Finite Group Databasebeta

← C3×#62998 #10681605

Subgroups — C3×#62998 #10681605

Order 768.

6930 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3523C218yesmaximal, complemented
2C3×#3523C214yesmaximal, complemented
3C3×#3518C214yesmaximal, complemented
4C3×#3516C218yesmaximal, complemented
5C3×#3509C216yesmaximal, complemented
6C3×#3502C211yesmaximal, characteristic, complemented
7C3×#3495C2112yesmaximal, complemented
8C3×#3486C212yesmaximal, complemented
9C3×#3482C214yesmaximal, complemented
10C3×Q8×#41C214yesmaximal, complemented
11C3×#3475C216yesmaximal, complemented
12C2×C3×D4×Q8C211yesmaximal, characteristic, complemented
13C3×C4×2−1+4C211yesmaximal, characteristic, complemented
14C2×C3×#519C212yesmaximal, complemented
15#62998C311yesmaximal, characteristic, direct product factor, Sylow
16C2×C3×2−1+4C2211yescharacteristic
17C23×C3×Q8C2212yes—
18C3×Q82C2214yescomplemented
19C3×#557C22112yescomplemented
20C3×#557C2214yescomplemented
21C3×#557C2218yescomplemented
22C3×#557C22112yescomplemented
23C3×#556C2216yes—
24C3×#556C22112yescomplemented
25C3×#556C22124yescomplemented
26C3×#556C22112yescomplemented
27C3×#555C2216yes—
28C3×#554C2216yes—
29C3×#554C22124yescomplemented
30C3×#553C22112yes—
31C3×#552C22112yes—
32C3×#552C22112yes—
33C3×#552C22124yes—
34C3×#552C22124yescomplemented
35C3×#552C22124yescomplemented
36C3×#551C22124yes—
37C3×D4×Q8C2214yes—
38C3×D4×Q8C2218yes—
39C3×D4×Q8C2214yes—
40C3×D4×Q8C2218yescomplemented
41C3×D4×Q8C2218yescomplemented
42C3×#548C2218yescomplemented
43C3×#548C2218yescomplemented
44C3×#547C2216yes—
45C3×#546C2214yes—
46C3×#544C2216yes—
47C3×#542C22124yescomplemented
48C3×#541C22124yescomplemented
49C3×#541C22124yescomplemented
50C3×#536C22112yes—
51C3×#533C2216yes—
52C3×#533C22124yescomplemented
53C3×#533C22112yescomplemented
54C3×#533C22112yescomplemented
55C2×C3×C4⋊Q8C2213yes—
56C3×#529C22124yes—
57C3×#529C22112yes—
58C3×#529C22124yescomplemented
59C3×#525C22112yes—
60C2×C3×C22⋊Q8C2216yes—
61C3×#520C2216yes—
62C3×#520C2214yescomplemented
63C3×#519C2211yescharacteristic
64C3×#519C2212yes—
65C3×#519C22112yes—
66C3×#519C2218yescomplemented
67C3×#519C2218yescomplemented
68C3×#519C2214yescomplemented
69C3×C4×#41C2216yes—
70C3×C4×#41C22112yes—
71C3×C4×#41C2214yescomplemented
72C2×C3×C4×Q8C2211yescharacteristic
73C2×C3×C4×Q8C2218yescomplemented
74C2×C3×C4×Q8C2218yescomplemented
75C2×C3×C4×Q8C2214yescomplemented
76C2×C3×C4×D4C2213yes—
77C2×C3×#117C22112yes—
78#3523C2×C318yescomplemented
79#3523C2×C314yescomplemented
80#3518C2×C314yescomplemented
81#3516C2×C318yescomplemented
82#3509C2×C316yescomplemented
83#3502C2×C311yescharacteristic, complemented
84#3495C2×C3112yescomplemented
85#3486C2×C312yescomplemented
86#3482C2×C314yescomplemented
87Q8×#41C2×C314yescomplemented
88#3475C2×C316yescomplemented
89C2×D4×Q8C2×C311yescharacteristic, complemented
90C4×2−1+4C2×C311yescharacteristic, complemented
91C2×#519C2×C312yescomplemented
92C3×2−1+4—28no—
93C2×C3×#41C2316yes—
94C2×C3×#41C2314yes—
95C2×C3×#41C2314yes—
96C22×C3×Q8—216no—
97C22×C3×Q8C2318yes—
98C22×C3×Q8C2316yes—
99C22×C3×Q8C2318yes—
100C22×C3×Q8C2314yes—
101C22×C3×Q8C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4C2316yes—
104C3×C4⋊Q8C2316yes—
105C3×C4⋊Q8C23124yes—
106C3×C4⋊Q8C23112yes—
107C3×C4⋊Q8C23112yes—
108C3×C4⋊Q8C2316yes—
109C3×C4⋊Q8C23124yes—
110C3×#126C23124yes—
111C3×#126C23124yes—
112C3×#126C23124yes—
113C3×#126C23148yes—
114C3×#125C23112yes—
115C3×#125C23124yes—
116C3×#125C23124yes—
117C3×#125C23112yes—
118C3×#125C23124yes—
119C3×#125C23148yes—
120C3×#124C2314yes—
121C3×#124C23124yes—
122C3×#124C23124yes—
123C3×#123C23124yes—
124C3×#123C2318yes—
125C3×#123C23124yes—
126C3×#123C23124yes—
127C3×C22⋊Q8C23124yes—
128C3×C22⋊Q8C23124yes—
129C3×C22⋊Q8C23112yes—
130C3×C22⋊Q8C23112yes—
131C3×C22⋊Q8C23112yes—
132C3×C22⋊Q8C23124yes—
133C3×C22⋊Q8C2314yes—
134C3×C22⋊Q8C23112yes—
135C3×C22⋊Q8C23124yes—
136C3×C22⋊Q8C23124yes—
137C3×C22⋊Q8C23124yes—
138C3×#121C23112yes—
139C3×#121C23112yes—
140C3×#121C2318yes—
141C3×#121C2314yes—
142C3×#120C2318yes—
143C3×C4×Q8C2314yes—
144C3×C4×Q8C2318yes—
145C3×C4×Q8C23112yes—
146C3×C4×Q8C2314yes—
147C3×C4×Q8C2314yes—
148C3×C4×Q8C2316yes—
149C3×C4×Q8C2314yes—
150C3×C4×Q8C23124yes—
151C3×C4×Q8C23124yes—
152C3×C4×Q8C2318yes—
153C3×C4×Q8C23124yes—
154C3×C4×Q8C23124yes—
155C3×C4×Q8C23112yes—
156C3×C4×Q8C2316yes—
157C3×C4×Q8C23112yes—
158C3×C4×Q8C23112yes—
159C3×C4×Q8C23124yes—
160C3×C4×D4C2316yes—
161C3×C4×D4C23112yes—
162C3×C4×D4C2316yes—
163C3×C4×D4C2314yes—
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×#117C2316yes—
173C3×#117C23112yes—
174C3×#117C23124yes—
175C3×#117C23124yes—
176C3×#117C23112yes—
177C3×#117C23112yes—
178C3×#117C23112yes—
179C3×#117C23124yes—
180C3×#117C23112yes—
181C3×#117C23112yes—
182C3×#117C23124yes—
183C2×C3×C4⋊C4C23112yes—
184C2×C3×C4⋊C4C23112yes—
185C2×C3×C4⋊C4C2313yes—
186C2×C3×C4⋊C4C2313yes—
187C2×C3×C4⋊C4C23112yes—
188C2×C3×C4⋊C4C2316yes—
189C2×C3×C22⋊C4C2318yes—
190C2×C3×C22⋊C4C2316yes—
191C2×C3×C42C23124yes—
192C2×C3×C42C2313yes—
193C2×C3×C42C23112yes—
194C2×2−1+4C22×C311yescharacteristic
195C23×Q8C22×C312yes—
196Q82C22×C314yescomplemented
197#557C22×C3112yescomplemented
198#557C22×C314yescomplemented
199#557C22×C318yescomplemented
200#557C22×C3112yescomplemented
201#556C22×C316yes—
202#556C22×C3112yescomplemented
203#556C22×C3124yescomplemented
204#556C22×C3112yescomplemented
205#555C22×C316yes—
206#554C22×C316yes—
207#554C22×C3124yescomplemented
208#553C22×C3112yes—
209#552C22×C3112yes—
210#552C22×C3112yes—
211#552C22×C3124yes—
212#552C22×C3124yescomplemented
213#552C22×C3124yescomplemented
214#551C22×C3124yes—
215D4×Q8C22×C314yes—
216D4×Q8C22×C318yes—
217D4×Q8C22×C314yes—
218D4×Q8C22×C318yescomplemented
219D4×Q8C22×C318yescomplemented
220#548C22×C318yescomplemented
221#548C22×C318yescomplemented
222#547C22×C316yes—
223#546C22×C314yes—
224#544C22×C316yes—
225#542C22×C3124yescomplemented
226#541C22×C3124yescomplemented
227#541C22×C3124yescomplemented
228#536C22×C3112yes—
229#533C22×C316yes—
230#533C22×C3124yescomplemented
231#533C22×C3112yescomplemented
232#533C22×C3112yescomplemented
233C2×C4⋊Q8C22×C313yes—
234#529C22×C3124yes—
235#529C22×C3112yes—
236#529C22×C3124yescomplemented
237#525C22×C3112yes—
238C2×C22⋊Q8C22×C316yes—
239#520C22×C316yes—
240#520C22×C314yescomplemented
241#519C22×C311yescharacteristic
242#519C22×C312yes—
243#519C22×C3112yes—
244#519C22×C318yescomplemented
245#519C22×C318yescomplemented
246#519C22×C314yescomplemented
247C4×#41C22×C316yes—
248C4×#41C22×C3112yes—
249C4×#41C22×C314yescomplemented
250C2×C4×Q8C22×C311yescharacteristic
251C2×C4×Q8C22×C318yescomplemented
252C2×C4×Q8C22×C318yescomplemented
253C2×C4×Q8C22×C314yescomplemented
254C2×C4×D4C22×C313yes—
255C2×#117C22×C3112yes—
256C24×C3C2412yes—
257C3×#41—216no—
258C3×#41—216no—
259C3×#41—224no—
260C2×C3×Q8—232no—
261C2×C3×Q8—232no—
262C2×C3×Q8—216no—
263C2×C3×Q8—224no—
264C2×C3×Q8#4118yescomplemented
265C2×C3×Q8C2414yes—
266C2×C3×Q8C24124yes—
267C2×C3×Q8C2416yes—
268C2×C3×Q8C24112yes—
269C2×C3×Q8C2414yes—
270C2×C3×D4—24no—
271C2×C3×D4C2418yes—
272C2×C3×D4C2412yes—
273C2×C3×D4C2411yescharacteristic
274C2×C3×D4C2414yes—
275C2×C3×D4C2416yes—
276C2×C3×D4C2418yes—
277C2×C3×D4C2411yescharacteristic
278C22×C3×C4—224no—
279C22×C3×C4C2418yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2414yes—
282C22×C3×C4C24112yes—
283C22×C3×C4C24112yes—
284C22×C3×C4C2416yes—
285C22×C3×C4C24112yes—
286C22×C3×C4C2418yes—
287C22×C3×C4C2413yes—
288C22×C3×C4C24112yes—
289C22×C3×C4C2413yes—
290C3×C4⋊C4C2416yes—
291C3×C4⋊C4C2416yes—
292C3×C4⋊C4C24112yes—
293C3×C4⋊C4C24112yes—
294C3×C4⋊C4C2416yes—
295C3×C4⋊C4C24112yes—
296C3×C4⋊C4C24112yes—
297C3×C4⋊C4C24124yes—
298C3×C4⋊C4C24124yes—
299C3×C4⋊C4C24124yes—
300C3×C4⋊C4C2416yes—
301C3×C4⋊C4C2414yes—
302C3×C4⋊C4C2414yes—
303C3×C4⋊C4C24112yes—
304C3×C4⋊C4C24124yes—
305C3×C4⋊C4C24124yes—
306C3×C4⋊C4C24124yes—
307C3×C4⋊C4C2418yes—
308C3×C22⋊C4C2414yes—
309C3×C22⋊C4C2418yes—
310C3×C22⋊C4C2418yes—
311C3×C22⋊C4C2418yes—
312C3×C22⋊C4C24112yes—
313C3×C22⋊C4C24112yes—
314C3×C22⋊C4C2418yes—
315C3×C22⋊C4C2414yes—
316C3×C22⋊C4C24112yes—
317C3×C22⋊C4C24124yes—
318C3×C22⋊C4C24124yes—
319C3×C22⋊C4C2418yes—
320C3×C42C24112yes—
321C3×C42C2416yes—
322C3×C42C2414yes—
323C3×C42C24112yes—
324C3×C42C24124yes—
325C3×C42C24124yes—
326C3×C42C2416yes—
327C3×C42C24124yes—
3282−1+4—28no—
329C2×#41C23×C314yes—
330C2×#41C23×C316yes—
331C2×#41C23×C314yes—
332C22×Q8—216no—
333C22×Q8C23×C318yes—
334C22×Q8C23×C314yes—
335C22×Q8C23×C316yes—
336C22×Q8C23×C318yes—
337C22×Q8C23×C311yescharacteristic
338C22×D4C23×C311yescharacteristic
339C23×C4C23×C316yes—
340C4⋊Q8C23×C3112yes—
341C4⋊Q8C23×C3112yes—
342C4⋊Q8C23×C316yes—
343C4⋊Q8C23×C316yes—
344C4⋊Q8C23×C3124yes—
345C4⋊Q8C23×C3124yes—
346#126C23×C3124yes—
347#126C23×C3124yes—
348#126C23×C3124yes—
349#126C23×C3148yes—
350#125C23×C3112yes—
351#125C23×C3124yes—
352#125C23×C3124yes—
353#125C23×C3112yes—
354#125C23×C3124yes—
355#125C23×C3148yes—
356#124C23×C314yes—
357#124C23×C3124yes—
358#124C23×C3124yes—
359#123C23×C3124yes—
360#123C23×C318yes—
361#123C23×C3124yes—
362#123C23×C3124yes—
363C22⋊Q8C23×C3124yes—
364C22⋊Q8C23×C3124yes—
365C22⋊Q8C23×C3112yes—
366C22⋊Q8C23×C3112yes—
367C22⋊Q8C23×C3112yes—
368C22⋊Q8C23×C3124yes—
369C22⋊Q8C23×C314yes—
370C22⋊Q8C23×C3112yes—
371C22⋊Q8C23×C3124yes—
372C22⋊Q8C23×C3124yes—
373C22⋊Q8C23×C3124yes—
374#121C23×C3112yes—
375#121C23×C3112yes—
376#121C23×C318yes—
377#121C23×C314yes—
378#120C23×C318yes—
379C4×Q8C23×C314yes—
380C4×Q8C23×C314yes—
381C4×Q8C23×C314yes—
382C4×Q8C23×C316yes—
383C4×Q8C23×C314yes—
384C4×Q8C23×C3124yes—
385C4×Q8C23×C3124yes—
386C4×Q8C23×C318yes—
387C4×Q8C23×C318yes—
388C4×Q8C23×C3124yes—
389C4×Q8C23×C3124yes—
390C4×Q8C23×C3112yes—
391C4×Q8C23×C316yes—
392C4×Q8C23×C3112yes—
393C4×Q8C23×C3112yes—
394C4×Q8C23×C3112yes—
395C4×Q8C23×C3124yes—
396C4×D4C23×C316yes—
397C4×D4C23×C3112yes—
398C4×D4C23×C316yes—
399C4×D4C23×C314yes—
400C4×D4C23×C314yes—
401C4×D4C23×C316yes—
402C4×D4C23×C3112yes—
403C4×D4C23×C316yes—
404C4×D4C23×C3124yes—
405C4×D4C23×C3124yes—
406C4×D4C23×C3112yes—
407C4×D4C23×C3124yes—
408#117C23×C316yes—
409#117C23×C3112yes—
410#117C23×C3124yes—
411#117C23×C3124yes—
412#117C23×C3112yes—
413#117C23×C3112yes—
414#117C23×C3112yes—
415#117C23×C3124yes—
416#117C23×C3112yes—
417#117C23×C3112yes—
418#117C23×C3124yes—
419C2×C4⋊C4C23×C3112yes—
420C2×C4⋊C4C23×C3112yes—
421C2×C4⋊C4C23×C313yes—
422C2×C4⋊C4C23×C313yes—
423C2×C4⋊C4C23×C3112yes—
424C2×C4⋊C4C23×C316yes—
425C2×C22⋊C4C23×C318yes—
426C2×C22⋊C4C23×C316yes—
427C2×C42C23×C3124yes—
428C2×C42C23×C313yes—
429C2×C42C23×C3112yes—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3—42no—
433C23×C3C2512yes—
434C23×C3C2514yes—
435C23×C3C2511yescharacteristic
436C23×C3C2512yes—
437C3×Q8—248no—
438C3×Q8—212no—
439C3×Q8—28no—
440C3×Q8—412no—
441C3×Q8C2×#41116yes—
442C3×D4—28no—
443C3×D4—24no—
444C3×D4—216no—
445C3×D4—212no—
446C3×D4—22no—
447C3×D4—48no—
448C3×D42−1+414yescomplemented
449C2×C3×C4—212no—
450C2×C3×C4—216no—
451C2×C3×C4—224no—
452C2×C3×C4—224no—
453C2×C3×C4—224no—
454C2×C3×C4—22no—
455C2×C3×C4—28no—
456C2×C3×C4—412no—
457C2×C3×C4—48no—
458C2×C3×C4—43no—
459C2×C3×C4C2×#41112yes—
460C2×C3×C4C2514yes—
461C2×C3×C4C2514yes—
462C2×C3×C4C2518yes—
463C2×C3×C4C2518yes—
464C2×C3×C4C2511yescharacteristic
465C2×C3×C4C2516yes—
466C2×C3×C4C25112yes—
467C2×C3×C4C2514yes—
468C2×C3×C4C2516yes—
469C2×C3×C4C2511yescharacteristic
470C24C24×C312yes—
471#41—216no—
472#41—216no—
473#41—224no—
474C2×Q8—232no—
475C2×Q8—232no—
476C2×Q8—216no—
477C2×Q8—224no—
478C2×Q8C3×#4118yescomplemented
479C2×Q8C24×C314yes—
480C2×Q8C24×C3124yes—
481C2×Q8C24×C316yes—
482C2×Q8C24×C3112yes—
483C2×Q8C24×C314yes—
484C2×D4—24no—
485C2×D4C24×C318yes—
486C2×D4C24×C312yes—
487C2×D4C24×C311yescharacteristic
488C2×D4C24×C314yes—
489C2×D4C24×C316yes—
490C2×D4C24×C318yes—
491C2×D4C24×C311yescharacteristic
492C22×C4—224no—
493C22×C4C24×C318yes—
494C22×C4C24×C311yescharacteristic
495C22×C4C24×C314yes—
496C22×C4C24×C3112yes—
497C22×C4C24×C3112yes—
498C22×C4C24×C316yes—
499C22×C4C24×C3112yes—
500C22×C4C24×C318yes—
501C22×C4C24×C313yes—
502C22×C4C24×C3112yes—
503C22×C4C24×C313yes—
504C4⋊C4C24×C316yes—
505C4⋊C4C24×C316yes—
506C4⋊C4C24×C3112yes—
507C4⋊C4C24×C3112yes—
508C4⋊C4C24×C316yes—
509C4⋊C4C24×C3112yes—
510C4⋊C4C24×C3112yes—
511C4⋊C4C24×C3124yes—
512C4⋊C4C24×C3124yes—
513C4⋊C4C24×C3124yes—
514C4⋊C4C24×C316yes—
515C4⋊C4C24×C314yes—
516C4⋊C4C24×C314yes—
517C4⋊C4C24×C3112yes—
518C4⋊C4C24×C3124yes—
519C4⋊C4C24×C3124yes—
520C4⋊C4C24×C3124yes—
521C4⋊C4C24×C318yes—
522C22⋊C4C24×C314yes—
523C22⋊C4C24×C318yes—
524C22⋊C4C24×C318yes—
525C22⋊C4C24×C318yes—
526C22⋊C4C24×C3112yes—
527C22⋊C4C24×C3112yes—
528C22⋊C4C24×C318yes—
529C22⋊C4C24×C314yes—
530C22⋊C4C24×C3112yes—
531C22⋊C4C24×C3124yes—
532C22⋊C4C24×C3124yes—
533C22⋊C4C24×C318yes—
534C42C24×C3112yes—
535C42C24×C316yes—
536C42C24×C314yes—
537C42C24×C3112yes—
538C42C24×C3124yes—
539C42C24×C3124yes—
540C42C24×C316yes—
541C42C24×C3124yes—
542C22×C3—22no—
543C22×C3—21no—
544C22×C3—22no—
545C22×C3—21no—
546C22×C3—22no—
547C22×C3—24no—
548C22×C3—24no—
549C22×C3—22no—
550C22×C3—24no—
551C22×C3—22no—
552C22×C3—48no—
553C22×C3C22×#4112yes—
554C22×C3C2×2−1+414yes—
555C22×C3C2611yescharacteristic
556C3×C4—24no—
557C3×C4—212no—
558C3×C4—24no—
559C3×C4—21no—
560C3×C4—28no—
561C3×C4—24no—
562C3×C4—26no—
563C3×C4—28no—
564C3×C4C22×#41112yes—
565C3×C4C2×2−1+412yes—
566C23—24no—
567C23—24no—
568C23—42no—
569C23C25×C312yes—
570C23C25×C314yes—
571C23C25×C311yescharacteristic
572C23C25×C312yes—
573Q8—248no—
574Q8—212no—
575Q8—28no—
576Q8—412no—
577Q8C2×C3×#41116yes—
578D4—28no—
579D4—24no—
580D4—216no—
581D4—212no—
582D4—22no—
583D4—48no—
584D4C3×2−1+414yescomplemented
585C2×C4—212no—
586C2×C4—216no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—22no—
591C2×C4—28no—
592C2×C4—412no—
593C2×C4—48no—
594C2×C4—43no—
595C2×C4C2×C3×#41112yes—
596C2×C4C25×C314yes—
597C2×C4C25×C314yes—
598C2×C4C25×C318yes—
599C2×C4C25×C318yes—
600C2×C4C25×C311yescharacteristic
601C2×C4C25×C316yes—
602C2×C4C25×C3112yes—
603C2×C4C25×C314yes—
604C2×C4C25×C316yes—
605C2×C4C25×C311yescharacteristic
606C2×C3—22no—
607C2×C3—24no—
608C2×C3—44no—
609C2×C3—42no—
610C2×C3C23×#4111yescharacteristic
611C2×C3C22×2−1+411yescharacteristic
612C2×C32−1+611yescharacteristic
613C22—22no—
614C22—21no—
615C22—22no—
616C22—21no—
617C22—22no—
618C22—24no—
619C22—24no—
620C22—22no—
621C22—24no—
622C22—22no—
623C22—48no—
624C22C22×C3×#4112yes—
625C22C2×C3×2−1+414yes—
626C22C26×C311yescharacteristic
627C4—24no—
628C4—212no—
629C4—24no—
630C4—21no—
631C4—28no—
632C4—24no—
633C4—26no—
634C4—28no—
635C4C22×C3×#41112yes—
636C4C2×C3×2−1+412yes—
637C3#6299811yescharacteristic, direct product factor, Sylow
638C2—22no—
639C2—24no—
640C2—42no—
641C2—44no—
642C2C23×C3×#4111yescharacteristic
643C2C22×C3×2−1+411yescharacteristic
644C2C3×2−1+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×#3523C2semidirect
3. C3×#3518C2semidirect
4. C3×#3516C2semidirect
5. C3×#3509C2semidirect
6. C3×#3502C2semidirect
7. C3×#3495C2semidirect
8. C3×#3486C2semidirect
9. C3×#3482C2semidirect
10. C3×Q8×#41C2semidirect
11. C3×#3475C2semidirect
12. C2×C3×D4×Q8C2semidirect
13. C3×C4×2−1+4C2semidirect
14. C2×C3×#519C2semidirect
15. #62998C3direct (N × H)
18. C3×Q82C22semidirect
19. C3×#557C22semidirect
20. C3×#557C22semidirect
21. C3×#557C22semidirect
22. C3×#557C22semidirect
24. C3×#556C22semidirect
25. C3×#556C22semidirect
26. C3×#556C22semidirect
29. C3×#554C22semidirect
34. C3×#552C22semidirect
35. C3×#552C22semidirect
40. C3×D4×Q8C22semidirect
41. C3×D4×Q8C22semidirect
42. C3×#548C22semidirect
43. C3×#548C22semidirect
47. C3×#542C22semidirect
48. C3×#541C22semidirect
49. C3×#541C22semidirect
52. C3×#533C22semidirect
53. C3×#533C22semidirect
54. C3×#533C22semidirect
58. C3×#529C22semidirect
62. C3×#520C22semidirect
66. C3×#519C22semidirect
67. C3×#519C22semidirect
68. C3×#519C22semidirect
71. C3×C4×#41C22semidirect
73. C2×C3×C4×Q8C22semidirect
74. C2×C3×C4×Q8C22semidirect
75. C2×C3×C4×Q8C22semidirect
78. #3523C2×C3semidirect
79. #3523C2×C3semidirect
80. #3518C2×C3semidirect
81. #3516C2×C3semidirect
82. #3509C2×C3semidirect
83. #3502C2×C3semidirect
84. #3495C2×C3semidirect
85. #3486C2×C3semidirect
86. #3482C2×C3semidirect
87. Q8×#41C2×C3semidirect
88. #3475C2×C3semidirect
89. C2×D4×Q8C2×C3semidirect
90. C4×2−1+4C2×C3semidirect
91. C2×#519C2×C3semidirect
196. Q82C22×C3semidirect
197. #557C22×C3semidirect
198. #557C22×C3semidirect
199. #557C22×C3semidirect
200. #557C22×C3semidirect
202. #556C22×C3semidirect
203. #556C22×C3semidirect
204. #556C22×C3semidirect
207. #554C22×C3semidirect
212. #552C22×C3semidirect
213. #552C22×C3semidirect
218. D4×Q8C22×C3semidirect
219. D4×Q8C22×C3semidirect
220. #548C22×C3semidirect
221. #548C22×C3semidirect
225. #542C22×C3semidirect
226. #541C22×C3semidirect
227. #541C22×C3semidirect
230. #533C22×C3semidirect
231. #533C22×C3semidirect
232. #533C22×C3semidirect
236. #529C22×C3semidirect
240. #520C22×C3semidirect
244. #519C22×C3semidirect
245. #519C22×C3semidirect
246. #519C22×C3semidirect
249. C4×#41C22×C3semidirect
251. C2×C4×Q8C22×C3semidirect
252. C2×C4×Q8C22×C3semidirect
253. C2×C4×Q8C22×C3semidirect
264. C2×C3×Q8#41semidirect
448. C3×D42−1+4semidirect
478. C2×Q8C3×#41semidirect
584. D4C3×2−1+4semidirect
637. C3#62998direct (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×#35182
C3×#35162
C3×#35092
C3×#35022
C3×#34952
C3×#34862
C3×#34822
C3×Q8×#412
C3×#34752
C2×C3×D4×Q82
C3×C4×2−1+42
C2×C3×#5192
#629983