Finite Group Databasebeta

← #17045431

Subgroups — #17045431

Order 4352.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762887C211yesmaximal, characteristic, complemented
2C2×#11762773C211yesmaximal, characteristic, complemented
3#14529583C211yesmaximal, characteristic, complemented
4#14529579C211yesmaximal, characteristic, complemented
5#14529399C211yesmaximal, characteristic, complemented
6#14529392C211yesmaximal, characteristic, complemented
7#14529392C211yesmaximal, characteristic, complemented
8#14529392C211yesmaximal, characteristic, complemented
9#14529082C211yesmaximal, characteristic, complemented
10#14529082C211yesmaximal, characteristic, complemented
11#14529082C211yesmaximal, characteristic, complemented
12#14528969C211yesmaximal, characteristic, complemented
13#14528694C211yesmaximal, characteristic, complemented
14#14528568C211yesmaximal, characteristic, complemented
15C4×C17×#120C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C22×#63223C2211yescharacteristic, complemented
19#11762887—24no—
20C2×C4⋊#3622C2211yescharacteristic, complemented
21C2×C4⋊#3622C2211yescharacteristic, complemented
22C2×C4⋊#3622C2211yescharacteristic, complemented
23#11762773—24no—
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×C22⋊#3622C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×C22⋊#3622C2211yescharacteristic
29C2×C22⋊#3622C2211yescharacteristic
30C2×C22⋊#3622C2211yescharacteristic
31C2×C22⋊#3622C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33C2×C22⋊#3622C2211yescharacteristic
34C2×C22⋊#3622C2211yescharacteristic, complemented
35C2×C22⋊#3622C2211yescharacteristic, complemented
36C2×C22⋊#3622C2211yescharacteristic, complemented
37C2×#10587474C2211yescharacteristic, complemented
38C2×C4×#3622C2211yescharacteristic, complemented
39C2×C4×#3622C2211yescharacteristic, complemented
40#11762564C2211yescharacteristic, complemented
41#11762564C2211yescharacteristic, complemented
42#11762564C2211yescharacteristic, complemented
43#11762564C2211yescharacteristic, complemented
44#11762564C2211yescharacteristic, complemented
45#11762564C2211yescharacteristic, complemented
46C24×C4×C17C2211yescharacteristic
47C2×C17×#120C411yescharacteristic
48C2×C4×D4×C17C2211yescharacteristic
49C2×C4×D4×C17C2211yescharacteristic
50C2×C4×D4×C17C2211yescharacteristic
51C17×#386C411yescharacteristic
52C17×#386C411yescharacteristic
53C17×#386C411yescharacteristic
54C17×#385C411yescharacteristic
55C17×#385C411yescharacteristic
56C17×#385C411yescharacteristic
57C17×#379C411yescharacteristic
58C4×C22⋊C4×C17C2211yescharacteristic
59C4×C22⋊C4×C17C2211yescharacteristic
60C4×C22⋊C4×C17C2211yescharacteristic
61C25×C17C2×C411yescharacteristic
62C22×D4×C17C2×C411yescharacteristic
63C22×D4×C17C2×C411yescharacteristic
64C22×D4×C17C2×C411yescharacteristic
65C23×C4×C17—22no—
66C23×C4×C17—22no—
67C23×C4×C17—41no—
68C23×C4×C17—41no—
69C23×C4×C17—41no—
70C23×C4×C17—41no—
71C23×C4×C17C2×C411yescharacteristic
72C23×C4×C17C2×C411yescharacteristic
73C23×C4×C17C2×C411yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C17×#120—24no—
79C4×D4×C17—22no—
80C4×D4×C17—22no—
81C4×D4×C17—41no—
82C4×D4×C17—41no—
83C4×D4×C17—41no—
84C4×D4×C17—41no—
85C2×C4⋊C4×C17C2×C411yescharacteristic
86C2×C4⋊C4×C17C2×C411yescharacteristic
87C2×C4⋊C4×C17C2×C411yescharacteristic
88C2×C22⋊C4×C17C2×C411yescharacteristic
89C2×C22⋊C4×C17C2×C411yescharacteristic
90C2×C22⋊C4×C17C2×C411yescharacteristic
91C2×C22⋊C4×C17C2×C411yescharacteristic
92C2×C22⋊C4×C17C2×C411yescharacteristic
93C2×C22⋊C4×C17C2×C411yescharacteristic
94C2×C22⋊C4×C17C2×C411yescharacteristic
95C2×C22⋊C4×C17C2×C411yescharacteristic
96C2×C22⋊C4×C17C2×C411yescharacteristic
97C2×C22⋊C4×C17C2×C411yescharacteristic
98C2×C22⋊C4×C17C2×C411yescharacteristic
99C2×C22⋊C4×C17C2×C411yescharacteristic
100C2×C42×C17C2311yescharacteristic
101C2×C42×C17C2311yescharacteristic
102C2×C42×C17C2311yescharacteristic
103C2×#63223—22no—
104C2×#63223—22no—
105C2×#63223—41no—
106C2×#63223—41no—
107C2×#63223—41no—
108C2×#63223—41no—
109C2×#63223—41no—
110C2×#63223—41no—
111C2×#63223D414yescomplemented
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C22×#3622C2311yescharacteristic
120C17×#95C2×C411yescharacteristic
121C17×#95C2×C411yescharacteristic
122C17×#95C2×C411yescharacteristic
123C17×#95C2×C411yescharacteristic
124C17×#95C2×C411yescharacteristic
125C17×#95C2×C411yescharacteristic
126C22⋊#3622—22no—
127C22⋊#3622—22no—
128C22⋊#3622—22no—
129C22⋊#3622—22no—
130C22⋊#3622—22no—
131C22⋊#3622—22no—
132C22⋊#3622—22no—
133C22⋊#3622—41no—
134C22⋊#3622—41no—
135C22⋊#3622—41no—
136C22⋊#3622—41no—
137C22⋊#3622—41no—
138C22⋊#3622—41no—
139C4⋊#3622—22no—
140C4⋊#3622—41no—
141C4⋊#3622—41no—
142#10587474—41no—
143C4×#3622—22no—
144C4×#3622—41no—
145C24×C17—22no—
146C24×C17—22no—
147C24×C17—22no—
148C24×C17—41no—
149C24×C17—41no—
150C24×C17—41no—
151C24×C17—41no—
152C24×C17C22×C411yescharacteristic
153C24×C17C22×C411yescharacteristic
154C24×C17C22×C411yescharacteristic
155C24×C17C22×C411yescharacteristic
156C2×D4×C17—22no—
157C2×D4×C17—22no—
158C2×D4×C17—22no—
159C2×D4×C17—22no—
160C2×D4×C17—22no—
161C2×D4×C17—41no—
162C2×D4×C17—41no—
163C2×D4×C17—41no—
164C2×D4×C17—41no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—41no—
191C22×C4×C17—41no—
192C22×C4×C17—41no—
193C22×C4×C17—41no—
194C22×C4×C17—41no—
195C22×C4×C17—41no—
196C22×C4×C17—44no—
197C22×C4×C17—44no—
198C22×C4×C17—44no—
199C22×C4×C17—44no—
200C22×C4×C17C22×C411yescharacteristic
201C22×C4×C17C22×C411yescharacteristic
202C22×C4×C17C22×C411yescharacteristic
203C22×C4×C17C22×C411yescharacteristic
204C22×C4×C17C22×C411yescharacteristic
205C22×C4×C17C22×C411yescharacteristic
206C22×C4×C17C22×C411yescharacteristic
207C22×C4×C17C22×C411yescharacteristic
208C22×C4×C17C22×C411yescharacteristic
209C22×C4×C17C22×C411yescharacteristic
210C22×C4×C17C2×D412yes—
211C22×C4×C17#4112yes—
212C22×C4×C17C2411yescharacteristic
213C4⋊C4×C17—22no—
214C4⋊C4×C17—41no—
215C4⋊C4×C17—41no—
216C22⋊C4×C17—22no—
217C22⋊C4×C17—22no—
218C22⋊C4×C17—22no—
219C22⋊C4×C17—22no—
220C22⋊C4×C17—22no—
221C22⋊C4×C17—41no—
222C22⋊C4×C17—41no—
223C22⋊C4×C17—41no—
224C22⋊C4×C17—41no—
225C22⋊C4×C17—41no—
226C22⋊C4×C17—41no—
227C22⋊C4×C17M1614yescomplemented
228C42×C17—21no—
229C42×C17—21no—
230C42×C17—21no—
231C42×C17—21no—
232C42×C17—21no—
233C42×C17—21no—
234#63223—44no—
235#63223—44no—
236#63223—44no—
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—21no—
250C2×#3622—21no—
251C2×#3622—21no—
252C2×#3622—21no—
253C2×#3622—21no—
254C2×#3622—21no—
255C2×#3622—21no—
256C2×#3622—21no—
257C2×#3622—21no—
258C2×#3622—21no—
259C2×#3622C2×D412yes—
260C2×#3622C2×D412yes—
261#22038—171nomaximal, Sylow
262C23×C17—21no—
263C23×C17—21no—
264C23×C17—21no—
265C23×C17—21no—
266C23×C17—21no—
267C23×C17—21no—
268C23×C17—21no—
269C23×C17—21no—
270C23×C17—21no—
271C23×C17—21no—
272C23×C17—21no—
273C23×C17—21no—
274C23×C17—21no—
275C23×C17—21no—
276C23×C17—21no—
277C23×C17—21no—
278C23×C17—21no—
279C23×C17—21no—
280C23×C17—21no—
281C23×C17—21no—
282C23×C17—21no—
283C23×C17—21no—
284C23×C17—21no—
285C23×C17—21no—
286C23×C17—21no—
287C23×C17—44no—
288C23×C17—44no—
289C23×C17—44no—
290C23×C17—44no—
291C23×C17—44no—
292C23×C17—44no—
293C23×C17—44no—
294C23×C17C4×D412yes—
295C23×C17C2×M1612yes—
296C23×C17#13112yes—
297C23×C17C23×C411yescharacteristic
298D4×C17—44no—
299D4×C17—44no—
300D4×C17—44no—
301C2×C4×C17—21no—
302C2×C4×C17—21no—
303C2×C4×C17—21no—
304C2×C4×C17—21no—
305C2×C4×C17—21no—
306C2×C4×C17—21no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—21no—
312C2×C4×C17—21no—
313C2×C4×C17—21no—
314C2×C4×C17—21no—
315C2×C4×C17—21no—
316C2×C4×C17—21no—
317C2×C4×C17—21no—
318C2×C4×C17—21no—
319C2×C4×C17—21no—
320C2×C4×C17—21no—
321C2×C4×C17—21no—
322C2×C4×C17—21no—
323C2×C4×C17—21no—
324C2×C4×C17—21no—
325C2×C4×C17—21no—
326C2×C4×C17—21no—
327C2×C4×C17—21no—
328C2×C4×C17—21no—
329C2×C4×C17—21no—
330C2×C4×C17—21no—
331C2×C4×C17—21no—
332C2×C4×C17—44no—
333C2×C4×C17—44no—
334C2×C4×C17—44no—
335C2×C4×C17—41no—
336C2×C4×C17—41no—
337C2×C4×C17—41no—
338C2×C4×C17—41no—
339C2×C4×C17—41no—
340C2×C4×C17—41no—
341C2×C4×C17—41no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17C4×D412yes—
348C2×C4×C17C2×M1612yes—
349C2×C4×C17C2×M1612yes—
350C2×C4×C17C22×D411yescharacteristic
351C2×C4×C17C2×#4111yescharacteristic
352C2×C4×C17H(5,𝔽2)11yescharacteristic
353C2×C4×C17H(5,𝔽2)11yescharacteristic
354C2×C4×C17H(5,𝔽2)11yescharacteristic
355C2×C4×C17H(5,𝔽2)11yescharacteristic
356#3622—22no—
357#3622—22no—
358#3622—41no—
359#3622—41no—
360#3622—41no—
361#3622—41no—
362#3622—41no—
363#3622—41no—
364C2×#436—171no—
365C2×#407—171no—
366C4×#120D1711yescharacteristic
367#1955—171no—
368#1954—171no—
369#1924—171no—
370#1923—171no—
371#1923—171no—
372#1923—171no—
373#1870—171no—
374#1870—171no—
375#1870—171no—
376#1851—171no—
377#1779—171no—
378#1753—171no—
379C22×C17—22no—
380C22×C17—22no—
381C22×C17—22no—
382C22×C17—22no—
383C22×C17—22no—
384C22×C17—22no—
385C22×C17—22no—
386C22×C17—22no—
387C22×C17—22no—
388C22×C17—416no—
389C22×C17—41no—
390C22×C17—41no—
391C22×C17—41no—
392C22×C17—41no—
393C22×C17—41no—
394C22×C17—41no—
395C22×C17—41no—
396C22×C17—41no—
397C22×C17—41no—
398C22×C17—41no—
399C22×C17—41no—
400C22×C17—41no—
401C22×C17—41no—
402C22×C17—41no—
403C22×C17—41no—
404C22×C17—41no—
405C22×C17—41no—
406C22×C17—41no—
407C22×C17—41no—
408C22×C17C2×C4×D411yescharacteristic
409C22×C17#51811yescharacteristic
410C22×C17#51811yescharacteristic
411C22×C17C22×M1611yescharacteristic
412C22×C17C2×#13111yescharacteristic
413C22×C17#56811yescharacteristic
414C22×C17#56811yescharacteristic
415C4×C17—22no—
416C4×C17—22no—
417C4×C17—22no—
418C4×C17—41no—
419C4×C17—41no—
420C4×C17—41no—
421C4×C17—41no—
422C4×C17—41no—
423C4×C17—41no—
424C4×C17—41no—
425C4×C17#53411yescharacteristic
426C4×C17#53511yescharacteristic
427C4×C17#53811yescharacteristic
428C4×C17#53811yescharacteristic
429C24×C4C2×D1711yescharacteristic
430C22×M16—171no—
431C22×M16—171no—
432C22×M16—171no—
433C2×#120Dic1711yescharacteristic
434C2×C4×D4C2×D1711yescharacteristic
435C2×C4×D4C2×D1711yescharacteristic
436C2×C4×D4C2×D1711yescharacteristic
437#436—344no—
438C2×C4⋊C8—171no—
439C2×C4⋊C8—171no—
440C2×C4⋊C8—171no—
441#407—344no—
442C2×C22⋊C8—171no—
443C2×C22⋊C8—171no—
444C2×C22⋊C8—171no—
445C2×C22⋊C8—171no—
446C2×C22⋊C8—171no—
447C2×C22⋊C8—171no—
448C2×C22⋊C8—171no—
449C2×C22⋊C8—171no—
450C2×C22⋊C8—171no—
451C2×C22⋊C8—171no—
452C2×C22⋊C8—171no—
453C2×C22⋊C8—171no—
454C2×C22⋊C8—171no—
455C2×#97—171no—
456C2×C4×C8—171no—
457C2×C4×C8—171no—
458#386Dic1711yescharacteristic
459#386Dic1711yescharacteristic
460#386Dic1711yescharacteristic
461#385Dic1711yescharacteristic
462#385Dic1711yescharacteristic
463#385Dic1711yescharacteristic
464#379Dic1711yescharacteristic
465C4×C22⋊C4C2×D1711yescharacteristic
466C4×C22⋊C4C2×D1711yescharacteristic
467C4×C22⋊C4C2×D1711yescharacteristic
468#336—171no—
469#336—171no—
470#336—171no—
471#336—171no—
472#336—171no—
473#336—171no—
474C2×C17—42no—
475C2×C17—42no—
476C2×C17—42no—
477C2×C17—81no—
478C2×C17#232111yescharacteristic
479C2×C17#293311yescharacteristic
480C2×C17D4×M1611yescharacteristic
481C2×C17#297411yescharacteristic
482C2×C17#297511yescharacteristic
483C2×C17#297611yescharacteristic
484C2×C17#297811yescharacteristic
485C25C2×Dic1711yescharacteristic
486C22×D4C2×Dic1711yescharacteristic
487C22×D4C2×Dic1711yescharacteristic
488C22×D4C2×Dic1711yescharacteristic
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—41no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4C2×Dic1711yescharacteristic
496C23×C4C2×Dic1711yescharacteristic
497C23×C4C2×Dic1711yescharacteristic
498C23×C4C22×D1711yescharacteristic
499C23×C4C22×D1711yescharacteristic
500C23×C4C22×D1711yescharacteristic
501C23×C4C22×D1711yescharacteristic
502C2×M16—174no—
503C2×M16—342no—
504C2×M16—342no—
505C2×M16—681no—
506C2×M16—681no—
507C2×M16—681no—
508C2×M16—681no—
509C2×M16—681no—
510C2×M16—681no—
511C22×C8—171no—
512C22×C8—171no—
513C22×C8—171no—
514C22×C8—171no—
515C22×C8—171no—
516C22×C8—171no—
517C22×C8—171no—
518C22×C8—171no—
519#120—24no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—41no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—41no—
526C2×C4⋊C4C2×Dic1711yescharacteristic
527C2×C4⋊C4C2×Dic1711yescharacteristic
528C2×C4⋊C4C2×Dic1711yescharacteristic
529C2×C22⋊C4C2×Dic1711yescharacteristic
530C2×C22⋊C4C2×Dic1711yescharacteristic
531C2×C22⋊C4C2×Dic1711yescharacteristic
532C2×C22⋊C4C2×Dic1711yescharacteristic
533C2×C22⋊C4C2×Dic1711yescharacteristic
534C2×C22⋊C4C2×Dic1711yescharacteristic
535C2×C22⋊C4C2×Dic1711yescharacteristic
536C2×C22⋊C4C2×Dic1711yescharacteristic
537C2×C22⋊C4C2×Dic1711yescharacteristic
538C2×C22⋊C4C2×Dic1711yescharacteristic
539C2×C22⋊C4C2×Dic1711yescharacteristic
540C2×C22⋊C4C2×Dic1711yescharacteristic
541C2×C42C22×D1711yescharacteristic
542C2×C42C22×D1711yescharacteristic
543C2×C42C22×D1711yescharacteristic
544C4⋊C8—342no—
545C4⋊C8—681no—
546C4⋊C8—681no—
547C22⋊C8—342no—
548C22⋊C8—342no—
549C22⋊C8—342no—
550C22⋊C8—342no—
551C22⋊C8—342no—
552C22⋊C8—342no—
553C22⋊C8—342no—
554C22⋊C8—681no—
555C22⋊C8—681no—
556C22⋊C8—681no—
557C22⋊C8—681no—
558C22⋊C8—681no—
559C22⋊C8—681no—
560#97—681no—
561C4×C8—342no—
562C4×C8—681no—
563#95C2×Dic1711yescharacteristic
564#95C2×Dic1711yescharacteristic
565#95C2×Dic1711yescharacteristic
566#95C2×Dic1711yescharacteristic
567#95C2×Dic1711yescharacteristic
568#95C2×Dic1711yescharacteristic
569C17#2203811yescharacteristic, complemented, Sylow
570C24—22no—
571C24—22no—
572C24—22no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24C22×Dic1711yescharacteristic
578C24C22×Dic1711yescharacteristic
579C24C22×Dic1711yescharacteristic
580C24C22×Dic1711yescharacteristic
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4D4×D1712yes—
626C22×C4#6325412yes—
627C22×C4C22×Dic1711yescharacteristic
628C22×C4C22×Dic1711yescharacteristic
629C22×C4C22×Dic1711yescharacteristic
630C22×C4C22×Dic1711yescharacteristic
631C22×C4C22×Dic1711yescharacteristic
632C22×C4C22×Dic1711yescharacteristic
633C22×C4C22×Dic1711yescharacteristic
634C22×C4C22×Dic1711yescharacteristic
635C22×C4C22×Dic1711yescharacteristic
636C22×C4C22×Dic1711yescharacteristic
637C22×C4C23×D1711yescharacteristic
638M16—684no—
639M16—684no—
640M16—684no—
641C2×C8—172no—
642C2×C8—172no—
643C2×C8—341no—
644C2×C8—341no—
645C2×C8—341no—
646C2×C8—341no—
647C2×C8—341no—
648C2×C8—341no—
649C2×C8—341no—
650C2×C8—341no—
651C2×C8—341no—
652C2×C8—341no—
653C2×C8—341no—
654C2×C8—341no—
655C2×C8—341no—
656C2×C8—341no—
657C2×C8—341no—
658C2×C8—341no—
659C2×C8—341no—
660C2×C8—341no—
661C2×C8—341no—
662C2×C8—341no—
663C2×C8—341no—
664C2×C8—341no—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4#6322314yescomplemented
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23C2×#6322312yes—
719C23D4×Dic1712yes—
720C23#1058763412yes—
721C23C23×Dic1711yescharacteristic
722D4—44no—
723D4—44no—
724D4—44no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4C2×#6322312yes—
772C2×C4C2×#6322312yes—
773C2×C4D4×Dic1712yes—
774C2×C4C2×D4×D1711yescharacteristic
775C2×C4C2×#6325411yescharacteristic
776C2×C4#1058769111yescharacteristic
777C2×C4#1058769111yescharacteristic
778C2×C4#1058769111yescharacteristic
779C2×C4#1058769111yescharacteristic
780C8—342no—
781C8—342no—
782C8—681no—
783C8—681no—
784C8—681no—
785C8—681no—
786C8—681no—
787C8—681no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22C2×D4×Dic1711yescharacteristic
818C22#1176328411yescharacteristic
819C22#1176328411yescharacteristic
820C22C22×#6322311yescharacteristic
821C22C2×#1058763411yescharacteristic
822C22#1176357611yescharacteristic
823C22#1176357611yescharacteristic
824C4—22no—
825C4—22no—
826C4—22no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4#1176336911yescharacteristic
835C4#1176337411yescharacteristic
836C4#1176339411yescharacteristic
837C4#1176339411yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—81no—
842C2#1453144511yescharacteristic
843C2#1453751111yescharacteristic
844C2D4×#6322311yescharacteristic
845C2#1453781911yescharacteristic
846C2#1453782511yescharacteristic
847C2#1453783211yescharacteristic
848C2#1453784611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC4×C17×#120C2
prime radicalC2×C17×#120C4
cosocleC22×C4×C17C24
hypercenterC4×#120D17
hypocenterC17#22038
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#11762887C2semidirect
2. C2×#11762773C2semidirect
3. #14529583C2semidirect
4. #14529579C2semidirect
5. #14529399C2semidirect
6. #14529392C2semidirect
7. #14529392C2semidirect
8. #14529392C2semidirect
9. #14529082C2semidirect
10. #14529082C2semidirect
11. #14529082C2semidirect
12. #14528969C2semidirect
13. #14528694C2semidirect
14. #14528568C2semidirect
18. C22×#63223C22semidirect
20. C2×C4⋊#3622C22semidirect
21. C2×C4⋊#3622C22semidirect
22. C2×C4⋊#3622C22semidirect
34. C2×C22⋊#3622C22semidirect
35. C2×C22⋊#3622C22semidirect
36. C2×C22⋊#3622C22semidirect
37. C2×#10587474C22semidirect
38. C2×C4×#3622C22semidirect
39. C2×C4×#3622C22semidirect
40. #11762564C22semidirect
41. #11762564C22semidirect
42. #11762564C22semidirect
43. #11762564C22semidirect
44. #11762564C22semidirect
45. #11762564C22semidirect
111. C2×#63223D4semidirect
227. C22⋊C4×C17M16semidirect
569. C17#22038semidirect
679. C22⋊C4#63223semidirect

Maximal subgroups

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

subgroupindex
C2×#117628872
C2×#117627732
#145295832
#145295792
#145293992
#145293922
#145290822
#145289692
#145286942
#145285682
C4×C17×#1202
#2203817