Finite Group Databasebeta

← #16965632

Subgroups — #16965632

Order 4352.

1422 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762693C211yesmaximal, characteristic
2C2×#11762691C211yesmaximal, characteristic
3C2×C42×Dic17C211yesmaximal, characteristic
4#14527019C211yesmaximal, characteristic
5#14527019C211yesmaximal, characteristic
6#14527019C211yesmaximal, characteristic
7#14527015C211yesmaximal, characteristic
8#14527015C211yesmaximal, characteristic
9#14527015C211yesmaximal, characteristic
10#14527015C211yesmaximal, characteristic
11#14527015C211yesmaximal, characteristic
12#14527009C211yesmaximal, characteristic
13#14527009C211yesmaximal, characteristic
14#14527009C211yesmaximal, characteristic
15C17×#1434C211yesmaximal, characteristic
16C22×#63225C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C4×Dic17C2211yescharacteristic
21C22×C4×Dic17C2211yescharacteristic
22C22×C4×Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26#11762693C418yescomplemented
27#11762691—24no—
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C42×Dic17—24no—
47C22×C42×C17C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17C2311yescharacteristic
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C2×C42×C17—22no—
70C2×C42×C17—22no—
71C2×C42×C17C2×C414yes—
72C2×#63225—22no—
73C2×#63225—22no—
74C2×#63225—22no—
75C2×#63225—22no—
76C2×#63225—22no—
77C2×#63225—22no—
78C2×#63225—22no—
79C2×#63225—22no—
80C2×#63225—22no—
81C2×#63225—22no—
82C2×#63225C2×C414yes—
83C2×#63225C2×C414yes—
84C2×C4×Dic17—22no—
85C2×C4×Dic17—22no—
86C2×C4×Dic17—22no—
87C2×C4×Dic17—22no—
88C2×C4×Dic17—22no—
89C2×C4×Dic17—22no—
90C2×C4×Dic17—22no—
91C2×C4×Dic17—22no—
92C2×C4×Dic17—22no—
93C2×C4×Dic17—22no—
94C2×C4×Dic17—22no—
95C2×C4×Dic17—22no—
96C2×C4×Dic17—22no—
97C2×C4×Dic17—22no—
98C2×C4×Dic17—22no—
99C2×C4×Dic17—22no—
100C2×C4×Dic17D414yes—
101C2×C4×Dic17Q814yes—
102C17×#95—22no—
103C17×#95—22no—
104C17×#95—22no—
105C17×#95—22no—
106C17×#95—22no—
107C17×#95—22no—
108#10587502—22no—
109#10587502—22no—
110#10587502—22no—
111#10587502—22no—
112#10587502—22no—
113#10587502—22no—
114#10587502—22no—
115#10587502—22no—
116#10587502—22no—
117#10587502—22no—
118#10587502—22no—
119#10587502—22no—
120#10587502—22no—
121#10587502—22no—
122#10587502C2×C414yes—
123#10587502C2×C414yes—
124#10587502C2×C414yes—
125#10587502C2×C414yes—
126C24×C17C2411yescharacteristic
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17C22×C412yes—
168C22×C4×C17C22×C412yes—
169C22×C4×C17C22×C412yes—
170C22×C4×C17C2×D412yes—
171C22×C4×C17C2×Q812yes—
172C22×C4×C17#4112yes—
173C22×C4×C17#4112yes—
174C22×C4×C17#4112yes—
175C22×C4×C17#4112yes—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—21no—
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—21no—
192C22×Dic17—21no—
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17C22×C412yes—
217C22×Dic17C22×C412yes—
218C22×Dic17C22×C412yes—
219C22×Dic17C22×C412yes—
220C22×Dic17C2×D412yes—
221C22×Dic17C2×D412yes—
222C22×Dic17C2×Q812yes—
223C22×Dic17C2×Q812yes—
224C22×Dic17#4112yes—
225C22×Dic17#4112yes—
226C22×Dic17#4112yes—
227C22×Dic17#4112yes—
228C22×Dic17#4112yes—
229C22×Dic17#4112yes—
230C22×Dic17#4112yes—
231C22×Dic17#4112yes—
232C42×C17—28no—
233#63225—28no—
234#63225—28no—
235#63225—44no—
236#63225—44no—
237C4×Dic17—28no—
238C4×Dic17—28no—
239C4×Dic17—28no—
240C4×Dic17—28no—
241C4×Dic17—28no—
242C4×Dic17—28no—
243#14704—171nomaximal, Sylow
244C23×C17C23×C411yescharacteristic
245C23×C17C22×D411yescharacteristic
246C23×C17C22×Q811yescharacteristic
247C23×C17C2×#4111yescharacteristic
248C23×C17C2×#4111yescharacteristic
249C23×C17C2×#4111yescharacteristic
250C23×C17C2×#4111yescharacteristic
251C23×C17C2×#4111yescharacteristic
252C23×C17C2×#4111yescharacteristic
253C23×C17C2×#4111yescharacteristic
254C23×C17C2×#4111yescharacteristic
255C23×C17C2×#4111yescharacteristic
256C23×C17C2×#4111yescharacteristic
257C23×C17C2×#4111yescharacteristic
258C23×C17C2×#4111yescharacteristic
259C2×C4×C17—22no—
260C2×C4×C17—22no—
261C2×C4×C17—22no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—41no—
278C2×C4×C17—41no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17#11714yes—
306C2×C4×C17C4×D414yes—
307C2×C4×C17C4×Q814yes—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—41no—
345C2×Dic17—41no—
346C2×Dic17—41no—
347C2×Dic17—41no—
348C2×Dic17—41no—
349C2×Dic17—41no—
350C2×Dic17—41no—
351C2×Dic17—41no—
352C2×Dic17—41no—
353C2×Dic17—41no—
354C2×Dic17—41no—
355C2×Dic17—41no—
356C2×Dic17—41no—
357C2×Dic17—41no—
358C2×Dic17—41no—
359C2×Dic17—41no—
360C2×Dic17C22⋊Q814yes—
361C2×Dic17#12314yes—
362C2×Dic17#12514yes—
363C2×Dic17#12614yes—
364C2×#387—171no—
365C2×#387—171no—
366C2×C43—171no—
367#1436—171no—
368#1436—171no—
369#1436—171no—
370#1436—171no—
371#1436—171no—
372#1436—171no—
373#1436—171no—
374#1436—171no—
375#1434—171no—
376#1434—171no—
377#1434—171no—
378#1434D1711yescharacteristic
379C22×C17C2×#11711yescharacteristic
380C22×C17C2×C4×D411yescharacteristic
381C22×C17C2×C4×Q811yescharacteristic
382C22×C17C4×#4111yescharacteristic
383C22×C17C4×#4111yescharacteristic
384C22×C17C4×#4111yescharacteristic
385C22×C17C4×#4111yescharacteristic
386C22×C17C2×C22⋊Q811yescharacteristic
387C22×C17C2×#12311yescharacteristic
388C22×C17#52511yescharacteristic
389C22×C17#52511yescharacteristic
390C22×C17#52511yescharacteristic
391C22×C17#52511yescharacteristic
392C22×C17C2×#12511yescharacteristic
393C22×C17C2×#12611yescharacteristic
394C22×C17#52911yescharacteristic
395C22×C17#52911yescharacteristic
396C22×C17#52911yescharacteristic
397C22×C17#52911yescharacteristic
398C22×C17#52911yescharacteristic
399C22×C17#52911yescharacteristic
400C22×C17#52911yescharacteristic
401C22×C17#52911yescharacteristic
402C22×C17#52911yescharacteristic
403C22×C17#52911yescharacteristic
404C22×C17#52911yescharacteristic
405C22×C17#52911yescharacteristic
406C22×C17#52911yescharacteristic
407C22×C17#52911yescharacteristic
408C22×C17#52911yescharacteristic
409C22×C17#52911yescharacteristic
410C22×C17#53311yescharacteristic
411C22×C17#53311yescharacteristic
412C22×C17#53311yescharacteristic
413C22×C17#53311yescharacteristic
414C4×C17—24no—
415C4×C17—24no—
416C4×C17—24no—
417C4×C17—81no—
418C4×C17—81no—
419C4×C17—81no—
420C4×C17—81no—
421Dic17—24no—
422Dic17—24no—
423Dic17—24no—
424Dic17—24no—
425Dic17—42no—
426Dic17—42no—
427Dic17—42no—
428Dic17—42no—
429C22×C4⋊C4—171no—
430C22×C4⋊C4—171no—
431C22×C4⋊C4—171no—
432C22×C4⋊C4—171no—
433C22×C42—171no—
434C22×C42—171no—
435C22×C42—171no—
436C22×C42—171no—
437C22×C42—171no—
438C22×C42—171no—
439C22×C42C2×D1711yescharacteristic
440#387—178no—
441#387—344no—
442C2×#95—171no—
443C2×#95—171no—
444C2×#95—171no—
445C2×#95—171no—
446C2×#95—171no—
447C2×#95—171no—
448C2×#95—171no—
449C2×#95—171no—
450C2×#95—171no—
451C2×#95—171no—
452C2×#95—171no—
453C2×#95—171no—
454C2×#95—171no—
455C2×#95—171no—
456C2×#95—171no—
457C2×#95—171no—
458C2×#95—171no—
459C2×#95—171no—
460C2×#95C2×D1711yescharacteristic
461C2×#95C2×D1711yescharacteristic
462C2×#95C2×D1711yescharacteristic
463C2×#95C2×D1711yescharacteristic
464C2×#95C2×D1711yescharacteristic
465C2×#95C2×D1711yescharacteristic
466C43—344no—
467C2×C17#229011yescharacteristic
468C2×C17#229511yescharacteristic
469C2×C17#229811yescharacteristic
470C2×C17C4×#12311yescharacteristic
471C2×C17C4×C22⋊Q811yescharacteristic
472C2×C17C4×#12611yescharacteristic
473C2×C17C4×#12511yescharacteristic
474C2×C17#285111yescharacteristic
475C2×C17#285211yescharacteristic
476C2×C17#285311yescharacteristic
477C2×C17#285511yescharacteristic
478C2×C17#286311yescharacteristic
479C2×C17#286411yescharacteristic
480C2×C17#286511yescharacteristic
481C2×C17#286611yescharacteristic
482C23×C4—171no—
483C23×C4—171no—
484C23×C4—171no—
485C23×C4—171no—
486C23×C4—171no—
487C23×C4—171no—
488C23×C4—171no—
489C23×C4—171no—
490C23×C4C22×D1711yescharacteristic
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1711yescharacteristic
493C23×C4C22×D1711yescharacteristic
494C23×C4C22×D1711yescharacteristic
495C23×C4C22×D1711yescharacteristic
496C23×C4C22×D1711yescharacteristic
497C2×C4⋊C4—174no—
498C2×C4⋊C4—174no—
499C2×C4⋊C4—342no—
500C2×C4⋊C4—342no—
501C2×C4⋊C4—342no—
502C2×C4⋊C4—342no—
503C2×C4⋊C4—342no—
504C2×C4⋊C4—342no—
505C2×C4⋊C4—342no—
506C2×C4⋊C4—342no—
507C2×C4⋊C4—342no—
508C2×C4⋊C4—342no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—174no—
512C2×C42—174no—
513C2×C42—342no—
514C2×C42—342no—
515C2×C42—342no—
516C2×C42—342no—
517C2×C42—342no—
518C2×C42—342no—
519C2×C42—342no—
520C2×C42—342no—
521C2×C42—342no—
522C2×C42—342no—
523C2×C42—342no—
524C2×C42—342no—
525C2×C42—342no—
526C2×C42—342no—
527C2×C42—342no—
528C2×C42—342no—
529C2×C42C4×D1714yes—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—174no—
537#95—174no—
538#95—174no—
539#95—174no—
540#95—342no—
541#95—342no—
542#95—342no—
543#95—342no—
544#95—342no—
545#95—342no—
546#95—342no—
547#95—342no—
548#95—342no—
549#95—342no—
550#95—342no—
551#95—342no—
552#95—342no—
553#95—342no—
554C17#1470411yescharacteristic, complemented, Sylow
555C24C23×D1711yescharacteristic
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—172no—
597C22×C4—172no—
598C22×C4—172no—
599C22×C4—172no—
600C22×C4—172no—
601C22×C4—172no—
602C22×C4—172no—
603C22×C4—172no—
604C22×C4—172no—
605C22×C4—172no—
606C22×C4—172no—
607C22×C4—172no—
608C22×C4—172no—
609C22×C4—172no—
610C22×C4—172no—
611C22×C4—172no—
612C22×C4—341no—
613C22×C4—341no—
614C22×C4—341no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—341no—
618C22×C4—341no—
619C22×C4—341no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—341no—
623C22×C4—341no—
624C22×C4—341no—
625C22×C4—341no—
626C22×C4—341no—
627C22×C4—341no—
628C22×C4—341no—
629C22×C4—341no—
630C22×C4—341no—
631C22×C4—341no—
632C22×C4—341no—
633C22×C4—341no—
634C22×C4—341no—
635C22×C4—341no—
636C22×C4—341no—
637C22×C4—341no—
638C22×C4—341no—
639C22×C4—341no—
640C22×C4—341no—
641C22×C4—341no—
642C22×C4—341no—
643C22×C4—341no—
644C22×C4—341no—
645C22×C4—341no—
646C22×C4—341no—
647C22×C4—341no—
648C22×C4—341no—
649C22×C4—341no—
650C22×C4—341no—
651C22×C4—341no—
652C22×C4C2×C4×D1712yes—
653C22×C4C2×C4×D1712yes—
654C22×C4C2×C4×D1712yes—
655C22×C4#6325212yes—
656C22×C4#6325212yes—
657C22×C4D4×D1712yes—
658C22×C4#6325412yes—
659C22×C4#6325412yes—
660C22×C4Q8×D1712yes—
661C4⋊C4—348no—
662C4⋊C4—348no—
663C4⋊C4—684no—
664C4⋊C4—684no—
665C42—28no—
666C42—348no—
667C42—348no—
668C42—348no—
669C42—348no—
670C42—348no—
671C42—348no—
672C23C22×C4×D1711yescharacteristic
673C23C2×#6325211yescharacteristic
674C23C2×#6325211yescharacteristic
675C23C2×D4×D1711yescharacteristic
676C23C2×#6325411yescharacteristic
677C23C2×#6325411yescharacteristic
678C23C2×Q8×D1711yescharacteristic
679C23#41×D1711yescharacteristic
680C23#41×D1711yescharacteristic
681C23#41×D1711yescharacteristic
682C23#41×D1711yescharacteristic
683C23#41×D1711yescharacteristic
684C23#41×D1711yescharacteristic
685C23#41×D1711yescharacteristic
686C23#41×D1711yescharacteristic
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—174no—
734C2×C4—174no—
735C2×C4—174no—
736C2×C4—174no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—342no—
744C2×C4—342no—
745C2×C4—342no—
746C2×C4—342no—
747C2×C4—342no—
748C2×C4—342no—
749C2×C4—342no—
750C2×C4—342no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—342no—
756C2×C4—342no—
757C2×C4—342no—
758C2×C4—342no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—342no—
766C2×C4—342no—
767C2×C4—342no—
768C2×C4—342no—
769C2×C4—342no—
770C2×C4—342no—
771C2×C4—342no—
772C2×C4—342no—
773C2×C4—681no—
774C2×C4—681no—
775C2×C4—681no—
776C2×C4—681no—
777C2×C4—681no—
778C2×C4—681no—
779C2×C4—681no—
780C2×C4—681no—
781C2×C4—681no—
782C2×C4—681no—
783C2×C4—681no—
784C2×C4—681no—
785C2×C4—681no—
786C2×C4—681no—
787C2×C4—681no—
788C2×C4—681no—
789C2×C4#1058755814yes—
790C2×C4#1058756714yes—
791C2×C4#1058757314yes—
792C22C2×#1058755811yescharacteristic
793C22C2×#1058756711yescharacteristic
794C22C2×#1058757311yescharacteristic
795C22#1176327711yescharacteristic
796C22#1176327711yescharacteristic
797C22#1176327711yescharacteristic
798C22#1176327711yescharacteristic
799C22C22⋊Q8×D1711yescharacteristic
800C22#123×D1711yescharacteristic
801C22#1176331711yescharacteristic
802C22#1176331811yescharacteristic
803C22#1176331811yescharacteristic
804C22#1176331911yescharacteristic
805C22#125×D1711yescharacteristic
806C22#126×D1711yescharacteristic
807C22#1176333611yescharacteristic
808C22#1176333611yescharacteristic
809C22#1176333711yescharacteristic
810C22#1176333711yescharacteristic
811C22#1176333711yescharacteristic
812C22#1176333711yescharacteristic
813C22#1176333811yescharacteristic
814C22#1176333811yescharacteristic
815C22#1176333911yescharacteristic
816C22#1176333911yescharacteristic
817C22#1176334011yescharacteristic
818C22#1176334111yescharacteristic
819C22#1176334111yescharacteristic
820C22#1176334211yescharacteristic
821C22#1176334211yescharacteristic
822C22#1176334211yescharacteristic
823C22#1176336111yescharacteristic
824C22#1176336311yescharacteristic
825C22#1176336311yescharacteristic
826C22#1176336511yescharacteristic
827C4—24no—
828C4—24no—
829C4—24no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4—344no—
835C4—344no—
836C4—344no—
837C4—344no—
838C4—682no—
839C4—682no—
840C4—682no—
841C4—682no—
842C2#1453122311yescharacteristic
843C2#1453125811yescharacteristic
844C2#1453127911yescharacteristic
845C2#1453130111yescharacteristic
846C2#1453131211yescharacteristic
847C2#1453133211yescharacteristic
848C2#1453133911yescharacteristic
849C2#1453709111yescharacteristic
850C2#1453709811yescharacteristic
851C2#1453710411yescharacteristic
852C2#1453711911yescharacteristic
853C2#1453716511yescharacteristic
854C2#1453716811yescharacteristic
855C2#1453717211yescharacteristic
856C2#1453717511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, prime radical, cosocleC24×C17C24
hypercenter#1434D17
hypocenterC17#14704
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
26. #11762693C4semidirect
554. C17#14704semidirect

Maximal subgroups

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

subgroupindex
C2×#117626932
C2×#117626912
C2×C42×Dic172
#145270192
#145270152
#145270092
C17×#14342
#1470417