Finite Group Databasebeta

← #10764081

Subgroups — #10764081

Order 768.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3511C211yesmaximal, characteristic
2#82522C211yesmaximal, characteristic, complemented
3#82522C211yesmaximal, characteristic, complemented
4#71833C211yesmaximal, characteristic, complemented
5#71832C211yesmaximal, characteristic, complemented
6#71830C211yesmaximal, characteristic, complemented
7#71828C211yesmaximal, characteristic, complemented
8#71809C211yesmaximal, characteristic, complemented
9#71808C211yesmaximal, characteristic, complemented
10#71807C211yesmaximal, characteristic, complemented
11#71807C211yesmaximal, characteristic, complemented
12#71806C211yesmaximal, characteristic, complemented
13#71804C211yesmaximal, characteristic, complemented
14#71776C211yesmaximal, characteristic, complemented
15C2×#4547C211yesmaximal, characteristic, complemented
16#17775—31nomaximal, Sylow
17C3×#556—21no—
18C3×#555—21no—
19C3×#554—21no—
20C3×#553—21no—
21C3×#553—21no—
22C3×#548—21no—
23C3×#548—21no—
24C3×#547—21no—
25C3×#542C412yes—
26C3×#542C412yes—
27C3×#537C412yes—
28C3×#533C2211yescharacteristic
29C3×#533C2211yescharacteristic
30C3×#532C2211yescharacteristic
31C3×#532C2211yescharacteristic
32C3×#532C2211yescharacteristic
33C2×C3×C4⋊Q8C2211yescharacteristic
34C3×#520C412yes—
35C3×C4×#41C2211yescharacteristic
36#5024—21no—
37#5024—21no—
38#5011—21no—
39#5011—21no—
40#5011—21no—
41#5011—21no—
42D4×C3⋊C8—21no—
43D4×C3⋊C8—21no—
44#4926C2211yescharacteristic
45#4926C2211yescharacteristic
46#4926C2211yescharacteristic
47#4926C2211yescharacteristic
48#4925C2211yescharacteristic
49#4925C2211yescharacteristic
50#4924C2211yescharacteristic
51#4924C2211yescharacteristic
52C2×C4⋊(C3⋊C8)C2211yescharacteristic
53C2×C4⋊(C3⋊C8)C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55C2×C4⋊(C3⋊C8)C2211yescharacteristic
56#4547C2211yescharacteristic
57#4547C2211yescharacteristic
58#4547C2211yescharacteristic
59#4547C2211yescharacteristic
60#4547C2211yescharacteristic
61#4547C2211yescharacteristic
62#4547C2211yescharacteristic
63#4547C2211yescharacteristic
64#4546C2211yescharacteristic
65#4546C2211yescharacteristic
66#4546C2211yescharacteristic
67#4546C2211yescharacteristic
68#4544C2211yescharacteristic
69#4544C2211yescharacteristic
70#4544C2211yescharacteristic
71#4544C2211yescharacteristic
72#3511D311yescharacteristic
73#2990—31no—
74#2990—31no—
75#1559—31no—
76#1557—31no—
77#1556—31no—
78#1554—31no—
79#1553—31no—
80#1551—31no—
81#1551—31no—
82#1550—31no—
83#1547—31no—
84#1542—31no—
85#1540—31no—
86C2×#332—31no—
87C2×C3×#41—21no—
88C2×C3×#41—21no—
89C2×C3×#41C2×C412yes—
90C2×C3×#41C2×C411yescharacteristic
91C22×C3×Q8—21no—
92C3×C4⋊Q8—21no—
93C3×C4⋊Q8—21no—
94C3×C4⋊Q8C2×C412yes—
95C3×C4⋊Q8C2311yescharacteristic
96C3×C4⋊Q8C2311yescharacteristic
97C3×C4⋊Q8C2311yescharacteristic
98C3×#127C2311yescharacteristic
99C3×#126—22no—
100C3×#126—22no—
101C3×#125—21no—
102C3×#125—21no—
103C3×#124—22no—
104C3×#124—22no—
105C3×#124—21no—
106C3×#124—21no—
107C3×#124C2×C412yes—
108C3×#123—22no—
109C3×#123—22no—
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—21no—
112C3×C22⋊Q8—21no—
113C3×C22⋊Q8—22no—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8C2×C412yes—
116C3×C22⋊Q8C2×C412yes—
117C3×#121—22no—
118C3×#121—22no—
119C3×#121—22no—
120C3×#121—21no—
121C3×#121—21no—
122C3×#121—21no—
123C3×#121—21no—
124C3×#121C2×C412yes—
125C3×#121C2×C412yes—
126C3×C4×Q8—21no—
127C3×C4×Q8—21no—
128C3×C4×Q8C2×C412yes—
129C3×C4×Q8C2×C412yes—
130C3×C4×Q8D411yescharacteristic
131C3×C4×Q8D411yescharacteristic
132C3×C4×D4—22no—
133C3×C4×D4—22no—
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×C4×D4—21no—
137C3×C4×D4—21no—
138C3×C4×D4C2×C412yes—
139C3×C4×D4C2×C412yes—
140C3×C4×D4D411yescharacteristic
141C3×C4×D4D411yescharacteristic
142C3×C4×D4D411yescharacteristic
143C3×C4×D4D411yescharacteristic
144C3×C4×D4D411yescharacteristic
145C3×C4×D4D411yescharacteristic
146C3×#117—21no—
147C3×#117—21no—
148C3×#117—22no—
149C3×#117C2×C411yescharacteristic
150C3×#117C2×C411yescharacteristic
151C3×#117C2×C411yescharacteristic
152C2×C3×C4⋊C4—21no—
153C2×C3×C4⋊C4—22no—
154C2×C3×C4⋊C4C2×C412yes—
155C2×C3×C42C2311yescharacteristic
156C2×C3×C42C2311yescharacteristic
157C2×C3×C42C2311yescharacteristic
158C2×#208—21no—
159C2×#208—21no—
160C22×C3⋊C8—21no—
161C22×C3⋊C8—21no—
162C22×C3⋊C8—21no—
163C22×C3⋊C8—21no—
164#830—21no—
165#830—21no—
166#830—21no—
167#830—21no—
168#830—21no—
169#830—21no—
170C4⋊(C3⋊C8)—21no—
171C4⋊(C3⋊C8)—21no—
172C4⋊(C3⋊C8)—21no—
173C4⋊(C3⋊C8)—21no—
174C4⋊(C3⋊C8)—21no—
175C4⋊(C3⋊C8)—21no—
176C4⋊(C3⋊C8)C2311yescharacteristic
177C4⋊(C3⋊C8)C2311yescharacteristic
178C4⋊(C3⋊C8)C2311yescharacteristic
179C4⋊(C3⋊C8)C2311yescharacteristic
180C4⋊(C3⋊C8)C2311yescharacteristic
181C4⋊(C3⋊C8)C2311yescharacteristic
182C4⋊(C3⋊C8)C2311yescharacteristic
183C4⋊(C3⋊C8)C2311yescharacteristic
184#803—21no—
185#803—21no—
186#803—21no—
187#803—21no—
188C4×C3⋊C8—21no—
189C4×C3⋊C8—21no—
190#556—21no—
191#555—21no—
192#554—21no—
193#553—21no—
194#553—21no—
195#548—21no—
196#548—21no—
197#547—21no—
198#542Dic312yes—
199#542Dic312yes—
200#537Dic312yes—
201#533C2×D311yescharacteristic
202#533C2×D311yescharacteristic
203#532C2×D311yescharacteristic
204#532C2×D311yescharacteristic
205#532C2×D311yescharacteristic
206C2×C4⋊Q8C2×D311yescharacteristic
207#520Dic312yes—
208C4×#41C2×D311yescharacteristic
209#446—61no—
210#446—61no—
211#435—61no—
212#435—61no—
213#435—61no—
214#435—61no—
215C8×D4—61no—
216C8×D4—61no—
217#432—31no—
218#432—31no—
219#432—31no—
220#432—31no—
221#431—31no—
222#431—31no—
223#423—31no—
224#423—31no—
225C2×C4⋊C8—31no—
226C2×C4⋊C8—31no—
227C2×C4⋊C8—31no—
228C2×C4⋊C8—31no—
229#333—31no—
230#333—31no—
231#333—31no—
232#333—31no—
233#332—31no—
234#332—31no—
235#332—31no—
236#332—31no—
237#332—31no—
238#332—31no—
239#332—31no—
240#332—31no—
241#331—31no—
242#331—31no—
243#331—31no—
244#331—31no—
245C3×#41—42no—
246C3×#41—44no—
247C3×#41—81no—
248C3×#41—81no—
249C3×#41—81no—
250C3×#41—81no—
251C2×C3×Q8—22no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—81no—
255C2×C3×Q8—81no—
256C2×C3×Q8C22⋊C411yescharacteristic
257C2×C3×Q8C22×C412yes—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4C22⋊C411yescharacteristic
264C2×C3×D4C22⋊C411yescharacteristic
265C2×C3×D4C22⋊C411yescharacteristic
266C2×C3×D4C22×C412yes—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4C22×C411yescharacteristic
272C22×C3×C4C22×C411yescharacteristic
273C22×C3×C4C22×C411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C3×C4⋊C4—22no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4—22no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4C22⋊C411yescharacteristic
291C3×C4⋊C4C22⋊C411yescharacteristic
292C3×C4⋊C4C22⋊C411yescharacteristic
293C3×C4⋊C4C22⋊C411yescharacteristic
294C3×C4⋊C4C22⋊C411yescharacteristic
295C3×C4⋊C4C22⋊C411yescharacteristic
296C3×C4⋊C4C22×C412yes—
297C3×C4⋊C4C22×C412yes—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—22no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4C22⋊C411yescharacteristic
307C3×C22⋊C4C22⋊C411yescharacteristic
308C3×C22⋊C4C22⋊C411yescharacteristic
309C3×C22⋊C4C22⋊C411yescharacteristic
310C3×C22⋊C4C22⋊C411yescharacteristic
311C3×C22⋊C4C22⋊C411yescharacteristic
312C3×C42—22no—
313C3×C42—22no—
314C3×C42C22×C411yescharacteristic
315C3×C42C22×C411yescharacteristic
316C3×C42C22×C411yescharacteristic
317C3×C42C2×D411yescharacteristic
318C3×C42C2×D411yescharacteristic
319C3×C42C2×D411yescharacteristic
320C3×C42C2×D411yescharacteristic
321C3×C42C2×D411yescharacteristic
322C3×C42C2×D411yescharacteristic
323C3×C42C2411yescharacteristic
324#208—81no—
325#208—81no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—81no—
335C2×C3⋊C8—81no—
336C2×C3⋊C8—81no—
337C2×C3⋊C8—81no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41C2×Dic312yes—
341C2×#41C2×Dic311yescharacteristic
342C22×Q8—21no—
343C2×M16—61no—
344C2×M16—61no—
345C22×C8—61no—
346C22×C8—61no—
347C22×C8—61no—
348C22×C8—61no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8C2×Dic312yes—
352C4⋊Q8C22×D311yescharacteristic
353C4⋊Q8C22×D311yescharacteristic
354C4⋊Q8C22×D311yescharacteristic
355#127C22×D311yescharacteristic
356#126—22no—
357#126—22no—
358#125—21no—
359#125—21no—
360#124—22no—
361#124—22no—
362#124—21no—
363#124—21no—
364#124C2×Dic312yes—
365#123—22no—
366#123—22no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8C2×Dic312yes—
373C22⋊Q8C2×Dic312yes—
374#121—22no—
375#121—22no—
376#121—22no—
377#121—21no—
378#121—21no—
379#121—21no—
380#121—21no—
381#121C2×Dic312yes—
382#121C2×Dic312yes—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C2×Dic312yes—
386C4×Q8C2×Dic312yes—
387C4×Q8#6711yescharacteristic
388C4×Q8#6711yescharacteristic
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4C2×Dic312yes—
396C4×D4C2×Dic312yes—
397C4×D4#6711yescharacteristic
398C4×D4#6711yescharacteristic
399C4×D4#6711yescharacteristic
400C4×D4#6711yescharacteristic
401C4×D4#6711yescharacteristic
402C4×D4#6711yescharacteristic
403#117—21no—
404#117—21no—
405#117—22no—
406#117C2×Dic311yescharacteristic
407#117C2×Dic311yescharacteristic
408#117C2×Dic311yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4C2×Dic312yes—
412C2×C42C22×D311yescharacteristic
413C2×C42C22×D311yescharacteristic
414C2×C42C22×D311yescharacteristic
415C4⋊C8—31no—
416C4⋊C8—31no—
417C4⋊C8—31no—
418C4⋊C8—31no—
419C4⋊C8—31no—
420C4⋊C8—31no—
421C4⋊C8—31no—
422C4⋊C8—31no—
423C4⋊C8—61no—
424C4⋊C8—61no—
425C4⋊C8—61no—
426C4⋊C8—61no—
427C4⋊C8—61no—
428C4⋊C8—61no—
429C22⋊C8—61no—
430C22⋊C8—61no—
431C22⋊C8—61no—
432C22⋊C8—61no—
433C22⋊C8—61no—
434C22⋊C8—61no—
435#97—61no—
436#97—61no—
437#97—61no—
438#97—61no—
439C4×C8—61no—
440C4×C8—61no—
441C23×C3—22no—
442C23×C3C2×C22⋊C411yescharacteristic
443C23×C3C2×C22⋊C411yescharacteristic
444C23×C3C2×C22⋊C411yescharacteristic
445C3×Q8—41no—
446C3×Q8—42no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8—82no—
452C3×D4—22no—
453C3×D4—22no—
454C3×D4—41no—
455C3×D4—42no—
456C3×D4—44no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—41no—
461C3×D4—82no—
462C3×D4—82no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—44no—
482C2×C3×C4—82no—
483C2×C3×C4—82no—
484C2×C3×C4—82no—
485C2×C3×C4C2×C22⋊C411yescharacteristic
486C2×C3×C4C2×C22⋊C411yescharacteristic
487C2×C3×C4C2×C22⋊C411yescharacteristic
488C2×C3×C4C2×C22⋊C411yescharacteristic
489C2×C3×C4C2×C22⋊C411yescharacteristic
490C2×C3×C4C2×C22⋊C411yescharacteristic
491C2×C3×C4C2×C22⋊C411yescharacteristic
492C2×C3×C4C2×C22⋊C411yescharacteristic
493C2×C3×C4C2×C22⋊C411yescharacteristic
494C2×C3×C4C23×C411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C3⋊C8—41no—
498C3⋊C8—41no—
499C3⋊C8—41no—
500C3⋊C8—41no—
501C3⋊C8—41no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C3⋊C8—41no—
505#41—42no—
506#41—44no—
507#41—81no—
508#41—81no—
509#41—81no—
510#41—81no—
511C2×Q8—22no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—81no—
515C2×Q8—81no—
516C2×Q8#21711yescharacteristic
517C2×Q8C22×Dic312yes—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4#21711yescharacteristic
524C2×D4#21711yescharacteristic
525C2×D4#21711yescharacteristic
526C2×D4C22×Dic312yes—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4C22×Dic311yescharacteristic
532C22×C4C22×Dic311yescharacteristic
533C22×C4C22×Dic311yescharacteristic
534C22×C4C2×#6711yescharacteristic
535C22×C4C2×#6711yescharacteristic
536C22×C4C2×#6711yescharacteristic
537C22×C4C2×#6711yescharacteristic
538C22×C4C2×#6711yescharacteristic
539C22×C4C2×#6711yescharacteristic
540M16—241no—
541M16—241no—
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—241no—
551C2×C8—241no—
552C2×C8—241no—
553C2×C8—241no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4#21711yescharacteristic
565C4⋊C4#21711yescharacteristic
566C4⋊C4#21711yescharacteristic
567C4⋊C4#21711yescharacteristic
568C4⋊C4#21711yescharacteristic
569C4⋊C4#21711yescharacteristic
570C4⋊C4C22×Dic312yes—
571C4⋊C4C22×Dic312yes—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4#21711yescharacteristic
581C22⋊C4#21711yescharacteristic
582C22⋊C4#21711yescharacteristic
583C22⋊C4#21711yescharacteristic
584C22⋊C4#21711yescharacteristic
585C22⋊C4#21711yescharacteristic
586C42—22no—
587C42—22no—
588C42C22×Dic311yescharacteristic
589C42C22×Dic311yescharacteristic
590C42C22×Dic311yescharacteristic
591C42C2×#6711yescharacteristic
592C42C2×#6711yescharacteristic
593C42C2×#6711yescharacteristic
594C42C2×#6711yescharacteristic
595C42C2×#6711yescharacteristic
596C42C2×#6711yescharacteristic
597C42C23×D311yescharacteristic
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3#41312yes—
610C22×C3C22×C22⋊C411yescharacteristic
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4#57611yescharacteristic
625C3×C4#57711yescharacteristic
626C3×C4#57711yescharacteristic
627C3×C4#57811yescharacteristic
628C23—22no—
629C23C2×#21711yescharacteristic
630C23C2×#21711yescharacteristic
631C23C2×#21711yescharacteristic
632Q8—41no—
633Q8—42no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—82no—
639D4—22no—
640D4—22no—
641D4—41no—
642D4—42no—
643D4—44no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—82no—
649D4—82no—
650C2×C4—22no—
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—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—44no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4C2×#21711yescharacteristic
673C2×C4C2×#21711yescharacteristic
674C2×C4C2×#21711yescharacteristic
675C2×C4C2×#21711yescharacteristic
676C2×C4C2×#21711yescharacteristic
677C2×C4C2×#21711yescharacteristic
678C2×C4C2×#21711yescharacteristic
679C2×C4C2×#21711yescharacteristic
680C2×C4C2×#21711yescharacteristic
681C2×C4C23×Dic311yescharacteristic
682C2×C4C22×#6711yescharacteristic
683C2×C4C22×#6711yescharacteristic
684C8—121no—
685C8—121no—
686C8—121no—
687C8—121no—
688C8—121no—
689C8—121no—
690C8—121no—
691C8—121no—
692C2×C3—22no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3—82no—
696C2×C3C2×#41311yescharacteristic
697C2×C3#289711yescharacteristic
698C2×C3#289811yescharacteristic
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22#523712yes—
711C22C22×#21711yescharacteristic
712C4—21no—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4#583511yescharacteristic
726C4#583611yescharacteristic
727C4#583711yescharacteristic
728C4#583811yescharacteristic
729C3#1777511yescharacteristic, complemented, Sylow
730C2—22no—
731C2—41no—
732C2—41no—
733C2—82no—
734C2C2×#523711yescharacteristic
735C2#8409911yescharacteristic
736C2#8411111yescharacteristic
subgroupG/H
centerC22C22×#217
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
Fitting, prime radicalC3×#3511C2
socleC22×C3C22×C22⋊C4
cosocleC3×C42C24
hypercenter#3511D3
hypocenterC3#17775
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
2. #82522C2semidirect
3. #82522C2semidirect
4. #71833C2semidirect
5. #71832C2semidirect
6. #71830C2semidirect
7. #71828C2semidirect
8. #71809C2semidirect
9. #71808C2semidirect
10. #71807C2semidirect
11. #71807C2semidirect
12. #71806C2semidirect
13. #71804C2semidirect
14. #71776C2semidirect
15. C2×#4547C2semidirect
729. C3#17775semidirect

Maximal subgroups

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

subgroupindex
C3×#35112
#825222
#718332
#718322
#718302
#718282
#718092
#718082
#718072
#718062
#718042
#717762
C2×#45472
#177753