Finite Group Databasebeta

← #17044346

Subgroups — #17044346

Order 4352.

1122 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊C4×D17C211yesmaximal, characteristic
2#14529393C211yesmaximal, characteristic, complemented
3#14529392C211yesmaximal, characteristic, complemented
4#14529391C211yesmaximal, characteristic, complemented
5#14529390C211yesmaximal, characteristic, complemented
6#14529389C211yesmaximal, characteristic, complemented
7#14529388C211yesmaximal, characteristic, complemented
8#14529387C211yesmaximal, characteristic, complemented
9#14528763C211yesmaximal, characteristic, complemented
10#14528761C211yesmaximal, characteristic, complemented
11#14528693C211yesmaximal, characteristic
12#14528693C211yesmaximal, characteristic
13C4×#10587491C211yesmaximal, characteristic, complemented
14#14528541C211yesmaximal, characteristic, complemented
15C17×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C2×C22⋊C4×D17C411yescharacteristic
18C2×C22⋊C4×D17C411yescharacteristic
19C2×C42×D17C2211yescharacteristic
20C2×C42×D17C2211yescharacteristic
21C2×C4⋊#3622C2211yescharacteristic, complemented
22C2×#10587485C2211yescharacteristic, complemented
23C2×#10587485C2211yescharacteristic, complemented
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×#10587491C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34C2×C4×#3622C2211yescharacteristic, complemented
35C2×C8×Dic17C2211yescharacteristic, complemented
36C2×C8×Dic17C2211yescharacteristic, complemented
37C22⋊C4×Dic17C411yescharacteristic
38C22⋊C4×Dic17C411yescharacteristic
39C4×#63227C2211yescharacteristic
40C4×#63227C2211yescharacteristic
41C4×C22⋊Dic17C2211yescharacteristic
42#11762656C411yescharacteristic
43#11762656C411yescharacteristic
44#95×D17C411yescharacteristic
45#95×D17C411yescharacteristic
46#11762564C2211yescharacteristic, complemented
47#11762564C2211yescharacteristic, complemented
48#11762563C2211yescharacteristic, complemented
49#11762563C2211yescharacteristic, complemented
50#11762563C2211yescharacteristic, complemented
51#11762563C2211yescharacteristic, complemented
52C2×C17×C4⋊C8C2211yescharacteristic, complemented
53C2×C17×C22⋊C8C2211yescharacteristic
54C2×C17×C22⋊C8C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic, complemented
56C4×C22⋊C4×C17C2211yescharacteristic
57C17×#336C2211yescharacteristic, complemented
58C17×#336C2211yescharacteristic, complemented
59C24×D17C2×C411yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17C2×C411yescharacteristic
62C22×C4×D17—22no—
63C22×C4×D17—22no—
64C22×C4×D17—41no—
65C22×C4×D17—41no—
66C22×C4×D17—41no—
67C22×C4×D17—41no—
68C22×C4×D17C2×C411yescharacteristic
69C22×C4×D17C2×C411yescharacteristic
70C22×C4×D17C2×C411yescharacteristic
71C22×C4×D17C2×C411yescharacteristic
72C22×C4×D17C2×C411yescharacteristic
73C22×C4×D17C2×C411yescharacteristic
74C22×C4×D17C2311yescharacteristic
75C22×C4×D17C2311yescharacteristic
76C22×C8×C17C2311yescharacteristic
77C22×C8×C17C2311yescharacteristic
78C22×C8×C17C2311yescharacteristic
79C22×C8×C17C2311yescharacteristic
80C2×C22⋊C4×C17C2×C411yescharacteristic
81C2×C22⋊C4×C17C2×C411yescharacteristic
82C2×C42×C17C2311yescharacteristic
83C2×C42×C17C2311yescharacteristic
84C2×C22⋊Dic17C2×C411yescharacteristic
85C2×C22⋊Dic17C2×C411yescharacteristic
86C2×#63227C2×C411yescharacteristic
87C2×#63227C2×C411yescharacteristic
88C2×#63227C2×C411yescharacteristic
89C2×#63227C2×C411yescharacteristic
90C2×C4×Dic17C2×C411yescharacteristic
91C2×C4×Dic17C2×C411yescharacteristic
92C2×C4×Dic17C2×C411yescharacteristic
93C2×C4×Dic17C2×C411yescharacteristic
94C2×C4×Dic17C2311yescharacteristic
95C2×C4×Dic17C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100C22⋊C4×D17—24no—
101C22⋊C4×D17C818yescomplemented
102C42×D17—41no—
103C42×D17—41no—
104C42×D17—41no—
105C42×D17—41no—
106C17×C4⋊C8—41no—
107C17×C22⋊C8—41no—
108C17×C22⋊C8—41no—
109C4×C8×C17—41no—
110C17×#95C2×C411yescharacteristic
111C17×#95C2×C411yescharacteristic
112#10587502C2×C411yescharacteristic
113#10587502C2×C411yescharacteristic
114#10587502C2×C411yescharacteristic
115#10587502C2×C411yescharacteristic
116#10587502C2×C411yescharacteristic
117#10587502C2×C411yescharacteristic
118C22⋊#3622—41no—
119C22⋊#3622—41no—
120#10587491—22no—
121#10587491—22no—
122#10587491—22no—
123#10587491—22no—
124#10587491—41no—
125#10587491—41no—
126#10587491—41no—
127#10587491—41no—
128#10587485—41no—
129#10587485—41no—
130C8×Dic17—41no—
131C8×Dic17—41no—
132C4⋊#3622—41no—
133C4×#3622—41no—
134C24×C17C22×C411yescharacteristic
135C23×D17—22no—
136C23×D17—22no—
137C23×D17—41no—
138C23×D17—41no—
139C23×D17—41no—
140C23×D17—41no—
141C23×D17C2×C814yes—
142C23×D17C22×C411yescharacteristic
143C23×D17C22×C411yescharacteristic
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×C17C22×C411yescharacteristic
151C22×C4×C17C22×C411yescharacteristic
152C22×C4×C17C22×C411yescharacteristic
153C22×C4×C17C22×C411yescharacteristic
154C22×C4×C17C22×C411yescharacteristic
155C22×C4×C17C2411yescharacteristic
156C22×Dic17—22no—
157C22×Dic17—41no—
158C22×Dic17—41no—
159C22×Dic17C22×C411yescharacteristic
160C22×Dic17C22×C411yescharacteristic
161C22×Dic17C22×C411yescharacteristic
162C22×Dic17C22×C411yescharacteristic
163C22×Dic17C22×C411yescharacteristic
164C22×Dic17C22×C411yescharacteristic
165C2×C4×D17—21no—
166C2×C4×D17—21no—
167C2×C4×D17—21no—
168C2×C4×D17—21no—
169C2×C4×D17—22no—
170C2×C4×D17—22no—
171C2×C4×D17—21no—
172C2×C4×D17—21no—
173C2×C4×D17—21no—
174C2×C4×D17—21no—
175C2×C4×D17—21no—
176C2×C4×D17—21no—
177C2×C4×D17—22no—
178C2×C4×D17—44no—
179C2×C4×D17—44no—
180C2×C4×D17—44no—
181C2×C4×D17—44no—
182C2×C4×D17—41no—
183C2×C4×D17—41no—
184C2×C4×D17—41no—
185C2×C4×D17—41no—
186C2×C4×D17—41no—
187C2×C4×D17—41no—
188C2×C4×D17—41no—
189C2×C4×D17—41no—
190C2×C4×D17—41no—
191C2×C4×D17—41no—
192C2×C4×D17—41no—
193C2×C4×D17—41no—
194C2×C4×D17C2×C814yes—
195C2×C4×D17C2×C814yes—
196C2×C4×D17M1614yes—
197C2×C4×D17#4112yes—
198C2×C4×D17#4112yes—
199C2×C8×C17—21no—
200C2×C8×C17—21no—
201C2×C8×C17—21no—
202C2×C8×C17—21no—
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—
211C22⋊C4×C17—22no—
212C22⋊C4×C17C2×C814yes—
213C42×C17—21no—
214C42×C17—21no—
215C42×C17—21no—
216C42×C17—21no—
217C22⋊Dic17—22no—
218C22⋊Dic17C2×C814yes—
219#63227—22no—
220#63227—22no—
221#63227C2×C814yes—
222#63227C2×C814yes—
223C4×Dic17—21no—
224C4×Dic17—21no—
225C4×Dic17—21no—
226C4×Dic17—21no—
227C4×Dic17—41no—
228C4×Dic17—41no—
229C4×Dic17—41no—
230C4×Dic17—41no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243#21902—171nomaximal, Sylow
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17C22×C812yes—
251C23×C17C23×C411yescharacteristic
252C22×D17—21no—
253C22×D17—21no—
254C22×D17—21no—
255C22×D17—21no—
256C22×D17—21no—
257C22×D17—21no—
258C22×D17—21no—
259C22×D17—21no—
260C22×D17—21no—
261C22×D17—21no—
262C22×D17—28no—
263C22×D17—44no—
264C22×D17—44no—
265C22×D17—44no—
266C22×D17—44no—
267C22×D17—44no—
268C22×D17—44no—
269C22×D17#11712yes—
270C22×D17C22×C812yes—
271C22×D17C22×C812yes—
272C22×D17C2×M1612yes—
273C2×C4×C17—21no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—21no—
280C2×C4×C17—21no—
281C2×C4×C17—21no—
282C2×C4×C17—21no—
283C2×C4×C17—21no—
284C2×C4×C17—21no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17C22×C812yes—
290C2×C4×C17C22×C812yes—
291C2×C4×C17C2×M1612yes—
292C2×C4×C17C2×#4111yescharacteristic
293C2×C4×C17C2×#4111yescharacteristic
294C2×C4×C17H(5,𝔽2)11yescharacteristic
295C2×C4×C17H(5,𝔽2)11yescharacteristic
296C2×C4×C17H(5,𝔽2)11yescharacteristic
297C2×C4×C17H(5,𝔽2)11yescharacteristic
298C2×Dic17—21no—
299C2×Dic17—21no—
300C2×Dic17—21no—
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—21no—
305C2×Dic17—21no—
306C2×Dic17—21no—
307C2×Dic17—21no—
308C2×Dic17—21no—
309C2×Dic17—21no—
310C2×Dic17—21no—
311C2×Dic17—21no—
312C2×Dic17—44no—
313C2×Dic17#11712yes—
314C2×Dic17C22×C812yes—
315C2×Dic17C22×C812yes—
316C2×Dic17C2×M1612yes—
317C4×D17—22no—
318C4×D17—22no—
319C4×D17—22no—
320C4×D17—22no—
321C4×D17—44no—
322C4×D17—44no—
323C4×D17—44no—
324C4×D17—44no—
325C4×D17—44no—
326C4×D17—44no—
327C4×D17—41no—
328C4×D17—41no—
329C4×D17—41no—
330C4×D17—41no—
331C8×C17—41no—
332C8×C17—41no—
333C8×C17—41no—
334C8×C17—41no—
335#3622—41no—
336#3622—41no—
337#3622—41no—
338#3622—41no—
339C2×C4×C22⋊C4—171no—
340#1923—171no—
341#1923—171no—
342#1923—171no—
343#1923—171no—
344#1923—171no—
345#1923—171no—
346#1923—171no—
347#1923D1711yescharacteristic, complemented
348#1797—171no—
349#1797—171no—
350#1779—171no—
351#1779—171no—
352C4×C22⋊C8—171no—
353C4×C22⋊C8—171no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—22no—
357C22×C17—41no—
358C22×C17—41no—
359C22×C17—41no—
360C22×C17—41no—
361C22×C17C2×#11711yescharacteristic
362C22×C17#51811yescharacteristic
363C22×C17#51811yescharacteristic
364C22×C17C23×C811yescharacteristic
365C22×C17C22×M1611yescharacteristic
366C22×C17#56811yescharacteristic
367C22×C17#56811yescharacteristic
368C2×D17—22no—
369C2×D17—22no—
370C2×D17—22no—
371C2×D17—22no—
372C2×D17—22no—
373C2×D17—22no—
374C2×D17—22no—
375C2×D17—22no—
376C2×D17—22no—
377C2×D17—416no—
378C2×D17—41no—
379C2×D17—41no—
380C2×D17—41no—
381C2×D17—41no—
382C2×D17#43114yes—
383C4×C17—22no—
384C4×C17—22no—
385C4×C17—22no—
386C4×C17—41no—
387C4×C17—41no—
388C4×C17#53811yescharacteristic
389C4×C17#53811yescharacteristic
390C4×C17#53811yescharacteristic
391C4×C17#53811yescharacteristic
392Dic17—22no—
393Dic17—22no—
394Dic17—22no—
395Dic17—22no—
396Dic17—41no—
397Dic17—41no—
398C24×C4—171no—
399C22×C22⋊C4—171no—
400C22×C22⋊C4—171no—
401C22×C42—171no—
402C22×C42—171no—
403C2×C4⋊C8—171no—
404C2×C4⋊C8—171no—
405C2×C4⋊C8—171no—
406C2×C4⋊C8C2×D1711yescharacteristic, complemented
407C2×C22⋊C8—171no—
408C2×C22⋊C8—171no—
409C2×C22⋊C8—171no—
410C2×C22⋊C8—171no—
411C2×C22⋊C8—171no—
412C2×C22⋊C8—171no—
413C2×C22⋊C8—171no—
414C2×C22⋊C8—171no—
415C2×C22⋊C8—171no—
416C2×C22⋊C8—171no—
417C2×C22⋊C8C2×D1711yescharacteristic
418C2×C22⋊C8C2×D1711yescharacteristic
419C2×C4×C8—171no—
420C2×C4×C8—171no—
421C2×C4×C8—171no—
422C2×C4×C8C2×D1711yescharacteristic, complemented
423C4×C22⋊C4—171no—
424C4×C22⋊C4—171no—
425C4×C22⋊C4—171no—
426C4×C22⋊C4—171no—
427C4×C22⋊C4—171no—
428C4×C22⋊C4—171no—
429C4×C22⋊C4—171no—
430C4×C22⋊C4C2×D1711yescharacteristic
431C2×#95—171no—
432C2×#95—171no—
433#336—171no—
434#336—171no—
435#336—171no—
436#336—171no—
437#336—171no—
438#336—171no—
439#336C2×D1711yescharacteristic, complemented
440#336C2×D1711yescharacteristic, complemented
441C2×C17—42no—
442C2×C17#231211yescharacteristic
443C2×C17C2×#43111yescharacteristic
444C2×C17#292111yescharacteristic
445C2×C17#297211yescharacteristic
446C2×C17#297211yescharacteristic
447C2×C17#297311yescharacteristic
448C2×C17#297511yescharacteristic
449D17—24no—
450D17—42no—
451C25—171no—
452C23×C4—171no—
453C23×C4—171no—
454C23×C4—171no—
455C23×C4—171no—
456C23×C4—171no—
457C23×C4—171no—
458C23×C4—171no—
459C23×C4—171no—
460C23×C4—171no—
461C23×C4—342no—
462C23×C4—342no—
463C23×C4—681no—
464C23×C4—681no—
465C23×C4—681no—
466C23×C4—681no—
467C23×C4C22×D1711yescharacteristic
468C22×C8—171no—
469C22×C8—171no—
470C22×C8—171no—
471C22×C8—171no—
472C22×C8C22×D1711yescharacteristic
473C22×C8C22×D1711yescharacteristic
474C22×C8C22×D1711yescharacteristic
475C22×C8C22×D1711yescharacteristic
476C2×C22⋊C4—171no—
477C2×C22⋊C4—171no—
478C2×C22⋊C4—171no—
479C2×C22⋊C4—178no—
480C2×C22⋊C4—171no—
481C2×C22⋊C4—171no—
482C2×C22⋊C4—171no—
483C2×C22⋊C4—344no—
484C2×C22⋊C4C4×D1711yescharacteristic
485C2×C22⋊C4C4×D1711yescharacteristic
486C2×C42—171no—
487C2×C42—171no—
488C2×C42—171no—
489C2×C42—171no—
490C2×C42—171no—
491C2×C42—171no—
492C2×C42—681no—
493C2×C42—681no—
494C2×C42—681no—
495C2×C42—681no—
496C2×C42C22×D1711yescharacteristic
497C2×C42C22×D1711yescharacteristic
498C4⋊C8—41no—
499C4⋊C8—681no—
500C4⋊C8—681no—
501C4⋊C8—681no—
502C22⋊C8—41no—
503C22⋊C8—41no—
504C22⋊C8—342no—
505C22⋊C8—342no—
506C22⋊C8—342no—
507C22⋊C8—342no—
508C22⋊C8—681no—
509C22⋊C8—681no—
510C22⋊C8—681no—
511C22⋊C8—681no—
512C22⋊C8—681no—
513C22⋊C8—681no—
514C4×C8—41no—
515C4×C8—681no—
516C4×C8—681no—
517C4×C8—681no—
518#95—171no—
519#95—171no—
520#95—171no—
521#95—171no—
522#95—171no—
523#95—171no—
524#95C4×D1711yescharacteristic
525#95C4×D1711yescharacteristic
526C17#2190211yescharacteristic, complemented, Sylow
527C24—171no—
528C24—171no—
529C24—174no—
530C24—342no—
531C24—342no—
532C24—681no—
533C24—681no—
534C24—681no—
535C24—681no—
536C24C2×C4×D1711yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—171no—
544C22×C4—171no—
545C22×C4—171no—
546C22×C4—171no—
547C22×C4—172no—
548C22×C4—172no—
549C22×C4—174no—
550C22×C4—174no—
551C22×C4—174no—
552C22×C4—171no—
553C22×C4—171no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—342no—
557C22×C4—342no—
558C22×C4—341no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—341no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—681no—
569C22×C4—681no—
570C22×C4—681no—
571C22×C4—681no—
572C22×C4—681no—
573C22×C4—681no—
574C22×C4—681no—
575C22×C4—681no—
576C22×C4—681no—
577C22×C4—681no—
578C22×C4—681no—
579C22×C4—681no—
580C22×C4—684no—
581C22×C4—684no—
582C22×C4—684no—
583C22×C4—684no—
584C22×C4—681no—
585C22×C4—681no—
586C22×C4C2×C4×D1711yescharacteristic
587C22×C4C2×C4×D1711yescharacteristic
588C22×C4C2×C4×D1711yescharacteristic
589C22×C4C2×C4×D1711yescharacteristic
590C22×C4C2×C4×D1711yescharacteristic
591C22×C4C23×D1711yescharacteristic
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—341no—
605C2×C8—341no—
606C2×C8—341no—
607C2×C8—341no—
608C2×C8—341no—
609C2×C8—341no—
610C2×C8—341no—
611C2×C8—341no—
612C2×C8—341no—
613C2×C8—341no—
614C2×C8—341no—
615C2×C8—341no—
616C22⋊C4—22no—
617C22⋊C4—174no—
618C22⋊C4—174no—
619C22⋊C4—174no—
620C22⋊C4—342no—
621C22⋊C4—342no—
622C22⋊C4—342no—
623C22⋊C4C8×D1714yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—341no—
629C42—341no—
630C42—341no—
631C42—341no—
632C42—681no—
633C42—681no—
634C42—681no—
635C42—681no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—172no—
643C23—172no—
644C23—172no—
645C23—172no—
646C23—348no—
647C23—341no—
648C23—341no—
649C23—341no—
650C23—341no—
651C23—341no—
652C23—341no—
653C23—341no—
654C23—341no—
655C23—341no—
656C23—341no—
657C23—684no—
658C23—684no—
659C23—684no—
660C23—684no—
661C23—684no—
662C23—684no—
663C23C2×C8×D1712yes—
664C23C22×C4×D1711yescharacteristic
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—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—172no—
682C2×C4—172no—
683C2×C4—172no—
684C2×C4—172no—
685C2×C4—341no—
686C2×C4—341no—
687C2×C4—341no—
688C2×C4—341no—
689C2×C4—341no—
690C2×C4—341no—
691C2×C4—341no—
692C2×C4—341no—
693C2×C4—342no—
694C2×C4—342no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—341no—
698C2×C4—341no—
699C2×C4—341no—
700C2×C4—341no—
701C2×C4—341no—
702C2×C4—341no—
703C2×C4—684no—
704C2×C4—684no—
705C2×C4—684no—
706C2×C4—684no—
707C2×C4—684no—
708C2×C4—684no—
709C2×C4—684no—
710C2×C4—681no—
711C2×C4—681no—
712C2×C4—681no—
713C2×C4—681no—
714C2×C4C2×C8×D1712yes—
715C2×C4C2×C8×D1712yes—
716C2×C4M16×D1712yes—
717C2×C4#1058769111yescharacteristic
718C2×C4#1058769111yescharacteristic
719C2×C4#41×D1711yescharacteristic
720C2×C4#41×D1711yescharacteristic
721C2×C4#1058769611yescharacteristic
722C2×C4#1058769611yescharacteristic
723C8—41no—
724C8—41no—
725C8—41no—
726C8—41no—
727C8—681no—
728C8—681no—
729C8—681no—
730C8—681no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—174no—
739C22—342no—
740C22—342no—
741C22—342no—
742C22—342no—
743C22—342no—
744C22—342no—
745C22—342no—
746C22—342no—
747C22—342no—
748C22—6816no—
749C22—681no—
750C22—681no—
751C22—681no—
752C22—681no—
753C22#117×D1711yescharacteristic
754C22#1176328111yescharacteristic
755C22#1176328111yescharacteristic
756C22C22×C8×D1711yescharacteristic
757C22C2×M16×D1711yescharacteristic
758C22#1176357411yescharacteristic
759C22#1176357411yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—41no—
764C4—41no—
765C4—342no—
766C4—342no—
767C4—342no—
768C4—342no—
769C4—681no—
770C4—681no—
771C4#1176339111yescharacteristic
772C4#1176339311yescharacteristic
773C4#1176339511yescharacteristic
774C4#1176339811yescharacteristic
775C2—42no—
776C2—344no—
777C2—682no—
778C2#1453137811yescharacteristic
779C2D17×#43111yescharacteristic
780C2#1453741811yescharacteristic
781C2#1453780511yescharacteristic
782C2#1453780511yescharacteristic
783C2#1453780911yescharacteristic
784C2#1453782211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutatorC22×C17C23×C8
FittingC17×#1923C2
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenter#1923D17
hypocenterC17#21902
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #14529393C2semidirect
3. #14529392C2semidirect
4. #14529391C2semidirect
5. #14529390C2semidirect
6. #14529389C2semidirect
7. #14529388C2semidirect
8. #14529387C2semidirect
9. #14528763C2semidirect
10. #14528761C2semidirect
13. C4×#10587491C2semidirect
14. #14528541C2semidirect
15. C17×#1923C2semidirect
21. C2×C4⋊#3622C22semidirect
22. C2×#10587485C22semidirect
23. C2×#10587485C22semidirect
34. C2×C4×#3622C22semidirect
35. C2×C8×Dic17C22semidirect
36. C2×C8×Dic17C22semidirect
46. #11762564C22semidirect
47. #11762564C22semidirect
48. #11762563C22semidirect
49. #11762563C22semidirect
50. #11762563C22semidirect
51. #11762563C22semidirect
52. C2×C17×C4⋊C8C22semidirect
55. C2×C4×C8×C17C22semidirect
57. C17×#336C22semidirect
58. C17×#336C22semidirect
101. C22⋊C4×D17C8semidirect
347. #1923D17semidirect
406. C2×C4⋊C8C2×D17semidirect
422. C2×C4×C8C2×D17semidirect
439. #336C2×D17semidirect
440. #336C2×D17semidirect
526. C17#21902semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊C4×D172
#145293932
#145293922
#145293912
#145293902
#145293892
#145293882
#145293872
#145287632
#145287612
#145286932
C4×#105874912
#145285412
C17×#19232
#2190217