Finite Group Databasebeta

← #16939600

Subgroups — #16939600

Order 4352.

1822 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D17C211yesmaximal, characteristic
2C22×#10587491C211yesmaximal, characteristic
3C2×#11762666C211yesmaximal, characteristic
4C2×#11762572C211yesmaximal, characteristic, complemented
5C2×#11762571C211yesmaximal, characteristic, complemented
6C2×#11762571C211yesmaximal, characteristic, complemented
7C2×C17×#340C211yesmaximal, characteristic, complemented
8C23×C4×D17—21no—
9C23×C4×D17C2211yescharacteristic
10C23×#3622C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×#63225—21no—
14C2×C4⋊C4×D17—22no—
15C2×C4⋊C4×D17—22no—
16C2×C4⋊C4×D17—22no—
17C2×C4⋊C4×D17—22no—
18C2×C4⋊C4×D17—22no—
19C2×C4⋊C4×D17C414yescomplemented
20C22×#63227—21no—
21C2×#10587491—22no—
22C2×#10587491—22no—
23C2×#10587491C414yescomplemented
24#11762666—22no—
25#11762666C414yescomplemented
26C2×#10587502—21no—
27#11762572—22no—
28#11762571—22no—
29#11762571—22no—
30C23×C8×C17C2211yescharacteristic
31C22×C4⋊C4×C17C2211yescharacteristic
32C22×C4⋊C4×C17C2211yescharacteristic
33C17×#340—22no—
34C24×D17D411yescharacteristic
35C23×C4×C17—21no—
36C23×C4×C17—21no—
37C23×C4×C17C2311yescharacteristic
38C23×Dic17—21no—
39C23×Dic17—21no—
40C23×Dic17D411yescharacteristic
41C22×C4×D17—21no—
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—21no—
45C22×C4×D17—21no—
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17—21no—
49C22×C4×D17—24no—
50C22×C4×D17—24no—
51C22×C4×D17—24no—
52C22×C4×D17—42no—
53C22×C4×D17—42no—
54C22×C4×D17—42no—
55C22×C4×D17—42no—
56C22×C4×D17C2×C412yes—
57C22×C4×D17C2×C412yes—
58C22×C4×D17C2×C412yes—
59C22×C4×D17D412yes—
60C22×C4×D17D412yes—
61C22×C4×D17Q812yes—
62C22×C8×C17—21no—
63C22×C8×C17—21no—
64C22×C8×C17—21no—
65C22×C8×C17—21no—
66C22×C8×C17—21no—
67C22×C8×C17—21no—
68C22×C8×C17C2×C412yescomplemented
69C2×C4⋊C4×C17—21no—
70C2×C4⋊C4×C17—21no—
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17—21no—
74C2×C4⋊C4×C17—21no—
75C2×C4⋊C4×C17—21no—
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17C2×C412yes—
78C2×C4⋊C4×C17C2×C412yescomplemented
79C2×C4⋊C4×C17D412yes—
80C2×C4⋊C4×C17D412yes—
81C2×#63227—24no—
82C2×#63227—42no—
83C2×#63227—42no—
84C2×C4⋊Dic17—21no—
85C2×C4⋊Dic17—21no—
86C2×C4⋊Dic17—21no—
87C2×C4⋊Dic17—21no—
88C2×C4⋊Dic17—21no—
89C2×C4⋊Dic17—21no—
90C2×C4⋊Dic17—21no—
91C2×C4⋊Dic17—21no—
92C2×C4⋊Dic17C2×C412yes—
93C2×C4⋊Dic17C2×C412yescomplemented
94C2×C4⋊Dic17D412yes—
95C2×C4⋊Dic17D412yes—
96C2×#63225—24no—
97C2×#63225—24no—
98C2×#63225—24no—
99C22×#3622—21no—
100C22×#3622—21no—
101C22×#3622—21no—
102C22×#3622—21no—
103C22×#3622—21no—
104C22×#3622—21no—
105C22×#3622C2×C412yescomplemented
106C4⋊C4×D17—28no—
107C4⋊C4×D17—28no—
108C4⋊C4×D17—28no—
109C4⋊C4×D17—28no—
110#10587502—24no—
111#10587491—28no—
112C24×C17C2×D411yescharacteristic
113C23×D17—21no—
114C23×D17—21no—
115C23×D17—21no—
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17C22⋊C412yes—
122C23×D17C22⋊C412yes—
123C23×D17C4⋊C412yes—
124C23×D17D812yes—
125C23×D17SD1612yes—
126C23×D17SD1612yes—
127C23×D17Q1612yes—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17—41no—
133C22×C4×C17—41no—
134C22×C4×C17—41no—
135C22×C4×C17—41no—
136C22×C4×C17—41no—
137C22×C4×C17—41no—
138C22×C4×C17—41no—
139C22×C4×C17—41no—
140C22×C4×C17—41no—
141C22×C4×C17—41no—
142C22×C4×C17C22×C411yescharacteristic
143C22×C4×C17C22×C411yescharacteristic
144C22×C4×C17C22×C411yescharacteristic
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17C2×D411yescharacteristic
147C22×C4×C17C2×D411yescharacteristic
148C22×C4×C17C2×D411yescharacteristic
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17C2×D411yescharacteristic
151C22×C4×C17C2×Q811yescharacteristic
152C22×C4×C17#4111yescharacteristic
153C22×C4×C17#4111yescharacteristic
154C22×C4×C17#4111yescharacteristic
155C22×C4×C17#4111yescharacteristic
156C22×Dic17—21no—
157C22×Dic17—21no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—22no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17—41no—
165C22×Dic17—41no—
166C22×Dic17—41no—
167C22×Dic17—41no—
168C22×Dic17—41no—
169C22×Dic17—41no—
170C22×Dic17—41no—
171C22×Dic17—41no—
172C22×Dic17—41no—
173C22×Dic17—41no—
174C22×Dic17C22⋊C412yes—
175C22×Dic17C22⋊C412yes—
176C22×Dic17C4⋊C412yes—
177C2×C4×D17—22no—
178C2×C4×D17—22no—
179C2×C4×D17—22no—
180C2×C4×D17—22no—
181C2×C4×D17—22no—
182C2×C4×D17—22no—
183C2×C4×D17—22no—
184C2×C4×D17—22no—
185C2×C4×D17—22no—
186C2×C4×D17—22no—
187C2×C4×D17—22no—
188C2×C4×D17—22no—
189C2×C4×D17—22no—
190C2×C4×D17—22no—
191C2×C4×D17—22no—
192C2×C4×D17—22no—
193C2×C4×D17—22no—
194C2×C4×D17—22no—
195C2×C4×D17—22no—
196C2×C4×D17—22no—
197C2×C4×D17—22no—
198C2×C4×D17—22no—
199C2×C4×D17—22no—
200C2×C4×D17—22no—
201C2×C4×D17—216no—
202C2×C4×D17—48no—
203C2×C4×D17—48no—
204C2×C4×D17—48no—
205C2×C4×D17—48no—
206C2×C4×D17—48no—
207C2×C4×D17—48no—
208C2×C4×D17C4214yes—
209C2×C4×D17C22⋊C414yes—
210C2×C4×D17C4⋊C414yes—
211C2×C4×D17C4⋊C414yes—
212C2×C8×C17—22no—
213C2×C8×C17—22no—
214C2×C8×C17—22no—
215C2×C8×C17—41no—
216C2×C8×C17—41no—
217C2×C8×C17—41no—
218C2×C8×C17—41no—
219C4⋊C4×C17—22no—
220C4⋊C4×C17—22no—
221C4⋊C4×C17—22no—
222C4⋊C4×C17—22no—
223C4⋊C4×C17—22no—
224C4⋊C4×C17—41no—
225C4⋊C4×C17—41no—
226C4⋊C4×C17C22⋊C414yescomplemented
227#63227—48no—
228C4⋊Dic17—22no—
229C4⋊Dic17—22no—
230C4⋊Dic17—22no—
231C4⋊Dic17—22no—
232C4⋊Dic17—22no—
233C4⋊Dic17—41no—
234C4⋊Dic17—41no—
235C4⋊Dic17C22⋊C414yescomplemented
236#63225—216no—
237C2×#3622—22no—
238C2×#3622—22no—
239C2×#3622—22no—
240C2×#3622—41no—
241C2×#3622—41no—
242C2×#3622—41no—
243C2×#3622—41no—
244#10730—171nomaximal, Sylow
245C23×C17C2×C22⋊C411yescharacteristic
246C23×C17C2×C22⋊C411yescharacteristic
247C23×C17C2×C4⋊C411yescharacteristic
248C23×C17#12011yescharacteristic
249C23×C17#12011yescharacteristic
250C23×C17#12311yescharacteristic
251C23×C17#12311yescharacteristic
252C23×C17C2×D811yescharacteristic
253C23×C17C2×SD1611yescharacteristic
254C23×C17C2×SD1611yescharacteristic
255C23×C17C2×Q1611yescharacteristic
256C23×C17AGL(1,ℤ/8)11yescharacteristic
257C23×C17AGL(1,ℤ/8)11yescharacteristic
258C23×C17#13711yescharacteristic
259C23×C17#13711yescharacteristic
260C22×D17—22no—
261C22×D17—22no—
262C22×D17—22no—
263C22×D17—22no—
264C22×D17—22no—
265C22×D17—22no—
266C22×D17—22no—
267C22×D17—22no—
268C22×D17—22no—
269C22×D17—22no—
270C22×D17—22no—
271C22×D17—22no—
272C22×D17—22no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17—22no—
278C22×D17—22no—
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17—22no—
287C22×D17—22no—
288C22×D17#9514yes—
289C22×D17#10214yes—
290C22×D17#10214yes—
291C22×D17#10314yes—
292C22×D17#10314yes—
293C22×D17#10614yes—
294C22×D17#10714yes—
295C2×C4×C17—24no—
296C2×C4×C17—42no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—42no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—81no—
306C2×C4×C17—81no—
307C2×C4×C17—81no—
308C2×C4×C17—81no—
309C2×C4×C17C2×C4211yescharacteristic
310C2×C4×C17C2×C22⋊C411yescharacteristic
311C2×C4×C17C2×C22⋊C411yescharacteristic
312C2×C4×C17C2×C22⋊C411yescharacteristic
313C2×C4×C17C2×C4⋊C411yescharacteristic
314C2×C4×C17C2×C4⋊C411yescharacteristic
315C2×C4×C17#11711yescharacteristic
316C2×C4×C17#11711yescharacteristic
317C2×C4×C17C4×D411yescharacteristic
318C2×C4×C17C4×D411yescharacteristic
319C2×C4×C17C4×D411yescharacteristic
320C2×C4×C17C4×D411yescharacteristic
321C2×C4×C17C4×D411yescharacteristic
322C2×C4×C17C4×D411yescharacteristic
323C2×C4×C17C4×D411yescharacteristic
324C2×C4×C17C4×D411yescharacteristic
325C2×C4×C17#12011yescharacteristic
326C2×C4×C17#12011yescharacteristic
327C2×C4×C17#12111yescharacteristic
328C2×C4×C17#12111yescharacteristic
329C2×C4×C17#12111yescharacteristic
330C2×C4×C17#12111yescharacteristic
331C2×C4×C17C22⋊Q811yescharacteristic
332C2×C4×C17C22⋊Q811yescharacteristic
333C2×C4×C17C22⋊Q811yescharacteristic
334C2×C4×C17C22⋊Q811yescharacteristic
335C2×C4×C17#12311yescharacteristic
336C2×C4×C17#12311yescharacteristic
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—24no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17—42no—
350C2×Dic17—42no—
351C2×Dic17—42no—
352C2×Dic17—42no—
353C2×Dic17—81no—
354C2×Dic17—81no—
355C2×Dic17—81no—
356C2×Dic17—81no—
357C2×Dic17#9514yes—
358C4×D17—24no—
359C4×D17—24no—
360C4×D17—24no—
361C4×D17—24no—
362C4×D17—24no—
363C4×D17—24no—
364C4×D17—24no—
365C4×D17—24no—
366C4×D17—432no—
367C8×C17—42no—
368#3622—42no—
369C23×C4⋊C4—171no—
370C22×C22⋊C8—171no—
371C2×#380—171no—
372C2×#340—171no—
373C2×#340—171no—
374C2×#340—171no—
375C2×#340D1711yescharacteristic, complemented
376C22×C17C2×#9511yescharacteristic
377C22×C17#37911yescharacteristic
378C22×C17#38111yescharacteristic
379C22×C17#38511yescharacteristic
380C22×C17#38511yescharacteristic
381C22×C17#38611yescharacteristic
382C22×C17#38611yescharacteristic
383C22×C17C2×#10211yescharacteristic
384C22×C17C2×#10211yescharacteristic
385C22×C17C2×#10311yescharacteristic
386C22×C17C2×#10311yescharacteristic
387C22×C17#41711yescharacteristic
388C22×C17#41711yescharacteristic
389C22×C17#41811yescharacteristic
390C22×C17#41911yescharacteristic
391C22×C17C2×#10611yescharacteristic
392C22×C17C2×#10711yescharacteristic
393C22×C17#42811yescharacteristic
394C22×C17#42811yescharacteristic
395C22×C17#44711yescharacteristic
396C22×C17#44711yescharacteristic
397C22×C17#44811yescharacteristic
398C22×C17#44811yescharacteristic
399C22×C17#45011yescharacteristic
400C22×C17#45011yescharacteristic
401C22×C17#45111yescharacteristic
402C22×C17#45111yescharacteristic
403C22×C17#48011yescharacteristic
404C22×C17#48011yescharacteristic
405C22×C17#48111yescharacteristic
406C22×C17#48111yescharacteristic
407C22×C17#48311yescharacteristic
408C22×C17#48311yescharacteristic
409C22×C17#48411yescharacteristic
410C22×C17#48411yescharacteristic
411C2×D17—24no—
412C2×D17—24no—
413C2×D17—24no—
414C2×D17—24no—
415C2×D17—24no—
416C2×D17—24no—
417C2×D17—24no—
418C2×D17—24no—
419C2×D17—24no—
420C2×D17—24no—
421C2×D17—24no—
422C2×D17—24no—
423C2×D17—24no—
424C2×D17—24no—
425C2×D17#34018yescomplemented
426C4×C17—44no—
427C4×C17—82no—
428C4×C17C4×C22⋊C411yescharacteristic
429C4×C17C4×C22⋊C411yescharacteristic
430C4×C17#38011yescharacteristic
431C4×C17#38011yescharacteristic
432C4×C17#38511yescharacteristic
433C4×C17#38511yescharacteristic
434C4×C17#38611yescharacteristic
435C4×C17#38611yescharacteristic
436Dic17—24no—
437Dic17—44no—
438Dic17—82no—
439C24×C4—171no—
440C24×C4—341no—
441C23×C8—171no—
442C23×C8C2×D1711yescharacteristic
443C22×C4⋊C4—171no—
444C22×C4⋊C4—171no—
445C22×C4⋊C4—174no—
446C22×C4⋊C4—342no—
447C22×C4⋊C4—342no—
448C22×C4⋊C4—342no—
449C22×C4⋊C4—341no—
450C22×C4⋊C4—342no—
451C22×C4⋊C4—342no—
452C22×C4⋊C4C2×D1711yescharacteristic
453C22×C4⋊C4C2×D1711yescharacteristic
454C22×C22⋊C4—341no—
455C2×C22⋊C8—174no—
456C2×C22⋊C8—342no—
457C2×C22⋊C8—342no—
458#380—174no—
459#380—342no—
460C2×#95—341no—
461#340—22no—
462#340—342no—
463#340—342no—
464#340—342no—
465C2×C17C22⋊#9511yescharacteristic
466C2×C17C2×#34011yescharacteristic
467C2×C17#173611yescharacteristic
468C2×C17#178611yescharacteristic
469C2×C17#178711yescharacteristic
470C2×C17#182311yescharacteristic
471C2×C17#182411yescharacteristic
472C2×C17#185211yescharacteristic
473C2×C17#185211yescharacteristic
474C2×C17#185311yescharacteristic
475C2×C17#185311yescharacteristic
476C2×C17#187211yescharacteristic
477C2×C17#187211yescharacteristic
478C2×C17#187411yescharacteristic
479C2×C17#187411yescharacteristic
480D17—28no—
481C25—171no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—171no—
485C23×C4—172no—
486C23×C4—172no—
487C23×C4—172no—
488C23×C4—172no—
489C23×C4—172no—
490C23×C4—172no—
491C23×C4—344no—
492C23×C4—344no—
493C23×C4—344no—
494C23×C4—341no—
495C23×C4—341no—
496C23×C4—341no—
497C23×C4—341no—
498C23×C4—341no—
499C23×C4—341no—
500C23×C4—341no—
501C23×C4—341no—
502C23×C4—341no—
503C23×C4—341no—
504C23×C4—682no—
505C23×C4—682no—
506C23×C4—682no—
507C23×C4—682no—
508C23×C4C22×D1711yescharacteristic
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—21no—
513C22×C8—21no—
514C22×C8—21no—
515C22×C8—172no—
516C22×C8—341no—
517C22×C8—341no—
518C22×C8—341no—
519C22×C8—341no—
520C22×C8—341no—
521C22×C8—341no—
522C22×C8C4×D1712yescomplemented
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—172no—
532C2×C4⋊C4—172no—
533C2×C4⋊C4—172no—
534C2×C4⋊C4—172no—
535C2×C4⋊C4—348no—
536C2×C4⋊C4—348no—
537C2×C4⋊C4—348no—
538C2×C4⋊C4—344no—
539C2×C4⋊C4—344no—
540C2×C4⋊C4—344no—
541C2×C4⋊C4—341no—
542C2×C4⋊C4—341no—
543C2×C4⋊C4—341no—
544C2×C4⋊C4—348no—
545C2×C4⋊C4—341no—
546C2×C4⋊C4—341no—
547C2×C4⋊C4—341no—
548C2×C4⋊C4—341no—
549C2×C4⋊C4—341no—
550C2×C4⋊C4C4×D1712yes—
551C2×C4⋊C4C4×D1712yescomplemented
552C2×C4⋊C4D6812yes—
553C2×C4⋊C4C22⋊D1712yes—
554C2×C22⋊C4—344no—
555C2×C22⋊C4—682no—
556C2×C22⋊C4—682no—
557C22⋊C8—348no—
558#95—344no—
559C17#1073011yescharacteristic, complemented, Sylow
560C24—172no—
561C24—172no—
562C24—172no—
563C24—172no—
564C24—172no—
565C24—172no—
566C24—172no—
567C24—341no—
568C24—341no—
569C24—341no—
570C24—341no—
571C24—341no—
572C24—341no—
573C24—341no—
574C24—341no—
575C24D4×D1711yescharacteristic
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—172no—
591C22×C4—172no—
592C22×C4—172no—
593C22×C4—174no—
594C22×C4—174no—
595C22×C4—174no—
596C22×C4—174no—
597C22×C4—3416no—
598C22×C4—341no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—342no—
611C22×C4—342no—
612C22×C4—342no—
613C22×C4—342no—
614C22×C4—342no—
615C22×C4—342no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4—342no—
630C22×C4—688no—
631C22×C4—688no—
632C22×C4—688no—
633C22×C4—688no—
634C22×C4—688no—
635C22×C4—688no—
636C22×C4—681no—
637C22×C4—681no—
638C22×C4—681no—
639C22×C4—681no—
640C22×C4—681no—
641C22×C4—681no—
642C22×C4—681no—
643C22×C4—681no—
644C22×C4—681no—
645C22×C4—681no—
646C22×C4C2×C4×D1711yescharacteristic
647C22×C4C2×C4×D1711yescharacteristic
648C22×C4C2×C4×D1711yescharacteristic
649C22×C4C2×D6811yescharacteristic
650C22×C4#6325211yescharacteristic
651C22×C4#6325211yescharacteristic
652C22×C4D4×D1711yescharacteristic
653C22×C4D4×D1711yescharacteristic
654C22×C4D4×D1711yescharacteristic
655C22×C4D4×D1711yescharacteristic
656C22×C4#6325411yescharacteristic
657C22×C4Q8×D1711yescharacteristic
658C22×C4#6325611yescharacteristic
659C22×C4C2×C22⋊D1711yescharacteristic
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—342no—
668C2×C8—342no—
669C2×C8—342no—
670C2×C8—681no—
671C2×C8—681no—
672C2×C8—681no—
673C2×C8—681no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—174no—
682C4⋊C4—3416no—
683C4⋊C4—342no—
684C4⋊C4—342no—
685C4⋊C4—342no—
686C4⋊C4—342no—
687C4⋊C4—342no—
688C4⋊C4—681no—
689C4⋊C4—681no—
690C4⋊C4#6322714yescomplemented
691C22⋊C4—688no—
692C23—174no—
693C23—174no—
694C23—174no—
695C23—174no—
696C23—174no—
697C23—174no—
698C23—174no—
699C23—342no—
700C23—342no—
701C23—342no—
702C23—342no—
703C23—342no—
704C23—342no—
705C23—342no—
706C23—342no—
707C23—342no—
708C23—342no—
709C23—342no—
710C23—342no—
711C23—342no—
712C23—342no—
713C23—342no—
714C23—342no—
715C23—342no—
716C23—342no—
717C23—342no—
718C23—342no—
719C23—342no—
720C23—342no—
721C23—342no—
722C23—342no—
723C23—342no—
724C23—342no—
725C23—342no—
726C23—342no—
727C23C22⋊C4×D1711yescharacteristic
728C23C22⋊C4×D1711yescharacteristic
729C23#1058756811yescharacteristic
730C23#1058756911yescharacteristic
731C23C4⋊C4×D1711yescharacteristic
732C23#1058758011yescharacteristic
733C23D8×D1711yescharacteristic
734C23#1058759711yescharacteristic
735C23SD16×D1711yescharacteristic
736C23SD16×D1711yescharacteristic
737C23#1058760011yescharacteristic
738C23#1058760111yescharacteristic
739C23Q16×D1711yescharacteristic
740C23#1058760411yescharacteristic
741C23#1058762311yescharacteristic
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—174no—
757C2×C4—342no—
758C2×C4—342no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—344no—
764C2×C4—344no—
765C2×C4—344no—
766C2×C4—344no—
767C2×C4—344no—
768C2×C4—344no—
769C2×C4—344no—
770C2×C4—344no—
771C2×C4—344no—
772C2×C4—6832no—
773C2×C4—682no—
774C2×C4—682no—
775C2×C4—682no—
776C2×C4—682no—
777C2×C4—682no—
778C2×C4—682no—
779C2×C4—682no—
780C2×C4—682no—
781C2×C4—682no—
782C2×C4—1361no—
783C2×C4—1361no—
784C2×C4—1361no—
785C2×C4—1361no—
786C2×C4C42×D1711yescharacteristic
787C2×C4#1058755811yescharacteristic
788C2×C4C4×D6811yescharacteristic
789C2×C4C4×D6811yescharacteristic
790C2×C4C22⋊C4×D1711yescharacteristic
791C2×C4C22⋊C4×D1711yescharacteristic
792C2×C4#1058756711yescharacteristic
793C2×C4#1058756711yescharacteristic
794C2×C4#1058756811yescharacteristic
795C2×C4#1058756911yescharacteristic
796C2×C4#1058757011yescharacteristic
797C2×C4#1058757011yescharacteristic
798C2×C4C4⋊C4×D1711yescharacteristic
799C2×C4C4⋊C4×D1711yescharacteristic
800C2×C4#1058757811yescharacteristic
801C2×C4#1058757911yescharacteristic
802C2×C4#1058757911yescharacteristic
803C2×C4#1058758011yescharacteristic
804C2×C4#1058758111yescharacteristic
805C2×C4#1058758211yescharacteristic
806C2×C4#1058758211yescharacteristic
807C2×C4#1058758311yescharacteristic
808C2×C4C2×#6322711yescharacteristic
809C2×C4C4×C22⋊D1711yescharacteristic
810C2×C4C4×C22⋊D1711yescharacteristic
811C2×C4#1058762311yescharacteristic
812C2×C4#1058762411yescharacteristic
813C2×C4#1058763211yescharacteristic
814C8—42no—
815C8—682no—
816C22—178no—
817C22—344no—
818C22—344no—
819C22—344no—
820C22—344no—
821C22—344no—
822C22—344no—
823C22—344no—
824C22—344no—
825C22—344no—
826C22—344no—
827C22—344no—
828C22—344no—
829C22—344no—
830C22—344no—
831C22#95×D1711yescharacteristic
832C22#1176266411yescharacteristic
833C22#1176267111yescharacteristic
834C22#1176268011yescharacteristic
835C22#1176268311yescharacteristic
836C22#1176268511yescharacteristic
837C22#1176268711yescharacteristic
838C22#102×D1711yescharacteristic
839C22#102×D1711yescharacteristic
840C22#103×D1711yescharacteristic
841C22#103×D1711yescharacteristic
842C22#1176280711yescharacteristic
843C22#1176280911yescharacteristic
844C22#1176281211yescharacteristic
845C22#1176281611yescharacteristic
846C22#106×D1711yescharacteristic
847C22#107×D1711yescharacteristic
848C22#1176284811yescharacteristic
849C22#1176285011yescharacteristic
850C22#1176294111yescharacteristic
851C22#1176294411yescharacteristic
852C22#1176294611yescharacteristic
853C22#1176294911yescharacteristic
854C22#1176295811yescharacteristic
855C22#1176296111yescharacteristic
856C22#1176296311yescharacteristic
857C22#1176296611yescharacteristic
858C22#1176312111yescharacteristic
859C22#1176312411yescharacteristic
860C22#1176312611yescharacteristic
861C22#1176312911yescharacteristic
862C22#1176313811yescharacteristic
863C22#1176314111yescharacteristic
864C22#1176314311yescharacteristic
865C22#1176314611yescharacteristic
866C4—44no—
867C4—82no—
868C4—344no—
869C4—684no—
870C4—1362no—
871C4#1176265611yescharacteristic
872C4C4×#6322711yescharacteristic
873C4#1176266611yescharacteristic
874C4#1176266811yescharacteristic
875C4#1176268011yescharacteristic
876C4#1176268311yescharacteristic
877C4#1176268511yescharacteristic
878C4#1176268711yescharacteristic
879C2—348no—
880C2#1452700511yescharacteristic
881C2D17×#34011yescharacteristic
882C2#1452850211yescharacteristic
883C2#1452871311yescharacteristic
884C2#1452871711yescharacteristic
885C2#1452886911yescharacteristic
886C2#1452887311yescharacteristic
887C2#1452897011yescharacteristic
888C2#1452897311yescharacteristic
889C2#1452897511yescharacteristic
890C2#1452897811yescharacteristic
891C2#1452908811yescharacteristic
892C2#1452909011yescharacteristic
893C2#1452909811yescharacteristic
894C2#1452910011yescharacteristic
subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#340C2
socleC24×C17C2×D4
prime radicalC24×D17D4
cosocleC23×C4×C17C23
hypercenterC2×#340D17
hypocenterC17#10730
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#11762572C2semidirect
5. C2×#11762571C2semidirect
6. C2×#11762571C2semidirect
7. C2×C17×#340C2semidirect
19. C2×C4⋊C4×D17C4semidirect
23. C2×#10587491C4semidirect
25. #11762666C4semidirect
68. C22×C8×C17C2×C4semidirect
78. C2×C4⋊C4×C17C2×C4semidirect
93. C2×C4⋊Dic17C2×C4semidirect
105. C22×#3622C2×C4semidirect
226. C4⋊C4×C17C22⋊C4semidirect
235. C4⋊Dic17C22⋊C4semidirect
375. C2×#340D17semidirect
425. C2×D17#340semidirect
522. C22×C8C4×D17semidirect
551. C2×C4⋊C4C4×D17semidirect
559. C17#10730semidirect
690. C4⋊C4#63227semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D172
C22×#105874912
C2×#117626662
C2×#117625722
C2×#117625712
C2×C17×#3402
#1073017