Finite Group Databasebeta

← #17060880

Subgroups — #17060880

Order 4352.

914 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14532063C211yesmaximal, characteristic
2#14529080C211yesmaximal, characteristic, complemented
3#14529078C211yesmaximal, characteristic, complemented
4#14529078C211yesmaximal, characteristic, complemented
5#14529077C211yesmaximal, characteristic, complemented
6#14529076C211yesmaximal, characteristic, complemented
7#14529076C211yesmaximal, characteristic, complemented
8#14529075C211yesmaximal, characteristic, complemented
9#14529074C211yesmaximal, characteristic, complemented
10#14529074C211yesmaximal, characteristic, complemented
11#14529073C211yesmaximal, characteristic, complemented
12#14529073C211yesmaximal, characteristic, complemented
13#14528928C211yesmaximal, characteristic, complemented
14#14528928C211yesmaximal, characteristic, complemented
15C17×#1869C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C22×C8×D17C2211yescharacteristic
19C2×C4×D68C2211yescharacteristic
20C2×C4×C22⋊D17C2211yescharacteristic
21C2×C4×C22⋊D17C2211yescharacteristic
22C2×C4×C22⋊D17C2211yescharacteristic
23C2×C4×C22⋊D17C2211yescharacteristic
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×C22⋊#3622C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33#11762745C411yescharacteristic
34#11762745C411yescharacteristic
35#11762744C411yescharacteristic
36#11762744C411yescharacteristic
37#11762718C411yescharacteristic
38#11762718C411yescharacteristic
39#11762717C411yescharacteristic
40#11762717C411yescharacteristic
41#11762655C2211yescharacteristic
42#11762564C2211yescharacteristic
43#11762564C2211yescharacteristic
44#11762563C2211yescharacteristic
45#11762563C2211yescharacteristic
46#11762563C2211yescharacteristic
47#11762563C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C23×C8×C17C2211yescharacteristic
53C2×C4×D4×C17C2211yescharacteristic
54C2×C17×C22⋊C8C2211yescharacteristic
55C2×C17×C22⋊C8C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C22×D4×C17C2×C411yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C22×C22⋊D17C2×C411yescharacteristic
63C22×C22⋊D17C2×C411yescharacteristic
64C22×C22⋊D17C2×C411yescharacteristic
65C22×C22⋊D17C2×C411yescharacteristic
66C22×D68C2×C411yescharacteristic
67C22×C4×D17C2311yescharacteristic
68C22×C4×D17C2311yescharacteristic
69C22×C8×C17—41no—
70C22×C8×C17—41no—
71C22×C8×C17—41no—
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C22×C8×C17C2311yescharacteristic
75C22×C8×C17C2311yescharacteristic
76C4×D4×C17—41no—
77C4×D4×C17—41no—
78C2×C4⋊C4×C17C2×C411yescharacteristic
79C2×C22⋊C4×C17C2×C411yescharacteristic
80C2×C22⋊C4×C17C2×C411yescharacteristic
81C2×C42×C17C2311yescharacteristic
82C2×C22⋊Dic17C2×C411yescharacteristic
83C2×C22⋊Dic17C2×C411yescharacteristic
84C2×C22⋊Dic17C2×C411yescharacteristic
85C2×C22⋊Dic17C2×C411yescharacteristic
86C4×C22⋊D17—41no—
87C4×C22⋊D17—41no—
88C4×C22⋊D17—41no—
89C4×C22⋊D17—41no—
90C4×C22⋊D17—41no—
91C4×C22⋊D17—41no—
92C4×C22⋊D17—41no—
93C4×C22⋊D17—41no—
94C2×#63227C2×C411yescharacteristic
95C2×#63227C2×C411yescharacteristic
96C2×#63227C2×C411yescharacteristic
97C2×#63227C2×C411yescharacteristic
98C2×#63227C2×C411yescharacteristic
99C2×#63227C2×C411yescharacteristic
100C2×C4⋊Dic17C2×C411yescharacteristic
101C2×#63225C2×C411yescharacteristic
102C2×#63225C2×C411yescharacteristic
103C2×#63225C2×C411yescharacteristic
104C2×#63225C2×C411yescharacteristic
105C2×C4×Dic17C2311yescharacteristic
106C2×C4×Dic17C2311yescharacteristic
107C22×#3622—41no—
108C22×#3622—41no—
109C22×#3622—41no—
110C22×#3622C2311yescharacteristic
111C22×#3622C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C2×#63218—41no—
115C2×#63218—41no—
116C2×#63218—41no—
117C2×C8×D17—41no—
118C2×C8×D17—41no—
119C2×C8×D17—41no—
120C4×D68—41no—
121C4×D68—41no—
122C17×C22⋊C8—41no—
123C17×C22⋊C8—41no—
124C17×C22⋊C8—41no—
125#10587502C2×C411yescharacteristic
126#10587502C2×C411yescharacteristic
127#10587502C2×C411yescharacteristic
128#10587502C2×C411yescharacteristic
129C22⋊#3622—41no—
130C22⋊#3622—41no—
131C22⋊#3622—41no—
132#10587491—41no—
133#10587491—41no—
134#10587491—41no—
135#10587491—41no—
136#10587491—41no—
137#10587491—41no—
138C24×C17C22×C411yescharacteristic
139C24×C17C22×C411yescharacteristic
140C23×D17C22×C411yescharacteristic
141C23×D17C22×C411yescharacteristic
142C2×D4×C17—22no—
143C2×D4×C17—22no—
144C2×D4×C17—41no—
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×C17C22×C411yescharacteristic
158C22×C4×C17C22×C411yescharacteristic
159C22×C4×C17C22×C411yescharacteristic
160C22×C4×C17C22×C411yescharacteristic
161C22×C4×C17C2411yescharacteristic
162C2×C22⋊D17—22no—
163C2×C22⋊D17—22no—
164C2×C22⋊D17—22no—
165C2×C22⋊D17—22no—
166C2×C22⋊D17—22no—
167C2×C22⋊D17—22no—
168C2×C22⋊D17—41no—
169C2×C22⋊D17—41no—
170C2×C22⋊D17—41no—
171C2×C22⋊D17—41no—
172C2×C22⋊D17—41no—
173C2×C22⋊D17—41no—
174C22×Dic17C22×C411yescharacteristic
175C22×Dic17C22×C411yescharacteristic
176C22×Dic17C22×C411yescharacteristic
177C22×Dic17C22×C411yescharacteristic
178C22×Dic17C22×C411yescharacteristic
179C22×Dic17C22×C411yescharacteristic
180C2×D68—22no—
181C2×D68—41no—
182C2×D68—41no—
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×C8×C17—21no—
196C2×C8×C17—21no—
197C2×C8×C17—21no—
198C2×C8×C17—21no—
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—44no—
208C4⋊C4×C17—41no—
209C22⋊C4×C17—41no—
210C22⋊C4×C17—41no—
211C42×C17—21no—
212C42×C17—21no—
213C22⋊Dic17—41no—
214C22⋊Dic17—41no—
215C22⋊Dic17—41no—
216C22⋊Dic17—41no—
217#63227—41no—
218#63227—41no—
219#63227—41no—
220#63227—41no—
221#63227—41no—
222#63227—41no—
223C4⋊Dic17—41no—
224#63225—41no—
225#63225—41no—
226#63225—41no—
227#63225—41no—
228C4×Dic17—21no—
229C4×Dic17—21no—
230C4×Dic17—21no—
231C4×Dic17—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—
243C2×#3622—21no—
244C2×#3622—44no—
245#63218—44no—
246C8×D17—44no—
247#23358—171nomaximal, Sylow
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17—21no—
257C23×C17—21no—
258C23×C17—21no—
259C23×C17—21no—
260C23×C17#13112yes—
261C23×C17#13112yes—
262C23×C17C23×C411yescharacteristic
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#13112yes—
277D4×C17—44no—
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—21no—
286C2×C4×C17—21no—
287C2×C4×C17—21no—
288C2×C4×C17—21no—
289C2×C4×C17—21no—
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×C17H(5,𝔽2)11yescharacteristic
299C2×C4×C17H(5,𝔽2)11yescharacteristic
300C2×C4×C17H(5,𝔽2)11yescharacteristic
301C2×C4×C17H(5,𝔽2)11yescharacteristic
302C2×C4×C17H(5,𝔽2)11yescharacteristic
303C2×C4×C17H(5,𝔽2)11yescharacteristic
304C22⋊D17—44no—
305C22⋊D17—44no—
306C22⋊D17—44no—
307C22⋊D17—44no—
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—
320C2×Dic17—21no—
321C2×Dic17—21no—
322C2×Dic17—21no—
323C2×Dic17—21no—
324C2×Dic17—21no—
325C2×Dic17—21no—
326D68—44no—
327C4×D17—41no—
328C4×D17—41no—
329C4×D17—41no—
330C4×D17—41no—
331C4×D17—41no—
332C4×D17—41no—
333C4×D17—41no—
334C4×D17—41no—
335C8×C17—41no—
336C8×C17—41no—
337C8×C17—41no—
338C8×C17—41no—
339#3622—41no—
340#3622—41no—
341#3622—41no—
342#3622—41no—
343#2397—171no—
344#1870—171no—
345#1870—171no—
346#1870—171no—
347#1869—171no—
348#1869—171no—
349#1869—171no—
350#1869—171no—
351#1869—171no—
352#1869—171no—
353#1869—171no—
354#1869—171no—
355#1869D1711yescharacteristic, complemented
356#1840—171no—
357#1840—171no—
358C22×C17—22no—
359C22×C17—22no—
360C22×C17—22no—
361C22×C17—22no—
362C22×C17—22no—
363C22×C17—22no—
364C22×C17—41no—
365C22×C17—41no—
366C22×C17—41no—
367C22×C17—41no—
368C22×C17—41no—
369C22×C17—41no—
370C22×C17—41no—
371C22×C17—41no—
372C22×C17#51811yescharacteristic
373C22×C17#51811yescharacteristic
374C22×C17#51811yescharacteristic
375C22×C17C2×#13111yescharacteristic
376C22×C17C2×#13111yescharacteristic
377C22×C17C2×#13111yescharacteristic
378C22×C17#56811yescharacteristic
379C2×D17—22no—
380C2×D17—22no—
381C2×D17—22no—
382C2×D17—41no—
383C2×D17—41no—
384C2×D17—41no—
385C2×D17—41no—
386C2×D17—41no—
387C2×D17—41no—
388C2×D17—41no—
389C2×D17—41no—
390C2×D17—41no—
391C2×D17—41no—
392C2×D17—41no—
393C4×C17—41no—
394C4×C17—41no—
395C4×C17—41no—
396C4×C17—41no—
397C4×C17#56011yescharacteristic
398C4×C17#56011yescharacteristic
399C4×C17#56011yescharacteristic
400C4×C17#56011yescharacteristic
401Dic17—41no—
402Dic17—41no—
403Dic17—41no—
404Dic17—41no—
405Dic17—41no—
406Dic17—41no—
407C22×M16—171no—
408C23×C8—171no—
409C23×C8—171no—
410C23×C8C2×D1711yescharacteristic
411C2×C4×D4—171no—
412C2×C4×D4—171no—
413C2×C4×D4—171no—
414C2×C4×D4—171no—
415C2×C4×D4—171no—
416C2×C4×D4C2×D1711yescharacteristic
417C2×C22⋊C8—171no—
418C2×C22⋊C8—171no—
419C2×C22⋊C8—171no—
420C2×C22⋊C8—171no—
421C2×C22⋊C8—171no—
422C2×C22⋊C8—171no—
423C2×C22⋊C8—171no—
424C2×C22⋊C8—171no—
425C2×C22⋊C8—171no—
426C2×C22⋊C8C2×D1711yescharacteristic
427C2×C22⋊C8C2×D1711yescharacteristic
428C2×C22⋊C8C2×D1711yescharacteristic
429#399—171no—
430#399—171no—
431#399—171no—
432#399—171no—
433#392—171no—
434#392—171no—
435#392—171no—
436#392—171no—
437#376—171no—
438#336—171no—
439#336—171no—
440#336—171no—
441#336—171no—
442#336—171no—
443#336—171no—
444#336—171no—
445#336—171no—
446#336—171no—
447#336—171no—
448#336C2×D1711yescharacteristic
449#336C2×D1711yescharacteristic
450C2×C17—42no—
451C2×C17—42no—
452C2×C17#238011yescharacteristic
453C2×C17#297611yescharacteristic
454C2×C17#297611yescharacteristic
455C2×C17#297611yescharacteristic
456C2×C17#297711yescharacteristic
457C2×C17#297711yescharacteristic
458C2×C17#297711yescharacteristic
459D17—42no—
460D17—81no—
461C22×D4—171no—
462C22×D4—171no—
463C22×D4—171no—
464C22×D4—171no—
465C22×D4—171no—
466C22×D4C4×D1711yescharacteristic
467C23×C4—171no—
468C23×C4—171no—
469C23×C4C22×D1711yescharacteristic
470C23×C4C22×D1711yescharacteristic
471C2×M16—681no—
472C2×M16—681no—
473C2×M16—681no—
474C22×C8—41no—
475C22×C8—41no—
476C22×C8—41no—
477C22×C8—171no—
478C22×C8—171no—
479C22×C8—171no—
480C22×C8—171no—
481C22×C8—681no—
482C22×C8—681no—
483C22×C8—681no—
484C22×C8—681no—
485C22×C8—681no—
486C22×C8—681no—
487C22×C8C22×D1711yescharacteristic
488C22×C8C22×D1711yescharacteristic
489C22×C8C22×D1711yescharacteristic
490C22×C8C22×D1711yescharacteristic
491C4×D4—41no—
492C4×D4—41no—
493C4×D4—681no—
494C4×D4—681no—
495C4×D4—681no—
496C4×D4—681no—
497C4×D4—681no—
498C4×D4—681no—
499C4×D4—681no—
500C4×D4—681no—
501C4×D4—681no—
502C4×D4—681no—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—171no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4C4×D1711yescharacteristic
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×C22⋊C4—171no—
518C2×C22⋊C4—171no—
519C2×C22⋊C4C4×D1711yescharacteristic
520C2×C22⋊C4C4×D1711yescharacteristic
521C2×C42—171no—
522C2×C42—171no—
523C2×C42C22×D1711yescharacteristic
524C22⋊C8—41no—
525C22⋊C8—41no—
526C22⋊C8—41no—
527C22⋊C8—681no—
528C22⋊C8—681no—
529C22⋊C8—681no—
530C22⋊C8—681no—
531C22⋊C8—681no—
532C22⋊C8—681no—
533C22⋊C8—681no—
534C22⋊C8—681no—
535C22⋊C8—681no—
536#95—171no—
537#95—171no—
538#95—171no—
539#95—171no—
540C17#2335811yescharacteristic, complemented, Sylow
541C24—171no—
542C24—171no—
543C24C2×C4×D1711yescharacteristic
544C24C2×C4×D1711yescharacteristic
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—41no—
548C2×D4—342no—
549C2×D4—342no—
550C2×D4—342no—
551C2×D4—342no—
552C2×D4—342no—
553C2×D4—342no—
554C2×D4—342no—
555C2×D4—681no—
556C2×D4—681no—
557C2×D4—681no—
558C2×D4—681no—
559C2×D4—681no—
560C2×D4—681no—
561C2×D4—681no—
562C2×D4—681no—
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—171no—
576C22×C4—171no—
577C22×C4—171no—
578C22×C4—171no—
579C22×C4—171no—
580C22×C4—171no—
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—341no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4C2×C4×D1711yescharacteristic
594C22×C4C2×C4×D1711yescharacteristic
595C22×C4C2×C4×D1711yescharacteristic
596C22×C4C2×C4×D1711yescharacteristic
597C22×C4C23×D1711yescharacteristic
598M16—684no—
599C2×C8—21no—
600C2×C8—21no—
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—44no—
612C2×C8—341no—
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—684no—
625C2×C8—684no—
626C4⋊C4—41no—
627C4⋊C4—681no—
628C4⋊C4—681no—
629C4⋊C4—681no—
630C4⋊C4—681no—
631C4⋊C4—681no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—681no—
635C22⋊C4—681no—
636C22⋊C4—681no—
637C22⋊C4—681no—
638C22⋊C4—681no—
639C22⋊C4—681no—
640C22⋊C4—681no—
641C22⋊C4—681no—
642C22⋊C4—681no—
643C22⋊C4—681no—
644C42—21no—
645C42—21no—
646C42—341no—
647C42—341no—
648C42—341no—
649C42—341no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—172no—
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—
676C23#1058758712yes—
677C23#1058759312yes—
678C23C22×C4×D1711yescharacteristic
679D4—44no—
680D4—684no—
681D4—684no—
682D4—684no—
683D4—684no—
684D4—684no—
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—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—341no—
706C2×C4—341no—
707C2×C4—341no—
708C2×C4—341no—
709C2×C4—341no—
710C2×C4—341no—
711C2×C4—341no—
712C2×C4—341no—
713C2×C4—341no—
714C2×C4—341no—
715C2×C4—341no—
716C2×C4—341no—
717C2×C4—341no—
718C2×C4—341no—
719C2×C4—341no—
720C2×C4—341no—
721C2×C4—341no—
722C2×C4—341no—
723C2×C4—681no—
724C2×C4—681no—
725C2×C4—681no—
726C2×C4—681no—
727C2×C4—681no—
728C2×C4—681no—
729C2×C4—681no—
730C2×C4—681no—
731C2×C4#1058769111yescharacteristic
732C2×C4#1058769111yescharacteristic
733C2×C4#1058769111yescharacteristic
734C2×C4#1058769111yescharacteristic
735C2×C4#1058769611yescharacteristic
736C2×C4#1058769611yescharacteristic
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—681no—
742C8—681no—
743C8—681no—
744C8—681no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—342no—
760C22—342no—
761C22—342no—
762C22—681no—
763C22—681no—
764C22—681no—
765C22—681no—
766C22—681no—
767C22—681no—
768C22—681no—
769C22—681no—
770C22—681no—
771C22—681no—
772C22—681no—
773C22#1176328111yescharacteristic
774C22#1176328111yescharacteristic
775C22#1176328211yescharacteristic
776C22#131×D1711yescharacteristic
777C22C2×#1058758711yescharacteristic
778C22C2×#1058759311yescharacteristic
779C22#1176357411yescharacteristic
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—681no—
785C4—681no—
786C4—681no—
787C4—681no—
788C4—681no—
789C4—681no—
790C4#1176354711yescharacteristic
791C4#1176354711yescharacteristic
792C4#1176354811yescharacteristic
793C4#1176354911yescharacteristic
794C2—42no—
795C2—42no—
796C2—682no—
797C2—1361no—
798C2#1453195911yescharacteristic
799C2#1453782611yescharacteristic
800C2#1453782711yescharacteristic
801C2#1453783311yescharacteristic
802C2#1453783511yescharacteristic
803C2#1453783711yescharacteristic
804C2#1453783811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1869C2
prime radical#14532063C2
cosocleC22×C4×C17C24
hypercenter#1869D17
hypocenterC17#23358
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #14529080C2semidirect
3. #14529078C2semidirect
4. #14529078C2semidirect
5. #14529077C2semidirect
6. #14529076C2semidirect
7. #14529076C2semidirect
8. #14529075C2semidirect
9. #14529074C2semidirect
10. #14529074C2semidirect
11. #14529073C2semidirect
12. #14529073C2semidirect
13. #14528928C2semidirect
14. #14528928C2semidirect
15. C17×#1869C2semidirect
355. #1869D17semidirect
540. C17#23358semidirect

Maximal subgroups

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

subgroupindex
#145320632
#145290802
#145290782
#145290772
#145290762
#145290752
#145290742
#145290732
#145289282
C17×#18692
#2335817