Finite Group Databasebeta

← C3×#63006 #10681613

Subgroups — C3×#63006 #10681613

Order 768.

7230 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3524C218yesmaximal, complemented
2C3×#3522C214yesmaximal, complemented
3C3×#3517C218yesmaximal, complemented
4C3×#3517C214yesmaximal, complemented
5C3×#3508C216yesmaximal, complemented
6C3×#3502C211yesmaximal, characteristic, complemented
7C3×#3494C2112yesmaximal, complemented
8C3×#3487C212yesmaximal, complemented
9C3×#3483C214yesmaximal, complemented
10C3×#3480C214yesmaximal, complemented
11C3×#3475C216yesmaximal, complemented
12C2×C3×#550C211yesmaximal, characteristic, complemented
13C3×C4×2−1+4C211yesmaximal, characteristic, complemented
14C3×#3428C212yesmaximal, complemented
15#63006C311yesmaximal, characteristic, direct product factor, Sylow
16C2×C3×2−1+4C2211yescharacteristic
17C22×C3×#41C2212yes—
18C3×#559C22112yescomplemented
19C3×#559C22112yescomplemented
20C3×Q82C2214yescomplemented
21C3×#557C2214yescomplemented
22C3×#557C2218yescomplemented
23C3×#556C2216yescomplemented
24C3×#555C2216yescomplemented
25C3×#555C22124yescomplemented
26C3×#554C2216yescomplemented
27C3×#553C22112yescomplemented
28C3×#553C22124yescomplemented
29C3×#553C22124yescomplemented
30C3×#552C2214yes—
31C3×#552C22112yescomplemented
32C3×#551C22124yes—
33C3×#550C2214yes—
34C3×#550C2214yes—
35C3×#550C2218yes—
36C3×#550C2218yescomplemented
37C3×#550C22112yescomplemented
38C3×#550C2218yescomplemented
39C3×#550C22112yescomplemented
40C3×#548C2218yescomplemented
41C3×#548C2218yescomplemented
42C3×#547C2216yescomplemented
43C3×#547C22124yescomplemented
44C3×#546C22112yes—
45C3×#546C22124yes—
46C3×#544C2216yes—
47C3×#542C22124yescomplemented
48C3×#540C22124yescomplemented
49C3×#540C22124yescomplemented
50C3×#535C22112yes—
51C3×#533C2216yes—
52C3×#532C22112yescomplemented
53C3×#532C22124yescomplemented
54C3×#532C22112yescomplemented
55C2×C3×#127C2213yes—
56C3×#529C22112yescomplemented
57C3×#529C22124yescomplemented
58C3×#529C22124yescomplemented
59C3×#525C22112yes—
60C2×C3×#121C2216yes—
61C3×#520C2216yes—
62C3×#520C2218yescomplemented
63C3×#520C2218yescomplemented
64C3×#520C2214yescomplemented
65C3×#519C2211yescharacteristic
66C3×#519C2212yes—
67C3×#519C2214yescomplemented
68C3×#518C22112yes—
69C3×C4×#41C2216yes—
70C3×C4×#41C2218yescomplemented
71C3×C4×#41C2218yescomplemented
72C3×C4×#41C2214yescomplemented
73C3×C4×#41C22112yescomplemented
74C2×C3×C4×Q8C2211yescharacteristic
75C2×C3×C4×Q8C2214yescomplemented
76C2×C3×C4×D4C2213yes—
77C2×C3×#117C22112yes—
78#3524C2×C318yescomplemented
79#3522C2×C314yescomplemented
80#3517C2×C318yescomplemented
81#3517C2×C314yescomplemented
82#3508C2×C316yescomplemented
83#3502C2×C311yescharacteristic, complemented
84#3494C2×C3112yescomplemented
85#3487C2×C312yescomplemented
86#3483C2×C314yescomplemented
87#3480C2×C314yescomplemented
88#3475C2×C316yescomplemented
89C2×#550C2×C311yescharacteristic, complemented
90C4×2−1+4C2×C311yescharacteristic, complemented
91#3428C2×C312yescomplemented
92C3×2−1+4—28no—
93C2×C3×#41—216no—
94C2×C3×#41C2318yes—
95C2×C3×#41C2318yes—
96C2×C3×#41C2316yes—
97C2×C3×#41C2314yes—
98C2×C3×#41C23112yes—
99C2×C3×#41C23124yes—
100C22×C3×Q8C2314yes—
101C22×C3×Q8C2311yescharacteristic
102C22×C3×D4C2316yes—
103C22×C3×D4C2313yes—
104C22×C3×D4C2316yes—
105C23×C3×C4C2316yes—
106C3×C4⋊Q8C2316yes—
107C3×C4⋊Q8C23124yes—
108C3×C4⋊Q8C2316yes—
109C3×#127C23112yes—
110C3×#127C23112yes—
111C3×#127C23124yes—
112C3×#126C23124yes—
113C3×#126C2318yes—
114C3×#126C23124yes—
115C3×#125C2318yes—
116C3×#125C2314yes—
117C3×#125C23124yes—
118C3×#125C23112yes—
119C3×#124C23112yes—
120C3×#124C23124yes—
121C3×#124C23124yes—
122C3×#124C23124yes—
123C3×#123C23124yes—
124C3×#123C23148yes—
125C3×#123C2318yes—
126C3×#123C23124yes—
127C3×#123C23124yes—
128C3×C22⋊Q8C23112yes—
129C3×C22⋊Q8C23112yes—
130C3×C22⋊Q8C2314yes—
131C3×C22⋊Q8C23124yes—
132C3×C22⋊Q8C2314yes—
133C3×C22⋊Q8C23112yes—
134C3×#121C23124yes—
135C3×#121C23124yes—
136C3×#121C23112yes—
137C3×#121C23112yes—
138C3×#121C23112yes—
139C3×#121C23124yes—
140C3×#121C23124yes—
141C3×#121C23124yes—
142C3×#121C23124yes—
143C3×#121C23148yes—
144C3×#120C23124yes—
145C3×C4×Q8C23112yes—
146C3×C4×Q8C2314yes—
147C3×C4×Q8C2318yes—
148C3×C4×Q8C2316yes—
149C3×C4×Q8C2316yes—
150C3×C4×Q8C23112yes—
151C3×C4×Q8C2314yes—
152C3×C4×Q8C2314yes—
153C3×C4×Q8C23112yes—
154C3×C4×Q8C2314yes—
155C3×C4×Q8C2314yes—
156C3×C4×Q8C2318yes—
157C3×C4×D4C23112yes—
158C3×C4×D4C23124yes—
159C3×C4×D4C23124yes—
160C3×C4×D4C23124yes—
161C3×C4×D4C2316yes—
162C3×C4×D4C2316yes—
163C3×C4×D4C23112yes—
164C3×C4×D4C2314yes—
165C3×C4×D4C2316yes—
166C3×C4×D4C23112yes—
167C3×C4×D4C2316yes—
168C3×C4×D4C23124yes—
169C3×C4×D4C23124yes—
170C3×C4×D4C23112yes—
171C3×C4×D4C23124yes—
172C3×C4×D4C23124yes—
173C3×C4×D4C23124yes—
174C3×#117C2318yes—
175C3×#117C2316yes—
176C3×#117C23112yes—
177C3×#117C23112yes—
178C3×#117C23112yes—
179C3×#117C23124yes—
180C3×#117C23112yes—
181C3×#117C2314yes—
182C3×#117C23112yes—
183C3×#117C23124yes—
184C2×C3×C4⋊C4C23112yes—
185C2×C3×C4⋊C4C23112yes—
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2313yes—
188C2×C3×C4⋊C4C23112yes—
189C2×C3×C22⋊C4C23124yes—
190C2×C3×C22⋊C4C2316yes—
191C2×C3×C42C23124yes—
192C2×C3×C42C2313yes—
193C2×C3×C42C23112yes—
194C2×2−1+4C22×C311yescharacteristic
195C22×#41C22×C312yes—
196#559C22×C3112yescomplemented
197#559C22×C3112yescomplemented
198Q82C22×C314yescomplemented
199#557C22×C314yescomplemented
200#557C22×C318yescomplemented
201#556C22×C316yescomplemented
202#555C22×C316yescomplemented
203#555C22×C3124yescomplemented
204#554C22×C316yescomplemented
205#553C22×C3112yescomplemented
206#553C22×C3124yescomplemented
207#553C22×C3124yescomplemented
208#552C22×C314yes—
209#552C22×C3112yescomplemented
210#551C22×C3124yes—
211#550C22×C314yes—
212#550C22×C314yes—
213#550C22×C318yes—
214#550C22×C318yescomplemented
215#550C22×C3112yescomplemented
216#550C22×C318yescomplemented
217#550C22×C3112yescomplemented
218#548C22×C318yescomplemented
219#548C22×C318yescomplemented
220#547C22×C316yescomplemented
221#547C22×C3124yescomplemented
222#546C22×C3112yes—
223#546C22×C3124yes—
224#544C22×C316yes—
225#542C22×C3124yescomplemented
226#540C22×C3124yescomplemented
227#540C22×C3124yescomplemented
228#535C22×C3112yes—
229#533C22×C316yes—
230#532C22×C3112yescomplemented
231#532C22×C3124yescomplemented
232#532C22×C3112yescomplemented
233C2×#127C22×C313yes—
234#529C22×C3112yescomplemented
235#529C22×C3124yescomplemented
236#529C22×C3124yescomplemented
237#525C22×C3112yes—
238C2×#121C22×C316yes—
239#520C22×C316yes—
240#520C22×C318yescomplemented
241#520C22×C318yescomplemented
242#520C22×C314yescomplemented
243#519C22×C311yescharacteristic
244#519C22×C312yes—
245#519C22×C314yescomplemented
246#518C22×C3112yes—
247C4×#41C22×C316yes—
248C4×#41C22×C318yescomplemented
249C4×#41C22×C318yescomplemented
250C4×#41C22×C314yescomplemented
251C4×#41C22×C3112yescomplemented
252C2×C4×Q8C22×C311yescharacteristic
253C2×C4×Q8C22×C314yescomplemented
254C2×C4×D4C22×C313yes—
255C2×#117C22×C3112yes—
256C24×C3C2416yes—
257C3×#41—232no—
258C3×#41—232no—
259C3×#41—216no—
260C3×#41—224no—
261C3×#41—424no—
262C3×#41—824no—
263C2×C3×Q8—216no—
264C2×C3×Q8#4118yescomplemented
265C2×C3×Q8C2416yes—
266C2×C3×Q8C2414yes—
267C2×C3×Q8C24112yes—
268C2×C3×Q8C2414yes—
269C2×C3×D4—224no—
270C2×C3×D4—46no—
271C2×C3×D4—86no—
272C2×C3×D4C2414yes—
273C2×C3×D4C24124yes—
274C2×C3×D4C2416yes—
275C2×C3×D4C2416yes—
276C2×C3×D4C24124yes—
277C2×C3×D4C2416yes—
278C2×C3×D4C24124yes—
279C2×C3×D4C24124yes—
280C22×C3×C4—224no—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2414yes—
283C22×C3×C4C24112yes—
284C22×C3×C4C24112yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C24112yes—
287C22×C3×C4C2413yes—
288C22×C3×C4C24124yes—
289C22×C3×C4C24124yes—
290C22×C3×C4C24112yes—
291C22×C3×C4C2413yes—
292C3×C4⋊C4C2416yes—
293C3×C4⋊C4C2418yes—
294C3×C4⋊C4C2418yes—
295C3×C4⋊C4C2416yes—
296C3×C4⋊C4C24112yes—
297C3×C4⋊C4C24112yes—
298C3×C4⋊C4C2411yescharacteristic
299C3×C4⋊C4C24112yes—
300C3×C4⋊C4C24112yes—
301C3×C4⋊C4C2411yescharacteristic
302C3×C4⋊C4C2412yes—
303C3×C4⋊C4C2418yes—
304C3×C4⋊C4C2414yes—
305C3×C4⋊C4C2414yes—
306C3×C4⋊C4C24124yes—
307C3×C4⋊C4C2418yes—
308C3×C4⋊C4C24112yes—
309C3×C4⋊C4C2418yes—
310C3×C22⋊C4C2414yes—
311C3×C22⋊C4C2418yes—
312C3×C22⋊C4C24112yes—
313C3×C22⋊C4C24124yes—
314C3×C22⋊C4C24124yes—
315C3×C22⋊C4C24112yes—
316C3×C22⋊C4C2414yes—
317C3×C22⋊C4C24112yes—
318C3×C22⋊C4C2418yes—
319C3×C22⋊C4C24124yes—
320C3×C22⋊C4C24124yes—
321C3×C22⋊C4C2418yes—
322C3×C42C2418yes—
323C3×C42C24112yes—
324C3×C42C2418yes—
325C3×C42C2414yes—
326C3×C42C2416yes—
327C3×C42C24112yes—
328C3×C42C24124yes—
329C3×C42C2416yes—
3302−1+4—28no—
331C2×#41—216no—
332C2×#41C23×C316yes—
333C2×#41C23×C318yes—
334C2×#41C23×C314yes—
335C2×#41C23×C318yes—
336C2×#41C23×C3112yes—
337C2×#41C23×C3124yes—
338C22×Q8C23×C314yes—
339C22×Q8C23×C311yescharacteristic
340C22×D4C23×C316yes—
341C22×D4C23×C313yes—
342C22×D4C23×C316yes—
343C23×C4C23×C316yes—
344C4⋊Q8C23×C316yes—
345C4⋊Q8C23×C316yes—
346C4⋊Q8C23×C3124yes—
347#127C23×C3112yes—
348#127C23×C3112yes—
349#127C23×C3124yes—
350#126C23×C3124yes—
351#126C23×C318yes—
352#126C23×C3124yes—
353#125C23×C318yes—
354#125C23×C314yes—
355#125C23×C3124yes—
356#125C23×C3112yes—
357#124C23×C3112yes—
358#124C23×C3124yes—
359#124C23×C3124yes—
360#124C23×C3124yes—
361#123C23×C318yes—
362#123C23×C3124yes—
363#123C23×C3124yes—
364#123C23×C3124yes—
365#123C23×C3148yes—
366C22⋊Q8C23×C3112yes—
367C22⋊Q8C23×C3112yes—
368C22⋊Q8C23×C314yes—
369C22⋊Q8C23×C3124yes—
370C22⋊Q8C23×C314yes—
371C22⋊Q8C23×C3112yes—
372#121C23×C3124yes—
373#121C23×C3124yes—
374#121C23×C3112yes—
375#121C23×C3112yes—
376#121C23×C3112yes—
377#121C23×C3124yes—
378#121C23×C3124yes—
379#121C23×C3124yes—
380#121C23×C3124yes—
381#121C23×C3148yes—
382#120C23×C3124yes—
383C4×Q8C23×C314yes—
384C4×Q8C23×C314yes—
385C4×Q8C23×C316yes—
386C4×Q8C23×C314yes—
387C4×Q8C23×C3112yes—
388C4×Q8C23×C316yes—
389C4×Q8C23×C314yes—
390C4×Q8C23×C314yes—
391C4×Q8C23×C318yes—
392C4×Q8C23×C318yes—
393C4×Q8C23×C3112yes—
394C4×Q8C23×C3112yes—
395C4×D4C23×C316yes—
396C4×D4C23×C316yes—
397C4×D4C23×C3112yes—
398C4×D4C23×C314yes—
399C4×D4C23×C316yes—
400C4×D4C23×C3112yes—
401C4×D4C23×C316yes—
402C4×D4C23×C3124yes—
403C4×D4C23×C3124yes—
404C4×D4C23×C3124yes—
405C4×D4C23×C3124yes—
406C4×D4C23×C3112yes—
407C4×D4C23×C3124yes—
408C4×D4C23×C3112yes—
409C4×D4C23×C3124yes—
410C4×D4C23×C3124yes—
411C4×D4C23×C3124yes—
412#117C23×C318yes—
413#117C23×C316yes—
414#117C23×C3112yes—
415#117C23×C3112yes—
416#117C23×C3112yes—
417#117C23×C3124yes—
418#117C23×C3112yes—
419#117C23×C314yes—
420#117C23×C3112yes—
421#117C23×C3124yes—
422C2×C4⋊C4C23×C3112yes—
423C2×C4⋊C4C23×C3112yes—
424C2×C4⋊C4C23×C311yescharacteristic
425C2×C4⋊C4C23×C313yes—
426C2×C4⋊C4C23×C3112yes—
427C2×C22⋊C4C23×C3124yes—
428C2×C22⋊C4C23×C316yes—
429C2×C42C23×C3124yes—
430C2×C42C23×C313yes—
431C2×C42C23×C3112yes—
432C23×C3—212no—
433C23×C3—46no—
434C23×C3—46no—
435C23×C3C25112yes—
436C23×C3C2514yes—
437C23×C3C2511yescharacteristic
438C3×Q8—212no—
439C3×Q8—28no—
440C3×Q8—412no—
441C3×Q8C2×#41116yes—
442C3×D4—28no—
443C3×D4—248no—
444C3×D4—212no—
445C3×D4—212no—
446C3×D4—46no—
447C3×D4—424no—
448C3×D4—424no—
449C3×D4—424no—
450C2×C3×C4—24no—
451C2×C3×C4—224no—
452C2×C3×C4—224no—
453C2×C3×C4—224no—
454C2×C3×C4—22no—
455C2×C3×C4—28no—
456C2×C3×C4—43no—
457C2×C3×C4—424no—
458C2×C3×C4—412no—
459C2×C3×C4—424no—
460C2×C3×C4C2×#41112yes—
461C2×C3×C4C2512yes—
462C2×C3×C4C2514yes—
463C2×C3×C4C2514yes—
464C2×C3×C4C2511yescharacteristic
465C2×C3×C4C2514yes—
466C2×C3×C4C2518yes—
467C2×C3×C4C2518yes—
468C2×C3×C4C2516yes—
469C2×C3×C4C2512yes—
470C2×C3×C4C2516yes—
471C2×C3×C4C2511yescharacteristic
472C24C24×C316yes—
473#41—232no—
474#41—232no—
475#41—216no—
476#41—224no—
477#41—424no—
478#41—824no—
479C2×Q8—216no—
480C2×Q8C3×#4118yescomplemented
481C2×Q8C24×C316yes—
482C2×Q8C24×C314yes—
483C2×Q8C24×C3112yes—
484C2×Q8C24×C314yes—
485C2×D4—224no—
486C2×D4—46no—
487C2×D4—86no—
488C2×D4C24×C314yes—
489C2×D4C24×C3124yes—
490C2×D4C24×C316yes—
491C2×D4C24×C316yes—
492C2×D4C24×C3124yes—
493C2×D4C24×C316yes—
494C2×D4C24×C3124yes—
495C2×D4C24×C3124yes—
496C22×C4—224no—
497C22×C4C24×C311yescharacteristic
498C22×C4C24×C314yes—
499C22×C4C24×C3112yes—
500C22×C4C24×C3112yes—
501C22×C4C24×C312yes—
502C22×C4C24×C3112yes—
503C22×C4C24×C313yes—
504C22×C4C24×C3124yes—
505C22×C4C24×C3124yes—
506C22×C4C24×C3112yes—
507C22×C4C24×C313yes—
508C4⋊C4C24×C316yes—
509C4⋊C4C24×C318yes—
510C4⋊C4C24×C318yes—
511C4⋊C4C24×C316yes—
512C4⋊C4C24×C3112yes—
513C4⋊C4C24×C3112yes—
514C4⋊C4C24×C311yescharacteristic
515C4⋊C4C24×C3112yes—
516C4⋊C4C24×C3112yes—
517C4⋊C4C24×C311yescharacteristic
518C4⋊C4C24×C312yes—
519C4⋊C4C24×C318yes—
520C4⋊C4C24×C314yes—
521C4⋊C4C24×C314yes—
522C4⋊C4C24×C3124yes—
523C4⋊C4C24×C318yes—
524C4⋊C4C24×C3112yes—
525C4⋊C4C24×C318yes—
526C22⋊C4C24×C314yes—
527C22⋊C4C24×C318yes—
528C22⋊C4C24×C3112yes—
529C22⋊C4C24×C3124yes—
530C22⋊C4C24×C3124yes—
531C22⋊C4C24×C3112yes—
532C22⋊C4C24×C314yes—
533C22⋊C4C24×C3112yes—
534C22⋊C4C24×C318yes—
535C22⋊C4C24×C3124yes—
536C22⋊C4C24×C3124yes—
537C22⋊C4C24×C318yes—
538C42C24×C318yes—
539C42C24×C3112yes—
540C42C24×C318yes—
541C42C24×C314yes—
542C42C24×C316yes—
543C42C24×C3112yes—
544C42C24×C3124yes—
545C42C24×C316yes—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—24no—
549C22×C3—212no—
550C22×C3—24no—
551C22×C3—212no—
552C22×C3—24no—
553C22×C3—212no—
554C22×C3—812no—
555C22×C3C22×#4112yes—
556C22×C3C2611yescharacteristic
557C3×C4—22no—
558C3×C4—22no—
559C3×C4—24no—
560C3×C4—24no—
561C3×C4—21no—
562C3×C4—28no—
563C3×C4—24no—
564C3×C4—26no—
565C3×C4—28no—
566C3×C4C22×#41112yes—
567C3×C4#58512yes—
568C23—212no—
569C23—46no—
570C23—46no—
571C23C25×C3112yes—
572C23C25×C314yes—
573C23C25×C311yescharacteristic
574Q8—212no—
575Q8—28no—
576Q8—412no—
577Q8C2×C3×#41116yes—
578D4—28no—
579D4—248no—
580D4—212no—
581D4—212no—
582D4—46no—
583D4—424no—
584D4—424no—
585D4—424no—
586C2×C4—24no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—22no—
591C2×C4—28no—
592C2×C4—43no—
593C2×C4—424no—
594C2×C4—412no—
595C2×C4—424no—
596C2×C4C2×C3×#41112yes—
597C2×C4C25×C312yes—
598C2×C4C25×C314yes—
599C2×C4C25×C314yes—
600C2×C4C25×C311yescharacteristic
601C2×C4C25×C314yes—
602C2×C4C25×C318yes—
603C2×C4C25×C318yes—
604C2×C4C25×C316yes—
605C2×C4C25×C312yes—
606C2×C4C25×C316yes—
607C2×C4C25×C311yescharacteristic
608C2×C3—22no—
609C2×C3—44no—
610C2×C3—412no—
611C2×C3C23×#4111yescharacteristic
612C2×C3C2×#58511yescharacteristic
613C2×C3H(7,𝔽2)11yescharacteristic
614C22—21no—
615C22—21no—
616C22—24no—
617C22—212no—
618C22—24no—
619C22—212no—
620C22—24no—
621C22—212no—
622C22—812no—
623C22C22×C3×#4112yes—
624C22C26×C311yescharacteristic
625C4—22no—
626C4—22no—
627C4—24no—
628C4—24no—
629C4—21no—
630C4—28no—
631C4—24no—
632C4—26no—
633C4—28no—
634C4C22×C3×#41112yes—
635C4C3×#58512yes—
636C3#6300611yescharacteristic, direct product factor, Sylow
637C2—22no—
638C2—412no—
639C2—44no—
640C2C23×C3×#4111yescharacteristic
641C2C2×C3×#58511yescharacteristic
642C2C3×H(7,𝔽2)11yescharacteristic
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×#3522C2semidirect
3. C3×#3517C2semidirect
4. C3×#3517C2semidirect
5. C3×#3508C2semidirect
6. C3×#3502C2semidirect
7. C3×#3494C2semidirect
8. C3×#3487C2semidirect
9. C3×#3483C2semidirect
10. C3×#3480C2semidirect
11. C3×#3475C2semidirect
12. C2×C3×#550C2semidirect
13. C3×C4×2−1+4C2semidirect
14. C3×#3428C2semidirect
15. #63006C3direct (N × H)
18. C3×#559C22semidirect
19. C3×#559C22semidirect
20. C3×Q82C22semidirect
21. C3×#557C22semidirect
22. C3×#557C22semidirect
23. C3×#556C22semidirect
24. C3×#555C22semidirect
25. C3×#555C22semidirect
26. C3×#554C22semidirect
27. C3×#553C22semidirect
28. C3×#553C22semidirect
29. C3×#553C22semidirect
31. C3×#552C22semidirect
36. C3×#550C22semidirect
37. C3×#550C22semidirect
38. C3×#550C22semidirect
39. C3×#550C22semidirect
40. C3×#548C22semidirect
41. C3×#548C22semidirect
42. C3×#547C22semidirect
43. C3×#547C22semidirect
47. C3×#542C22semidirect
48. C3×#540C22semidirect
49. C3×#540C22semidirect
52. C3×#532C22semidirect
53. C3×#532C22semidirect
54. C3×#532C22semidirect
56. C3×#529C22semidirect
57. C3×#529C22semidirect
58. C3×#529C22semidirect
62. C3×#520C22semidirect
63. C3×#520C22semidirect
64. C3×#520C22semidirect
67. C3×#519C22semidirect
70. C3×C4×#41C22semidirect
71. C3×C4×#41C22semidirect
72. C3×C4×#41C22semidirect
73. C3×C4×#41C22semidirect
75. C2×C3×C4×Q8C22semidirect
78. #3524C2×C3semidirect
79. #3522C2×C3semidirect
80. #3517C2×C3semidirect
81. #3517C2×C3semidirect
82. #3508C2×C3semidirect
83. #3502C2×C3semidirect
84. #3494C2×C3semidirect
85. #3487C2×C3semidirect
86. #3483C2×C3semidirect
87. #3480C2×C3semidirect
88. #3475C2×C3semidirect
89. C2×#550C2×C3semidirect
90. C4×2−1+4C2×C3semidirect
91. #3428C2×C3semidirect
196. #559C22×C3semidirect
197. #559C22×C3semidirect
198. Q82C22×C3semidirect
199. #557C22×C3semidirect
200. #557C22×C3semidirect
201. #556C22×C3semidirect
202. #555C22×C3semidirect
203. #555C22×C3semidirect
204. #554C22×C3semidirect
205. #553C22×C3semidirect
206. #553C22×C3semidirect
207. #553C22×C3semidirect
209. #552C22×C3semidirect
214. #550C22×C3semidirect
215. #550C22×C3semidirect
216. #550C22×C3semidirect
217. #550C22×C3semidirect
218. #548C22×C3semidirect
219. #548C22×C3semidirect
220. #547C22×C3semidirect
221. #547C22×C3semidirect
225. #542C22×C3semidirect
226. #540C22×C3semidirect
227. #540C22×C3semidirect
230. #532C22×C3semidirect
231. #532C22×C3semidirect
232. #532C22×C3semidirect
234. #529C22×C3semidirect
235. #529C22×C3semidirect
236. #529C22×C3semidirect
240. #520C22×C3semidirect
241. #520C22×C3semidirect
242. #520C22×C3semidirect
245. #519C22×C3semidirect
248. C4×#41C22×C3semidirect
249. C4×#41C22×C3semidirect
250. C4×#41C22×C3semidirect
251. C4×#41C22×C3semidirect
253. C2×C4×Q8C22×C3semidirect
264. C2×C3×Q8#41semidirect
480. C2×Q8C3×#41semidirect
636. C3#63006direct (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×#35172
C3×#35082
C3×#35022
C3×#34942
C3×#34872
C3×#34832
C3×#34802
C3×#34752
C2×C3×#5502
C3×C4×2−1+42
C3×#34282
#630063