Finite Group Databasebeta

← #10801349

Subgroups — #10801349

Order 768.

1044 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2392C211yesmaximal, characteristic
2C2×#5012C211yesmaximal, characteristic, complemented
3C2×#5011C211yesmaximal, characteristic, complemented
4C2×#5011C211yesmaximal, characteristic, complemented
5C2×#4997C211yesmaximal, characteristic, complemented
6#71614C211yesmaximal, characteristic, complemented
7#71610C211yesmaximal, characteristic, complemented
8#71610C211yesmaximal, characteristic, complemented
9#71583C211yesmaximal, characteristic, complemented
10#69484C211yesmaximal, characteristic, complemented
11#69478C211yesmaximal, characteristic, complemented
12#69452C211yesmaximal, characteristic, complemented
13#69452C211yesmaximal, characteristic, complemented
14#69448C211yesmaximal, characteristic, complemented
15C22⋊C4×C3⋊C8C211yesmaximal, characteristic, complemented
16#21496—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21C22×#208C2211yescharacteristic
22C22×#208C2211yescharacteristic
23C23×C3⋊C8C2211yescharacteristic
24C23×C3⋊C8C2211yescharacteristic
25C3×#398C411yescharacteristic
26C3×#397C411yescharacteristic
27C3×#396C411yescharacteristic
28C3×#396C411yescharacteristic
29C3×#394C411yescharacteristic
30C3×#394C411yescharacteristic
31C3×#394C411yescharacteristic
32C3×#392C411yescharacteristic
33C3×C4×C4⋊C4C2211yescharacteristic
34C3×C4×C22⋊C4C2211yescharacteristic
35C3×C4×C22⋊C4C2211yescharacteristic
36C2×#830C2211yescharacteristic
37C2×#830C2211yescharacteristic
38C2×#830C2211yescharacteristic
39C2×#830C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5012—24no—
45#5011—24no—
46#5011—24no—
47#4997—24no—
48C2×C4⋊(C3⋊C8)C2211yescharacteristic
49C2×C4⋊(C3⋊C8)C2211yescharacteristic
50C2×C4⋊(C3⋊C8)C2211yescharacteristic
51C2×C4⋊(C3⋊C8)C2211yescharacteristic
52C2×#803C2211yescharacteristic
53C2×#803C2211yescharacteristic
54C2×#803C2211yescharacteristic
55C2×C4×C3⋊C8C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4524C2211yescharacteristic
59#4524C2211yescharacteristic
60#4524C2211yescharacteristic
61#4524C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#436—31no—
65C2×#435—31no—
66C2×#435—31no—
67C2×#405—31no—
68#2392D311yescharacteristic
69#1954—31no—
70#1939—31no—
71#1924—31no—
72#1924—31no—
73#1869—31no—
74#1869—31no—
75#1798—31no—
76#1771—31no—
77#1753—31no—
78C8×C22⋊C4—31no—
79C22×C3×D4C2×C411yescharacteristic
80C22×C3×D4C2×C411yescharacteristic
81C22×C3×D4C2×C411yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C3×C4×D4—22no—
86C3×C4×D4—22no—
87C3×C4×D4—22no—
88C3×C4×D4—22no—
89C3×C4×D4—22no—
90C3×C4×D4—22no—
91C3×#117—22no—
92C3×#117—22no—
93C2×C3×C4⋊C4C2×C411yescharacteristic
94C2×C3×C4⋊C4C2×C411yescharacteristic
95C2×C3×C4⋊C4C2×C411yescharacteristic
96C2×C3×C4⋊C4C2×C411yescharacteristic
97C2×C3×C4⋊C4C2×C411yescharacteristic
98C2×C3×C4⋊C4C2×C411yescharacteristic
99C2×C3×C4⋊C4C2×C411yescharacteristic
100C2×C3×C22⋊C4C2×C411yescharacteristic
101C2×C3×C22⋊C4C2×C411yescharacteristic
102C2×C3×C22⋊C4C2×C411yescharacteristic
103C2×C3×C22⋊C4C2×C411yescharacteristic
104C2×C3×C22⋊C4C2×C411yescharacteristic
105C2×C3×C22⋊C4C2×C411yescharacteristic
106C2×C3×C22⋊C4C2×C411yescharacteristic
107C2×C3×C22⋊C4C2×C411yescharacteristic
108C2×C3×C22⋊C4C2×C411yescharacteristic
109C2×C3×C22⋊C4C2×C411yescharacteristic
110C2×C3×C22⋊C4C2×C411yescharacteristic
111C2×C3×C22⋊C4C2×C411yescharacteristic
112C2×C3×C42C2311yescharacteristic
113C2×C3×C42C2311yescharacteristic
114C2×C3×C42C2311yescharacteristic
115C2×C3×C42C2311yescharacteristic
116C2×#208—22no—
117C2×#208—22no—
118C2×#208—22no—
119C2×#208—22no—
120C2×#208—22no—
121C2×#208D414yescomplemented
122C22×C3⋊C8—22no—
123C22×C3⋊C8—22no—
124C22×C3⋊C8—22no—
125C22×C3⋊C8—22no—
126C22×C3⋊C8—22no—
127C22×C3⋊C8—22no—
128C22×C3⋊C8C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C3×#95C2×C411yescharacteristic
137C3×#95C2×C411yescharacteristic
138C3×#95C2×C411yescharacteristic
139C3×#95C2×C411yescharacteristic
140C3×#95C2×C411yescharacteristic
141C3×#95C2×C411yescharacteristic
142#830—22no—
143#830—22no—
144#830—22no—
145#830—22no—
146#830—22no—
147#830—22no—
148#830—22no—
149#830—22no—
150C4⋊(C3⋊C8)—22no—
151C4⋊(C3⋊C8)—22no—
152C4⋊(C3⋊C8)—22no—
153C4⋊(C3⋊C8)—22no—
154#803—22no—
155#803—22no—
156#803D414yescomplemented
157C4×C3⋊C8—22no—
158C4×C3⋊C8—22no—
159C4×C3⋊C8—22no—
160C22×M16—31no—
161C22×M16—31no—
162C23×C8—31no—
163C23×C8—31no—
164C2×C4×D4C2×D311yescharacteristic
165C2×C4×D4C2×D311yescharacteristic
166C2×C4×D4C2×D311yescharacteristic
167C2×#117C2×D311yescharacteristic
168#436—64no—
169#435—64no—
170#435—64no—
171C2×C4⋊C8—31no—
172C2×C4⋊C8—31no—
173C2×C4⋊C8—31no—
174C2×C4⋊C8—31no—
175C2×C22⋊C8—31no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8—31no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—31no—
180C2×C22⋊C8—31no—
181C2×C22⋊C8—31no—
182C2×C22⋊C8—31no—
183#405—64no—
184C2×#97—31no—
185C2×#97—31no—
186C2×#97—31no—
187C2×C4×C8—31no—
188C2×C4×C8—31no—
189C2×C4×C8—31no—
190#398Dic311yescharacteristic
191#397Dic311yescharacteristic
192#396Dic311yescharacteristic
193#396Dic311yescharacteristic
194#394Dic311yescharacteristic
195#394Dic311yescharacteristic
196#394Dic311yescharacteristic
197#392Dic311yescharacteristic
198C4×C4⋊C4C2×D311yescharacteristic
199C4×C22⋊C4C2×D311yescharacteristic
200C4×C22⋊C4C2×D311yescharacteristic
201#336—31no—
202#336—31no—
203#336—31no—
204#336—31no—
205#336—31no—
206#336—31no—
207C24×C3C22×C411yescharacteristic
208C24×C3C22×C411yescharacteristic
209C24×C3C22×C411yescharacteristic
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—22no—
216C2×C3×D4—41no—
217C2×C3×D4—41no—
218C2×C3×D4—41no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
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—21no—
235C22×C3×C4C22×C411yescharacteristic
236C22×C3×C4C22×C411yescharacteristic
237C22×C3×C4C22×C411yescharacteristic
238C22×C3×C4C22×C411yescharacteristic
239C22×C3×C4C22×C411yescharacteristic
240C22×C3×C4C22×C411yescharacteristic
241C22×C3×C4C22×C411yescharacteristic
242C22×C3×C4C22×C411yescharacteristic
243C22×C3×C4C22×C411yescharacteristic
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C2×D412yes—
247C22×C3×C4#4112yes—
248C22×C3×C4C2411yescharacteristic
249C3×C4⋊C4—22no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—22no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—22no—
255C3×C4⋊C4—41no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—41no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42—21no—
274C3×C42C2×D412yes—
275C3×C42#4112yes—
276#208—28no—
277#208—44no—
278C2×C3⋊C8—28no—
279C2×C3⋊C8—21no—
280C2×C3⋊C8—21no—
281C2×C3⋊C8—21no—
282C2×C3⋊C8—21no—
283C2×C3⋊C8—21no—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—21no—
286C2×C3⋊C8—21no—
287C2×C3⋊C8—21no—
288C2×C3⋊C8—21no—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—44no—
298C2×C3⋊C8C2×D412yes—
299C2×C3⋊C8C2×D412yes—
300C2×C3⋊C8C2×D412yes—
301C2×C3⋊C8C2×D412yes—
302C2×C3⋊C8#4112yes—
303C2×C3⋊C8#4112yes—
304C22×D4C2×Dic311yescharacteristic
305C22×D4C2×Dic311yescharacteristic
306C22×D4C2×Dic311yescharacteristic
307C23×C4C22×D311yescharacteristic
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D311yescharacteristic
310C2×M16—34no—
311C2×M16—62no—
312C2×M16—62no—
313C2×M16—62no—
314C2×M16—62no—
315C2×M16—62no—
316C22×C8—31no—
317C22×C8—31no—
318C22×C8—31no—
319C22×C8—31no—
320C22×C8—31no—
321C22×C8—31no—
322C22×C8—31no—
323C22×C8—31no—
324C22×C8—62no—
325C22×C8—62no—
326C22×C8—62no—
327C22×C8—62no—
328C22×C8—62no—
329C22×C8—62no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336#117—22no—
337#117—22no—
338C2×C4⋊C4C2×Dic311yescharacteristic
339C2×C4⋊C4C2×Dic311yescharacteristic
340C2×C4⋊C4C2×Dic311yescharacteristic
341C2×C4⋊C4C2×Dic311yescharacteristic
342C2×C4⋊C4C2×Dic311yescharacteristic
343C2×C4⋊C4C2×Dic311yescharacteristic
344C2×C4⋊C4C2×Dic311yescharacteristic
345C2×C22⋊C4C2×Dic311yescharacteristic
346C2×C22⋊C4C2×Dic311yescharacteristic
347C2×C22⋊C4C2×Dic311yescharacteristic
348C2×C22⋊C4C2×Dic311yescharacteristic
349C2×C22⋊C4C2×Dic311yescharacteristic
350C2×C22⋊C4C2×Dic311yescharacteristic
351C2×C22⋊C4C2×Dic311yescharacteristic
352C2×C22⋊C4C2×Dic311yescharacteristic
353C2×C22⋊C4C2×Dic311yescharacteristic
354C2×C22⋊C4C2×Dic311yescharacteristic
355C2×C22⋊C4C2×Dic311yescharacteristic
356C2×C22⋊C4C2×Dic311yescharacteristic
357C2×C42C22×D311yescharacteristic
358C2×C42C22×D311yescharacteristic
359C2×C42C22×D311yescharacteristic
360C2×C42C22×D311yescharacteristic
361C4⋊C8—62no—
362C4⋊C8—62no—
363C4⋊C8—62no—
364C4⋊C8—62no—
365C22⋊C8—62no—
366C22⋊C8—62no—
367C22⋊C8—62no—
368C22⋊C8—62no—
369C22⋊C8—62no—
370C22⋊C8—62no—
371C22⋊C8—62no—
372C22⋊C8—62no—
373#97—34no—
374#97—62no—
375#97—62no—
376C4×C8—62no—
377C4×C8—62no—
378C4×C8—62no—
379#95C2×Dic311yescharacteristic
380#95C2×Dic311yescharacteristic
381#95C2×Dic311yescharacteristic
382#95C2×Dic311yescharacteristic
383#95C2×Dic311yescharacteristic
384#95C2×Dic311yescharacteristic
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3C4×D412yes—
405C23×C3#13112yes—
406C23×C3C23×C411yescharacteristic
407C3×D4—44no—
408C3×D4—44no—
409C3×D4—44no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
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×C4C4×D412yes—
452C2×C3×C4C4×D412yes—
453C2×C3×C4C4×D412yes—
454C2×C3×C4#13112yes—
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C3⋊C8—22no—
462C3⋊C8—22no—
463C3⋊C8—22no—
464C3⋊C8—41no—
465C3⋊C8—41no—
466C3⋊C8—41no—
467C3⋊C8—41no—
468C3⋊C8#12114yes—
469C24C22×Dic311yescharacteristic
470C24C22×Dic311yescharacteristic
471C24C22×Dic311yescharacteristic
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4D3×D412yes—
498C22×C4#23712yes—
499C22×C4C22×Dic311yescharacteristic
500C22×C4C22×Dic311yescharacteristic
501C22×C4C22×Dic311yescharacteristic
502C22×C4C22×Dic311yescharacteristic
503C22×C4C22×Dic311yescharacteristic
504C22×C4C22×Dic311yescharacteristic
505C22×C4C22×Dic311yescharacteristic
506C22×C4C22×Dic311yescharacteristic
507C22×C4C22×Dic311yescharacteristic
508C22×C4C22×Dic311yescharacteristic
509C22×C4C22×Dic311yescharacteristic
510C22×C4C23×D311yescharacteristic
511M16—68no—
512M16—124no—
513C2×C8—32no—
514C2×C8—32no—
515C2×C8—32no—
516C2×C8—32no—
517C2×C8—32no—
518C2×C8—32no—
519C2×C8—68no—
520C2×C8—61no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—61no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—61no—
529C2×C8—61no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—124no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—41no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42D3×D412yes—
565C42#23712yes—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3C2×C4×D411yescharacteristic
588C22×C3C2×C4×D411yescharacteristic
589C22×C3C4×#4111yescharacteristic
590C22×C3C2×#13111yescharacteristic
591C22×C3C2×#13111yescharacteristic
592C22×C3#56811yescharacteristic
593C22×C3#56811yescharacteristic
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4C2×#12111yescharacteristic
606C3×C4#52511yescharacteristic
607C3×C4#52911yescharacteristic
608C3×C4#53211yescharacteristic
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23D4×Dic312yes—
629C23#94812yes—
630C23C23×Dic311yescharacteristic
631D4—44no—
632D4—44no—
633D4—44no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4D4×Dic312yes—
676C2×C4D4×Dic312yes—
677C2×C4D4×Dic312yes—
678C2×C4#94812yes—
679C2×C4C2×D3×D411yescharacteristic
680C2×C4C2×D3×D411yescharacteristic
681C2×C4C2×#23711yescharacteristic
682C2×C4C2×#23711yescharacteristic
683C2×C4D3×#4111yescharacteristic
684C2×C4D3×#4111yescharacteristic
685C8—34no—
686C8—62no—
687C8—62no—
688C8—62no—
689C8—121no—
690C8—121no—
691C8—121no—
692C8—121no—
693C2×C3—42no—
694C2×C3—42no—
695C2×C3—81no—
696C2×C3C4×#12111yescharacteristic
697C2×C3#293311yescharacteristic
698C2×C3#293311yescharacteristic
699C2×C3#293311yescharacteristic
700C2×C3#293511yescharacteristic
701C2×C3#296611yescharacteristic
702C2×C3#296711yescharacteristic
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22C2×D4×Dic311yescharacteristic
725C22C2×D4×Dic311yescharacteristic
726C22C2×#94811yescharacteristic
727C22C2×#94811yescharacteristic
728C22#581911yescharacteristic
729C22#581911yescharacteristic
730C22Dic3×#4111yescharacteristic
731C4—22no—
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4#559611yescharacteristic
743C4#560011yescharacteristic
744C4D3×#12111yescharacteristic
745C4#560611yescharacteristic
746C3#2149611yescharacteristic, complemented, Sylow
747C2—42no—
748C2—42no—
749C2—81no—
750C2Dic3×#12111yescharacteristic
751C2#8291811yescharacteristic
752C2#8291811yescharacteristic
753C2#8291811yescharacteristic
754C2#8312611yescharacteristic
755C2#8312711yescharacteristic
756C2#8327711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#2392C2
prime radicalC3×#392C4
cosocleC22×C3×C4C24
hypercenter#2392D3
hypocenterC3#21496
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
2. C2×#5012C2semidirect
3. C2×#5011C2semidirect
4. C2×#5011C2semidirect
5. C2×#4997C2semidirect
6. #71614C2semidirect
7. #71610C2semidirect
8. #71610C2semidirect
9. #71583C2semidirect
10. #69484C2semidirect
11. #69478C2semidirect
12. #69452C2semidirect
13. #69452C2semidirect
14. #69448C2semidirect
15. C22⋊C4×C3⋊C8C2semidirect
121. C2×#208D4semidirect
156. #803D4semidirect
746. C3#21496semidirect

Maximal subgroups

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

subgroupindex
C3×#23922
C2×#50122
C2×#50112
C2×#49972
#716142
#716102
#715832
#694842
#694782
#694522
#694482
C22⋊C4×C3⋊C82
#214963