Finite Group Databasebeta

← C3×#32968 #10651575

Subgroups — C3×#32968 #10651575

Order 768.

1274 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#520C211yesmaximal, characteristic
2C2×C3×#479C211yesmaximal, characteristic, complemented
3C2×C3×#478C211yesmaximal, characteristic, complemented
4C3×#2629C211yesmaximal, characteristic, complemented
5C3×#1865C211yesmaximal, characteristic, complemented
6C3×#1864C211yesmaximal, characteristic, complemented
7C3×#1863C211yesmaximal, characteristic, complemented
8C3×#1862C211yesmaximal, characteristic, complemented
9C3×#1853C211yesmaximal, characteristic, complemented
10C3×#1852C211yesmaximal, characteristic, complemented
11C3×#1803C211yesmaximal, characteristic, complemented
12C3×#1802C211yesmaximal, characteristic, complemented
13C3×#1798C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic
15C3×#1788C211yesmaximal, characteristic
16#32968C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C3×#520—24no—
20C3×#520—24no—
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×D4—21no—
24C2×C3×C4×D4—21no—
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×#117—21no—
28C2×C3×#117C2211yescharacteristic
29C22×C3×C4⋊C4—21no—
30C22×C3×C4⋊C4C2211yescharacteristic
31C3×#479—24no—
32C3×#478—24no—
33C2×C3×#107C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#398—21no—
50C3×#398—21no—
51C3×#396—21no—
52C3×#396—21no—
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#384C2211yescharacteristic
56C3×#380C2211yescharacteristic
57C3×#380C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#520C2×C311yescharacteristic
65C2×#479C2×C311yescharacteristic, complemented
66C2×#478C2×C311yescharacteristic, complemented
67#2629C2×C311yescharacteristic, complemented
68#1865C2×C311yescharacteristic, complemented
69#1864C2×C311yescharacteristic, complemented
70#1863C2×C311yescharacteristic, complemented
71#1862C2×C311yescharacteristic, complemented
72#1853C2×C311yescharacteristic, complemented
73#1852C2×C311yescharacteristic, complemented
74#1803C2×C311yescharacteristic, complemented
75#1802C2×C311yescharacteristic, complemented
76#1798C2×C311yescharacteristic, complemented
77#1788C2×C311yescharacteristic
78#1788C2×C311yescharacteristic
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41Q814yes—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×#125—22no—
98C3×#125—22no—
99C3×C4×Q8—22no—
100C3×C4×Q8—22no—
101C3×C4×Q8—22no—
102C3×C4×Q8D414yes—
103C3×C4×D4—28no—
104C3×C4×D4—28no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×C4×D4—22no—
108C3×C4×D4D414yes—
109C3×#117—28no—
110C3×#117—22no—
111C3×#117—22no—
112C2×C3×C4⋊C4—28no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4D411yescharacteristic
125C2×C3×C4⋊C4D411yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4D411yescharacteristic
137C2×C3×C22⋊C4D411yescharacteristic
138C2×C3×C42—21no—
139C2×C3×C42—21no—
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C3×#107—22no—
143C3×#107—22no—
144C3×#106—22no—
145C3×#106—22no—
146C3×C4⋊C8—22no—
147C3×C4⋊C8—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#103—22no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×C22⋊C8—22no—
157C3×C22⋊C8—22no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162C22×#41C22×C311yescharacteristic
163C2×#125C22×C311yescharacteristic
164#520—24no—
165#520—24no—
166C2×C4×Q8C22×C311yescharacteristic
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×D4—21no—
169C2×C4×D4—21no—
170C2×C4×D4C22×C311yescharacteristic
171C2×C4×D4C22×C311yescharacteristic
172C2×#117—21no—
173C2×#117C22×C311yescharacteristic
174C22×C4⋊C4—21no—
175C22×C4⋊C4C22×C311yescharacteristic
176#479—24no—
177#478—24no—
178C2×#107C22×C311yescharacteristic
179C2×#107C22×C311yescharacteristic
180C2×#106C22×C311yescharacteristic
181C2×#106C22×C311yescharacteristic
182C2×C4⋊C8C22×C311yescharacteristic
183C2×C4⋊C8C22×C311yescharacteristic
184C2×#103C22×C311yescharacteristic
185C2×#103C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#102C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×C22⋊C8C22×C311yescharacteristic
193C2×C22⋊C8C22×C311yescharacteristic
194#398—21no—
195#398—21no—
196#396—21no—
197#396—21no—
198#389C22×C311yescharacteristic
199#389C22×C311yescharacteristic
200#384C22×C311yescharacteristic
201#380C22×C311yescharacteristic
202#380C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#336C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209C24×C3—21no—
210C24×C3C2×D411yescharacteristic
211C3×#41—28no—
212C3×#41—28no—
213C3×#41—28no—
214C3×#41—28no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8C2×D412yes—
219C2×C3×Q8C2×Q812yes—
220C2×C3×Q8#4112yes—
221C2×C3×D4—24no—
222C2×C3×D4—24no—
223C2×C3×D4—24no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4C2×D412yes—
228C2×C3×D4C2×Q812yes—
229C2×C3×D4#4112yes—
230C22×C3×C4—24no—
231C22×C3×C4—24no—
232C22×C3×C4—21no—
233C22×C3×C4—24no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—24no—
241C22×C3×C4—24no—
242C22×C3×C4—24no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—81no—
248C22×C3×C4—81no—
249C22×C3×C4—81no—
250C22×C3×C4—81no—
251C22×C3×C4—81no—
252C22×C3×C4—81no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×Q812yes—
259C22×C3×C4#4112yes—
260C22×C3×C4C2411yescharacteristic
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—42no—
289C3×C4⋊C4—42no—
290C3×C4⋊C4—81no—
291C3×C4⋊C4—81no—
292C3×C4⋊C4—81no—
293C3×C4⋊C4—81no—
294C3×C4⋊C4C2×D412yes—
295C3×C4⋊C4C2×D412yes—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—81no—
301C3×C22⋊C4—81no—
302C3×C42—24no—
303C3×C42—24no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42C2×D412yes—
307C3×C42C2×D412yes—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41C3×Q814yes—
314C22×Q8C23×C311yescharacteristic
315C22×D4—21no—
316C22×D4C23×C311yescharacteristic
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C23×C311yescharacteristic
322C22×C8C23×C311yescharacteristic
323C22×C8C23×C311yescharacteristic
324C22×C8C23×C311yescharacteristic
325C22×C8C23×C311yescharacteristic
326#125—22no—
327#125—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8C3×D414yes—
332C4×D4—28no—
333C4×D4—28no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4C3×D414yes—
338#117—28no—
339#117—22no—
340#117—22no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4C3×D411yescharacteristic
354C2×C4⋊C4C3×D411yescharacteristic
355C2×C4⋊C4C23×C311yescharacteristic
356C2×C4⋊C4C23×C311yescharacteristic
357C2×C4⋊C4C23×C311yescharacteristic
358C2×C4⋊C4C23×C311yescharacteristic
359C2×C4⋊C4C23×C311yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4C3×D411yescharacteristic
366C2×C22⋊C4C3×D411yescharacteristic
367C2×C42—21no—
368C2×C42—21no—
369C2×C42C23×C311yescharacteristic
370C2×C42C23×C311yescharacteristic
371#107—22no—
372#107—22no—
373#106—22no—
374#106—22no—
375C4⋊C8—22no—
376C4⋊C8—22no—
377#103—22no—
378#103—22no—
379#103—22no—
380#103—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385C22⋊C8—22no—
386C22⋊C8—22no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391C23×C3—21no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—22no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3C22⋊Q812yes—
405C23×C3C22×D411yescharacteristic
406C3×Q8—22no—
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8C22⋊Q814yes—
410C3×D4—216no—
411C3×D4—22no—
412C3×D4—22no—
413C3×D4—22no—
414C3×D4C22⋊Q814yes—
415C2×C3×C4—216no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—84no—
454C2×C3×C4—84no—
455C2×C3×C4—84no—
456C2×C3×C4#12012yes—
457C2×C3×C4#12012yes—
458C2×C3×C4C22⋊Q812yes—
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×Q811yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C3×C8—41no—
466C3×C8—41no—
467C3×C8—41no—
468C3×C8—41no—
469C24—21no—
470C24C2×C3×D411yescharacteristic
471#41—28no—
472#41—28no—
473#41—28no—
474#41—28no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8C2×C3×D412yes—
479C2×Q8C2×C3×Q812yes—
480C2×Q8C3×#4112yes—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×C3×D412yes—
488C2×D4C2×C3×Q812yes—
489C2×D4C3×#4112yes—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4C2×C3×D411yescharacteristic
514C22×C4C2×C3×D411yescharacteristic
515C22×C4C2×C3×D411yescharacteristic
516C22×C4C2×C3×D411yescharacteristic
517C22×C4C2×C3×D411yescharacteristic
518C22×C4C2×C3×Q812yes—
519C22×C4C3×#4112yes—
520C22×C4C24×C311yescharacteristic
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—24no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4C2×C3×D412yes—
555C4⋊C4C2×C3×D412yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C42—24no—
563C42—24no—
564C42—21no—
565C42—21no—
566C42C2×C3×D412yes—
567C42C2×C3×D412yes—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—24no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—41no—
575C22×C3—42no—
576C22×C3—41no—
577C22×C3—42no—
578C22×C3—41no—
579C22×C3—42no—
580C22×C3—41no—
581C22×C3—42no—
582C22×C3C2×#12011yescharacteristic
583C22×C3C2×C22⋊Q811yescharacteristic
584C22×C3#52511yescharacteristic
585C22×C3#57611yescharacteristic
586C22×C3#57711yescharacteristic
587C22×C3#57711yescharacteristic
588C22×C3#57811yescharacteristic
589C3×C4—22no—
590C3×C4—24no—
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—41no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—41no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4—81no—
600C3×C4—81no—
601C3×C4C2×C22⋊Q811yescharacteristic
602C3×C4C2×C22⋊Q811yescharacteristic
603C3×C4#52511yescharacteristic
604C3×C4#52511yescharacteristic
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—22no—
611C23—22no—
612C23—21no—
613C23—22no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23C3×C22⋊Q812yes—
619C23C22×C3×D411yescharacteristic
620Q8—22no—
621Q8—22no—
622Q8—22no—
623Q8C3×C22⋊Q814yes—
624D4—216no—
625D4—22no—
626D4—22no—
627D4—22no—
628D4C3×C22⋊Q814yes—
629C2×C4—216no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4C3×#12012yes—
671C2×C4C3×#12012yes—
672C2×C4C3×C22⋊Q812yes—
673C2×C4C22×C3×D411yescharacteristic
674C2×C4C22×C3×D411yescharacteristic
675C2×C4C22×C3×Q811yescharacteristic
676C2×C4C2×C3×#4111yescharacteristic
677C2×C4C2×C3×#4111yescharacteristic
678C2×C4C2×C3×#4111yescharacteristic
679C8—41no—
680C8—41no—
681C8—41no—
682C8—41no—
683C2×C3—42no—
684C2×C3—44no—
685C2×C3#284811yescharacteristic
686C2×C3#301211yescharacteristic
687C2×C3#301311yescharacteristic
688C2×C3#308311yescharacteristic
689C2×C3#308411yescharacteristic
690C2×C3#311911yescharacteristic
691C2×C3#312011yescharacteristic
692C22—22no—
693C22—22no—
694C22—22no—
695C22—24no—
696C22—41no—
697C22—42no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—41no—
705C22—42no—
706C22C2×C3×#12011yescharacteristic
707C22C2×C3×C22⋊Q811yescharacteristic
708C22C3×#52511yescharacteristic
709C22C3×#57611yescharacteristic
710C22C3×#57711yescharacteristic
711C22C3×#57711yescharacteristic
712C22C3×#57811yescharacteristic
713C4—22no—
714C4—22no—
715C4—22no—
716C4—24no—
717C4—41no—
718C4—42no—
719C4—42no—
720C4—41no—
721C4—81no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4C2×C3×C22⋊Q811yescharacteristic
726C4C2×C3×C22⋊Q811yescharacteristic
727C4C3×#52511yescharacteristic
728C4C3×#52511yescharacteristic
729C3#3296811yescharacteristic, direct product factor, Sylow
730C2—42no—
731C2—44no—
732C2C3×#284811yescharacteristic
733C2C3×#301211yescharacteristic
734C2C3×#301311yescharacteristic
735C2C3×#308311yescharacteristic
736C2C3×#308411yescharacteristic
737C2C3×#311911yescharacteristic
738C2C3×#312011yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#479C2semidirect
3. C2×C3×#478C2semidirect
4. C3×#2629C2semidirect
5. C3×#1865C2semidirect
6. C3×#1864C2semidirect
7. C3×#1863C2semidirect
8. C3×#1862C2semidirect
9. C3×#1853C2semidirect
10. C3×#1852C2semidirect
11. C3×#1803C2semidirect
12. C3×#1802C2semidirect
13. C3×#1798C2semidirect
16. #32968C3direct (N × H)
65. C2×#479C2×C3semidirect
66. C2×#478C2×C3semidirect
67. #2629C2×C3semidirect
68. #1865C2×C3semidirect
69. #1864C2×C3semidirect
70. #1863C2×C3semidirect
71. #1862C2×C3semidirect
72. #1853C2×C3semidirect
73. #1852C2×C3semidirect
74. #1803C2×C3semidirect
75. #1802C2×C3semidirect
76. #1798C2×C3semidirect
729. C3#32968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5202
C2×C3×#4792
C2×C3×#4782
C3×#26292
C3×#18652
C3×#18642
C3×#18632
C3×#18622
C3×#18532
C3×#18522
C3×#18032
C3×#18022
C3×#17982
C3×#17882
#329683