Finite Group Databasebeta

← C3×#62995 #10681602

Subgroups — C3×#62995 #10681602

Order 768.

7030 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3521C2112yesmaximal, complemented
2C3×#3520C216yesmaximal, complemented
3C3×#3518C212yesmaximal, complemented
4C3×#3516C214yesmaximal, complemented
5C3×#3510C216yesmaximal, complemented
6C3×#3509C213yesmaximal, complemented
7C3×#3507C216yesmaximal, complemented
8C3×#3506C213yesmaximal, complemented
9C3×#3500C212yesmaximal, complemented
10C3×#3499C211yesmaximal, characteristic, complemented
11C3×#3482C212yesmaximal, complemented
12C3×#3480C213yesmaximal, complemented
13C3×Q8×#41C211yesmaximal, characteristic, complemented
14C3×#3475C216yesmaximal, complemented
15C2×C3×#556C213yesmaximal, complemented
16C3×C4×2−1+4C212yesmaximal, complemented
17C3×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
18#62995C311yesmaximal, characteristic, direct product factor, Sylow
19C2×C3×2−1+4C2212yes—
20C2×C3×H(5,𝔽2)C2211yescharacteristic
21C3×#559C2211yescharacteristic, complemented
22C3×#559C2216yescomplemented
23C3×#559C22112yescomplemented
24C3×Q82C2211yescharacteristic, complemented
25C3×#557C2211yescharacteristic, complemented
26C3×#557C2212yescomplemented
27C3×#557C2213yescomplemented
28C3×#557C2216yescomplemented
29C3×#556C2213yescomplemented
30C3×#556C2216yescomplemented
31C3×#556C2216yescomplemented
32C3×#556C22112yescomplemented
33C3×#556C22112yescomplemented
34C3×#556C2216yescomplemented
35C3×#556C2216yescomplemented
36C3×#556C22112yescomplemented
37C3×#556C2216yescomplemented
38C3×#555C2216yescomplemented
39C3×#554C2213yescomplemented
40C3×#554C2216yescomplemented
41C3×#554C22112yescomplemented
42C3×#553C2216yescomplemented
43C3×#553C22112yescomplemented
44C3×#553C22112yescomplemented
45C3×#552C22112yescomplemented
46C3×#552C22112yescomplemented
47C3×#552C22112yescomplemented
48C3×#552C22112yescomplemented
49C3×#551C22124yescomplemented
50C3×#551C22124yescomplemented
51C3×#550C2213yescomplemented
52C3×D4×Q8C2213yescomplemented
53C3×D4×Q8C2212yescomplemented
54C3×D4×Q8C2212yescomplemented
55C3×#548C2214yes—
56C3×#548C2214yes—
57C3×#548C2216yescomplemented
58C3×#547C2216yescomplemented
59C3×#547C2216yescomplemented
60C3×#547C2216yescomplemented
61C3×#546C22112yes—
62C3×#546C22112yes—
63C3×#542C22112yescomplemented
64C3×#542C22112yescomplemented
65C3×#541C22112yescomplemented
66C3×#539C22124yescomplemented
67C3×#538C22112yescomplemented
68C3×#536C2216yes—
69C3×#536C2216yescomplemented
70C3×#535C2216yes—
71C3×#533C2216yescomplemented
72C3×#533C2213yescomplemented
73C3×#533C2216yescomplemented
74C3×#533C2216yescomplemented
75C3×#532C2216yes—
76C3×#532C2213yescomplemented
77C2×C3×C4⋊Q8C2213yescomplemented
78C3×#529C22124yescomplemented
79C3×#529C22112yescomplemented
80C3×#529C22112yescomplemented
81C3×#529C2216yescomplemented
82C3×#529C22112yescomplemented
83C2×C3×#126C22112yescomplemented
84C2×C3×#124C2216yes—
85C3×#525C22112yescomplemented
86C2×C3×C22⋊Q8C2216yescomplemented
87C3×#520C2211yescharacteristic
88C3×#520C2213yes—
89C3×#520C2212yes—
90C3×#520C2216yescomplemented
91C3×#520C22112yescomplemented
92C3×#519C2216yescomplemented
93C3×#519C2214yescomplemented
94C3×#518C2213yes—
95C3×#518C2216yes—
96C3×C4×#41C2211yescharacteristic
97C3×C4×#41C2213yes—
98C3×C4×#41C2212yes—
99C3×C4×#41C2212yes—
100C3×C4×#41C22112yescomplemented
101C3×C4×#41C2216yescomplemented
102C3×C4×#41C2216yescomplemented
103C2×C3×C4×Q8C2216yescomplemented
104C2×C3×C4×Q8C2214yescomplemented
105C2×C3×C4×Q8C2213yescomplemented
106C2×C3×C4×D4C2213yes—
107C2×C3×C4×D4C2216yes—
108C2×C3×#117C2216yescomplemented
109#3521C2×C3112yescomplemented
110#3520C2×C316yescomplemented
111#3518C2×C312yescomplemented
112#3516C2×C314yescomplemented
113#3510C2×C316yescomplemented
114#3509C2×C313yescomplemented
115#3507C2×C316yescomplemented
116#3506C2×C313yescomplemented
117#3500C2×C312yescomplemented
118#3499C2×C311yescharacteristic, complemented
119#3482C2×C312yescomplemented
120#3480C2×C313yescomplemented
121Q8×#41C2×C311yescharacteristic, complemented
122#3475C2×C316yescomplemented
123C2×#556C2×C313yescomplemented
124C4×2−1+4C2×C312yescomplemented
125C4×H(5,𝔽2)C2×C311yescharacteristic, complemented
126C3×2−1+4—216no—
127C3×H(5,𝔽2)—28no—
128C2×C3×#41C2313yes—
129C2×C3×#41C2312yes—
130C2×C3×#41C2316yes—
131C2×C3×#41C23112yes—
132C2×C3×#41C2316yes—
133C2×C3×#41C2311yescharacteristic
134C22×C3×Q8C2316yes—
135C22×C3×Q8C2314yes—
136C22×C3×Q8C2313yes—
137C22×C3×D4C2313yes—
138C22×C3×D4C2316yes—
139C23×C3×C4C2316yes—
140C3×C4⋊Q8C2313yes—
141C3×C4⋊Q8C2316yes—
142C3×C4⋊Q8C2313yes—
143C3×C4⋊Q8C2316yes—
144C3×C4⋊Q8C2316yes—
145C3×C4⋊Q8C2316yes—
146C3×C4⋊Q8C2316yes—
147C3×C4⋊Q8C2313yes—
148C3×C4⋊Q8C2316yes—
149C3×#127C2316yes—
150C3×#127C2311yescharacteristic
151C3×#126C23112yes—
152C3×#126C23124yes—
153C3×#126C23124yes—
154C3×#126C23124yes—
155C3×#126C23112yes—
156C3×#126C23112yes—
157C3×#126C23124yes—
158C3×#125C2316yes—
159C3×#125C2316yes—
160C3×#125C2316yes—
161C3×#125C23124yes—
162C3×#125C23112yes—
163C3×#125C23112yes—
164C3×#125C2316yes—
165C3×#124C2316yes—
166C3×#124C2316yes—
167C3×#124C23112yes—
168C3×#124C2312yes—
169C3×#124C23124yes—
170C3×#124C23112yes—
171C3×#124C2312yes—
172C3×#124C23112yes—
173C3×#124C23112yes—
174C3×#123C23124yes—
175C3×#123C23112yes—
176C3×#123C2314yes—
177C3×#123C23124yes—
178C3×#123C23112yes—
179C3×#123C23124yes—
180C3×#123C23124yes—
181C3×C22⋊Q8C2316yes—
182C3×C22⋊Q8C23112yes—
183C3×C22⋊Q8C23124yes—
184C3×C22⋊Q8C2316yes—
185C3×C22⋊Q8C23112yes—
186C3×C22⋊Q8C23112yes—
187C3×C22⋊Q8C23112yes—
188C3×C22⋊Q8C23112yes—
189C3×C22⋊Q8C23112yes—
190C3×C22⋊Q8C23112yes—
191C3×C22⋊Q8C2316yes—
192C3×C22⋊Q8C23112yes—
193C3×C22⋊Q8C23112yes—
194C3×#121C2316yes—
195C3×#121C2316yes—
196C3×#121C23112yes—
197C3×#121C23112yes—
198C3×#121C23112yes—
199C3×#121C23112yes—
200C3×#121C23112yes—
201C3×#121C2316yes—
202C3×#120C23124yes—
203C3×C4×Q8C2313yes—
204C3×C4×Q8C2311yescharacteristic
205C3×C4×Q8C2312yes—
206C3×C4×Q8C2316yes—
207C3×C4×Q8C2311yescharacteristic
208C3×C4×Q8C23112yes—
209C3×C4×Q8C2316yes—
210C3×C4×Q8C2311yescharacteristic
211C3×C4×Q8C2316yes—
212C3×C4×Q8C2312yes—
213C3×C4×Q8C2312yes—
214C3×C4×Q8C23112yes—
215C3×C4×Q8C2316yes—
216C3×C4×Q8C2313yes—
217C3×C4×Q8C23112yes—
218C3×C4×Q8C23112yes—
219C3×C4×Q8C2316yes—
220C3×C4×Q8C2313yes—
221C3×C4×Q8C2311yescharacteristic
222C3×C4×Q8C2313yes—
223C3×C4×Q8C23112yes—
224C3×C4×Q8C2316yes—
225C3×C4×Q8C23112yes—
226C3×C4×D4C2312yes—
227C3×C4×D4C2316yes—
228C3×C4×D4C2313yes—
229C3×C4×D4C2316yes—
230C3×C4×D4C2312yes—
231C3×C4×D4C23112yes—
232C3×C4×D4C23124yes—
233C3×C4×D4C2313yes—
234C3×C4×D4C2316yes—
235C3×C4×D4C2316yes—
236C3×C4×D4C2313yes—
237C3×C4×D4C2316yes—
238C3×C4×D4C23112yes—
239C3×C4×D4C2316yes—
240C3×C4×D4C2316yes—
241C3×C4×D4C2316yes—
242C3×C4×D4C2316yes—
243C3×C4×D4C2313yes—
244C3×C4×D4C2316yes—
245C3×C4×D4C2316yes—
246C3×C4×D4C23112yes—
247C3×C4×D4C23124yes—
248C3×C4×D4C23112yes—
249C3×C4×D4C23112yes—
250C3×C4×D4C2316yes—
251C3×C4×D4C23112yes—
252C3×C4×D4C2316yes—
253C3×#117C2316yes—
254C3×#117C23112yes—
255C3×#117C23124yes—
256C3×#117C2313yes—
257C3×#117C2316yes—
258C3×#117C2313yes—
259C3×#117C2316yes—
260C3×#117C2316yes—
261C3×#117C23112yes—
262C3×#117C23124yes—
263C3×#117C23112yes—
264C3×#117C23112yes—
265C3×#117C23112yes—
266C2×C3×C4⋊C4C2313yes—
267C2×C3×C4⋊C4C2316yes—
268C2×C3×C4⋊C4C2313yes—
269C2×C3×C4⋊C4C2316yes—
270C2×C3×C4⋊C4C23112yes—
271C2×C3×C4⋊C4C23112yes—
272C2×C3×C4⋊C4C2316yes—
273C2×C3×C4⋊C4C2316yes—
274C2×C3×C22⋊C4C23112yes—
275C2×C3×C22⋊C4C2316yes—
276C2×C3×C22⋊C4C23112yes—
277C2×C3×C22⋊C4C23112yes—
278C2×C3×C42C23112yes—
279C2×C3×C42C2313yes—
280C2×C3×C42C2316yes—
281C2×C3×C42C2316yes—
282C2×C3×C42C23112yes—
283C2×2−1+4C22×C312yes—
284C2×H(5,𝔽2)C22×C311yescharacteristic
285#559C22×C311yescharacteristic, complemented
286#559C22×C316yescomplemented
287#559C22×C3112yescomplemented
288Q82C22×C311yescharacteristic, complemented
289#557C22×C311yescharacteristic, complemented
290#557C22×C312yescomplemented
291#557C22×C313yescomplemented
292#557C22×C316yescomplemented
293#556C22×C313yescomplemented
294#556C22×C316yescomplemented
295#556C22×C316yescomplemented
296#556C22×C3112yescomplemented
297#556C22×C3112yescomplemented
298#556C22×C316yescomplemented
299#556C22×C316yescomplemented
300#556C22×C3112yescomplemented
301#556C22×C316yescomplemented
302#555C22×C316yescomplemented
303#554C22×C313yescomplemented
304#554C22×C316yescomplemented
305#554C22×C3112yescomplemented
306#553C22×C316yescomplemented
307#553C22×C3112yescomplemented
308#553C22×C3112yescomplemented
309#552C22×C3112yescomplemented
310#552C22×C3112yescomplemented
311#552C22×C3112yescomplemented
312#552C22×C3112yescomplemented
313#551C22×C3124yescomplemented
314#551C22×C3124yescomplemented
315#550C22×C313yescomplemented
316D4×Q8C22×C313yescomplemented
317D4×Q8C22×C312yescomplemented
318D4×Q8C22×C312yescomplemented
319#548C22×C314yes—
320#548C22×C314yes—
321#548C22×C316yescomplemented
322#547C22×C316yescomplemented
323#547C22×C316yescomplemented
324#547C22×C316yescomplemented
325#546C22×C3112yes—
326#546C22×C3112yes—
327#542C22×C3112yescomplemented
328#542C22×C3112yescomplemented
329#541C22×C3112yescomplemented
330#539C22×C3124yescomplemented
331#538C22×C3112yescomplemented
332#536C22×C316yes—
333#536C22×C316yescomplemented
334#535C22×C316yes—
335#533C22×C316yescomplemented
336#533C22×C313yescomplemented
337#533C22×C316yescomplemented
338#533C22×C316yescomplemented
339#532C22×C316yes—
340#532C22×C313yescomplemented
341C2×C4⋊Q8C22×C313yescomplemented
342#529C22×C3124yescomplemented
343#529C22×C3112yescomplemented
344#529C22×C3112yescomplemented
345#529C22×C316yescomplemented
346#529C22×C3112yescomplemented
347C2×#126C22×C3112yescomplemented
348C2×#124C22×C316yes—
349#525C22×C3112yescomplemented
350C2×C22⋊Q8C22×C316yescomplemented
351#520C22×C311yescharacteristic
352#520C22×C313yes—
353#520C22×C312yes—
354#520C22×C316yescomplemented
355#520C22×C3112yescomplemented
356#519C22×C316yescomplemented
357#519C22×C314yescomplemented
358#518C22×C313yes—
359#518C22×C316yes—
360C4×#41C22×C311yescharacteristic
361C4×#41C22×C313yes—
362C4×#41C22×C312yes—
363C4×#41C22×C312yes—
364C4×#41C22×C3112yescomplemented
365C4×#41C22×C316yescomplemented
366C4×#41C22×C316yescomplemented
367C2×C4×Q8C22×C316yescomplemented
368C2×C4×Q8C22×C314yescomplemented
369C2×C4×Q8C22×C313yescomplemented
370C2×C4×D4C22×C313yes—
371C2×C4×D4C22×C316yes—
372C2×#117C22×C316yescomplemented
373C24×C3C2416yes—
374C3×#41—28no—
375C3×#41—248no—
376C3×#41—212no—
377C3×#41—224no—
378C3×#41—412no—
379C3×#41#4118yescomplemented
380C2×C3×Q8—216no—
381C2×C3×Q8—224no—
382C2×C3×Q8—46no—
383C2×C3×Q8C2411yescharacteristic
384C2×C3×Q8C2413yes—
385C2×C3×Q8C24112yes—
386C2×C3×Q8C2416yes—
387C2×C3×Q8C2411yescharacteristic
388C2×C3×Q8C2416yes—
389C2×C3×Q8C2416yes—
390C2×C3×Q8C2411yescharacteristic
391C2×C3×D4—224no—
392C2×C3×D4—212no—
393C2×C3×D4C24112yes—
394C2×C3×D4C2412yes—
395C2×C3×D4C2416yes—
396C2×C3×D4C2416yes—
397C2×C3×D4C2413yes—
398C2×C3×D4C2412yes—
399C2×C3×D4C24112yes—
400C2×C3×D4C2412yes—
401C2×C3×D4C24112yes—
402C2×C3×D4C2413yes—
403C22×C3×C4—412no—
404C22×C3×C4C24112yes—
405C22×C3×C4C2413yes—
406C22×C3×C4C24112yes—
407C22×C3×C4C2416yes—
408C22×C3×C4C2416yes—
409C22×C3×C4C2416yes—
410C22×C3×C4C2414yes—
411C22×C3×C4C2416yes—
412C22×C3×C4C2413yes—
413C22×C3×C4C2416yes—
414C22×C3×C4C2416yes—
415C22×C3×C4C24112yes—
416C22×C3×C4C24112yes—
417C22×C3×C4C2413yes—
418C3×C4⋊C4C2416yes—
419C3×C4⋊C4C2411yescharacteristic
420C3×C4⋊C4C2412yes—
421C3×C4⋊C4C2416yes—
422C3×C4⋊C4C2413yes—
423C3×C4⋊C4C2413yes—
424C3×C4⋊C4C2416yes—
425C3×C4⋊C4C2416yes—
426C3×C4⋊C4C24112yes—
427C3×C4⋊C4C24124yes—
428C3×C4⋊C4C2416yes—
429C3×C4⋊C4C2413yes—
430C3×C4⋊C4C2416yes—
431C3×C4⋊C4C2416yes—
432C3×C4⋊C4C24112yes—
433C3×C4⋊C4C24112yes—
434C3×C4⋊C4C2416yes—
435C3×C4⋊C4C2416yes—
436C3×C4⋊C4C2411yescharacteristic
437C3×C4⋊C4C2413yes—
438C3×C4⋊C4C2412yes—
439C3×C4⋊C4C2416yes—
440C3×C4⋊C4C24112yes—
441C3×C4⋊C4C2416yes—
442C3×C4⋊C4C24112yes—
443C3×C4⋊C4C24112yes—
444C3×C4⋊C4C24112yes—
445C3×C22⋊C4C2416yes—
446C3×C22⋊C4C24112yes—
447C3×C22⋊C4C2416yes—
448C3×C22⋊C4C2416yes—
449C3×C22⋊C4C2416yes—
450C3×C22⋊C4C24112yes—
451C3×C22⋊C4C24112yes—
452C3×C22⋊C4C24124yes—
453C3×C22⋊C4C24124yes—
454C3×C22⋊C4C24112yes—
455C3×C22⋊C4C2414yes—
456C3×C22⋊C4C24112yes—
457C3×C22⋊C4C2414yes—
458C3×C22⋊C4C24112yes—
459C3×C22⋊C4C2414yes—
460C3×C22⋊C4C24112yes—
461C3×C42C2416yes—
462C3×C42C24112yes—
463C3×C42C2413yes—
464C3×C42C2412yes—
465C3×C42C2416yes—
466C3×C42C2411yescharacteristic
467C3×C42C2412yes—
468C3×C42C2416yes—
469C3×C42C24112yes—
470C3×C42C24124yes—
471C3×C42C2413yes—
472C3×C42C2416yes—
473C3×C42C2413yes—
474C3×C42C2416yes—
4752−1+4—216no—
476H(5,𝔽2)—28no—
477C2×#41C23×C313yes—
478C2×#41C23×C312yes—
479C2×#41C23×C316yes—
480C2×#41C23×C3112yes—
481C2×#41C23×C316yes—
482C2×#41C23×C311yescharacteristic
483C22×Q8C23×C316yes—
484C22×Q8C23×C314yes—
485C22×Q8C23×C313yes—
486C22×D4C23×C313yes—
487C22×D4C23×C316yes—
488C23×C4C23×C316yes—
489C4⋊Q8C23×C313yes—
490C4⋊Q8C23×C316yes—
491C4⋊Q8C23×C316yes—
492C4⋊Q8C23×C316yes—
493C4⋊Q8C23×C316yes—
494C4⋊Q8C23×C313yes—
495C4⋊Q8C23×C313yes—
496C4⋊Q8C23×C316yes—
497C4⋊Q8C23×C316yes—
498#127C23×C316yes—
499#127C23×C311yescharacteristic
500#126C23×C3112yes—
501#126C23×C3124yes—
502#126C23×C3124yes—
503#126C23×C3124yes—
504#126C23×C3112yes—
505#126C23×C3112yes—
506#126C23×C3124yes—
507#125C23×C316yes—
508#125C23×C316yes—
509#125C23×C316yes—
510#125C23×C3124yes—
511#125C23×C3112yes—
512#125C23×C3112yes—
513#125C23×C316yes—
514#124C23×C316yes—
515#124C23×C3112yes—
516#124C23×C3112yes—
517#124C23×C3112yes—
518#124C23×C312yes—
519#124C23×C3124yes—
520#124C23×C3112yes—
521#124C23×C312yes—
522#124C23×C316yes—
523#123C23×C3124yes—
524#123C23×C3112yes—
525#123C23×C314yes—
526#123C23×C3124yes—
527#123C23×C3124yes—
528#123C23×C3124yes—
529#123C23×C3112yes—
530C22⋊Q8C23×C316yes—
531C22⋊Q8C23×C3112yes—
532C22⋊Q8C23×C3124yes—
533C22⋊Q8C23×C316yes—
534C22⋊Q8C23×C3112yes—
535C22⋊Q8C23×C3112yes—
536C22⋊Q8C23×C3112yes—
537C22⋊Q8C23×C3112yes—
538C22⋊Q8C23×C3112yes—
539C22⋊Q8C23×C3112yes—
540C22⋊Q8C23×C316yes—
541C22⋊Q8C23×C3112yes—
542C22⋊Q8C23×C3112yes—
543#121C23×C316yes—
544#121C23×C316yes—
545#121C23×C3112yes—
546#121C23×C3112yes—
547#121C23×C3112yes—
548#121C23×C3112yes—
549#121C23×C3112yes—
550#121C23×C316yes—
551#120C23×C3124yes—
552C4×Q8C23×C311yescharacteristic
553C4×Q8C23×C312yes—
554C4×Q8C23×C312yes—
555C4×Q8C23×C3112yes—
556C4×Q8C23×C316yes—
557C4×Q8C23×C313yes—
558C4×Q8C23×C3112yes—
559C4×Q8C23×C3112yes—
560C4×Q8C23×C3112yes—
561C4×Q8C23×C313yes—
562C4×Q8C23×C316yes—
563C4×Q8C23×C313yes—
564C4×Q8C23×C316yes—
565C4×Q8C23×C311yescharacteristic
566C4×Q8C23×C311yescharacteristic
567C4×Q8C23×C312yes—
568C4×Q8C23×C311yescharacteristic
569C4×Q8C23×C313yes—
570C4×Q8C23×C3112yes—
571C4×Q8C23×C316yes—
572C4×Q8C23×C316yes—
573C4×Q8C23×C3112yes—
574C4×Q8C23×C316yes—
575C4×D4C23×C313yes—
576C4×D4C23×C316yes—
577C4×D4C23×C316yes—
578C4×D4C23×C313yes—
579C4×D4C23×C316yes—
580C4×D4C23×C3112yes—
581C4×D4C23×C316yes—
582C4×D4C23×C316yes—
583C4×D4C23×C316yes—
584C4×D4C23×C316yes—
585C4×D4C23×C316yes—
586C4×D4C23×C313yes—
587C4×D4C23×C316yes—
588C4×D4C23×C313yes—
589C4×D4C23×C316yes—
590C4×D4C23×C3112yes—
591C4×D4C23×C312yes—
592C4×D4C23×C312yes—
593C4×D4C23×C3124yes—
594C4×D4C23×C3112yes—
595C4×D4C23×C316yes—
596C4×D4C23×C3112yes—
597C4×D4C23×C3112yes—
598C4×D4C23×C316yes—
599C4×D4C23×C3124yes—
600C4×D4C23×C3112yes—
601C4×D4C23×C316yes—
602#117C23×C316yes—
603#117C23×C3112yes—
604#117C23×C3124yes—
605#117C23×C313yes—
606#117C23×C316yes—
607#117C23×C313yes—
608#117C23×C316yes—
609#117C23×C316yes—
610#117C23×C3112yes—
611#117C23×C3124yes—
612#117C23×C3112yes—
613#117C23×C3112yes—
614#117C23×C3112yes—
615C2×C4⋊C4C23×C313yes—
616C2×C4⋊C4C23×C316yes—
617C2×C4⋊C4C23×C313yes—
618C2×C4⋊C4C23×C316yes—
619C2×C4⋊C4C23×C3112yes—
620C2×C4⋊C4C23×C3112yes—
621C2×C4⋊C4C23×C316yes—
622C2×C4⋊C4C23×C316yes—
623C2×C22⋊C4C23×C3112yes—
624C2×C22⋊C4C23×C316yes—
625C2×C22⋊C4C23×C3112yes—
626C2×C22⋊C4C23×C3112yes—
627C2×C42C23×C3112yes—
628C2×C42C23×C313yes—
629C2×C42C23×C316yes—
630C2×C42C23×C316yes—
631C2×C42C23×C3112yes—
632C23×C3—212no—
633C23×C3—46no—
634C23×C3—46no—
635C23×C3C2516yes—
636C23×C3C2514yes—
637C23×C3C2513yes—
638C3×Q8—224no—
639C3×Q8—212no—
640C3×Q8—22no—
641C3×Q8—22no—
642C3×Q8—26no—
643C3×Q8—46no—
644C3×Q8—46no—
645C3×Q8C2×#4114yes—
646C3×D4—212no—
647C3×D4—224no—
648C3×D4—212no—
649C3×D4—26no—
650C3×D4—24no—
651C3×D4—24no—
652C3×D4—42no—
653C3×D4—412no—
654C3×D4—412no—
655C3×D4C2×#41112yes—
656C2×C3×C4—224no—
657C2×C3×C4—212no—
658C2×C3×C4—224no—
659C2×C3×C4—26no—
660C2×C3×C4—212no—
661C2×C3×C4—46no—
662C2×C3×C4—412no—
663C2×C3×C4—44no—
664C2×C3×C4—46no—
665C2×C3×C4—46no—
666C2×C3×C4—43no—
667C2×C3×C4—46no—
668C2×C3×C4—412no—
669C2×C3×C4C2×#41112yes—
670C2×C3×C4C2512yes—
671C2×C3×C4C2512yes—
672C2×C3×C4C2516yes—
673C2×C3×C4C2516yes—
674C2×C3×C4C2513yes—
675C2×C3×C4C2512yes—
676C2×C3×C4C25112yes—
677C2×C3×C4C2511yescharacteristic
678C2×C3×C4C2516yes—
679C2×C3×C4C2512yes—
680C2×C3×C4C2513yes—
681C2×C3×C4C2511yescharacteristic
682C2×C3×C4C2513yes—
683C2×C3×C4C2511yescharacteristic
684C24C24×C316yes—
685#41—28no—
686#41—248no—
687#41—212no—
688#41—224no—
689#41—412no—
690#41C3×#4118yescomplemented
691C2×Q8—216no—
692C2×Q8—224no—
693C2×Q8—46no—
694C2×Q8C24×C311yescharacteristic
695C2×Q8C24×C313yes—
696C2×Q8C24×C3112yes—
697C2×Q8C24×C316yes—
698C2×Q8C24×C311yescharacteristic
699C2×Q8C24×C316yes—
700C2×Q8C24×C316yes—
701C2×Q8C24×C311yescharacteristic
702C2×D4—224no—
703C2×D4—212no—
704C2×D4C24×C3112yes—
705C2×D4C24×C312yes—
706C2×D4C24×C316yes—
707C2×D4C24×C316yes—
708C2×D4C24×C313yes—
709C2×D4C24×C312yes—
710C2×D4C24×C3112yes—
711C2×D4C24×C312yes—
712C2×D4C24×C3112yes—
713C2×D4C24×C313yes—
714C22×C4—412no—
715C22×C4C24×C3112yes—
716C22×C4C24×C313yes—
717C22×C4C24×C3112yes—
718C22×C4C24×C316yes—
719C22×C4C24×C316yes—
720C22×C4C24×C316yes—
721C22×C4C24×C314yes—
722C22×C4C24×C316yes—
723C22×C4C24×C313yes—
724C22×C4C24×C316yes—
725C22×C4C24×C316yes—
726C22×C4C24×C3112yes—
727C22×C4C24×C3112yes—
728C22×C4C24×C313yes—
729C4⋊C4C24×C316yes—
730C4⋊C4C24×C311yescharacteristic
731C4⋊C4C24×C312yes—
732C4⋊C4C24×C316yes—
733C4⋊C4C24×C313yes—
734C4⋊C4C24×C313yes—
735C4⋊C4C24×C316yes—
736C4⋊C4C24×C316yes—
737C4⋊C4C24×C3112yes—
738C4⋊C4C24×C3124yes—
739C4⋊C4C24×C316yes—
740C4⋊C4C24×C313yes—
741C4⋊C4C24×C316yes—
742C4⋊C4C24×C316yes—
743C4⋊C4C24×C3112yes—
744C4⋊C4C24×C3112yes—
745C4⋊C4C24×C316yes—
746C4⋊C4C24×C316yes—
747C4⋊C4C24×C311yescharacteristic
748C4⋊C4C24×C313yes—
749C4⋊C4C24×C312yes—
750C4⋊C4C24×C316yes—
751C4⋊C4C24×C3112yes—
752C4⋊C4C24×C316yes—
753C4⋊C4C24×C3112yes—
754C4⋊C4C24×C3112yes—
755C4⋊C4C24×C3112yes—
756C22⋊C4C24×C316yes—
757C22⋊C4C24×C3112yes—
758C22⋊C4C24×C316yes—
759C22⋊C4C24×C316yes—
760C22⋊C4C24×C316yes—
761C22⋊C4C24×C3112yes—
762C22⋊C4C24×C3112yes—
763C22⋊C4C24×C3124yes—
764C22⋊C4C24×C3124yes—
765C22⋊C4C24×C3112yes—
766C22⋊C4C24×C314yes—
767C22⋊C4C24×C3112yes—
768C22⋊C4C24×C314yes—
769C22⋊C4C24×C3112yes—
770C22⋊C4C24×C314yes—
771C22⋊C4C24×C3112yes—
772C42C24×C316yes—
773C42C24×C3112yes—
774C42C24×C313yes—
775C42C24×C312yes—
776C42C24×C316yes—
777C42C24×C311yescharacteristic
778C42C24×C312yes—
779C42C24×C316yes—
780C42C24×C3112yes—
781C42C24×C3124yes—
782C42C24×C313yes—
783C42C24×C316yes—
784C42C24×C313yes—
785C42C24×C316yes—
786C22×C3—23no—
787C22×C3—23no—
788C22×C3—24no—
789C22×C3—26no—
790C22×C3—26no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—26no—
794C22×C3—812no—
795C22×C3C22×#4116yes—
796C22×C3C2611yescharacteristic
797C3×C4—22no—
798C3×C4—212no—
799C3×C4—26no—
800C3×C4—23no—
801C3×C4—26no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—21no—
806C3×C4—23no—
807C3×C4—26no—
808C3×C4C22×#4116yes—
809C3×C4C22×#4112yes—
810C3×C4#58512yes—
811C23—212no—
812C23—46no—
813C23—46no—
814C23C25×C316yes—
815C23C25×C314yes—
816C23C25×C313yes—
817Q8—224no—
818Q8—212no—
819Q8—22no—
820Q8—22no—
821Q8—26no—
822Q8—46no—
823Q8—46no—
824Q8C2×C3×#4114yes—
825D4—212no—
826D4—224no—
827D4—212no—
828D4—26no—
829D4—24no—
830D4—24no—
831D4—412no—
832D4—42no—
833D4—412no—
834D4C2×C3×#41112yes—
835C2×C4—224no—
836C2×C4—212no—
837C2×C4—224no—
838C2×C4—26no—
839C2×C4—212no—
840C2×C4—46no—
841C2×C4—412no—
842C2×C4—46no—
843C2×C4—412no—
844C2×C4—44no—
845C2×C4—46no—
846C2×C4—46no—
847C2×C4—43no—
848C2×C4C2×C3×#41112yes—
849C2×C4C25×C312yes—
850C2×C4C25×C312yes—
851C2×C4C25×C316yes—
852C2×C4C25×C316yes—
853C2×C4C25×C313yes—
854C2×C4C25×C312yes—
855C2×C4C25×C3112yes—
856C2×C4C25×C311yescharacteristic
857C2×C4C25×C316yes—
858C2×C4C25×C312yes—
859C2×C4C25×C313yes—
860C2×C4C25×C311yescharacteristic
861C2×C4C25×C313yes—
862C2×C4C25×C311yescharacteristic
863C2×C3—26no—
864C2×C3—44no—
865C2×C3—46no—
866C2×C3C23×#4111yescharacteristic
867C2×C3C2×#58511yescharacteristic
868C2×C32−1+611yescharacteristic
869C22—23no—
870C22—23no—
871C22—24no—
872C22—26no—
873C22—26no—
874C22—24no—
875C22—24no—
876C22—26no—
877C22—812no—
878C22C22×C3×#4116yes—
879C22C26×C311yescharacteristic
880C4—22no—
881C4—212no—
882C4—26no—
883C4—23no—
884C4—26no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—21no—
889C4—23no—
890C4—26no—
891C4C22×C3×#4116yes—
892C4C22×C3×#4112yes—
893C4C3×#58512yes—
894C3#6299511yescharacteristic, direct product factor, Sylow
895C2—26no—
896C2—46no—
897C2—44no—
898C2C23×C3×#4111yescharacteristic
899C2C2×C3×#58511yescharacteristic
900C2C3×2−1+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×#3521C2semidirect
2. C3×#3520C2semidirect
3. C3×#3518C2semidirect
4. C3×#3516C2semidirect
5. C3×#3510C2semidirect
6. C3×#3509C2semidirect
7. C3×#3507C2semidirect
8. C3×#3506C2semidirect
9. C3×#3500C2semidirect
10. C3×#3499C2semidirect
11. C3×#3482C2semidirect
12. C3×#3480C2semidirect
13. C3×Q8×#41C2semidirect
14. C3×#3475C2semidirect
15. C2×C3×#556C2semidirect
16. C3×C4×2−1+4C2semidirect
17. C3×C4×H(5,𝔽2)C2semidirect
18. #62995C3direct (N × H)
21. C3×#559C22semidirect
22. C3×#559C22semidirect
23. C3×#559C22semidirect
24. C3×Q82C22semidirect
25. C3×#557C22semidirect
26. C3×#557C22semidirect
27. C3×#557C22semidirect
28. C3×#557C22semidirect
29. C3×#556C22semidirect
30. C3×#556C22semidirect
31. C3×#556C22semidirect
32. C3×#556C22semidirect
33. C3×#556C22semidirect
34. C3×#556C22semidirect
35. C3×#556C22semidirect
36. C3×#556C22semidirect
37. C3×#556C22semidirect
38. C3×#555C22semidirect
39. C3×#554C22semidirect
40. C3×#554C22semidirect
41. C3×#554C22semidirect
42. C3×#553C22semidirect
43. C3×#553C22semidirect
44. C3×#553C22semidirect
45. C3×#552C22semidirect
46. C3×#552C22semidirect
47. C3×#552C22semidirect
48. C3×#552C22semidirect
49. C3×#551C22semidirect
50. C3×#551C22semidirect
51. C3×#550C22semidirect
52. C3×D4×Q8C22semidirect
53. C3×D4×Q8C22semidirect
54. C3×D4×Q8C22semidirect
57. C3×#548C22semidirect
58. C3×#547C22semidirect
59. C3×#547C22semidirect
60. C3×#547C22semidirect
63. C3×#542C22semidirect
64. C3×#542C22semidirect
65. C3×#541C22semidirect
66. C3×#539C22semidirect
67. C3×#538C22semidirect
69. C3×#536C22semidirect
71. C3×#533C22semidirect
72. C3×#533C22semidirect
73. C3×#533C22semidirect
74. C3×#533C22semidirect
76. C3×#532C22semidirect
77. C2×C3×C4⋊Q8C22semidirect
78. C3×#529C22semidirect
79. C3×#529C22semidirect
80. C3×#529C22semidirect
81. C3×#529C22semidirect
82. C3×#529C22semidirect
83. C2×C3×#126C22semidirect
85. C3×#525C22semidirect
86. C2×C3×C22⋊Q8C22semidirect
90. C3×#520C22semidirect
91. C3×#520C22semidirect
92. C3×#519C22semidirect
93. C3×#519C22semidirect
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
108. C2×C3×#117C22semidirect
109. #3521C2×C3semidirect
110. #3520C2×C3semidirect
111. #3518C2×C3semidirect
112. #3516C2×C3semidirect
113. #3510C2×C3semidirect
114. #3509C2×C3semidirect
115. #3507C2×C3semidirect
116. #3506C2×C3semidirect
117. #3500C2×C3semidirect
118. #3499C2×C3semidirect
119. #3482C2×C3semidirect
120. #3480C2×C3semidirect
121. Q8×#41C2×C3semidirect
122. #3475C2×C3semidirect
123. C2×#556C2×C3semidirect
124. C4×2−1+4C2×C3semidirect
125. C4×H(5,𝔽2)C2×C3semidirect
285. #559C22×C3semidirect
286. #559C22×C3semidirect
287. #559C22×C3semidirect
288. Q82C22×C3semidirect
289. #557C22×C3semidirect
290. #557C22×C3semidirect
291. #557C22×C3semidirect
292. #557C22×C3semidirect
293. #556C22×C3semidirect
294. #556C22×C3semidirect
295. #556C22×C3semidirect
296. #556C22×C3semidirect
297. #556C22×C3semidirect
298. #556C22×C3semidirect
299. #556C22×C3semidirect
300. #556C22×C3semidirect
301. #556C22×C3semidirect
302. #555C22×C3semidirect
303. #554C22×C3semidirect
304. #554C22×C3semidirect
305. #554C22×C3semidirect
306. #553C22×C3semidirect
307. #553C22×C3semidirect
308. #553C22×C3semidirect
309. #552C22×C3semidirect
310. #552C22×C3semidirect
311. #552C22×C3semidirect
312. #552C22×C3semidirect
313. #551C22×C3semidirect
314. #551C22×C3semidirect
315. #550C22×C3semidirect
316. D4×Q8C22×C3semidirect
317. D4×Q8C22×C3semidirect
318. D4×Q8C22×C3semidirect
321. #548C22×C3semidirect
322. #547C22×C3semidirect
323. #547C22×C3semidirect
324. #547C22×C3semidirect
327. #542C22×C3semidirect
328. #542C22×C3semidirect
329. #541C22×C3semidirect
330. #539C22×C3semidirect
331. #538C22×C3semidirect
333. #536C22×C3semidirect
335. #533C22×C3semidirect
336. #533C22×C3semidirect
337. #533C22×C3semidirect
338. #533C22×C3semidirect
340. #532C22×C3semidirect
341. C2×C4⋊Q8C22×C3semidirect
342. #529C22×C3semidirect
343. #529C22×C3semidirect
344. #529C22×C3semidirect
345. #529C22×C3semidirect
346. #529C22×C3semidirect
347. C2×#126C22×C3semidirect
349. #525C22×C3semidirect
350. C2×C22⋊Q8C22×C3semidirect
354. #520C22×C3semidirect
355. #520C22×C3semidirect
356. #519C22×C3semidirect
357. #519C22×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
372. C2×#117C22×C3semidirect
379. C3×#41#41semidirect
690. #41C3×#41semidirect
894. C3#62995direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35212
C3×#35202
C3×#35182
C3×#35162
C3×#35102
C3×#35092
C3×#35072
C3×#35062
C3×#35002
C3×#34992
C3×#34822
C3×#34802
C3×Q8×#412
C3×#34752
C2×C3×#5562
C3×C4×2−1+42
C3×C4×H(5,𝔽2)2
#629953