yes—
719C2×D4C24×C313yes—
720C22×C4—224no—
721C22×C4C24×C313yes—
722C22×C4C24×C312yes—
723C22×C4C24×C316yes—
724C22×C4C24×C316yes—
725C22×C4C24×C316yes—
726C22×C4C24×C316yes—
727C22×C4C24×C316yes—
728C22×C4C24×C312yes—
729C22×C4C24×C316yes—
730C22×C4C24×C316yes—
731C22×C4C24×C313yes—
732C22×C4C24×C3112yes—
733C22×C4C24×C3112yes—
734C22×C4C24×C3112yes—
735C22×C4C24×C316yes—
736C22×C4C24×C313yes—
737C4⋊C4C24×C311yescharacteristic
738C4⋊C4C24×C313yes—
739C4⋊C4C24×C312yes—
740C4⋊C4C24×C316yes—
741C4⋊C4C24×C311yescharacteristic
742C4⋊C4C24×C316yes—
743C4⋊C4C24×C313yes—
744C4⋊C4C24×C3112yes—
745C4⋊C4C24×C316yes—
746C4⋊C4C24×C3112yes—
747C4⋊C4C24×C316yes—
748C4⋊C4C24×C3112yes—
749C4⋊C4C24×C3112yes—
750C4⋊C4C24×C3112yes—
751C4⋊C4C24×C3112yes—
752C4⋊C4C24×C313yes—
753C4⋊C4C24×C316yes—
754C4⋊C4C24×C3124yes—
755C4⋊C4C24×C313yes—
756C4⋊C4C24×C316yes—
757C4⋊C4C24×C316yes—
758C4⋊C4C24×C3112yes—
759C4⋊C4C24×C3112yes—
760C4⋊C4C24×C312yes—
761C4⋊C4C24×C3112yes—
762C22⋊C4C24×C314yes—
763C22⋊C4C24×C3112yes—
764C22⋊C4C24×C312yes—
765C22⋊C4C24×C316yes—
766C22⋊C4C24×C3112yes—
767C22⋊C4C24×C3112yes—
768C22⋊C4C24×C316yes—
769C22⋊C4C24×C3124yes—
770C22⋊C4C24×C3124yes—
771C22⋊C4C24×C316yes—
772C22⋊C4C24×C316yes—
773C22⋊C4C24×C316yes—
774C22⋊C4C24×C316yes—
775C22⋊C4C24×C312yes—
776C22⋊C4C24×C3112yes—
777C22⋊C4C24×C3112yes—
778C22⋊C4C24×C314yes—
779C22⋊C4C24×C3112yes—
780C42C24×C314yes—
781C42C24×C316yes—
782C42C24×C3112yes—
783C42C24×C311yescharacteristic
784C42C24×C313yes—
785C42C24×C316yes—
786C42C24×C316yes—
787C42C24×C3124yes—
788C42C24×C3112yes—
789C42C24×C313yes—
790C42C24×C3112yes—
791C42C24×C313yes—
792C22×C3—23no—
793C22×C3—23no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—26no—
797C22×C3—22no—
798C22×C3—26no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—26no—
802C22×C3—22no—
803C22×C3—812no—
804C22×C3C22×#4116yes—
805C22×C3C2611yescharacteristic
806C3×C4—22no—
807C3×C4—26no—
808C3×C4—26no—
809C3×C4—22no—
810C3×C4—23no—
811C3×C4—212no—
812C3×C4—26no—
813C3×C4—23no—
814C3×C4—24no—
815C3×C4—21no—
816C3×C4C22×#4112yes—
817C3×C4C22×#4116yes—
818C3×C4#58512yes—
819C23—212no—
820C23—46no—
821C23—46no—
822C23C25×C312yes—
823C23C25×C316yes—
824C23C25×C312yes—
825C23C25×C313yes—
826Q8—26no—
827Q8—212no—
828Q8—212no—
829Q8—212no—
830Q8—412no—
831Q8—42no—
832Q8C2×C3×#4114yes—
833D4—224no—
834D4—212no—
835D4—212no—
836D4—22no—
837D4—22no—
838D4—26no—
839D4—46no—
840D4—412no—
841D4—46no—
842D4—44no—
843D4C2×C3×#41112yes—
844C2×C4—212no—
845C2×C4—212no—
846C2×C4—24no—
847C2×C4—212no—
848C2×C4—212no—
849C2×C4—212no—
850C2×C4—212no—
851C2×C4—26no—
852C2×C4—24no—
853C2×C4—412no—
854C2×C4—412no—
855C2×C4—46no—
856C2×C4—46no—
857C2×C4—412no—
858C2×C4—43no—
859C2×C4C2×C3×#41112yes—
860C2×C4C25×C316yes—
861C2×C4C25×C312yes—
862C2×C4C25×C312yes—
863C2×C4C25×C313yes—
864C2×C4C25×C311yescharacteristic
865C2×C4C25×C314yes—
866C2×C4C25×C316yes—
867C2×C4C25×C3112yes—
868C2×C4C25×C313yes—
869C2×C4C25×C316yes—
870C2×C4C25×C313yes—
871C2×C4C25×C311yescharacteristic
872C2×C4C25×C311yescharacteristic
873C2×C3—26no—
874C2×C3—42no—
875C2×C3—46no—
876C2×C3—42no—
877C2×C3C23×#4111yescharacteristic
878C2×C3C2×#58511yescharacteristic
879C2×C32−1+611yescharacteristic
880C22—23no—
881C22—23no—
882C22—22no—
883C22—22no—
884C22—26no—
885C22—22no—
886C22—26no—
887C22—22no—
888C22—22no—
889C22—26no—
890C22—22no—
891C22—812no—
892C22C22×C3×#4116yes—
893C22C26×C311yescharacteristic
894C4—22no—
895C4—26no—
896C4—26no—
897C4—22no—
898C4—23no—
899C4—212no—
900C4—26no—
901C4—23no—
902C4—24no—
903C4—21no—
904C4C22×C3×#4112yes—
905C4C22×C3×#4116yes—
906C4C3×#58512yes—
907C3#6300911yescharacteristic, direct product factor, Sylow
908C2—26no—
909C2—42no—
910C2—46no—
911C2—42no—
912C2C23×C3×#4111yescharacteristic
913C2C2×C3×#58511yescharacteristic
914C2C3×2−1+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×#3523C2semidirect
2. C3×#3521C2semidirect
3. C3×#3518C2semidirect
4. C3×#3514C2semidirect
5. C3×#3511C2semidirect
6. C3×#3507C2semidirect
7. C3×#3503C2semidirect
8. C3×#3495C2semidirect
9. C3×#3493C2semidirect
10. C3×#3489C2semidirect
11. C3×#3482C2semidirect
12. C3×#3480C2semidirect
13. C3×#3475C2semidirect
14. C2×C3×#556C2semidirect
15. C3×D4×#41C2semidirect
16. C3×C4×2−1+4C2semidirect
17. C3×#3428C2semidirect
18. #63009C3direct (N × H)
21. C3×#559C22semidirect
22. C3×Q82C22semidirect
23. C3×#557C22semidirect
24. C3×#557C22semidirect
27. C3×#556C22semidirect
28. C3×#556C22semidirect
29. C3×#556C22semidirect
30. C3×#556C22semidirect
31. C3×#556C22semidirect
32. C3×#556C22semidirect
34. C3×#555C22semidirect
35. C3×#555C22semidirect
36. C3×#554C22semidirect
37. C3×#554C22semidirect
38. C3×#554C22semidirect
39. C3×#553C22semidirect
40. C3×#553C22semidirect
41. C3×#553C22semidirect
42. C3×#552C22semidirect
43. C3×#552C22semidirect
44. C3×#552C22semidirect
45. C3×#552C22semidirect
46. C3×#552C22semidirect
47. C3×#551C22semidirect
48. C3×#551C22semidirect
51. C3×D4×Q8C22semidirect
52. C3×D4×Q8C22semidirect
54. C3×#548C22semidirect
55. C3×#548C22semidirect
57. C3×#547C22semidirect
58. C3×#547C22semidirect
61. C3×#546C22semidirect
63. C3×#544C22semidirect
64. C3×#542C22semidirect
65. C3×#542C22semidirect
66. C3×#541C22semidirect
67. C3×#539C22semidirect
68. C3×#538C22semidirect
69. C3×#537C22semidirect
70. C3×#536C22semidirect
71. C3×#533C22semidirect
72. C3×#533C22semidirect
73. C3×#533C22semidirect
75. C3×#532C22semidirect
76. C2×C3×C4⋊Q8C22semidirect
78. C3×#529C22semidirect
79. C3×#529C22semidirect
80. C3×#529C22semidirect
81. C3×#529C22semidirect
82. C2×C3×#126C22semidirect
85. C3×#525C22semidirect
86. C2×C3×C22⋊Q8C22semidirect
89. C3×#520C22semidirect
90. C3×#520C22semidirect
91. C3×#520C22semidirect
92. C3×#520C22semidirect
93. C3×#519C22semidirect
94. C3×#519C22semidirect
95. C3×#519C22semidirect
96. C3×#518C22semidirect
98. C3×C4×#41C22semidirect
99. C3×C4×#41C22semidirect
100. C3×C4×#41C22semidirect
101. C3×C4×#41C22semidirect
102. C3×C4×#41C22semidirect
103. C2×C3×C4×Q8C22semidirect
104. C2×C3×C4×Q8C22semidirect
105. C2×C3×C4×Q8C22semidirect
107. C2×C3×#117C22semidirect
108. C2×C3×#117C22semidirect
109. #3523C2×C3semidirect
110. #3521C2×C3semidirect
111. #3518C2×C3semidirect
112. #3514C2×C3semidirect
113. #3511C2×C3semidirect
114. #3507C2×C3semidirect
115. #3503C2×C3semidirect
116. #3495C2×C3semidirect
117. #3493C2×C3semidirect
118. #3489C2×C3semidirect
119. #3482C2×C3semidirect
120. #3480C2×C3semidirect
121. #3475C2×C3semidirect
122. C2×#556C2×C3semidirect
123. D4×#41C2×C3semidirect
124. C4×2−1+4C2×C3semidirect
125. #3428C2×C3semidirect
285. #559C22×C3semidirect
286. Q82C22×C3semidirect
287. #557C22×C3semidirect
288. #557C22×C3semidirect
291. #556C22×C3semidirect
292. #556C22×C3semidirect
293. #556C22×C3semidirect
294. #556C22×C3semidirect
295. #556C22×C3semidirect
296. #556C22×C3semidirect
298. #555C22×C3semidirect
299. #555C22×C3semidirect
300. #554C22×C3semidirect
301. #554C22×C3semidirect
302. #554C22×C3semidirect
303. #553C22×C3semidirect
304. #553C22×C3semidirect
305. #553C22×C3semidirect
306. #552C22×C3semidirect
307. #552C22×C3semidirect
308. #552C22×C3semidirect
309. #552C22×C3semidirect
310. #552C22×C3semidirect
311. #551C22×C3semidirect
312. #551C22×C3semidirect
315. D4×Q8C22×C3semidirect
316. D4×Q8C22×C3semidirect
318. #548C22×C3semidirect
319. #548C22×C3semidirect
321. #547C22×C3semidirect
322. #547C22×C3semidirect
325. #546C22×C3semidirect
327. #544C22×C3semidirect
328. #542C22×C3semidirect
329. #542C22×C3semidirect
330. #541C22×C3semidirect
331. #539C22×C3semidirect
332. #538C22×C3semidirect
333. #537C22×C3semidirect
334. #536C22×C3semidirect
335. #533C22×C3semidirect
336. #533C22×C3semidirect
337. #533C22×C3semidirect
339. #532C22×C3semidirect
340. C2×C4⋊Q8C22×C3semidirect
342. #529C22×C3semidirect
343. #529C22×C3semidirect
344. #529C22×C3semidirect
345. #529C22×C3semidirect
346. C2×#126C22×C3semidirect
349. #525C22×C3semidirect
350. C2×C22⋊Q8C22×C3semidirect
353. #520C22×C3semidirect
354. #520C22×C3semidirect
355. #520C22×C3semidirect
356. #520C22×C3semidirect
357. #519C22×C3semidirect
358. #519C22×C3semidirect
359. #519C22×C3semidirect
360. #518C22×C3semidirect
362. C4×#41C22×C3semidirect
363. C4×#41C22×C3semidirect
364. C4×#41C22×C3semidirect
365. C4×#41C22×C3semidirect
366. C4×#41C22×C3semidirect
367. C2×C4×Q8C22×C3semidirect
368. C2×C4×Q8C22×C3semidirect
369. C2×C4×Q8C22×C3semidirect
371. C2×#117C22×C3semidirect
372. C2×#117C22×C3semidirect
380. C3×#41#41semidirect
695. #41C3×#41semidirect
907. C3#63009direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35232
C3×#35212
C3×#35182
C3×#35142
C3×#35112
C3×#35072
C3×#35032
C3×#34952
C3×#34932
C3×#34892
C3×#34822
C3×#34802
C3×#34752
C2×C3×#5562
C3×D4×#412
C3×C4×2−1+42
C3×#34282
#630093