Finite Group Databasebeta

← #17051061

Subgroups — #17051061

Order 4352.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763346C211yesmaximal, characteristic
2C2×#11762940C211yesmaximal, characteristic, complemented
3#14529582C211yesmaximal, characteristic, complemented
4#14529582C211yesmaximal, characteristic, complemented
5#14529581C211yesmaximal, characteristic, complemented
6#14529581C211yesmaximal, characteristic, complemented
7#14529578C211yesmaximal, characteristic, complemented
8#14529577C211yesmaximal, characteristic, complemented
9#14528765C211yesmaximal, characteristic, complemented
10#14528765C211yesmaximal, characteristic, complemented
11#14528761C211yesmaximal, characteristic, complemented
12#14528553C211yesmaximal, characteristic, complemented
13#14528551C211yesmaximal, characteristic, complemented
14#14528547C211yesmaximal, characteristic, complemented
15C2×C17×#446C211yesmaximal, characteristic, complemented
16#11763346—24no—
17#11763346—24no—
18C2×#10587584C411yescharacteristic
19C2×#10587584C411yescharacteristic
20C2×#10587576C411yescharacteristic
21C2×#10587633C411yescharacteristic
22C2×#10587580C411yescharacteristic
23C2×#10587580C411yescharacteristic
24C2×#10587632C411yescharacteristic
25C2×#10587581C411yescharacteristic
26C2×C4×D68C2211yescharacteristic
27C2×C4×D68C2211yescharacteristic
28C2×C4×D68C2211yescharacteristic
29C2×#10587558C2211yescharacteristic
30C2×#10587558C2211yescharacteristic
31C2×C42×D17C2211yescharacteristic
32#11762940—24no—
33C2×C4⋊#3622C2211yescharacteristic
34C2×C4⋊#3622C2211yescharacteristic
35C2×C4⋊#3622C2211yescharacteristic
36C2×#10587491C2211yescharacteristic
37C2×#10587491C2211yescharacteristic
38C2×#10587491C2211yescharacteristic
39C2×#10587491C2211yescharacteristic
40C2×#10587491C2211yescharacteristic
41C2×#10587491C2211yescharacteristic
42C2×#10587491C2211yescharacteristic
43C2×#10587491C2211yescharacteristic
44C2×#10587491C2211yescharacteristic
45C2×#10587491C2211yescharacteristic
46C2×#10587491C2211yescharacteristic
47C2×#10587491C2211yescharacteristic
48C2×#10587474C2211yescharacteristic
49C2×#10587474C2211yescharacteristic
50C2×C4×#3622C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54#11762563C2211yescharacteristic
55C2×C4×Q8×C17C2211yescharacteristic
56C17×#446—24no—
57C2×C17×C4⋊C8C2211yescharacteristic
58C2×C17×C4⋊C8C2211yescharacteristic
59C2×C17×C4⋊C8C2211yescharacteristic
60C2×C17×#97C2211yescharacteristic
61C2×C17×#97C2211yescharacteristic
62C2×C4×C8×C17C2211yescharacteristic
63C22×Q8×C17C2×C411yescharacteristic
64C22×D68C2×C411yescharacteristic
65C22×D68C2×C411yescharacteristic
66C22×D68C2×C411yescharacteristic
67C22×C4×D17C2×C411yescharacteristic
68C22×C4×D17C2×C411yescharacteristic
69C22×C4×D17C2311yescharacteristic
70C22×C4×D17C2311yescharacteristic
71C22×C4×D17C2311yescharacteristic
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C22×C8×C17C2311yescharacteristic
75C22×C8×C17C2311yescharacteristic
76C4×Q8×C17D414yes—
77C4×Q8×C17D414yes—
78C2×C4⋊C4×C17C2×C411yescharacteristic
79C2×C4⋊C4×C17C2×C411yescharacteristic
80C2×C4⋊C4×C17C2×C411yescharacteristic
81C2×C42×C17C2311yescharacteristic
82C2×C42×C17C2311yescharacteristic
83C2×C42×C17C2311yescharacteristic
84#10587633—24no—
85#10587632—24no—
86C2×#63227C2×C411yescharacteristic
87C2×#63227C2×C411yescharacteristic
88C2×#63227C2×C411yescharacteristic
89C2×#63227C2×C411yescharacteristic
90C2×#63227C2×C411yescharacteristic
91C2×#63227C2×C411yescharacteristic
92C2×#63227C2×C411yescharacteristic
93C2×#63227C2×C411yescharacteristic
94C2×#63227C2×C411yescharacteristic
95C2×#63227C2×C411yescharacteristic
96C2×C4⋊Dic17C2×C411yescharacteristic
97C2×C4⋊Dic17C2×C411yescharacteristic
98C2×C4⋊Dic17C2×C411yescharacteristic
99C2×#63225C2×C411yescharacteristic
100C2×#63225C2×C411yescharacteristic
101C2×#63225C2×C411yescharacteristic
102C2×#63225C2×C411yescharacteristic
103C2×C4×Dic17C2×C411yescharacteristic
104C2×C4×Dic17C2×C411yescharacteristic
105C2×C4×Dic17C2311yescharacteristic
106C22×#3622C2311yescharacteristic
107C22×#3622C2311yescharacteristic
108C22×#3622C2311yescharacteristic
109C22×#3622C2311yescharacteristic
110#10587584—24no—
111#10587584—24no—
112#10587581—24no—
113#10587580—24no—
114#10587580—24no—
115#10587576—24no—
116C4×D68—22no—
117C4×D68—22no—
118C4×D68—22no—
119C4×D68—22no—
120C4×D68—22no—
121C4×D68—22no—
122#10587558—22no—
123#10587558—22no—
124#10587558—22no—
125#10587558—22no—
126C42×D17—22no—
127C42×D17—22no—
128C17×C4⋊C8—22no—
129C17×C4⋊C8—22no—
130C17×C4⋊C8—22no—
131C17×#97—22no—
132C17×#97—22no—
133C4×C8×C17—22no—
134#10587491—22no—
135#10587491—22no—
136#10587491—22no—
137#10587491—22no—
138#10587491—22no—
139#10587491—22no—
140#10587491—41no—
141#10587491—41no—
142#10587491—41no—
143#10587491—41no—
144#10587491—41no—
145#10587491—41no—
146C4⋊#3622—22no—
147C4⋊#3622—22no—
148C4⋊#3622—22no—
149#10587474—22no—
150#10587474—22no—
151C4×#3622—22no—
152C23×D17C22×C411yescharacteristic
153C23×D17C22×C411yescharacteristic
154C23×D17C22×C411yescharacteristic
155C2×Q8×C17—41no—
156C2×Q8×C17—41no—
157C2×Q8×C17C22⋊C414yes—
158C22×C4×C17C22×C411yescharacteristic
159C22×C4×C17C22×C411yescharacteristic
160C22×C4×C17C22×C411yescharacteristic
161C22×C4×C17C22×C411yescharacteristic
162C22×C4×C17C22×C411yescharacteristic
163C22×C4×C17C22×C411yescharacteristic
164C22×C4×C17C2411yescharacteristic
165C22×Dic17C22×C411yescharacteristic
166C22×Dic17C22×C411yescharacteristic
167C22×Dic17C22×C411yescharacteristic
168C22×Dic17C22×C411yescharacteristic
169C22×Dic17C22×C411yescharacteristic
170C2×D68—22no—
171C2×D68—22no—
172C2×D68—22no—
173C2×D68—22no—
174C2×D68—22no—
175C2×D68—41no—
176C2×D68—41no—
177C2×D68—41no—
178C2×D68—41no—
179C2×C4×D17—22no—
180C2×C4×D17—22no—
181C2×C4×D17—22no—
182C2×C4×D17—21no—
183C2×C4×D17—21no—
184C2×C4×D17—21no—
185C2×C4×D17—21no—
186C2×C4×D17—21no—
187C2×C4×D17—21no—
188C2×C4×D17—21no—
189C2×C4×D17—21no—
190C2×C4×D17—21no—
191C2×C4×D17—21no—
192C2×C4×D17—21no—
193C2×C4×D17—21no—
194C2×C4×D17—21no—
195C2×C4×D17—21no—
196C2×C4×D17—21no—
197C2×C4×D17—21no—
198C2×C4×D17—21no—
199C2×C4×D17—21no—
200C2×C4×D17—41no—
201C2×C4×D17—41no—
202C2×C4×D17—41no—
203C2×C8×C17—21no—
204C2×C8×C17—21no—
205C2×C8×C17—21no—
206C2×C8×C17—21no—
207C2×C8×C17—21no—
208C2×C8×C17—21no—
209C2×C8×C17—21no—
210C2×C8×C17—21no—
211C2×C8×C17—21no—
212C2×C8×C17—21no—
213C2×C8×C17—21no—
214C2×C8×C17#4112yes—
215C4⋊C4×C17C22⋊C414yes—
216C4⋊C4×C17C22⋊C414yes—
217C4⋊C4×C17C22⋊C414yes—
218C42×C17C2×D412yes—
219C42×C17C2×D412yes—
220C42×C17C2×D412yes—
221C42×C17C2×D412yes—
222C42×C17C2×D412yes—
223C42×C17C2×D412yes—
224#63227—22no—
225#63227—22no—
226#63227—22no—
227#63227—22no—
228#63227—22no—
229#63227—22no—
230#63227—22no—
231#63227—22no—
232#63227—22no—
233#63227—22no—
234C4⋊Dic17—22no—
235C4⋊Dic17—22no—
236C4⋊Dic17—22no—
237#63225—22no—
238#63225—22no—
239#63225—22no—
240#63225—22no—
241C4×Dic17—22no—
242C4×Dic17—22no—
243C4×Dic17—21no—
244C4×Dic17—21no—
245C2×#3622—21no—
246C2×#3622—21no—
247C2×#3622—21no—
248C2×#3622—21no—
249C2×#3622—21no—
250C2×#3622—21no—
251C2×#3622—21no—
252C2×#3622—21no—
253C2×#3622—21no—
254C2×#3622—21no—
255C2×#3622—21no—
256C2×#3622#4112yes—
257#22533—171nomaximal, Sylow
258C23×C17C23×C411yescharacteristic
259C22×D17—21no—
260C22×D17—21no—
261C22×D17—21no—
262C22×D17—21no—
263C22×D17—21no—
264C22×D17—21no—
265C22×D17—21no—
266C22×D17—21no—
267C22×D17—21no—
268C22×D17—21no—
269C22×D17—21no—
270C22×D17—21no—
271C22×D17—21no—
272C22×D17—21no—
273C22×D17—21no—
274C22×D17—21no—
275C22×D17—21no—
276C22×D17—21no—
277C22×D17—21no—
278C22×D17—21no—
279C22×D17#13112yes—
280Q8×C17—44no—
281C2×C4×C17—21no—
282C2×C4×C17—21no—
283C2×C4×C17—21no—
284C2×C4×C17—21no—
285C2×C4×C17—21no—
286C2×C4×C17—21no—
287C2×C4×C17—21no—
288C2×C4×C17—21no—
289C2×C4×C17—21no—
290C2×C4×C17—21no—
291C2×C4×C17—21no—
292C2×C4×C17—21no—
293C2×C4×C17C2×C22⋊C412yes—
294C2×C4×C17C2×C22⋊C412yes—
295C2×C4×C17C2×C22⋊C412yes—
296C2×C4×C17C2×C22⋊C412yes—
297C2×C4×C17C2×C22⋊C412yes—
298C2×C4×C17C2×C22⋊C412yes—
299C2×C4×C17C22×D411yescharacteristic
300C2×C4×C17C22×D411yescharacteristic
301C2×C4×C17C2×#4111yescharacteristic
302C2×C4×C17C2×#4111yescharacteristic
303C2×C4×C17H(5,𝔽2)11yescharacteristic
304C2×C4×C172−1+411yescharacteristic
305C2×Dic17—21no—
306C2×Dic17—21no—
307C2×Dic17—21no—
308C2×Dic17—21no—
309C2×Dic17—21no—
310C2×Dic17—21no—
311C2×Dic17—21no—
312C2×Dic17—21no—
313C2×Dic17—21no—
314C2×Dic17—21no—
315C2×Dic17—21no—
316C2×Dic17—21no—
317C2×Dic17—21no—
318C2×Dic17—21no—
319C2×Dic17—21no—
320D68—44no—
321D68—44no—
322D68—44no—
323C4×D17—44no—
324C4×D17—44no—
325C4×D17—41no—
326C4×D17—41no—
327C4×D17—41no—
328C4×D17—41no—
329C4×D17—41no—
330C4×D17—41no—
331C4×D17—41no—
332C4×D17—41no—
333C4×D17—41no—
334C4×D17—41no—
335C4×D17—41no—
336C4×D17—41no—
337C8×C17—22no—
338C8×C17—41no—
339C8×C17—41no—
340C8×C17—41no—
341#3622—22no—
342#3622—41no—
343#3622—41no—
344#3622—41no—
345C2×#529—171no—
346C2×#446—171no—
347C2×#446D1711yescharacteristic, complemented
348#1955—171no—
349#1955—171no—
350#1955—171no—
351#1955—171no—
352#1954—171no—
353#1954—171no—
354#1798—171no—
355#1798—171no—
356#1797—171no—
357#1750—171no—
358#1750—171no—
359#1749—171no—
360C22×C17C22×C22⋊C411yescharacteristic
361C22×C17C4×#4111yescharacteristic
362C22×C17#52011yescharacteristic
363C22×C17C2×#13111yescharacteristic
364C22×C17#56811yescharacteristic
365C22×C17#56811yescharacteristic
366C22×C17#56811yescharacteristic
367C2×D17—22no—
368C2×D17—22no—
369C2×D17—22no—
370C2×D17—41no—
371C2×D17—41no—
372C2×D17—41no—
373C2×D17—41no—
374C2×D17—41no—
375C2×D17—41no—
376C2×D17—41no—
377C2×D17—41no—
378C2×D17—41no—
379C2×D17—41no—
380C2×D17—41no—
381C2×D17—41no—
382C2×D17—41no—
383C2×D17—41no—
384C2×D17—41no—
385C2×D17—41no—
386C2×D17—41no—
387C2×D17—41no—
388C4×C17—22no—
389C4×C17—22no—
390C4×C17—22no—
391C4×C17—22no—
392C4×C17—22no—
393C4×C17—22no—
394C4×C17#54811yescharacteristic
395C4×C17#54811yescharacteristic
396C4×C17#55011yescharacteristic
397C4×C17#55011yescharacteristic
398Dic17—41no—
399Dic17—41no—
400Dic17—41no—
401Dic17—41no—
402Dic17—41no—
403#529—344no—
404#529—344no—
405C2×#126—171no—
406C2×#126—171no—
407C2×#125—171no—
408C2×#124—171no—
409C2×#123—171no—
410C2×#123—171no—
411C2×C22⋊Q8—171no—
412C2×#121—171no—
413C2×C4×Q8C2×D1711yescharacteristic
414C2×C4×D4—171no—
415C2×C4×D4—171no—
416C2×C4×D4—171no—
417C2×#117—171no—
418C2×#117—171no—
419C22×C42—171no—
420#446—24no—
421#446—344no—
422C2×C4⋊C8—171no—
423C2×C4⋊C8—171no—
424C2×C4⋊C8—171no—
425C2×C4⋊C8C2×D1711yescharacteristic
426C2×C4⋊C8C2×D1711yescharacteristic
427C2×C4⋊C8C2×D1711yescharacteristic
428C2×C22⋊C8—171no—
429C2×C22⋊C8—171no—
430C2×C22⋊C8—171no—
431C2×C22⋊C8—171no—
432C2×C22⋊C8—171no—
433C2×C22⋊C8—171no—
434C2×C22⋊C8—171no—
435C2×C22⋊C8—171no—
436C2×C22⋊C8—171no—
437C2×C22⋊C8—171no—
438C2×C22⋊C8—171no—
439C2×C22⋊C8—171no—
440C2×#97—171no—
441C2×#97—171no—
442C2×#97C2×D1711yescharacteristic
443C2×#97C2×D1711yescharacteristic
444C2×C4×C8—171no—
445C2×C4×C8C2×D1711yescharacteristic
446#336—171no—
447#336—171no—
448#336—171no—
449#336—171no—
450C2×C17#234111yescharacteristic
451C2×C17#287911yescharacteristic
452C2×C17#288011yescharacteristic
453C2×C17#296711yescharacteristic
454C2×C17#296811yescharacteristic
455C2×C17#299211yescharacteristic
456C2×C17#299511yescharacteristic
457D17—42no—
458D17—81no—
459D17—81no—
460C22×Q8C4×D1711yescharacteristic
461C22×D4—171no—
462C22×D4—171no—
463C22×D4—171no—
464C23×C4—171no—
465C23×C4—171no—
466C23×C4—171no—
467C23×C4—171no—
468C23×C4—171no—
469C22×C8—171no—
470C22×C8—171no—
471C22×C8—171no—
472C22×C8—171no—
473C22×C8C22×D1711yescharacteristic
474C22×C8C22×D1711yescharacteristic
475C22×C8C22×D1711yescharacteristic
476C22×C8C22×D1711yescharacteristic
477#126—344no—
478#126—344no—
479#125—344no—
480#124—344no—
481#123—344no—
482#123—344no—
483C22⋊Q8—344no—
484#121—344no—
485C4×Q8D6814yes—
486C4×Q8C22⋊D1714yes—
487C4×D4—342no—
488C4×D4—342no—
489C4×D4—342no—
490C4×D4—342no—
491C4×D4—342no—
492C4×D4—342no—
493#117—342no—
494#117—342no—
495#117—342no—
496#117—342no—
497C2×C4⋊C4—171no—
498C2×C4⋊C4—171no—
499C2×C4⋊C4—171no—
500C2×C4⋊C4—171no—
501C2×C4⋊C4—171no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—171no—
504C2×C4⋊C4C4×D1711yescharacteristic
505C2×C4⋊C4C4×D1711yescharacteristic
506C2×C4⋊C4C4×D1711yescharacteristic
507C2×C22⋊C4—171no—
508C2×C22⋊C4—171no—
509C2×C22⋊C4—171no—
510C2×C22⋊C4—171no—
511C2×C22⋊C4—171no—
512C2×C22⋊C4—171no—
513C2×C22⋊C4—171no—
514C2×C22⋊C4—171no—
515C2×C22⋊C4—171no—
516C2×C22⋊C4—171no—
517C2×C42—171no—
518C2×C42—171no—
519C2×C42—171no—
520C2×C42—342no—
521C2×C42—342no—
522C2×C42C22×D1711yescharacteristic
523C2×C42C22×D1711yescharacteristic
524C2×C42C22×D1711yescharacteristic
525C4⋊C8—22no—
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—342no—
529C4⋊C8—342no—
530C4⋊C8—342no—
531C22⋊C8—342no—
532C22⋊C8—342no—
533C22⋊C8—342no—
534C22⋊C8—342no—
535C22⋊C8—342no—
536C22⋊C8—342no—
537C22⋊C8—681no—
538C22⋊C8—681no—
539C22⋊C8—681no—
540C22⋊C8—681no—
541C22⋊C8—681no—
542C22⋊C8—681no—
543#97—22no—
544#97—22no—
545#97—342no—
546#97—342no—
547C4×C8—22no—
548C4×C8—342no—
549C17#2253311yescharacteristic, complemented, Sylow
550C24—171no—
551C24—171no—
552C24—171no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8#6322714yes—
556C2×D4—342no—
557C2×D4—342no—
558C2×D4—342no—
559C2×D4—342no—
560C2×D4—342no—
561C2×D4—681no—
562C2×D4—681no—
563C2×D4—681no—
564C2×D4—681no—
565C22×C4—171no—
566C22×C4—171no—
567C22×C4—171no—
568C22×C4—171no—
569C22×C4—171no—
570C22×C4—342no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—341no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—341no—
586C22×C4—341no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—681no—
592C22×C4—681no—
593C22×C4—681no—
594C22×C4C2×C4×D1711yescharacteristic
595C22×C4C2×C4×D1711yescharacteristic
596C22×C4C2×C4×D1711yescharacteristic
597C22×C4C2×C4×D1711yescharacteristic
598C22×C4C2×C4×D1711yescharacteristic
599C22×C4C2×C4×D1711yescharacteristic
600C22×C4C23×D1711yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—172no—
613C2×C8—341no—
614C2×C8—341no—
615C2×C8—341no—
616C2×C8—341no—
617C2×C8—341no—
618C2×C8—341no—
619C2×C8—341no—
620C2×C8—341no—
621C2×C8—341no—
622C2×C8—341no—
623C2×C8—341no—
624C2×C8#6325612yes—
625C4⋊C4—342no—
626C4⋊C4—342no—
627C4⋊C4—342no—
628C4⋊C4—342no—
629C4⋊C4—342no—
630C4⋊C4—342no—
631C4⋊C4—342no—
632C4⋊C4#6322714yes—
633C4⋊C4#6322714yes—
634C4⋊C4#6322714yes—
635C22⋊C4—342no—
636C22⋊C4—342no—
637C22⋊C4—342no—
638C22⋊C4—342no—
639C22⋊C4—342no—
640C22⋊C4—342no—
641C22⋊C4—342no—
642C22⋊C4—342no—
643C22⋊C4—342no—
644C22⋊C4—342no—
645C42—341no—
646C42—341no—
647C42—342no—
648C42—342no—
649C42C2×D6812yes—
650C42C2×D6812yes—
651C42C2×D6812yes—
652C42C2×C22⋊D1712yes—
653C42C2×C22⋊D1712yes—
654C42C2×C22⋊D1712yes—
655C23—172no—
656C23—341no—
657C23—341no—
658C23—341no—
659C23—341no—
660C23—341no—
661C23—341no—
662C23—341no—
663C23—341no—
664C23—341no—
665C23—341no—
666C23—341no—
667C23—341no—
668C23—341no—
669C23—341no—
670C23—341no—
671C23—341no—
672C23—341no—
673C23—341no—
674C23—341no—
675C23—341no—
676C23C22×C4×D1711yescharacteristic
677Q8—44no—
678D4—684no—
679D4—684no—
680D4—684no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—341no—
694C2×C4—341no—
695C2×C4—341no—
696C2×C4—341no—
697C2×C4—341no—
698C2×C4—341no—
699C2×C4—341no—
700C2×C4—341no—
701C2×C4—341no—
702C2×C4—341no—
703C2×C4—341no—
704C2×C4—341no—
705C2×C4—341no—
706C2×C4—341no—
707C2×C4—341no—
708C2×C4—684no—
709C2×C4—684no—
710C2×C4—681no—
711C2×C4—681no—
712C2×C4—681no—
713C2×C4—681no—
714C2×C4—681no—
715C2×C4—681no—
716C2×C4—681no—
717C2×C4—681no—
718C2×C4—681no—
719C2×C4—681no—
720C2×C4—681no—
721C2×C4—681no—
722C2×C4C2×#6322712yes—
723C2×C4C2×#6322712yes—
724C2×C4C2×#6322712yes—
725C2×C4C2×#6322712yes—
726C2×C4C2×#6322712yes—
727C2×C4C2×#6322712yes—
728C2×C4C22×D6811yescharacteristic
729C2×C4C2×#6325611yescharacteristic
730C2×C4#1058769411yescharacteristic
731C2×C4#41×D1711yescharacteristic
732C2×C4#1058769611yescharacteristic
733C2×C4C22×C22⋊D1711yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—342no—
739C8—681no—
740C8—681no—
741C8—681no—
742C22—342no—
743C22—342no—
744C22—342no—
745C22—681no—
746C22—681no—
747C22—681no—
748C22—681no—
749C22—681no—
750C22—681no—
751C22—681no—
752C22—681no—
753C22—681no—
754C22—681no—
755C22—681no—
756C22—681no—
757C22—681no—
758C22—681no—
759C22—681no—
760C22—681no—
761C22—681no—
762C22—681no—
763C22C22×#6322711yescharacteristic
764C22C4×#6325611yescharacteristic
765C22#1176329111yescharacteristic
766C22#131×D1711yescharacteristic
767C22#1176357411yescharacteristic
768C22#1176357511yescharacteristic
769C22#1176357511yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—681no—
777C4—681no—
778C4—681no—
779C4—681no—
780C4—681no—
781C4#1176347011yescharacteristic
782C4#1176347111yescharacteristic
783C4#1176347811yescharacteristic
784C4#1176348111yescharacteristic
785C2—682no—
786C2—1361no—
787C2—1361no—
788C2#1453162211yescharacteristic
789C2#1453722811yescharacteristic
790C2#1453723111yescharacteristic
791C2#1453776811yescharacteristic
792C2#1453777711yescharacteristic
793C2#1453792211yescharacteristic
794C2#1453795311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC2×C17×#446C2
prime radicalC2×#10587581C4
cosocleC22×C4×C17C24
hypercenterC2×#446D17
hypocenterC17#22533
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#11762940C2semidirect
3. #14529582C2semidirect
4. #14529582C2semidirect
5. #14529581C2semidirect
6. #14529581C2semidirect
7. #14529578C2semidirect
8. #14529577C2semidirect
9. #14528765C2semidirect
10. #14528765C2semidirect
11. #14528761C2semidirect
12. #14528553C2semidirect
13. #14528551C2semidirect
14. #14528547C2semidirect
15. C2×C17×#446C2semidirect
347. C2×#446D17semidirect
549. C17#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#117633462
C2×#117629402
#145295822
#145295812
#145295782
#145295772
#145287652
#145287612
#145285532
#145285512
#145285472
C2×C17×#4462
#2253317