Finite Group Databasebeta

← C3×#21397 #10640004

Subgroups — C3×#21397 #10640004

Order 768.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#542C211yesmaximal, characteristic
2C2×C3×#433C211yesmaximal, characteristic, complemented
3C3×#2274C211yesmaximal, characteristic, complemented
4C3×#1988C211yesmaximal, characteristic, complemented
5C3×#1987C211yesmaximal, characteristic, complemented
6C3×#1983C211yesmaximal, characteristic, complemented
7C3×#1983C211yesmaximal, characteristic, complemented
8C3×#1875C211yesmaximal, characteristic
9C3×#1874C211yesmaximal, characteristic
10C3×#1873C211yesmaximal, characteristic, complemented
11C3×#1872C211yesmaximal, characteristic, complemented
12C3×#1763C211yesmaximal, characteristic, complemented
13C3×#1762C211yesmaximal, characteristic, complemented
14C3×C4×#103C211yesmaximal, characteristic, complemented
15C3×C4×#102C211yesmaximal, characteristic, complemented
16#21397C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#542—24no—
18C3×#542C418yescomplemented
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#126—21no—
21C2×C3×#124—21no—
22C2×C3×#124C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C2×C3×#117C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C3×#433—24no—
33C2×C3×C4⋊C8C2211yescharacteristic
34C2×C3×C4⋊C8C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×C22⋊C8C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×#97C2211yescharacteristic
46C2×C3×C4×C8C2211yescharacteristic
47C3×C4×C4⋊C4—21no—
48C3×C4×C4⋊C4—21no—
49C3×C4×C4⋊C4C2211yescharacteristic
50C3×C4×C4⋊C4C2211yescharacteristic
51C3×C4×C4⋊C4C2211yescharacteristic
52C3×C4×C4⋊C4C2211yescharacteristic
53C3×C4×C22⋊C4—21no—
54C3×C4×C22⋊C4—21no—
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C2×#542C2×C311yescharacteristic
64C2×#433C2×C311yescharacteristic, complemented
65#2274C2×C311yescharacteristic, complemented
66#1988C2×C311yescharacteristic, complemented
67#1987C2×C311yescharacteristic, complemented
68#1983C2×C311yescharacteristic, complemented
69#1983C2×C311yescharacteristic, complemented
70#1875C2×C311yescharacteristic
71#1874C2×C311yescharacteristic
72#1873C2×C311yescharacteristic, complemented
73#1872C2×C311yescharacteristic, complemented
74#1763C2×C311yescharacteristic, complemented
75#1762C2×C311yescharacteristic, complemented
76C4×#103C2×C311yescharacteristic, complemented
77C4×#102C2×C311yescharacteristic, complemented
78C22×C3×Q8—21no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×C4⋊Q8—22no—
90C3×C4⋊Q8C2×C414yescomplemented
91C3×#126—28no—
92C3×#124—28no—
93C3×#124—22no—
94C3×#124C2×C414yescomplemented
95C3×#123—28no—
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—28no—
98C3×C22⋊Q8C2×C414yes—
99C3×#121—22no—
100C3×#121C2×C414yes—
101C3×C4×Q8—22no—
102C3×C4×Q8C2×C414yescomplemented
103C3×C4×D4—22no—
104C3×C4×D4C2×C414yescomplemented
105C3×#117—22no—
106C3×#117—22no—
107C3×#117C2×C414yes—
108C3×#117D414yes—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4D411yescharacteristic
116C2×C3×C4⋊C4D411yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4D411yescharacteristic
130C2×C3×C22⋊C4D411yescharacteristic
131C2×C3×C42—21no—
132C2×C3×C42—21no—
133C2×C3×C42—21no—
134C2×C3×C42—21no—
135C2×C3×C42—21no—
136C2×C3×C42—21no—
137C2×C3×C42C2311yescharacteristic
138C2×C3×C42C2311yescharacteristic
139C3×C4⋊C8—22no—
140C3×C4⋊C8—22no—
141C3×#103—22no—
142C3×#103—22no—
143C3×#103—22no—
144C3×#103—22no—
145C3×#102—22no—
146C3×#102—22no—
147C3×#102—22no—
148C3×#102—22no—
149C3×C22⋊C8—22no—
150C3×C22⋊C8—22no—
151C3×#97—22no—
152C3×C4×C8—22no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157#542—24no—
158#542C3×C418yescomplemented
159C2×C4⋊Q8C22×C311yescharacteristic
160C2×#126—21no—
161C2×#124—21no—
162C2×#124C22×C311yescharacteristic
163C2×#123—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×#121C22×C311yescharacteristic
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×D4C22×C311yescharacteristic
169C2×#117C22×C311yescharacteristic
170C2×#117C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172#433—24no—
173C2×C4⋊C8C22×C311yescharacteristic
174C2×C4⋊C8C22×C311yescharacteristic
175C2×#103C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×C22⋊C8C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185C2×#97C22×C311yescharacteristic
186C2×C4×C8C22×C311yescharacteristic
187C4×C4⋊C4—21no—
188C4×C4⋊C4—21no—
189C4×C4⋊C4C22×C311yescharacteristic
190C4×C4⋊C4C22×C311yescharacteristic
191C4×C4⋊C4C22×C311yescharacteristic
192C4×C4⋊C4C22×C311yescharacteristic
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203C24×C3—21no—
204C24×C3C2×D411yescharacteristic
205C2×C3×Q8—24no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—81no—
212C2×C3×Q8—81no—
213C2×C3×Q8C22×C412yes—
214C2×C3×D4—24no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—81no—
221C2×C3×D4—81no—
222C2×C3×D4C22×C412yes—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—24no—
235C22×C3×C4—24no—
236C22×C3×C4—81no—
237C22×C3×C4—81no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4C22×C412yes—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2411yescharacteristic
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4C22⋊C414yes—
271C3×C4⋊C4C22⋊C414yes—
272C3×C4⋊C4C22×C412yes—
273C3×C4⋊C4C22×C412yes—
274C3×C4⋊C4#4112yes—
275C3×C4⋊C4#4112yes—
276C3×C4⋊C4#4112yes—
277C3×C4⋊C4#4112yes—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4C22⋊C414yes—
285C3×C22⋊C4C22⋊C414yes—
286C3×C42—24no—
287C3×C42—24no—
288C3×C42—81no—
289C3×C42—81no—
290C3×C42—81no—
291C3×C42—81no—
292C3×C42C22×C412yes—
293C3×C42C22×C412yes—
294C3×C42C2×D412yes—
295C3×C42C2×D412yes—
296C22×Q8—21no—
297C22×Q8C23×C311yescharacteristic
298C22×D4—21no—
299C22×D4C23×C311yescharacteristic
300C23×C4—21no—
301C23×C4—21no—
302C23×C4C23×C311yescharacteristic
303C22×C8C23×C311yescharacteristic
304C22×C8C23×C311yescharacteristic
305C22×C8C23×C311yescharacteristic
306C22×C8C23×C311yescharacteristic
307C4⋊Q8—22no—
308C4⋊Q8C2×C3×C414yescomplemented
309#126—28no—
310#124—28no—
311#124—22no—
312#124C2×C3×C414yescomplemented
313#123—28no—
314C22⋊Q8—22no—
315C22⋊Q8—28no—
316C22⋊Q8C2×C3×C414yes—
317#121—22no—
318#121C2×C3×C414yes—
319C4×Q8—22no—
320C4×Q8C2×C3×C414yescomplemented
321C4×D4—22no—
322C4×D4C2×C3×C414yescomplemented
323#117—22no—
324#117—22no—
325#117C2×C3×C414yes—
326#117C3×D414yes—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4C3×D411yescharacteristic
334C2×C4⋊C4C3×D411yescharacteristic
335C2×C4⋊C4C23×C311yescharacteristic
336C2×C4⋊C4C23×C311yescharacteristic
337C2×C4⋊C4C23×C311yescharacteristic
338C2×C4⋊C4C23×C311yescharacteristic
339C2×C4⋊C4C23×C311yescharacteristic
340C2×C4⋊C4C23×C311yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4C3×D411yescharacteristic
348C2×C22⋊C4C3×D411yescharacteristic
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42C23×C311yescharacteristic
356C2×C42C23×C311yescharacteristic
357C4⋊C8—22no—
358C4⋊C8—22no—
359#103—22no—
360#103—22no—
361#103—22no—
362#103—22no—
363#102—22no—
364#102—22no—
365#102—22no—
366#102—22no—
367C22⋊C8—22no—
368C22⋊C8—22no—
369#97—22no—
370C4×C8—22no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—22no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3C2×C22⋊C412yes—
389C23×C3C22×D411yescharacteristic
390C3×Q8—22no—
391C3×Q8—22no—
392C3×Q8—41no—
393C3×Q8—41no—
394C3×Q8—84no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—41no—
398C3×D4—41no—
399C3×D4—84no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—84no—
436C2×C3×C4—84no—
437C2×C3×C4C2×C22⋊C412yes—
438C2×C3×C4C2×C22⋊C412yes—
439C2×C3×C4C2×C22⋊C412yes—
440C2×C3×C4C2×C22⋊C412yes—
441C2×C3×C4C2×C22⋊C412yes—
442C2×C3×C4C23×C411yescharacteristic
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C3×C8—41no—
449C3×C8—41no—
450C3×C8—41no—
451C3×C8—41no—
452C24—21no—
453C24C2×C3×D411yescharacteristic
454C2×Q8—24no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—81no—
461C2×Q8—81no—
462C2×Q8C22×C3×C412yes—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—81no—
470C2×D4—81no—
471C2×D4C22×C3×C412yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4C22×C3×C412yes—
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C2×C3×D411yescharacteristic
494C22×C4C2×C3×D411yescharacteristic
495C22×C4C2×C3×D412yes—
496C22×C4C24×C311yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4C3×C22⋊C414yes—
520C4⋊C4C3×C22⋊C414yes—
521C4⋊C4C22×C3×C412yes—
522C4⋊C4C22×C3×C412yes—
523C4⋊C4C3×#4112yes—
524C4⋊C4C3×#4112yes—
525C4⋊C4C3×#4112yes—
526C4⋊C4C3×#4112yes—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4C3×C22⋊C414yes—
534C22⋊C4C3×C22⋊C414yes—
535C42—24no—
536C42—24no—
537C42—81no—
538C42—81no—
539C42—81no—
540C42—81no—
541C42C22×C3×C412yes—
542C42C22×C3×C412yes—
543C42C2×C3×D412yes—
544C42C2×C3×D412yes—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—81no—
556C22×C3—81no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3C22×C22⋊C411yescharacteristic
560C22×C3#52511yescharacteristic
561C22×C3#52511yescharacteristic
562C22×C3#57611yescharacteristic
563C22×C3#57711yescharacteristic
564C22×C3#57711yescharacteristic
565C22×C3#57811yescharacteristic
566C3×C4—22no—
567C3×C4—22no—
568C3×C4—22no—
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—42no—
572C3×C4—42no—
573C3×C4—42no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—42no—
577C3×C4—42no—
578C3×C4C4×#4111yescharacteristic
579C3×C4C4×#4111yescharacteristic
580C3×C4#53211yescharacteristic
581C3×C4#53211yescharacteristic
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—22no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C2×C3×C22⋊C412yes—
596C23C22×C3×D411yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601Q8—84no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—84no—
643C2×C4—84no—
644C2×C4C2×C3×C22⋊C412yes—
645C2×C4C2×C3×C22⋊C412yes—
646C2×C4C2×C3×C22⋊C412yes—
647C2×C4C2×C3×C22⋊C412yes—
648C2×C4C2×C3×C22⋊C412yes—
649C2×C4C23×C3×C411yescharacteristic
650C2×C4C22×C3×D411yescharacteristic
651C2×C4C2×C3×#4111yescharacteristic
652C2×C4C2×C3×#4111yescharacteristic
653C2×C4C2×C3×#4111yescharacteristic
654C2×C4C2×C3×#4111yescharacteristic
655C8—41no—
656C8—41no—
657C8—41no—
658C8—41no—
659C2×C3—42no—
660C2×C3—82no—
661C2×C3#229711yescharacteristic
662C2×C3#289711yescharacteristic
663C2×C3#289811yescharacteristic
664C2×C3#311811yescharacteristic
665C2×C3#312111yescharacteristic
666C2×C3#312411yescharacteristic
667C2×C3#312511yescharacteristic
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22C22×C3×C22⋊C411yescharacteristic
683C22C3×#52511yescharacteristic
684C22C3×#52511yescharacteristic
685C22C3×#57611yescharacteristic
686C22C3×#57711yescharacteristic
687C22C3×#57711yescharacteristic
688C22C3×#57811yescharacteristic
689C4—22no—
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4C3×C4×#4111yescharacteristic
702C4C3×C4×#4111yescharacteristic
703C4C3×#53211yescharacteristic
704C4C3×#53211yescharacteristic
705C3#2139711yescharacteristic, direct product factor, Sylow
706C2—42no—
707C2—82no—
708C2C3×#229711yescharacteristic
709C2C3×#289711yescharacteristic
710C2C3×#289811yescharacteristic
711C2C3×#311811yescharacteristic
712C2C3×#312111yescharacteristic
713C2C3×#312411yescharacteristic
714C2C3×#312511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C2×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×#433C2semidirect
3. C3×#2274C2semidirect
4. C3×#1988C2semidirect
5. C3×#1987C2semidirect
6. C3×#1983C2semidirect
7. C3×#1983C2semidirect
10. C3×#1873C2semidirect
11. C3×#1872C2semidirect
12. C3×#1763C2semidirect
13. C3×#1762C2semidirect
14. C3×C4×#103C2semidirect
15. C3×C4×#102C2semidirect
16. #21397C3direct (N × H)
18. C3×#542C4semidirect
64. C2×#433C2×C3semidirect
65. #2274C2×C3semidirect
66. #1988C2×C3semidirect
67. #1987C2×C3semidirect
68. #1983C2×C3semidirect
69. #1983C2×C3semidirect
72. #1873C2×C3semidirect
73. #1872C2×C3semidirect
74. #1763C2×C3semidirect
75. #1762C2×C3semidirect
76. C4×#103C2×C3semidirect
77. C4×#102C2×C3semidirect
90. C3×C4⋊Q8C2×C4semidirect
94. C3×#124C2×C4semidirect
102. C3×C4×Q8C2×C4semidirect
104. C3×C4×D4C2×C4semidirect
158. #542C3×C4semidirect
308. C4⋊Q8C2×C3×C4semidirect
312. #124C2×C3×C4semidirect
320. C4×Q8C2×C3×C4semidirect
322. C4×D4C2×C3×C4semidirect
705. C3#21397direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×C3×#4332
C3×#22742
C3×#19882
C3×#19872
C3×#19832
C3×#18752
C3×#18742
C3×#18732
C3×#18722
C3×#17632
C3×#17622
C3×C4×#1032
C3×C4×#1022
#213973