Finite Group Databasebeta

← #17060871

Subgroups — #17060871

Order 4352.

944 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10587626C211yesmaximal, characteristic
2#14529081C211yesmaximal, characteristic, complemented
3#14529081C211yesmaximal, characteristic, complemented
4#14529080C211yesmaximal, characteristic, complemented
5#14529078C211yesmaximal, characteristic, complemented
6#14529078C211yesmaximal, characteristic, complemented
7#14529077C211yesmaximal, characteristic, complemented
8#14529075C211yesmaximal, characteristic, complemented
9#14529074C211yesmaximal, characteristic, complemented
10#14529074C211yesmaximal, characteristic, complemented
11#14529073C211yesmaximal, characteristic, complemented
12#14529073C211yesmaximal, characteristic, complemented
13#14528926C211yesmaximal, characteristic, complemented
14#14528926C211yesmaximal, characteristic, complemented
15C17×#1870C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C22×C8×D17C2211yescharacteristic
19C2×#10587626C411yescharacteristic
20C2×C4×D68C2211yescharacteristic
21C2×C4×C22⋊D17C2211yescharacteristic
22C2×C4×C22⋊D17C2211yescharacteristic
23C2×C4×C22⋊D17C2211yescharacteristic
24C2×C4×C22⋊D17C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×C22⋊#3622C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34#11762712C411yescharacteristic
35#11762710C411yescharacteristic
36#11762709C411yescharacteristic
37#11762709C411yescharacteristic
38#11762709C411yescharacteristic
39#11762709C411yescharacteristic
40#11762678C411yescharacteristic
41C42×Dic17C2211yescharacteristic
42#11762564C2211yescharacteristic
43#11762564C2211yescharacteristic
44#11762563C2211yescharacteristic
45#11762563C2211yescharacteristic
46#11762563C2211yescharacteristic
47#11762563C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C22×M16×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
69C2×M16×C17—41no—
70C2×M16×C17—41no—
71C2×M16×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
86#10587626—24no—
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—
94C4×C22⋊D17—41no—
95C2×#63227C2×C411yescharacteristic
96C2×#63227C2×C411yescharacteristic
97C2×#63227C2×C411yescharacteristic
98C2×#63227C2×C411yescharacteristic
99C2×#63227C2×C411yescharacteristic
100C2×#63227C2×C411yescharacteristic
101C2×C4⋊Dic17C2×C411yescharacteristic
102C2×#63225C2×C411yescharacteristic
103C2×#63225C2×C411yescharacteristic
104C2×#63225C2×C411yescharacteristic
105C2×#63225C2×C411yescharacteristic
106C2×C4×Dic17C2×C411yescharacteristic
107C2×C4×Dic17C2×C411yescharacteristic
108C2×C4×Dic17C2×C411yescharacteristic
109C2×C4×Dic17C2×C411yescharacteristic
110C2×C4×Dic17C2311yescharacteristic
111C2×C4×Dic17C2311yescharacteristic
112C22×#3622—41no—
113C22×#3622—41no—
114C22×#3622—41no—
115C22×#3622C2311yescharacteristic
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C2×#63218—41no—
120C2×#63218—41no—
121C2×#63218—41no—
122C2×C8×D17—41no—
123C2×C8×D17—41no—
124C2×C8×D17—41no—
125C4×D68—41no—
126C4×D68—41no—
127C17×C22⋊C8—41no—
128C17×C22⋊C8—41no—
129C17×C22⋊C8—41no—
130C22⋊#3622—41no—
131C22⋊#3622—41no—
132C22⋊#3622—41no—
133#10587491—41no—
134#10587491—41no—
135#10587491—41no—
136#10587491—41no—
137#10587491—41no—
138#10587491—41no—
139C24×C17C22×C411yescharacteristic
140C24×C17C22×C411yescharacteristic
141C23×D17C22×C411yescharacteristic
142C23×D17C22×C411yescharacteristic
143C2×D4×C17—22no—
144C2×D4×C17—22no—
145C2×D4×C17—41no—
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×C17C22×C411yescharacteristic
159C22×C4×C17C22×C411yescharacteristic
160C22×C4×C17C22×C411yescharacteristic
161C22×C4×C17C22×C411yescharacteristic
162C22×C4×C17C2411yescharacteristic
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—
174C2×C22⋊D17M1614yescomplemented
175C22×Dic17C22×C411yescharacteristic
176C22×Dic17C22×C411yescharacteristic
177C22×Dic17C22×C411yescharacteristic
178C22×Dic17C22×C411yescharacteristic
179C22×Dic17C22×C411yescharacteristic
180C22×Dic17C22×C411yescharacteristic
181C2×D68—22no—
182C2×D68—22no—
183C2×D68—41no—
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—
196M16×C17—44no—
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—21no—
208C2×C8×C17—21no—
209C4⋊C4×C17—41no—
210C22⋊C4×C17—41no—
211C22⋊C4×C17—41no—
212C42×C17—21no—
213C42×C17—21no—
214C22⋊Dic17—41no—
215C22⋊Dic17—41no—
216C22⋊Dic17—41no—
217C22⋊Dic17—41no—
218#63227—41no—
219#63227—41no—
220#63227—41no—
221#63227—41no—
222#63227—41no—
223#63227—41no—
224C4⋊Dic17—41no—
225#63225—41no—
226#63225—41no—
227#63225—41no—
228#63225—41no—
229C4×Dic17—22no—
230C4×Dic17—21no—
231C4×Dic17—21no—
232C4×Dic17—21no—
233C4×Dic17—21no—
234C4×Dic17—22no—
235C4×Dic17—22no—
236C4×Dic17—41no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243C2×#3622—21no—
244C2×#3622—21no—
245C2×#3622—21no—
246C2×#3622—21no—
247C2×#3622—21no—
248C2×#3622—21no—
249C2×#3622—44no—
250#63218—44no—
251C8×D17—44no—
252#23356—171nomaximal, Sylow
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17—21no—
257C23×C17—21no—
258C23×C17—21no—
259C23×C17—21no—
260C23×C17—21no—
261C23×C17—21no—
262C23×C17—21no—
263C23×C17—21no—
264C23×C17—21no—
265C23×C17—21no—
266C23×C17C2×M1612yes—
267C23×C17C23×C411yescharacteristic
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—21no—
280C22×D17—21no—
281C22×D17C2×M1612yes—
282D4×C17—44no—
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×C17—21no—
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#13112yes—
303C2×C4×C17H(5,𝔽2)11yescharacteristic
304C2×C4×C17H(5,𝔽2)11yescharacteristic
305C2×C4×C17H(5,𝔽2)11yescharacteristic
306C2×C4×C17H(5,𝔽2)11yescharacteristic
307C2×C4×C17H(5,𝔽2)11yescharacteristic
308C2×C4×C17H(5,𝔽2)11yescharacteristic
309C22⋊D17—44no—
310C22⋊D17—44no—
311C22⋊D17—44no—
312C22⋊D17—44no—
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—
326C2×Dic17—21no—
327C2×Dic17—21no—
328C2×Dic17—21no—
329C2×Dic17C2×M1612yes—
330C2×Dic17#13112yes—
331D68—44no—
332C4×D17—41no—
333C4×D17—41no—
334C4×D17—41no—
335C4×D17—41no—
336C4×D17—41no—
337C4×D17—41no—
338C4×D17—41no—
339C4×D17—41no—
340C8×C17—41no—
341C8×C17—41no—
342C8×C17—41no—
343C8×C17—41no—
344#3622—41no—
345#3622—41no—
346#3622—41no—
347#3622—41no—
348C4×#127—171no—
349#1870—171no—
350#1870—171no—
351#1870—171no—
352#1870—171no—
353#1870—171no—
354#1870D1711yescharacteristic, complemented
355#1869—171no—
356#1869—171no—
357#1869—171no—
358#1869—171no—
359#1869—171no—
360#1869—171no—
361#1839—171no—
362#1839—171no—
363C22×C17—22no—
364C22×C17—22no—
365C22×C17—22no—
366C22×C17—41no—
367C22×C17—41no—
368C22×C17—41no—
369C22×C17—41no—
370C22×C17—41no—
371C22×C17—41no—
372C22×C17—41no—
373C22×C17—41no—
374C22×C17—41no—
375C22×C17—41no—
376C22×C17—41no—
377C22×C17#51811yescharacteristic
378C22×C17#51811yescharacteristic
379C22×C17#51811yescharacteristic
380C22×C17C22×M1611yescharacteristic
381C22×C17C2×#13111yescharacteristic
382C22×C17C2×#13111yescharacteristic
383C22×C17#56811yescharacteristic
384C2×D17—22no—
385C2×D17—22no—
386C2×D17—22no—
387C2×D17—41no—
388C2×D17—41no—
389C2×D17—41no—
390C2×D17—41no—
391C2×D17—41no—
392C2×D17—41no—
393C2×D17—41no—
394C2×D17—41no—
395C2×D17—41no—
396C2×D17—41no—
397C2×D17—41no—
398C4×C17—22no—
399C4×C17—41no—
400C4×C17—41no—
401C4×C17—41no—
402C4×C17#56011yescharacteristic
403C4×C17#56011yescharacteristic
404C4×C17#56011yescharacteristic
405C4×C17#56011yescharacteristic
406Dic17—22no—
407Dic17—22no—
408Dic17—41no—
409Dic17—41no—
410Dic17—41no—
411Dic17—41no—
412C22×M16—171no—
413C22×M16C2×D1711yescharacteristic
414C23×C8—171no—
415C23×C8—171no—
416C2×#127—171no—
417C2×C4×D4—171no—
418C2×C4×D4—171no—
419C2×C4×D4—171no—
420C2×C4×D4—171no—
421C2×C4×D4—171no—
422C2×C4×D4C2×D1711yescharacteristic
423C2×C22⋊C8—171no—
424C2×C22⋊C8—171no—
425C2×C22⋊C8—171no—
426C2×C22⋊C8—171no—
427C2×C22⋊C8—171no—
428C2×C22⋊C8—171no—
429C2×C22⋊C8—171no—
430C2×C22⋊C8—171no—
431C2×C22⋊C8—171no—
432C2×C22⋊C8C2×D1711yescharacteristic
433C2×C22⋊C8C2×D1711yescharacteristic
434C2×C22⋊C8C2×D1711yescharacteristic
435#390—171no—
436#390—171no—
437#390—171no—
438#390—171no—
439#390—171no—
440#390—171no—
441#384—171no—
442C43—171no—
443#336—171no—
444#336—171no—
445#336—171no—
446#336—171no—
447#336—171no—
448#336—171no—
449#336—171no—
450#336—171no—
451#336—171no—
452#336—171no—
453#336C2×D1711yescharacteristic
454#336C2×D1711yescharacteristic
455C2×C17—42no—
456C2×C17—81no—
457C2×C17#238011yescharacteristic
458C2×C17#297311yescharacteristic
459C2×C17#297411yescharacteristic
460C2×C17#297411yescharacteristic
461C2×C17#297911yescharacteristic
462C2×C17#298111yescharacteristic
463C2×C17#298111yescharacteristic
464D17—42no—
465D17—81no—
466C22×D4—171no—
467C22×D4—171no—
468C22×D4—171no—
469C22×D4—171no—
470C22×D4—171no—
471C22×D4C4×D1711yescharacteristic
472C23×C4—171no—
473C23×C4—171no—
474C23×C4C22×D1711yescharacteristic
475C23×C4C22×D1711yescharacteristic
476C2×M16—41no—
477C2×M16—41no—
478C2×M16—41no—
479C2×M16—681no—
480C2×M16—681no—
481C2×M16—681no—
482C22×C8—171no—
483C22×C8—171no—
484C22×C8—171no—
485C22×C8—171no—
486C22×C8—681no—
487C22×C8—681no—
488C22×C8—681no—
489C22×C8—681no—
490C22×C8—681no—
491C22×C8—681no—
492C22×C8C22×D1711yescharacteristic
493C22×C8C22×D1711yescharacteristic
494C22×C8C22×D1711yescharacteristic
495C22×C8C22×D1711yescharacteristic
496#127—344no—
497C4×D4—41no—
498C4×D4—41no—
499C4×D4—681no—
500C4×D4—681no—
501C4×D4—681no—
502C4×D4—681no—
503C4×D4—681no—
504C4×D4—681no—
505C4×D4—681no—
506C4×D4—681no—
507C4×D4—681no—
508C4×D4—681no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—171no—
511C2×C4⋊C4—171no—
512C2×C4⋊C4—171no—
513C2×C4⋊C4—171no—
514C2×C4⋊C4C4×D1711yescharacteristic
515C2×C22⋊C4—171no—
516C2×C22⋊C4—171no—
517C2×C22⋊C4—171no—
518C2×C22⋊C4—171no—
519C2×C22⋊C4—171no—
520C2×C22⋊C4—171no—
521C2×C22⋊C4—171no—
522C2×C22⋊C4—171no—
523C2×C22⋊C4—171no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4C4×D1711yescharacteristic
526C2×C22⋊C4C4×D1711yescharacteristic
527C2×C42—171no—
528C2×C42—171no—
529C2×C42—171no—
530C2×C42—171no—
531C2×C42—171no—
532C2×C42—171no—
533C2×C42C22×D1711yescharacteristic
534C22⋊C8—41no—
535C22⋊C8—41no—
536C22⋊C8—41no—
537C22⋊C8—681no—
538C22⋊C8—681no—
539C22⋊C8—681no—
540C22⋊C8—681no—
541C22⋊C8—681no—
542C22⋊C8—681no—
543C22⋊C8—681no—
544C22⋊C8—681no—
545C22⋊C8—681no—
546C17#2335611yescharacteristic, complemented, Sylow
547C24—171no—
548C24—171no—
549C24C2×C4×D1711yescharacteristic
550C24C2×C4×D1711yescharacteristic
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—174no—
555C2×D4—342no—
556C2×D4—342no—
557C2×D4—342no—
558C2×D4—342no—
559C2×D4—342no—
560C2×D4—342no—
561C2×D4—342no—
562C2×D4—681no—
563C2×D4—681no—
564C2×D4—681no—
565C2×D4—681no—
566C2×D4—681no—
567C2×D4—681no—
568C2×D4—681no—
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—171no—
582C22×C4—171no—
583C22×C4—171no—
584C22×C4—171no—
585C22×C4—171no—
586C22×C4—171no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—341no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—341no—
597C22×C4—341no—
598C22×C4—341no—
599C22×C4C2×C4×D1711yescharacteristic
600C22×C4C2×C4×D1711yescharacteristic
601C22×C4C2×C4×D1711yescharacteristic
602C22×C4C2×C4×D1711yescharacteristic
603C22×C4C23×D1711yescharacteristic
604M16—44no—
605M16—684no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—341no—
619C2×C8—341no—
620C2×C8—341no—
621C2×C8—341no—
622C2×C8—341no—
623C2×C8—341no—
624C2×C8—341no—
625C2×C8—341no—
626C2×C8—341no—
627C2×C8—341no—
628C2×C8—341no—
629C2×C8—341no—
630C2×C8—684no—
631C2×C8—684no—
632C4⋊C4—41no—
633C4⋊C4—681no—
634C4⋊C4—681no—
635C4⋊C4—681no—
636C4⋊C4—681no—
637C4⋊C4—681no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—681no—
641C22⋊C4—681no—
642C22⋊C4—681no—
643C22⋊C4—681no—
644C22⋊C4—681no—
645C22⋊C4—681no—
646C22⋊C4—681no—
647C22⋊C4—681no—
648C22⋊C4—681no—
649C22⋊C4—681no—
650C42—21no—
651C42—21no—
652C42—342no—
653C42—342no—
654C42—341no—
655C42—341no—
656C42—341no—
657C42—341no—
658C42—342no—
659C42—681no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—172no—
674C23—341no—
675C23—341no—
676C23—341no—
677C23—341no—
678C23—341no—
679C23—341no—
680C23—341no—
681C23—341no—
682C23—341no—
683C23—341no—
684C23—341no—
685C23—341no—
686C23—341no—
687C23M16×D1712yes—
688C23C22×C4×D1711yescharacteristic
689D4—44no—
690D4—684no—
691D4—684no—
692D4—684no—
693D4—684no—
694D4—684no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
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—172no—
715C2×C4—172no—
716C2×C4—341no—
717C2×C4—341no—
718C2×C4—341no—
719C2×C4—341no—
720C2×C4—341no—
721C2×C4—341no—
722C2×C4—341no—
723C2×C4—341no—
724C2×C4—341no—
725C2×C4—341no—
726C2×C4—341no—
727C2×C4—341no—
728C2×C4—341no—
729C2×C4—341no—
730C2×C4—341no—
731C2×C4—341no—
732C2×C4—681no—
733C2×C4—681no—
734C2×C4—681no—
735C2×C4—681no—
736C2×C4—681no—
737C2×C4—681no—
738C2×C4—681no—
739C2×C4—681no—
740C2×C4#1058759312yes—
741C2×C4#1058769111yescharacteristic
742C2×C4#1058769111yescharacteristic
743C2×C4#1058769111yescharacteristic
744C2×C4#1058769111yescharacteristic
745C2×C4#1058769611yescharacteristic
746C2×C4#1058769611yescharacteristic
747C8—41no—
748C8—41no—
749C8—41no—
750C8—41no—
751C8—681no—
752C8—681no—
753C8—681no—
754C8—681no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—342no—
770C22—342no—
771C22—342no—
772C22—681no—
773C22—681no—
774C22—681no—
775C22—681no—
776C22—681no—
777C22—681no—
778C22—681no—
779C22—681no—
780C22—681no—
781C22—681no—
782C22—681no—
783C22#1176328111yescharacteristic
784C22#1176328111yescharacteristic
785C22#1176328211yescharacteristic
786C22C2×M16×D1711yescharacteristic
787C22#131×D1711yescharacteristic
788C22C2×#1058759311yescharacteristic
789C22#1176357411yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—342no—
795C4—342no—
796C4—681no—
797C4—681no—
798C4—681no—
799C4—681no—
800C4#1176354711yescharacteristic
801C4#1176354711yescharacteristic
802C4#1176354811yescharacteristic
803C4#1176354911yescharacteristic
804C2—42no—
805C2—81no—
806C2—682no—
807C2—1361no—
808C2#1453195911yescharacteristic
809C2#1453780911yescharacteristic
810C2#1453781411yescharacteristic
811C2#1453782011yescharacteristic
812C2#1453784911yescharacteristic
813C2#1453785711yescharacteristic
814C2#1453786111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1870C2
prime radicalC2×#10587626C4
cosocleC22×C4×C17C24
hypercenter#1870D17
hypocenterC17#23356
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #14529081C2semidirect
3. #14529081C2semidirect
4. #14529080C2semidirect
5. #14529078C2semidirect
6. #14529078C2semidirect
7. #14529077C2semidirect
8. #14529075C2semidirect
9. #14529074C2semidirect
10. #14529074C2semidirect
11. #14529073C2semidirect
12. #14529073C2semidirect
13. #14528926C2semidirect
14. #14528926C2semidirect
15. C17×#1870C2semidirect
174. C2×C22⋊D17M16semidirect
354. #1870D17semidirect
546. C17#23356semidirect

Maximal subgroups

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

subgroupindex
C4×#105876262
#145290812
#145290802
#145290782
#145290772
#145290752
#145290742
#145290732
#145289262
C17×#18702
#2335617