Finite Group Databasebeta

← #10801260

Subgroups — #10801260

Order 768.

1116 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#121C211yesmaximal, characteristic
2C2×#5011C211yesmaximal, characteristic, complemented
3C2×#5011C211yesmaximal, characteristic, complemented
4C2×D4×C3⋊C8C211yesmaximal, characteristic, complemented
5C22×#803C211yesmaximal, characteristic, complemented
6#71615C211yesmaximal, characteristic, complemented
7#71610C211yesmaximal, characteristic, complemented
8#71610C211yesmaximal, characteristic, complemented
9#71530C211yesmaximal, characteristic, complemented
10#69485C211yesmaximal, characteristic, complemented
11#69478C211yesmaximal, characteristic, complemented
12#69452C211yesmaximal, characteristic, complemented
13#69452C211yesmaximal, characteristic, complemented
14#69448C211yesmaximal, characteristic, complemented
15#69447C211yesmaximal, characteristic, complemented
16#21489—31nomaximal, Sylow
17C2×C3×#121C411yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×#208C2211yescharacteristic
23C23×C3⋊C8C2211yescharacteristic
24C23×C3⋊C8C2211yescharacteristic
25C23×C3⋊C8C2211yescharacteristic
26C3×#390C411yescharacteristic
27C3×#389C411yescharacteristic
28C3×#388C411yescharacteristic
29C3×#388C411yescharacteristic
30C3×#386C411yescharacteristic
31C3×#386C411yescharacteristic
32C3×#380C411yescharacteristic
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#5011—24no—
45#5011—24no—
46D4×C3⋊C8—24no—
47C2×C4⋊(C3⋊C8)C2211yescharacteristic
48C2×C4⋊(C3⋊C8)C2211yescharacteristic
49C2×C4⋊(C3⋊C8)C2211yescharacteristic
50C2×C4⋊(C3⋊C8)C2211yescharacteristic
51C2×#803—24no—
52C2×#803C2211yescharacteristic
53C2×#803C2211yescharacteristic
54C2×#803C2211yescharacteristic
55C2×#803C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4524C2211yescharacteristic
59#4524C2211yescharacteristic
60#4524C2211yescharacteristic
61#4524C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#435—31no—
65C2×#435—31no—
66C2×C8×D4—31no—
67C22×#97—31no—
68C4×#121D311yescharacteristic
69#1955—31no—
70#1940—31no—
71#1924—31no—
72#1924—31no—
73#1869—31no—
74#1869—31no—
75#1797—31no—
76#1771—31no—
77#1753—31no—
78#1752—31no—
79C22×C3×D4C2×C411yescharacteristic
80C22×C3×D4C2×C411yescharacteristic
81C22×C3×D4C2×C411yescharacteristic
82C23×C3×C4C2×C411yescharacteristic
83C23×C3×C4C2×C411yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C3×#121—24no—
88C3×C4×D4—22no—
89C3×C4×D4—22no—
90C3×C4×D4—22no—
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C3×C4×D4—22no—
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×C22⋊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×C42—22no—
110C2×C3×C42—22no—
111C2×C3×C42C2×C411yescharacteristic
112C2×C3×C42C2×C411yescharacteristic
113C2×C3×C42C2311yescharacteristic
114C2×C3×C42C2311yescharacteristic
115C2×C3×C42C2311yescharacteristic
116C2×C3×C42C2311yescharacteristic
117C2×#208—22no—
118C2×#208—22no—
119C2×#208—22no—
120C22×C3⋊C8—22no—
121C22×C3⋊C8—22no—
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⋊C8D414yescomplemented
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C3×#95C2×C411yescharacteristic
138C3×#95C2×C411yescharacteristic
139C3×#95C2×C411yescharacteristic
140C3×#95C2×C411yescharacteristic
141C3×#95C2×C411yescharacteristic
142C3×#95C2×C411yescharacteristic
143#830—22no—
144#830—22no—
145#830—22no—
146#830—22no—
147#830—22no—
148#830—22no—
149#830—22no—
150#830—22no—
151C4⋊(C3⋊C8)—22no—
152C4⋊(C3⋊C8)—22no—
153C4⋊(C3⋊C8)—22no—
154C4⋊(C3⋊C8)—22no—
155#803—22no—
156#803—22no—
157#803—22no—
158#803—22no—
159#803D414yescomplemented
160C4×C3⋊C8—22no—
161C22×M16—31no—
162C23×C8—31no—
163C23×C8—31no—
164C23×C8—31no—
165C2×#121Dic311yescharacteristic
166C2×C4×D4C2×D311yescharacteristic
167C2×C4×D4C2×D311yescharacteristic
168C2×C4×D4C2×D311yescharacteristic
169C22×C42C2×D311yescharacteristic
170#435—64no—
171#435—64no—
172C8×D4—64no—
173C2×C4⋊C8—31no—
174C2×C4⋊C8—31no—
175C2×C4⋊C8—31no—
176C2×C4⋊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—
183C2×C22⋊C8—31no—
184C2×C22⋊C8—31no—
185C2×#97—31no—
186C2×#97—31no—
187C2×#97—31no—
188C2×#97—31no—
189C2×#97—31no—
190C2×#97—64no—
191C2×C4×C8—31no—
192#390Dic311yescharacteristic
193#389Dic311yescharacteristic
194#388Dic311yescharacteristic
195#388Dic311yescharacteristic
196#386Dic311yescharacteristic
197#386Dic311yescharacteristic
198#380Dic311yescharacteristic
199C4×C4⋊C4C2×D311yescharacteristic
200C4×C22⋊C4C2×D311yescharacteristic
201C4×C22⋊C4C2×D311yescharacteristic
202#336—31no—
203#336—31no—
204#336—31no—
205#336—31no—
206#336—31no—
207#336—31no—
208C24×C3C22×C411yescharacteristic
209C24×C3C22×C411yescharacteristic
210C24×C3C22×C411yescharacteristic
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—41no—
219C2×C3×D4M1614yescomplemented
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
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×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—41no—
241C22×C3×C4—41no—
242C22×C3×C4C22×C411yescharacteristic
243C22×C3×C4C22×C411yescharacteristic
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C22×C411yescharacteristic
247C22×C3×C4C22×C411yescharacteristic
248C22×C3×C4C22×C411yescharacteristic
249C22×C3×C4C22×C411yescharacteristic
250C22×C3×C4C22×C411yescharacteristic
251C22×C3×C4C22×C411yescharacteristic
252C22×C3×C4C22×C411yescharacteristic
253C22×C3×C4C2×D412yes—
254C22×C3×C4#4112yes—
255C22×C3×C4C2411yescharacteristic
256C3×C4⋊C4—22no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—41no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—41no—
270C3×C22⋊C4—41no—
271C3×C42—22no—
272C3×C42—22no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42C2×D412yes—
280C3×C42#4112yes—
281#208—44no—
282C2×C3⋊C8—28no—
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—28no—
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—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—44no—
303C2×C3⋊C8C2×D412yes—
304C2×C3⋊C8C2×D412yes—
305C2×C3⋊C8C2×D412yes—
306C2×C3⋊C8C2×D412yes—
307C2×C3⋊C8#4112yes—
308C2×C3⋊C8#4112yes—
309C22×D4C2×Dic311yescharacteristic
310C22×D4C2×Dic311yescharacteristic
311C22×D4C2×Dic311yescharacteristic
312C23×C4C2×Dic311yescharacteristic
313C23×C4C2×Dic311yescharacteristic
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C2×M16—62no—
318C2×M16—62no—
319C2×M16—62no—
320C22×C8—31no—
321C22×C8—34no—
322C22×C8—31no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8—31no—
327C22×C8—31no—
328C22×C8—31no—
329C22×C8—62no—
330C22×C8—62no—
331C22×C8—62no—
332C22×C8—62no—
333C22×C8—62no—
334C22×C8—62no—
335C22×C8—62no—
336C22×C8—62no—
337#121—24no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C2×C4⋊C4C2×Dic311yescharacteristic
345C2×C4⋊C4C2×Dic311yescharacteristic
346C2×C4⋊C4C2×Dic311yescharacteristic
347C2×C4⋊C4C2×Dic311yescharacteristic
348C2×C4⋊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×C22⋊C4C2×Dic311yescharacteristic
358C2×C22⋊C4C2×Dic311yescharacteristic
359C2×C42—22no—
360C2×C42—22no—
361C2×C42C2×Dic311yescharacteristic
362C2×C42C2×Dic311yescharacteristic
363C2×C42C22×D311yescharacteristic
364C2×C42C22×D311yescharacteristic
365C2×C42C22×D311yescharacteristic
366C2×C42C22×D311yescharacteristic
367C4⋊C8—62no—
368C4⋊C8—62no—
369C4⋊C8—62no—
370C4⋊C8—62no—
371C22⋊C8—62no—
372C22⋊C8—62no—
373C22⋊C8—62no—
374C22⋊C8—62no—
375C22⋊C8—62no—
376C22⋊C8—62no—
377C22⋊C8—62no—
378C22⋊C8—62no—
379#97—34no—
380#97—62no—
381#97—62no—
382#97—62no—
383#97—62no—
384C4×C8—62no—
385#95C2×Dic311yescharacteristic
386#95C2×Dic311yescharacteristic
387#95C2×Dic311yescharacteristic
388#95C2×Dic311yescharacteristic
389#95C2×Dic311yescharacteristic
390#95C2×Dic311yescharacteristic
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×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3C4×D412yes—
409C23×C3C2×M1612yes—
410C23×C3C2×M1612yes—
411C23×C3#13112yes—
412C23×C3C23×C411yescharacteristic
413C3×D4—28no—
414C3×D4—44no—
415C3×D4—44no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
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—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—44no—
450C2×C3×C4—44no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4C4×D412yes—
460C2×C3×C4C4×D412yes—
461C2×C3×C4C4×D412yes—
462C2×C3×C4C2×M1612yes—
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C3⋊C8—22no—
470C3⋊C8—22no—
471C3⋊C8—22no—
472C3⋊C8—41no—
473C3⋊C8—41no—
474C3⋊C8—41no—
475C3⋊C8—41no—
476C3⋊C8#12114yescomplemented
477C24C22×Dic311yescharacteristic
478C24C22×Dic311yescharacteristic
479C24C22×Dic311yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—41no—
488C2×D4#20814yescomplemented
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4D3×D412yes—
512C22×C4#23712yes—
513C22×C4C22×Dic311yescharacteristic
514C22×C4C22×Dic311yescharacteristic
515C22×C4C22×Dic311yescharacteristic
516C22×C4C22×Dic311yescharacteristic
517C22×C4C22×Dic311yescharacteristic
518C22×C4C22×Dic311yescharacteristic
519C22×C4C22×Dic311yescharacteristic
520C22×C4C22×Dic311yescharacteristic
521C22×C4C22×Dic311yescharacteristic
522C22×C4C22×Dic311yescharacteristic
523C22×C4C22×Dic311yescharacteristic
524C22×C4C23×D311yescharacteristic
525M16—124no—
526C2×C8—32no—
527C2×C8—32no—
528C2×C8—32no—
529C2×C8—32no—
530C2×C8—32no—
531C2×C8—32no—
532C2×C8—68no—
533C2×C8—68no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—124no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—41no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C42—22no—
569C42—22no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42D3×D412yes—
577C42#23712yes—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3#43514yescomplemented
599C22×C3C2×C4×D411yescharacteristic
600C22×C3C2×C4×D411yescharacteristic
601C22×C3C4×#4111yescharacteristic
602C22×C3C22×M1611yescharacteristic
603C22×C3C2×#13111yescharacteristic
604C22×C3#56811yescharacteristic
605C22×C3#56811yescharacteristic
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—22no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4C2×#12111yescharacteristic
618C3×C4#52511yescharacteristic
619C3×C4#52911yescharacteristic
620C3×C4#53211yescharacteristic
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23C2×#20812yes—
639C23C2×#20812yes—
640C23D4×Dic312yes—
641C23#94812yes—
642C23C23×Dic311yescharacteristic
643D4—28no—
644D4—44no—
645D4—44no—
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—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
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—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4C2×#20812yes—
690C2×C4D4×Dic312yes—
691C2×C4D4×Dic312yes—
692C2×C4D4×Dic312yes—
693C2×C4C2×D3×D411yescharacteristic
694C2×C4C2×D3×D411yescharacteristic
695C2×C4C2×#23711yescharacteristic
696C2×C4C2×#23711yescharacteristic
697C2×C4D3×#4111yescharacteristic
698C2×C4D3×#4111yescharacteristic
699C8—34no—
700C8—62no—
701C8—62no—
702C8—62no—
703C8—121no—
704C8—121no—
705C8—121no—
706C8—121no—
707C2×C3—24no—
708C2×C3—42no—
709C2×C3—81no—
710C2×C3C4×#12111yescharacteristic
711C2×C3C2×#43511yescharacteristic
712C2×C3#293211yescharacteristic
713C2×C3#293311yescharacteristic
714C2×C3D4×M1611yescharacteristic
715C2×C3#296811yescharacteristic
716C2×C3#297011yescharacteristic
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22#501114yescomplemented
738C22C22×#20811yescharacteristic
739C22C2×D4×Dic311yescharacteristic
740C22C2×D4×Dic311yescharacteristic
741C22C2×#94811yescharacteristic
742C22#581911yescharacteristic
743C22#581911yescharacteristic
744C22Dic3×#4111yescharacteristic
745C4—22no—
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4#559611yescharacteristic
757C4#560011yescharacteristic
758C4D3×#12111yescharacteristic
759C4#560611yescharacteristic
760C3#2148911yescharacteristic, complemented, Sylow
761C2—24no—
762C2—42no—
763C2—81no—
764C2C2×#501111yescharacteristic
765C2D4×#20811yescharacteristic
766C2#8251811yescharacteristic
767C2Dic3×#12111yescharacteristic
768C2#8291811yescharacteristic
769C2#8312811yescharacteristic
770C2#8327611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×C4×#121C2
prime radicalC2×C3×#121C4
cosocleC22×C3×C4C24
hypercenterC4×#121D3
hypocenterC3#21489
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×#5011C2semidirect
3. C2×#5011C2semidirect
4. C2×D4×C3⋊C8C2semidirect
5. C22×#803C2semidirect
6. #71615C2semidirect
7. #71610C2semidirect
8. #71610C2semidirect
9. #71530C2semidirect
10. #69485C2semidirect
11. #69478C2semidirect
12. #69452C2semidirect
13. #69452C2semidirect
14. #69448C2semidirect
15. #69447C2semidirect
128. C22×C3⋊C8D4semidirect
159. #803D4semidirect
219. C2×C3×D4M16semidirect
476. C3⋊C8#121semidirect
488. C2×D4#208semidirect
598. C22×C3#435semidirect
737. C22#5011semidirect
760. C3#21489semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#1212
C2×#50112
C2×D4×C3⋊C82
C22×#8032
#716152
#716102
#715302
#694852
#694782
#694522
#694482
#694472
#214893