Finite Group Databasebeta

← C3×#62943 #10681550

Subgroups — C3×#62943 #10681550

Order 768.

6458 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3555C216yesmaximal, complemented
2C3×#3555C216yesmaximal, complemented
3C3×#3552C2112yesmaximal, complemented
4C3×#3550C216yesmaximal, complemented
5C3×#3544C216yesmaximal, complemented
6C3×#3522C212yesmaximal, complemented
7C3×#3518C212yesmaximal, complemented
8C3×#3516C214yesmaximal, complemented
9C3×#3511C213yesmaximal, complemented
10C3×#3507C213yesmaximal, complemented
11C3×#3503C212yesmaximal, complemented
12C3×#3503C213yesmaximal, complemented
13C3×#3502C212yesmaximal, complemented
14C3×#3480C211yesmaximal, characteristic, complemented
15C3×Q8×#41C211yesmaximal, characteristic, complemented
16C2×C3×Q82C211yesmaximal, characteristic, complemented
17C3×#3461C213yesmaximal, complemented
18#62943C311yesmaximal, characteristic, direct product factor, Sylow
19C3×#563C22124yes—
20C3×#563C22124yes—
21C3×#559C2213yes—
22C3×#559C2216yes—
23C3×Q82C2212yes—
24C3×Q82C2212yes—
25C3×Q82C2216yes—
26C3×Q82C2216yes—
27C3×Q82C2211yescharacteristic
28C3×Q82C2216yes—
29C3×#557C2213yes—
30C3×#557C2211yescharacteristic
31C3×#557C2214yes—
32C3×#557C2216yes—
33C3×#557C22112yes—
34C3×#557C2216yes—
35C3×#556C2213yes—
36C3×#556C2216yes—
37C3×#556C22112yes—
38C3×#556C2216yes—
39C3×#556C22112yes—
40C3×#556C22112yes—
41C3×#555C2216yes—
42C3×#554C2213yes—
43C3×#554C2216yes—
44C3×#554C2216yes—
45C3×#554C2216yes—
46C3×#554C22112yes—
47C3×#554C2216yes—
48C3×#553C2216yes—
49C3×#553C22112yes—
50C3×#552C22112yes—
51C3×#552C22112yes—
52C3×#550C2211yescharacteristic
53C3×D4×Q8C2212yes—
54C3×D4×Q8C2211yescharacteristic
55C3×D4×Q8C2216yes—
56C3×D4×Q8C22112yes—
57C3×D4×Q8C22112yes—
58C3×#548C2212yes—
59C3×#548C22112yes—
60C3×#548C2214yes—
61C3×#547C2216yes—
62C3×#547C22112yes—
63C3×#544C2213yes—
64C3×#544C22112yes—
65C3×#544C22112yes—
66C3×#544C22112yes—
67C3×#542C2216yes—
68C3×#542C2216yes—
69C3×#542C22112yes—
70C3×#542C22112yes—
71C3×#542C22112yes—
72C3×#542C22112yes—
73C3×#541C2216yes—
74C3×#541C2216yes—
75C3×#541C22112yes—
76C3×#541C22124yes—
77C3×#539C22112yes—
78C3×#539C22112yes—
79C3×#537C2213yes—
80C3×#536C2211yescharacteristic
81C3×#536C2213yes—
82C3×#536C22124yes—
83C3×#533C2216yes—
84C3×#533C2216yes—
85C3×#533C2213yes—
86C3×#533C2216yes—
87C3×#533C2216yes—
88C3×#533C2216yes—
89C3×#532C2213yes—
90C3×#532C2216yes—
91C2×C3×C4⋊Q8C2213yes—
92C2×C3×C4⋊Q8C2216yes—
93C2×C3×C4⋊Q8C2216yes—
94C3×#529C22112yes—
95C3×#529C2216yes—
96C3×#529C2216yes—
97C3×#529C2216yes—
98C3×#529C22112yes—
99C3×#520C2216yes—
100C3×#520C2214yes—
101C3×#519C2214yes—
102C3×C4×#41C2213yes—
103C3×C4×#41C2213yes—
104C3×C4×#41C2212yes—
105C2×C3×C4×Q8C2213yes—
106C2×C3×C4×Q8C2211yescharacteristic
107C2×C3×C4×Q8C2212yes—
108C2×C3×C4×Q8C2212yes—
109#3555C2×C316yescomplemented
110#3555C2×C316yescomplemented
111#3552C2×C3112yescomplemented
112#3550C2×C316yescomplemented
113#3544C2×C316yescomplemented
114#3522C2×C312yescomplemented
115#3518C2×C312yescomplemented
116#3516C2×C314yescomplemented
117#3511C2×C313yescomplemented
118#3507C2×C313yescomplemented
119#3503C2×C313yescomplemented
120#3503C2×C312yescomplemented
121#3502C2×C312yescomplemented
122#3480C2×C311yescharacteristic, complemented
123Q8×#41C2×C311yescharacteristic, complemented
124C2×Q82C2×C311yescharacteristic, complemented
125#3461C2×C313yescomplemented
126C2×C3×#41C2311yescharacteristic
127C2×C3×#41C2313yes—
128C2×C3×#41C2312yes—
129C2×C3×#41C23112yes—
130C22×C3×Q8C2311yescharacteristic
131C22×C3×Q8C2311yescharacteristic
132C22×C3×Q8C2312yes—
133C22×C3×Q8C2316yes—
134C22×C3×Q8C23112yes—
135C3×C4⋊Q8C2316yes—
136C3×C4⋊Q8C23124yes—
137C3×C4⋊Q8C2316yes—
138C3×C4⋊Q8C2316yes—
139C3×C4⋊Q8C23112yes—
140C3×C4⋊Q8C23112yes—
141C3×C4⋊Q8C2316yes—
142C3×C4⋊Q8C2316yes—
143C3×C4⋊Q8C23124yes—
144C3×C4⋊Q8C2313yes—
145C3×C4⋊Q8C23112yes—
146C3×C4⋊Q8C2316yes—
147C3×C4⋊Q8C23112yes—
148C3×C4⋊Q8C2316yes—
149C3×C4⋊Q8C2313yes—
150C3×C4⋊Q8C2312yes—
151C3×C4⋊Q8C2313yes—
152C3×C4⋊Q8C2316yes—
153C3×C4⋊Q8C2316yes—
154C3×#127C2313yes—
155C3×#126C23112yes—
156C3×#126C23112yes—
157C3×#126C23112yes—
158C3×#126C23124yes—
159C3×#126C23112yes—
160C3×#126C23124yes—
161C3×#126C23124yes—
162C3×#126C23112yes—
163C3×#125C23112yes—
164C3×#125C23112yes—
165C3×#125C23124yes—
166C3×#125C23124yes—
167C3×#125C2316yes—
168C3×#125C23112yes—
169C3×#125C2316yes—
170C3×#125C23112yes—
171C3×#125C2316yes—
172C3×#125C23112yes—
173C3×#125C23112yes—
174C3×#125C2316yes—
175C3×#124C2316yes—
176C3×#124C2316yes—
177C3×#124C23112yes—
178C3×#124C2316yes—
179C3×#124C23112yes—
180C3×#124C23124yes—
181C3×#124C2312yes—
182C3×#124C23112yes—
183C3×#123C23112yes—
184C3×#123C23124yes—
185C3×#123C23112yes—
186C3×#123C23124yes—
187C3×#123C2314yes—
188C3×#123C23112yes—
189C3×#123C23112yes—
190C3×C22⋊Q8C23112yes—
191C3×C22⋊Q8C23112yes—
192C3×C22⋊Q8C23112yes—
193C3×C22⋊Q8C23112yes—
194C3×C22⋊Q8C23124yes—
195C3×C22⋊Q8C23124yes—
196C3×C22⋊Q8C23124yes—
197C3×C22⋊Q8C23124yes—
198C3×C22⋊Q8C2312yes—
199C3×C22⋊Q8C2316yes—
200C3×C22⋊Q8C2316yes—
201C3×C22⋊Q8C23112yes—
202C3×C22⋊Q8C2316yes—
203C3×C22⋊Q8C2312yes—
204C3×C22⋊Q8C2316yes—
205C3×C22⋊Q8C23112yes—
206C3×C22⋊Q8C2316yes—
207C3×C22⋊Q8C2316yes—
208C3×C22⋊Q8C2316yes—
209C3×C22⋊Q8C23112yes—
210C3×C22⋊Q8C2316yes—
211C3×C22⋊Q8C2316yes—
212C3×#121C2316yes—
213C3×#121C2316yes—
214C3×#121C23112yes—
215C3×#121C2316yes—
216C3×#121C2316yes—
217C3×#121C2316yes—
218C3×#121C23112yes—
219C3×C4×Q8C2311yescharacteristic
220C3×C4×Q8C2316yes—
221C3×C4×Q8C2313yes—
222C3×C4×Q8C2313yes—
223C3×C4×Q8C2311yescharacteristic
224C3×C4×Q8C2314yes—
225C3×C4×Q8C2313yes—
226C3×C4×Q8C2316yes—
227C3×C4×Q8C2316yes—
228C3×C4×Q8C23112yes—
229C3×C4×Q8C2316yes—
230C3×C4×Q8C2316yes—
231C3×C4×Q8C2312yes—
232C3×C4×Q8C2313yes—
233C3×C4×Q8C23112yes—
234C3×C4×Q8C23112yes—
235C3×C4×Q8C2316yes—
236C3×C4×Q8C2312yes—
237C3×C4×Q8C2313yes—
238C3×C4×Q8C2313yes—
239C3×C4×Q8C23112yes—
240C3×C4×Q8C23112yes—
241C3×C4×Q8C2316yes—
242C3×C4×Q8C23112yes—
243C3×C4×Q8C23112yes—
244C3×C4×D4C2313yes—
245C3×C4×D4C2316yes—
246C3×C4×D4C23112yes—
247C3×C4×D4C23112yes—
248C3×C4×D4C2316yes—
249C3×C4×D4C2316yes—
250C3×C4×D4C2313yes—
251C3×C4×D4C2313yes—
252C3×C4×D4C2316yes—
253C3×C4×D4C2316yes—
254C3×C4×D4C2316yes—
255C3×C4×D4C2313yes—
256C3×C4×D4C23124yes—
257C3×C4×D4C23112yes—
258C3×C4×D4C23112yes—
259C3×C4×D4C2316yes—
260C3×#117C2311yescharacteristic
261C3×#117C2313yes—
262C3×#117C2316yes—
263C3×#117C2316yes—
264C3×#117C2316yes—
265C3×#117C23112yes—
266C3×#117C23112yes—
267C3×#117C23112yes—
268C3×#117C23112yes—
269C3×#117C23124yes—
270C2×C3×C4⋊C4C2313yes—
271C2×C3×C4⋊C4C2316yes—
272C2×C3×C4⋊C4C2313yes—
273C2×C3×C4⋊C4C2316yes—
274C2×C3×C4⋊C4C2316yes—
275C2×C3×C4⋊C4C23112yes—
276C2×C3×C4⋊C4C23112yes—
277C2×C3×C42C2313yes—
278C2×C3×C42C2316yes—
279C2×C3×C42C2316yes—
280C2×C3×C42C2316yes—
281#563C22×C3124yes—
282#563C22×C3124yes—
283#559C22×C313yes—
284#559C22×C316yes—
285Q82C22×C312yes—
286Q82C22×C312yes—
287Q82C22×C316yes—
288Q82C22×C316yes—
289Q82C22×C311yescharacteristic
290Q82C22×C316yes—
291#557C22×C313yes—
292#557C22×C311yescharacteristic
293#557C22×C314yes—
294#557C22×C316yes—
295#557C22×C3112yes—
296#557C22×C316yes—
297#556C22×C313yes—
298#556C22×C316yes—
299#556C22×C3112yes—
300#556C22×C316yes—
301#556C22×C3112yes—
302#556C22×C3112yes—
303#555C22×C316yes—
304#554C22×C313yes—
305#554C22×C316yes—
306#554C22×C316yes—
307#554C22×C316yes—
308#554C22×C3112yes—
309#554C22×C316yes—
310#553C22×C316yes—
311#553C22×C3112yes—
312#552C22×C3112yes—
313#552C22×C3112yes—
314#550C22×C311yescharacteristic
315D4×Q8C22×C312yes—
316D4×Q8C22×C311yescharacteristic
317D4×Q8C22×C316yes—
318D4×Q8C22×C3112yes—
319D4×Q8C22×C3112yes—
320#548C22×C312yes—
321#548C22×C3112yes—
322#548C22×C314yes—
323#547C22×C316yes—
324#547C22×C3112yes—
325#544C22×C313yes—
326#544C22×C3112yes—
327#544C22×C3112yes—
328#544C22×C3112yes—
329#542C22×C316yes—
330#542C22×C316yes—
331#542C22×C3112yes—
332#542C22×C3112yes—
333#542C22×C3112yes—
334#542C22×C3112yes—
335#541C22×C316yes—
336#541C22×C316yes—
337#541C22×C3112yes—
338#541C22×C3124yes—
339#539C22×C3112yes—
340#539C22×C3112yes—
341#537C22×C313yes—
342#536C22×C311yescharacteristic
343#536C22×C313yes—
344#536C22×C3124yes—
345#533C22×C316yes—
346#533C22×C316yes—
347#533C22×C313yes—
348#533C22×C316yes—
349#533C22×C316yes—
350#533C22×C316yes—
351#532C22×C313yes—
352#532C22×C316yes—
353C2×C4⋊Q8C22×C313yes—
354C2×C4⋊Q8C22×C316yes—
355C2×C4⋊Q8C22×C316yes—
356#529C22×C3112yes—
357#529C22×C316yes—
358#529C22×C316yes—
359#529C22×C316yes—
360#529C22×C3112yes—
361#520C22×C316yes—
362#520C22×C314yes—
363#519C22×C314yes—
364C4×#41C22×C313yes—
365C4×#41C22×C313yes—
366C4×#41C22×C312yes—
367C2×C4×Q8C22×C313yes—
368C2×C4×Q8C22×C311yescharacteristic
369C2×C4×Q8C22×C312yes—
370C2×C4×Q8C22×C312yes—
371C3×#41—28no—
372C3×#41—24no—
373C3×#41—212no—
374C3×#41—812no—
375C2×C3×Q8—24no—
376C2×C3×Q8—28no—
377C2×C3×Q8—24no—
378C2×C3×Q8—86no—
379C2×C3×Q8—812no—
380C2×C3×Q8C2412yes—
381C2×C3×Q8C2411yescharacteristic
382C2×C3×Q8C2413yes—
383C2×C3×Q8C2416yes—
384C2×C3×Q8C2412yes—
385C2×C3×Q8C2413yes—
386C2×C3×Q8C2416yes—
387C2×C3×Q8C24112yes—
388C2×C3×Q8C24112yes—
389C2×C3×Q8C24112yes—
390C2×C3×Q8C2411yescharacteristic
391C2×C3×D4C2416yes—
392C2×C3×D4C2412yes—
393C2×C3×D4C2411yescharacteristic
394C2×C3×D4C2416yes—
395C2×C3×D4C2413yes—
396C2×C3×D4C24112yes—
397C2×C3×D4C2416yes—
398C22×C3×C4C2413yes—
399C22×C3×C4C2412yes—
400C22×C3×C4C2412yes—
401C22×C3×C4C2416yes—
402C22×C3×C4C2416yes—
403C22×C3×C4C2416yes—
404C22×C3×C4C2413yes—
405C22×C3×C4C2416yes—
406C22×C3×C4C2416yes—
407C22×C3×C4C2416yes—
408C22×C3×C4C24124yes—
409C22×C3×C4C2411yescharacteristic
410C3×C4⋊C4C2413yes—
411C3×C4⋊C4C2416yes—
412C3×C4⋊C4C2416yes—
413C3×C4⋊C4C2413yes—
414C3×C4⋊C4C24112yes—
415C3×C4⋊C4C24112yes—
416C3×C4⋊C4C2413yes—
417C3×C4⋊C4C2416yes—
418C3×C4⋊C4C24124yes—
419C3×C4⋊C4C24112yes—
420C3×C4⋊C4C24112yes—
421C3×C4⋊C4C2416yes—
422C3×C4⋊C4C24112yes—
423C3×C4⋊C4C24112yes—
424C3×C4⋊C4C2413yes—
425C3×C4⋊C4C2416yes—
426C3×C4⋊C4C2414yes—
427C3×C4⋊C4C24112yes—
428C3×C4⋊C4C24112yes—
429C3×C4⋊C4C2411yescharacteristic
430C3×C4⋊C4C2411yescharacteristic
431C3×C4⋊C4C2416yes—
432C3×C4⋊C4C2416yes—
433C3×C4⋊C4C2416yes—
434C3×C4⋊C4C2416yes—
435C3×C4⋊C4C24112yes—
436C3×C4⋊C4C24112yes—
437C3×C4⋊C4C2416yes—
438C3×C4⋊C4C24112yes—
439C3×C4⋊C4C24112yes—
440C3×C4⋊C4C2416yes—
441C3×C4⋊C4C2414yes—
442C3×C22⋊C4C24112yes—
443C3×C22⋊C4C2414yes—
444C3×C22⋊C4C24112yes—
445C3×C22⋊C4C24112yes—
446C3×C22⋊C4C2416yes—
447C3×C22⋊C4C2412yes—
448C3×C22⋊C4C2416yes—
449C3×C22⋊C4C24112yes—
450C3×C22⋊C4C24124yes—
451C3×C22⋊C4C24112yes—
452C3×C22⋊C4C2416yes—
453C3×C22⋊C4C24112yes—
454C3×C22⋊C4C2416yes—
455C3×C22⋊C4C2416yes—
456C3×C22⋊C4C2414yes—
457C3×C42C2412yes—
458C3×C42C2413yes—
459C3×C42C2413yes—
460C3×C42C2413yes—
461C3×C42C2416yes—
462C3×C42C24112yes—
463C3×C42C2416yes—
464C3×C42C2416yes—
465C3×C42C2413yes—
466C3×C42C2416yes—
467C3×C42C24112yes—
468C3×C42C2416yes—
469C3×C42C24124yes—
470C2×#41C23×C311yescharacteristic
471C2×#41C23×C313yes—
472C2×#41C23×C312yes—
473C2×#41C23×C3112yes—
474C22×Q8C23×C311yescharacteristic
475C22×Q8C23×C311yescharacteristic
476C22×Q8C23×C312yes—
477C22×Q8C23×C316yes—
478C22×Q8C23×C3112yes—
479C4⋊Q8C23×C316yes—
480C4⋊Q8C23×C313yes—
481C4⋊Q8C23×C316yes—
482C4⋊Q8C23×C316yes—
483C4⋊Q8C23×C3124yes—
484C4⋊Q8C23×C316yes—
485C4⋊Q8C23×C3112yes—
486C4⋊Q8C23×C3112yes—
487C4⋊Q8C23×C3112yes—
488C4⋊Q8C23×C316yes—
489C4⋊Q8C23×C3112yes—
490C4⋊Q8C23×C313yes—
491C4⋊Q8C23×C312yes—
492C4⋊Q8C23×C313yes—
493C4⋊Q8C23×C316yes—
494C4⋊Q8C23×C316yes—
495C4⋊Q8C23×C316yes—
496C4⋊Q8C23×C316yes—
497C4⋊Q8C23×C3124yes—
498#127C23×C313yes—
499#126C23×C3112yes—
500#126C23×C3112yes—
501#126C23×C3112yes—
502#126C23×C3112yes—
503#126C23×C3124yes—
504#126C23×C3112yes—
505#126C23×C3124yes—
506#126C23×C3124yes—
507#125C23×C316yes—
508#125C23×C3112yes—
509#125C23×C316yes—
510#125C23×C3112yes—
511#125C23×C316yes—
512#125C23×C3112yes—
513#125C23×C3112yes—
514#125C23×C3112yes—
515#125C23×C3112yes—
516#125C23×C316yes—
517#125C23×C3124yes—
518#125C23×C3124yes—
519#124C23×C312yes—
520#124C23×C3112yes—
521#124C23×C316yes—
522#124C23×C316yes—
523#124C23×C3112yes—
524#124C23×C3112yes—
525#124C23×C316yes—
526#124C23×C3124yes—
527#123C23×C314yes—
528#123C23×C3112yes—
529#123C23×C3112yes—
530#123C23×C3112yes—
531#123C23×C3112yes—
532#123C23×C3124yes—
533#123C23×C3124yes—
534C22⋊Q8C23×C312yes—
535C22⋊Q8C23×C316yes—
536C22⋊Q8C23×C316yes—
537C22⋊Q8C23×C3112yes—
538C22⋊Q8C23×C316yes—
539C22⋊Q8C23×C312yes—
540C22⋊Q8C23×C316yes—
541C22⋊Q8C23×C3112yes—
542C22⋊Q8C23×C3112yes—
543C22⋊Q8C23×C316yes—
544C22⋊Q8C23×C316yes—
545C22⋊Q8C23×C316yes—
546C22⋊Q8C23×C3112yes—
547C22⋊Q8C23×C3112yes—
548C22⋊Q8C23×C3112yes—
549C22⋊Q8C23×C316yes—
550C22⋊Q8C23×C316yes—
551C22⋊Q8C23×C3112yes—
552C22⋊Q8C23×C3124yes—
553C22⋊Q8C23×C3124yes—
554C22⋊Q8C23×C3124yes—
555C22⋊Q8C23×C3124yes—
556#121C23×C316yes—
557#121C23×C316yes—
558#121C23×C3112yes—
559#121C23×C316yes—
560#121C23×C316yes—
561#121C23×C316yes—
562#121C23×C3112yes—
563C4×Q8C23×C311yescharacteristic
564C4×Q8C23×C311yescharacteristic
565C4×Q8C23×C314yes—
566C4×Q8C23×C312yes—
567C4×Q8C23×C313yes—
568C4×Q8C23×C316yes—
569C4×Q8C23×C316yes—
570C4×Q8C23×C316yes—
571C4×Q8C23×C313yes—
572C4×Q8C23×C316yes—
573C4×Q8C23×C3112yes—
574C4×Q8C23×C316yes—
575C4×Q8C23×C316yes—
576C4×Q8C23×C312yes—
577C4×Q8C23×C313yes—
578C4×Q8C23×C313yes—
579C4×Q8C23×C313yes—
580C4×Q8C23×C313yes—
581C4×Q8C23×C3112yes—
582C4×Q8C23×C3112yes—
583C4×Q8C23×C3112yes—
584C4×Q8C23×C3112yes—
585C4×Q8C23×C316yes—
586C4×Q8C23×C3112yes—
587C4×Q8C23×C3112yes—
588C4×D4C23×C316yes—
589C4×D4C23×C316yes—
590C4×D4C23×C313yes—
591C4×D4C23×C313yes—
592C4×D4C23×C316yes—
593C4×D4C23×C316yes—
594C4×D4C23×C316yes—
595C4×D4C23×C313yes—
596C4×D4C23×C316yes—
597C4×D4C23×C313yes—
598C4×D4C23×C3124yes—
599C4×D4C23×C3112yes—
600C4×D4C23×C3112yes—
601C4×D4C23×C3112yes—
602C4×D4C23×C3112yes—
603C4×D4C23×C316yes—
604#117C23×C311yescharacteristic
605#117C23×C313yes—
606#117C23×C316yes—
607#117C23×C316yes—
608#117C23×C316yes—
609#117C23×C3112yes—
610#117C23×C3112yes—
611#117C23×C3112yes—
612#117C23×C3112yes—
613#117C23×C3124yes—
614C2×C4⋊C4C23×C313yes—
615C2×C4⋊C4C23×C316yes—
616C2×C4⋊C4C23×C313yes—
617C2×C4⋊C4C23×C316yes—
618C2×C4⋊C4C23×C316yes—
619C2×C4⋊C4C23×C3112yes—
620C2×C4⋊C4C23×C3112yes—
621C2×C42C23×C313yes—
622C2×C42C23×C316yes—
623C2×C42C23×C316yes—
624C2×C42C23×C316yes—
625C23×C3C2512yes—
626C23×C3C2516yes—
627C23×C3C2511yescharacteristic
628C3×Q8—24no—
629C3×Q8—26no—
630C3×Q8—212no—
631C3×Q8—24no—
632C3×Q8—22no—
633C3×Q8—26no—
634C3×Q8—46no—
635C3×Q8—412no—
636C3×Q8—412no—
637C3×Q8—412no—
638C3×Q82−1+414yes—
639C3×D4—212no—
640C3×D4—24no—
641C3×D4—22no—
642C3×D4—212no—
643C3×D4—26no—
644C3×D4—46no—
645C3×D4—412no—
646C2×C3×C4—24no—
647C2×C3×C4—26no—
648C2×C3×C4—212no—
649C2×C3×C4—212no—
650C2×C3×C4—212no—
651C2×C3×C4—24no—
652C2×C3×C4—43no—
653C2×C3×C4—46no—
654C2×C3×C4—46no—
655C2×C3×C4—424no—
656C2×C3×C4—46no—
657C2×C3×C42−1+414yes—
658C2×C3×C4C2513yes—
659C2×C3×C4C2514yes—
660C2×C3×C4C2516yes—
661C2×C3×C4C2512yes—
662C2×C3×C4C2516yes—
663C2×C3×C4C2512yes—
664C2×C3×C4C2512yes—
665C2×C3×C4C2513yes—
666C2×C3×C4C25112yes—
667C2×C3×C4C2513yes—
668C2×C3×C4C2516yes—
669C2×C3×C4C2511yescharacteristic
670C2×C3×C4C2513yes—
671C2×C3×C4C2511yescharacteristic
672#41—28no—
673#41—24no—
674#41—212no—
675#41—812no—
676C2×Q8—24no—
677C2×Q8—28no—
678C2×Q8—24no—
679C2×Q8—86no—
680C2×Q8—812no—
681C2×Q8C24×C312yes—
682C2×Q8C24×C311yescharacteristic
683C2×Q8C24×C313yes—
684C2×Q8C24×C316yes—
685C2×Q8C24×C312yes—
686C2×Q8C24×C313yes—
687C2×Q8C24×C316yes—
688C2×Q8C24×C3112yes—
689C2×Q8C24×C3112yes—
690C2×Q8C24×C3112yes—
691C2×Q8C24×C311yescharacteristic
692C2×D4C24×C316yes—
693C2×D4C24×C312yes—
694C2×D4C24×C311yescharacteristic
695C2×D4C24×C316yes—
696C2×D4C24×C313yes—
697C2×D4C24×C3112yes—
698C2×D4C24×C316yes—
699C22×C4C24×C313yes—
700C22×C4C24×C312yes—
701C22×C4C24×C312yes—
702C22×C4C24×C316yes—
703C22×C4C24×C316yes—
704C22×C4C24×C316yes—
705C22×C4C24×C313yes—
706C22×C4C24×C316yes—
707C22×C4C24×C316yes—
708C22×C4C24×C316yes—
709C22×C4C24×C3124yes—
710C22×C4C24×C311yescharacteristic
711C4⋊C4C24×C313yes—
712C4⋊C4C24×C316yes—
713C4⋊C4C24×C316yes—
714C4⋊C4C24×C313yes—
715C4⋊C4C24×C3112yes—
716C4⋊C4C24×C3112yes—
717C4⋊C4C24×C313yes—
718C4⋊C4C24×C316yes—
719C4⋊C4C24×C3124yes—
720C4⋊C4C24×C3112yes—
721C4⋊C4C24×C3112yes—
722C4⋊C4C24×C316yes—
723C4⋊C4C24×C3112yes—
724C4⋊C4C24×C3112yes—
725C4⋊C4C24×C313yes—
726C4⋊C4C24×C316yes—
727C4⋊C4C24×C314yes—
728C4⋊C4C24×C3112yes—
729C4⋊C4C24×C3112yes—
730C4⋊C4C24×C311yescharacteristic
731C4⋊C4C24×C311yescharacteristic
732C4⋊C4C24×C316yes—
733C4⋊C4C24×C316yes—
734C4⋊C4C24×C316yes—
735C4⋊C4C24×C316yes—
736C4⋊C4C24×C3112yes—
737C4⋊C4C24×C3112yes—
738C4⋊C4C24×C316yes—
739C4⋊C4C24×C3112yes—
740C4⋊C4C24×C3112yes—
741C4⋊C4C24×C316yes—
742C4⋊C4C24×C314yes—
743C22⋊C4C24×C3112yes—
744C22⋊C4C24×C314yes—
745C22⋊C4C24×C3112yes—
746C22⋊C4C24×C3112yes—
747C22⋊C4C24×C316yes—
748C22⋊C4C24×C312yes—
749C22⋊C4C24×C316yes—
750C22⋊C4C24×C3112yes—
751C22⋊C4C24×C3124yes—
752C22⋊C4C24×C3112yes—
753C22⋊C4C24×C316yes—
754C22⋊C4C24×C3112yes—
755C22⋊C4C24×C316yes—
756C22⋊C4C24×C316yes—
757C22⋊C4C24×C314yes—
758C42C24×C312yes—
759C42C24×C313yes—
760C42C24×C313yes—
761C42C24×C313yes—
762C42C24×C316yes—
763C42C24×C3112yes—
764C42C24×C316yes—
765C42C24×C316yes—
766C42C24×C313yes—
767C42C24×C316yes—
768C42C24×C3112yes—
769C42C24×C316yes—
770C42C24×C3124yes—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—26no—
776C22×C3—26no—
777C22×C3—26no—
778C22×C3—22no—
779C22×C3C2×2−1+412yes—
780C22×C3C2611yescharacteristic
781C3×C4—22no—
782C3×C4—26no—
783C3×C4—22no—
784C3×C4—24no—
785C3×C4—23no—
786C3×C4—26no—
787C3×C4—26no—
788C3×C4—23no—
789C3×C4—212no—
790C3×C4—23no—
791C3×C4—22no—
792C3×C4C2×2−1+412yes—
793C3×C4C2×2−1+416yes—
794C3×C4C2×2−1+412yes—
795C23C25×C312yes—
796C23C25×C316yes—
797C23C25×C311yescharacteristic
798Q8—24no—
799Q8—26no—
800Q8—212no—
801Q8—24no—
802Q8—22no—
803Q8—26no—
804Q8—46no—
805Q8—412no—
806Q8—412no—
807Q8—412no—
808Q8C3×2−1+414yes—
809D4—212no—
810D4—24no—
811D4—22no—
812D4—212no—
813D4—26no—
814D4—46no—
815D4—412no—
816C2×C4—24no—
817C2×C4—26no—
818C2×C4—212no—
819C2×C4—212no—
820C2×C4—212no—
821C2×C4—24no—
822C2×C4—43no—
823C2×C4—46no—
824C2×C4—46no—
825C2×C4—424no—
826C2×C4—46no—
827C2×C4C3×2−1+414yes—
828C2×C4C25×C313yes—
829C2×C4C25×C314yes—
830C2×C4C25×C316yes—
831C2×C4C25×C312yes—
832C2×C4C25×C316yes—
833C2×C4C25×C312yes—
834C2×C4C25×C312yes—
835C2×C4C25×C313yes—
836C2×C4C25×C3112yes—
837C2×C4C25×C313yes—
838C2×C4C25×C316yes—
839C2×C4C25×C311yescharacteristic
840C2×C4C25×C313yes—
841C2×C4C25×C311yescharacteristic
842C2×C3—22no—
843C2×C3—42no—
844C2×C3—46no—
845C2×C3C22×2−1+411yescharacteristic
846C2×C3C22×2−1+411yescharacteristic
847C2×C3H(7,𝔽2)11yescharacteristic
848C22—21no—
849C22—21no—
850C22—22no—
851C22—22no—
852C22—26no—
853C22—26no—
854C22—26no—
855C22—22no—
856C22C2×C3×2−1+412yes—
857C22C26×C311yescharacteristic
858C4—22no—
859C4—26no—
860C4—22no—
861C4—24no—
862C4—23no—
863C4—26no—
864C4—26no—
865C4—23no—
866C4—212no—
867C4—23no—
868C4—22no—
869C4C2×C3×2−1+412yes—
870C4C2×C3×2−1+416yes—
871C4C2×C3×2−1+412yes—
872C3#6294311yescharacteristic, direct product factor, Sylow
873C2—22no—
874C2—42no—
875C2—46no—
876C2C22×C3×2−1+411yescharacteristic
877C2C22×C3×2−1+411yescharacteristic
878C2C3×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×#3555C2semidirect
2. C3×#3555C2semidirect
3. C3×#3552C2semidirect
4. C3×#3550C2semidirect
5. C3×#3544C2semidirect
6. C3×#3522C2semidirect
7. C3×#3518C2semidirect
8. C3×#3516C2semidirect
9. C3×#3511C2semidirect
10. C3×#3507C2semidirect
11. C3×#3503C2semidirect
12. C3×#3503C2semidirect
13. C3×#3502C2semidirect
14. C3×#3480C2semidirect
15. C3×Q8×#41C2semidirect
16. C2×C3×Q82C2semidirect
17. C3×#3461C2semidirect
18. #62943C3direct (N × H)
109. #3555C2×C3semidirect
110. #3555C2×C3semidirect
111. #3552C2×C3semidirect
112. #3550C2×C3semidirect
113. #3544C2×C3semidirect
114. #3522C2×C3semidirect
115. #3518C2×C3semidirect
116. #3516C2×C3semidirect
117. #3511C2×C3semidirect
118. #3507C2×C3semidirect
119. #3503C2×C3semidirect
120. #3503C2×C3semidirect
121. #3502C2×C3semidirect
122. #3480C2×C3semidirect
123. Q8×#41C2×C3semidirect
124. C2×Q82C2×C3semidirect
125. #3461C2×C3semidirect
872. C3#62943direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35552
C3×#35522
C3×#35502
C3×#35442
C3×#35222
C3×#35182
C3×#35162
C3×#35112
C3×#35072
C3×#35032
C3×#35022
C3×#34802
C3×Q8×#412
C2×C3×Q822
C3×#34612
#629433