Finite Group Databasebeta

← #16957112

Subgroups — #16957112

Order 4352.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587632C211yesmaximal, characteristic
2C2×#11762716C211yesmaximal, characteristic, complemented
3C2×#11762666C211yesmaximal, characteristic
4C2×C4×#63227C211yesmaximal, characteristic
5#14527034C212yesmaximal, complemented
6#14527026C212yesmaximal
7#14527022C212yesmaximal
8#14527017C212yesmaximal, complemented
9#14527014C211yesmaximal, characteristic, complemented
10#14527013C211yesmaximal, characteristic, complemented
11C22×C4×Q8×C17C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C2×#10587632—24no—
14C2×#10587632—24no—
15C2×#10587632C418yescomplemented
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2212yes—
19C22×#63227C2211yescharacteristic
20C22×#63227C2212yes—
21C22×#63227C2212yes—
22C22×#63227C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24#11762716—24no—
25#11762666—24no—
26C4×#63227—24no—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C23×Q8×C17C2211yescharacteristic
37C2×C4×Q8×C17—24no—
38C2×C4×Q8×C17—24no—
39C2×C4×Q8×C17—24no—
40C22×C4⋊C4×C17C2212yes—
41C22×C4⋊C4×C17C2211yescharacteristic
42C22×C42×C17C2212yes—
43C22×C42×C17C2211yescharacteristic
44C24×D17C2311yescharacteristic
45C22×Q8×C17—22no—
46C22×Q8×C17—22no—
47C22×Q8×C17—22no—
48C22×Q8×C17—22no—
49C22×Q8×C17C2×C414yes—
50C22×Q8×C17D414yes—
51C22×Q8×C17D414yes—
52C23×C4×C17C2312yes—
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2312yes—
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×Dic17C2312yes—
58C23×Dic17C2312yes—
59C23×Dic17C2311yescharacteristic
60C23×Dic17C2311yescharacteristic
61C23×Dic17C2311yescharacteristic
62C22×C4×D17—22no—
63C22×C4×D17—22no—
64C22×C4×D17—22no—
65C22×C4×D17—22no—
66C22×C4×D17—22no—
67C22×C4×D17—22no—
68C22×C4×D17C2×C414yes—
69C4×Q8×C17—232no—
70C2×C4⋊C4×C17—24no—
71C2×C4⋊C4×C17—24no—
72C2×C4⋊C4×C17—24no—
73C2×C4⋊C4×C17—22no—
74C2×C4⋊C4×C17—22no—
75C2×C4⋊C4×C17D414yes—
76C2×C42×C17—24no—
77C2×C42×C17—24no—
78C2×C42×C17—24no—
79C2×C42×C17—22no—
80C2×C42×C17—22no—
81C2×C42×C17D414yes—
82#10587632—232no—
83C2×#63227—22no—
84C2×#63227—24no—
85C2×#63227—24no—
86C2×#63227—24no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—24no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—42no—
93C2×#63227C2×C418yes—
94C2×#63227Q814yescomplemented
95C2×C4⋊Dic17—22no—
96C2×C4⋊Dic17—22no—
97C2×C4⋊Dic17—22no—
98C2×C4⋊Dic17—22no—
99C2×C4⋊Dic17—22no—
100C2×C4⋊Dic17C2×C414yes—
101C2×#63225—24no—
102C2×#63225—24no—
103C2×#63225C2×C418yes—
104C2×C4×Dic17—22no—
105C2×C4×Dic17—22no—
106C2×C4×Dic17—22no—
107#10587502—24no—
108#10587502—24no—
109#10587502—22no—
110#10587502—22no—
111#10587502—24no—
112#10587502—24no—
113#10587502—24no—
114#10587502—42no—
115#10587502—42no—
116C24×C17C2411yescharacteristic
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17—21no—
122C23×D17—21no—
123C23×D17—21no—
124C23×D17—21no—
125C23×D17—21no—
126C23×D17—21no—
127C23×D17—21no—
128C23×D17—21no—
129C23×D17C22×C412yes—
130C23×D17C2×Q812yes—
131C23×D17#4112yes—
132C2×Q8×C17—28no—
133C2×Q8×C17—28no—
134C2×Q8×C17—28no—
135C2×Q8×C17—28no—
136C2×Q8×C17—28no—
137C2×Q8×C17—28no—
138C2×Q8×C17C22⋊C4116yescomplemented
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—22no—
148C22×C4×C17—21no—
149C22×C4×C17—22no—
150C22×C4×C17—21no—
151C22×C4×C17—22no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—22no—
155C22×C4×C17—21no—
156C22×C4×C17—22no—
157C22×C4×C17—21no—
158C22×C4×C17—22no—
159C22×C4×C17C22×C414yes—
160C22×C4×C17C22×C412yes—
161C22×C4×C17C2×D414yes—
162C22×C4×C17C2×D412yes—
163C22×C4×C17C2×D414yes—
164C22×C4×C17C2×D412yes—
165C22×C4×C17C2×D414yes—
166C22×C4×C17C2×D412yes—
167C22×C4×C17C2×D412yes—
168C22×C4×C17C2×D412yes—
169C22×C4×C17C2×D412yes—
170C22×C4×C17C2×Q812yes—
171C22×C4×C17#4112yes—
172C22×C4×C17#4112yes—
173C22×C4×C17#4112yes—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—21no—
181C22×Dic17—21no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—21no—
192C22×Dic17—22no—
193C22×Dic17—21no—
194C22×Dic17—22no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17C22×C412yes—
206C22×Dic17C22×C414yes—
207C22×Dic17C2×Q812yes—
208C22×Dic17#4112yes—
209C2×C4×D17—28no—
210C2×C4×D17—28no—
211C2×C4×D17—28no—
212C2×C4×D17—44no—
213C2×C4×D17—44no—
214C2×C4×D17—44no—
215C2×C4×D17—44no—
216C4⋊C4×C17—216no—
217C4⋊C4×C17—28no—
218C42×C17—216no—
219C42×C17—28no—
220#63227—28no—
221#63227—216no—
222#63227—28no—
223#63227—48no—
224C4⋊Dic17—28no—
225C4⋊Dic17—44no—
226#63225—216no—
227C4×Dic17—44no—
228#13969—171nomaximal, Sylow
229C23×C17C23×C411yescharacteristic
230C23×C17C22×D411yescharacteristic
231C23×C17C22×D411yescharacteristic
232C23×C17C22×D411yescharacteristic
233C23×C17C22×D411yescharacteristic
234C23×C17C22×Q811yescharacteristic
235C23×C17C2×#4111yescharacteristic
236C23×C17C2×#4111yescharacteristic
237C23×C17C2×#4111yescharacteristic
238C23×C17C2×#4111yescharacteristic
239C23×C17C2×#4111yescharacteristic
240C23×C17H(5,𝔽2)11yescharacteristic
241C23×C172−1+411yescharacteristic
242C23×C172−1+411yescharacteristic
243C23×C172−1+411yescharacteristic
244C22×D17—22no—
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17—22no—
257C22×D17—22no—
258C22×D17—22no—
259C22×D17—22no—
260C22×D17—22no—
261C22×D17—22no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—41no—
268C22×D17—41no—
269C22×D17—41no—
270C22×D17—41no—
271C22×D17—41no—
272C22×D17—41no—
273C22×D17—41no—
274C22×D17—41no—
275C22×D17—41no—
276C22×D17—41no—
277C22×D17—41no—
278C22×D17C4×Q814yescomplemented
279Q8×C17—232no—
280C2×C4×C17—24no—
281C2×C4×C17—24no—
282C2×C4×C17—22no—
283C2×C4×C17—24no—
284C2×C4×C17—24no—
285C2×C4×C17—24no—
286C2×C4×C17—24no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—24no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—24no—
297C2×C4×C17—24no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—41no—
306C2×C4×C17C2×C22⋊C418yes—
307C2×C4×C17C2×C22⋊C414yes—
308C2×C4×C17C4×D414yes—
309C2×C4×C17C4×D414yes—
310C2×C4×C17#12014yes—
311C2×C4×C17#12114yes—
312C2×C4×C17#12114yes—
313C2×C4×C17C22⋊Q814yescomplemented
314C2×C4×C17#12314yes—
315C2×Dic17—22no—
316C2×Dic17—24no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—24no—
320C2×Dic17—24no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—41no—
328C2×Dic17—41no—
329C2×Dic17—41no—
330C2×Dic17—41no—
331C2×Dic17—41no—
332C2×Dic17—41no—
333C2×Dic17—41no—
334C2×Dic17—41no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—41no—
338C2×Dic17—42no—
339C2×Dic17—42no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17—42no—
350C4×D17—416no—
351C22×C22⋊Q8—171no—
352C22×C4×Q8D1711yescharacteristic, complemented
353C2×#391—171no—
354C2×#380—171no—
355C2×C4×C22⋊C4—171no—
356#1441—172no—
357#1439—172no—
358#1437—172no—
359#1436—172no—
360C4⋊#95—171no—
361C4⋊#95—171no—
362C22×C17C22×C22⋊C411yescharacteristic
363C22×C17C2×C4×D411yescharacteristic
364C22×C17C2×C4×D411yescharacteristic
365C22×C17C2×C4×Q811yescharacteristic
366C22×C17C4×#4111yescharacteristic
367C22×C17#51911yescharacteristic
368C22×C17#52011yescharacteristic
369C22×C17C2×#12011yescharacteristic
370C22×C17C2×#12111yescharacteristic
371C22×C17C2×#12111yescharacteristic
372C22×C17C2×C22⋊Q811yescharacteristic
373C22×C17C2×#12311yescharacteristic
374C22×C17#52511yescharacteristic
375C22×C17#52911yescharacteristic
376C22×C17#53311yescharacteristic
377C22×C17#53611yescharacteristic
378C22×C17#53711yescharacteristic
379C22×C17#54111yescharacteristic
380C22×C17#54211yescharacteristic
381C22×C17#54611yescharacteristic
382C22×C17#54711yescharacteristic
383C22×C17#54811yescharacteristic
384C22×C17#54811yescharacteristic
385C22×C17#54811yescharacteristic
386C22×C17#54811yescharacteristic
387C22×C17#54811yescharacteristic
388C22×C17D4×Q811yescharacteristic
389C22×C17D4×Q811yescharacteristic
390C22×C17D4×Q811yescharacteristic
391C22×C17#55011yescharacteristic
392C22×C17#55011yescharacteristic
393C22×C17#55211yescharacteristic
394C22×C17#55211yescharacteristic
395C22×C17#55411yescharacteristic
396C22×C17#55611yescharacteristic
397C2×D17—24no—
398C2×D17—24no—
399C2×D17—24no—
400C2×D17—42no—
401C2×D17—42no—
402C2×D17—42no—
403C2×D17—42no—
404C2×D17—42no—
405C2×D17—42no—
406C2×D17—42no—
407C2×D17—42no—
408C2×D17—42no—
409C2×D17—42no—
410C2×D17—42no—
411C2×D17—42no—
412C4×C17—24no—
413C4×C17—28no—
414C4×C17—42no—
415C4×C17—44no—
416C4×C17#38618yes—
417Dic17—44no—
418Dic17—42no—
419Dic17—42no—
420Dic17—42no—
421Dic17—82no—
422C23×Q8C2×D1711yescharacteristic
423C24×C4—171no—
424C2×C22⋊Q8—178no—
425C2×C22⋊Q8—344no—
426C2×C22⋊Q8—344no—
427C2×C4×Q8—24no—
428C2×C4×Q8—24no—
429C2×C4×Q8—24no—
430C22×C4⋊C4—172no—
431C22×C4⋊C4—171no—
432C22×C4⋊C4—171no—
433C22×C4⋊C4C2×D1712yes—
434C22×C4⋊C4C2×D1711yescharacteristic
435C22×C22⋊C4—172no—
436C22×C22⋊C4—171no—
437C22×C22⋊C4—171no—
438C22×C22⋊C4—172no—
439C22×C42—171no—
440C22×C42C2×D1712yes—
441C22×C42C2×D1711yescharacteristic
442#391—344no—
443#380—344no—
444C4×C22⋊C4—344no—
445C2×#95—172no—
446C2×#95—172no—
447C2×#95—171no—
448C2×#95—172no—
449C2×#95—172no—
450C2×#95—172no—
451C2×#95—171no—
452C2×#95—172no—
453C2×#95—172no—
454C2×C17C2×#38611yescharacteristic
455C2×C17C4×C22⋊Q811yescharacteristic
456C2×C17#232311yescharacteristic
457C2×C17Q8×C22⋊C411yescharacteristic
458C2×C17#234111yescharacteristic
459C2×C17#236011yescharacteristic
460C2×C17#236211yescharacteristic
461C2×C17#240711yescharacteristic
462C2×C17#240911yescharacteristic
463C2×C17#242111yescharacteristic
464C2×C17#242311yescharacteristic
465C2×C17#242611yescharacteristic
466C2×C17#242911yescharacteristic
467C2×C17#253611yescharacteristic
468C2×C17#253811yescharacteristic
469D17—44no—
470C25—171no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8C4×D1714yes—
476C22×Q8D6814yes—
477C22×Q8C22⋊D1714yes—
478C23×C4—172no—
479C23×C4—171no—
480C23×C4—171no—
481C23×C4—171no—
482C23×C4—174no—
483C23×C4—172no—
484C23×C4—342no—
485C23×C4—342no—
486C23×C4—342no—
487C23×C4—342no—
488C23×C4—342no—
489C23×C4—342no—
490C23×C4C22×D1712yes—
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1712yes—
493C23×C4C22×D1711yescharacteristic
494C23×C4C22×D1711yescharacteristic
495C22⋊Q8—3432no—
496C4×Q8—232no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—178no—
503C2×C4⋊C4—174no—
504C2×C4⋊C4—344no—
505C2×C4⋊C4—342no—
506C2×C4⋊C4—344no—
507C2×C4⋊C4—342no—
508C2×C4⋊C4—342no—
509C2×C4⋊C4—342no—
510C2×C4⋊C4—342no—
511C2×C4⋊C4C22⋊D1714yes—
512C2×C22⋊C4—178no—
513C2×C22⋊C4—174no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—342no—
516C2×C22⋊C4—344no—
517C2×C22⋊C4—342no—
518C2×C22⋊C4—344no—
519C2×C22⋊C4—342no—
520C2×C22⋊C4—342no—
521C2×C22⋊C4—344no—
522C2×C22⋊C4—344no—
523C2×C22⋊C4—682no—
524C2×C42—24no—
525C2×C42—24no—
526C2×C42—24no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—342no—
530C2×C42—342no—
531C2×C42—342no—
532C2×C42C22⋊D1714yes—
533#95—344no—
534#95—344no—
535#95—344no—
536#95—344no—
537#95—342no—
538#95—342no—
539#95—344no—
540#95—682no—
541#95—682no—
542C17#1396911yescharacteristic, complemented, Sylow
543C24—172no—
544C24—172no—
545C24—172no—
546C24—341no—
547C24—341no—
548C24—341no—
549C24—341no—
550C24—341no—
551C24—341no—
552C24—341no—
553C24—341no—
554C24—341no—
555C24—341no—
556C24—341no—
557C24—341no—
558C24C23×D1711yescharacteristic
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8#63227116yescomplemented
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—174no—
587C22×C4—172no—
588C22×C4—172no—
589C22×C4—172no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—342no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—341no—
597C22×C4—341no—
598C22×C4—342no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—341no—
605C22×C4—341no—
606C22×C4—342no—
607C22×C4—341no—
608C22×C4—341no—
609C22×C4—341no—
610C22×C4—341no—
611C22×C4—341no—
612C22×C4—342no—
613C22×C4—341no—
614C22×C4—348no—
615C22×C4—348no—
616C22×C4—348no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—684no—
625C22×C4—684no—
626C22×C4—684no—
627C22×C4—684no—
628C22×C4C2×C4×D1714yes—
629C22×C4C2×C4×D1712yes—
630C22×C4C2×D6814yes—
631C22×C4C2×D6812yes—
632C22×C4#6325212yes—
633C22×C4#6325212yes—
634C22×C4Q8×D1712yes—
635C22×C4#6325612yes—
636C22×C4C2×C22⋊D1714yes—
637C22×C4C2×C22⋊D1712yes—
638C22×C4C2×C22⋊D1714yes—
639C22×C4C2×C22⋊D1712yes—
640C22×C4C2×C22⋊D1712yes—
641C22×C4C2×C22⋊D1712yes—
642C22×C4C2×C22⋊D1712yes—
643C4⋊C4—216no—
644C4⋊C4—28no—
645C4⋊C4—3416no—
646C4⋊C4—348no—
647C4⋊C4—684no—
648C22⋊C4—348no—
649C22⋊C4—3416no—
650C22⋊C4—348no—
651C22⋊C4—688no—
652C42—216no—
653C42—28no—
654C42—684no—
655C23—174no—
656C23—342no—
657C23—342no—
658C23—342no—
659C23—342no—
660C23—342no—
661C23—342no—
662C23—342no—
663C23—342no—
664C23—342no—
665C23—342no—
666C23—342no—
667C23—342no—
668C23—342no—
669C23—342no—
670C23—342no—
671C23—342no—
672C23—342no—
673C23—342no—
674C23—681no—
675C23—681no—
676C23—681no—
677C23—681no—
678C23—681no—
679C23—681no—
680C23—681no—
681C23—681no—
682C23—681no—
683C23—681no—
684C23—681no—
685C23—681no—
686C23—681no—
687C23—681no—
688C23—681no—
689C23—681no—
690C23C22×C4×D1711yescharacteristic
691C23C22×D6811yescharacteristic
692C23C2×#6325211yescharacteristic
693C23C2×#6325211yescharacteristic
694C23C2×Q8×D1711yescharacteristic
695C23C2×#6325611yescharacteristic
696C23#1058769411yescharacteristic
697C23#1058769411yescharacteristic
698C23#41×D1711yescharacteristic
699C23#41×D1711yescharacteristic
700C23#1058769611yescharacteristic
701C23#1058769711yescharacteristic
702C23C22×C22⋊D1711yescharacteristic
703C23C22×C22⋊D1711yescharacteristic
704C23C22×C22⋊D1711yescharacteristic
705Q8—232no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—342no—
733C2×C4—342no—
734C2×C4—342no—
735C2×C4—344no—
736C2×C4—342no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—344no—
741C2×C4—344no—
742C2×C4—342no—
743C2×C4—342no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4—681no—
747C2×C4—682no—
748C2×C4—682no—
749C2×C4—681no—
750C2×C4—681no—
751C2×C4—681no—
752C2×C4—681no—
753C2×C4—681no—
754C2×C4—681no—
755C2×C4—681no—
756C2×C4—681no—
757C2×C4—681no—
758C2×C4—681no—
759C2×C4—681no—
760C2×C4—6816no—
761C2×C4—682no—
762C2×C4—682no—
763C2×C4—682no—
764C2×C4—682no—
765C2×C4—682no—
766C2×C4—682no—
767C2×C4—682no—
768C2×C4C2×#6322718yes—
769C2×C4C2×#6322714yes—
770C2×C4C4×C22⋊D1714yes—
771C2×C4C4×C22⋊D1714yes—
772C2×C4#1058761514yes—
773C2×C4#1058761614yes—
774C2×C4#1058761614yes—
775C2×C4#1058763214yescomplemented
776C2×C4#1058763914yes—
777C22—344no—
778C22—344no—
779C22—344no—
780C22—682no—
781C22—682no—
782C22—682no—
783C22—682no—
784C22—682no—
785C22—682no—
786C22—682no—
787C22—682no—
788C22—682no—
789C22—682no—
790C22—682no—
791C22—682no—
792C22C22×#6322711yescharacteristic
793C22C2×C4×C22⋊D1711yescharacteristic
794C22C2×C4×C22⋊D1711yescharacteristic
795C22C4×Q8×D1711yescharacteristic
796C22C4×#6325611yescharacteristic
797C22#1176328511yescharacteristic
798C22#1176329111yescharacteristic
799C22C2×#1058763911yescharacteristic
800C22C2×#1058761611yescharacteristic
801C22C2×#1058761611yescharacteristic
802C22C2×#1058763211yescharacteristic
803C22C2×#1058761511yescharacteristic
804C22#1176331611yescharacteristic
805C22#1176334611yescharacteristic
806C22#1176336311yescharacteristic
807C22#1176338311yescharacteristic
808C22#1176338711yescharacteristic
809C22#1176341711yescharacteristic
810C22#1176343111yescharacteristic
811C22#1176344711yescharacteristic
812C22#1176345811yescharacteristic
813C22#1176346611yescharacteristic
814C22#1176347011yescharacteristic
815C22#1176347011yescharacteristic
816C22#1176347111yescharacteristic
817C22#1176347111yescharacteristic
818C22Q8×C22⋊D1711yescharacteristic
819C22Q8×C22⋊D1711yescharacteristic
820C22Q8×D6811yescharacteristic
821C22#1176347811yescharacteristic
822C22#1176348111yescharacteristic
823C22#1176350011yescharacteristic
824C22#1176350011yescharacteristic
825C22#1176351911yescharacteristic
826C22#1176353211yescharacteristic
827C4—24no—
828C4—28no—
829C4—44no—
830C4—42no—
831C4—684no—
832C4—682no—
833C4—682no—
834C4—682no—
835C4—1362no—
836C4#1176268818yes—
837C2—684no—
838C2C2×#1176268811yescharacteristic
839C2C4×#1058763211yescharacteristic
840C2#1453146011yescharacteristic
841C2Q8×#6322711yescharacteristic
842C2#1453162211yescharacteristic
843C2#1453178511yescharacteristic
844C2#1453180711yescharacteristic
845C2#1453212311yescharacteristic
846C2#1453214311yescharacteristic
847C2#1453228111yescharacteristic
848C2#1453230311yescharacteristic
849C2#1453234411yescharacteristic
850C2#1453237711yescharacteristic
851C2#1453368911yescharacteristic
852C2#1453370211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C4×Q8×C17C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC22×C4×Q8D17
hypocenterC17#13969
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11762716C2semidirect
5. #14527034C2semidirect
8. #14527017C2semidirect
9. #14527014C2semidirect
10. #14527013C2semidirect
11. C22×C4×Q8×C17C2semidirect
15. C2×#10587632C4semidirect
94. C2×#63227Q8semidirect
138. C2×Q8×C17C22⋊C4semidirect
278. C22×D17C4×Q8semidirect
313. C2×C4×C17C22⋊Q8semidirect
352. C22×C4×Q8D17semidirect
542. C17#13969semidirect
565. C2×Q8#63227semidirect
775. C2×C4#10587632semidirect

Maximal subgroups

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

subgroupindex
C22×#105876322
C2×#117627162
C2×#117626662
C2×C4×#632272
#145270342
#145270262
#145270222
#145270172
#145270142
#145270132
C22×C4×Q8×C172
#1396917