Finite Group Databasebeta

← C2×#22569282 #31720611

Subgroups — C2×#22569282 #31720611

Order 17152.

2230 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863942C211yesmaximal, characteristic
2#22569282C2116yesmaximal, direct product factor
3C2×#16863472C211yesmaximal, characteristic, complemented
4C2×#16863471C211yesmaximal, characteristic, complemented
5C2×#16863470C211yesmaximal, characteristic, complemented
6C2×#16863467C211yesmaximal, characteristic, complemented
7C2×#16863465C211yesmaximal, characteristic, complemented
8C2×#16863464C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D67C211yesmaximal, characteristic, complemented
10C2×(C22⋊D67)⋊C8C211yesmaximal, characteristic, complemented
11C2×#16863450C211yesmaximal, characteristic, complemented
12C2×#16863446C211yesmaximal, characteristic, complemented
13C2×#16863363C211yesmaximal, characteristic, complemented
14C2×#16863361C211yesmaximal, characteristic, complemented
15C2×#16863361C211yesmaximal, characteristic, complemented
16C2×#408×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19C22×#11761611C2211yescharacteristic
20C22×#11761611C2211yescharacteristic
21C23×C67⋊C8C2211yescharacteristic
22C22×C8×D67C2211yescharacteristic
23C22×C8×D67C2211yescharacteristic
24#16863942C418yes—
25#16863942C2218yes—
26C2×#14524041C411yescharacteristic
27C2×#14524039C411yescharacteristic
28C2×#14524032C411yescharacteristic
29C2×#14524030C411yescharacteristic
30C2×#14524015C411yescharacteristic
31C2×#14524015C411yescharacteristic
32C2×#14524015C411yescharacteristic
33C2×#14524015C411yescharacteristic
34C2×C4×C22⋊D67C2211yescharacteristic
35C2×C4×C22⋊D67C2211yescharacteristic
36C2×C4×C22⋊D67C2211yescharacteristic
37C2×C4×C22⋊D67C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39#16863472C2218yescomplemented
40#16863471C2218yescomplemented
41#16863470C2218yescomplemented
42#16863467C2218yescomplemented
43#16863465C2218yescomplemented
44#16863464C2218yescomplemented
45C8×C22⋊D67C2218yescomplemented
46(C22⋊D67)⋊C8C2218yescomplemented
47#16863450C2218yescomplemented
48#16863446C2218yescomplemented
49C2×Dic67⋊C8C2211yescharacteristic
50C2×Dic67⋊C8C2211yescharacteristic
51C2×Dic67⋊C8C2211yescharacteristic
52C2×Dic67⋊C8C2211yescharacteristic
53#16863363C2218yescomplemented
54#16863361C2218yescomplemented
55#16863361C2218yescomplemented
56C2×C22⋊(C67⋊C8)C2211yescharacteristic
57C2×C22⋊(C67⋊C8)C2211yescharacteristic
58C2×C22⋊(C67⋊C8)C2211yescharacteristic
59C2×C22⋊(C67⋊C8)C2211yescharacteristic
60C2×(C2×D67)⋊C8C2211yescharacteristic
61C2×(C2×D67)⋊C8C2211yescharacteristic
62C2×(C2×D67)⋊C8C2211yescharacteristic
63C2×(C2×D67)⋊C8C2211yescharacteristic
64C2×#14523953C2211yescharacteristic
65C2×#14523953C2211yescharacteristic
66C2×C8×Dic67C2211yescharacteristic
67C2×C8×Dic67C2211yescharacteristic
68C22×#41×C67C2211yescharacteristic
69C22×M16×C67C2211yescharacteristic
70C23×C8×C67C2211yescharacteristic
71#408×C67C2218yescomplemented
72C2×C22⋊C8×C67C2211yescharacteristic
73C2×C22⋊C8×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C22⋊C8×C67C2211yescharacteristic
76C2×#11761628—42no—
77C2×#11761628—42no—
78C2×#11761628C2×C414yes—
79C2×#11761628C2314yes—
80C22×Dic134C2×C411yescharacteristic
81C22×D268C2×C411yescharacteristic
82C22×C22⋊D67C2×C411yescharacteristic
83C22×C22⋊D67C2×C411yescharacteristic
84C22×C22⋊D67C2×C411yescharacteristic
85C22×C22⋊D67C2×C411yescharacteristic
86C22×C22⋊D67C2×C411yescharacteristic
87C22×C22⋊D67C2×C411yescharacteristic
88C23×Dic67C2×C411yescharacteristic
89C23×Dic67C2×C411yescharacteristic
90C22×C4×D67C2311yescharacteristic
91C22×C4×D67C2311yescharacteristic
92C2×#11761612—42no—
93C2×#11761612C2314yes—
94C2×#11761611—42no—
95C2×#11761611—42no—
96C2×#11761611C2314yes—
97C2×#11761611C2314yes—
98C22×C67⋊C8—42no—
99C22×C67⋊C8C2311yescharacteristic
100C22×C67⋊C8C2311yescharacteristic
101C22×C67⋊C8C2311yescharacteristic
102C22×C67⋊C8C2311yescharacteristic
103C22×C67⋊C8C2314yes—
104C2×C8×D67—42no—
105C2×C8×D67—42no—
106C2×C8×D67C2314yes—
107C2×C8×D67C2314yes—
108#14524041C2×C418yes—
109#14524039C2×C418yes—
110#14524032C2×C418yes—
111#14524030C2×C418yes—
112#14524015C2×C418yes—
113#14524015C2×C418yes—
114#14524015C2×C418yes—
115#14524015C2×C418yes—
116C4×C22⋊D67C2×C414yes—
117C4×C22⋊D67C2×C414yes—
118C4×C22⋊D67C2×C414yes—
119C4×C22⋊D67C2×C414yes—
120C4×C22⋊D67C2314yes—
121C4×C22⋊D67C2314yes—
122C4×C22⋊D67C2314yes—
123C4×C22⋊D67C2314yes—
124C2×Dic67⋊C4C2×C411yescharacteristic
125C2×Dic67⋊C4C2×C411yescharacteristic
126C2×Dic67⋊C4C2×C411yescharacteristic
127C2×Dic67⋊C4C2×C411yescharacteristic
128C2×C22⋊Dic67C2×C411yescharacteristic
129C2×C22⋊Dic67C2×C411yescharacteristic
130C2×C22⋊Dic67C2×C411yescharacteristic
131C2×C22⋊Dic67C2×C411yescharacteristic
132C2×(C2×D67)⋊C4C2×C411yescharacteristic
133C2×(C2×D67)⋊C4C2×C411yescharacteristic
134C2×(C2×D67)⋊C4C2×C411yescharacteristic
135C2×(C2×D67)⋊C4C2×C411yescharacteristic
136C2×C4×Dic67C2×C411yescharacteristic
137C2×C4×Dic67C2×C411yescharacteristic
138C2×C4×Dic67C2×C414yes—
139C2×C4×Dic67C2311yescharacteristic
140C2×C4×Dic67C2311yescharacteristic
141C2×C4×Dic67C2314yes—
142Dic67⋊C8C2314yes—
143Dic67⋊C8C2314yes—
144Dic67⋊C8C2314yes—
145Dic67⋊C8C2314yes—
146C22⋊(C67⋊C8)C2314yes—
147C22⋊(C67⋊C8)C2314yes—
148C22⋊(C67⋊C8)C2314yes—
149C22⋊(C67⋊C8)C2314yes—
150(C2×D67)⋊C8C2314yes—
151(C2×D67)⋊C8C2314yes—
152(C2×D67)⋊C8C2314yes—
153(C2×D67)⋊C8C2314yes—
154#14523953C2314yes—
155#14523953C2314yes—
156C8×Dic67C2314yes—
157C8×Dic67C2314yes—
158C2×#41×C67—42no—
159C2×#41×C67—42no—
160C2×#41×C67C2×C414yes—
161C2×#41×C67C2314yes—
162C22×Q8×C67C2×C411yescharacteristic
163C22×D4×C67C2×C411yescharacteristic
164C22×D4×C67C2×C411yescharacteristic
165C22×D4×C67C2×C411yescharacteristic
166C23×C4×C67C2311yescharacteristic
167C23×C4×C67C2311yescharacteristic
168C23×C4×C67C2311yescharacteristic
169C2×M16×C67—42no—
170C2×M16×C67C2314yes—
171C22×C8×C67—42no—
172C22×C8×C67C2311yescharacteristic
173C22×C8×C67C2311yescharacteristic
174C22×C8×C67C2311yescharacteristic
175C22×C8×C67C2311yescharacteristic
176C22×C8×C67C2314yes—
177C22⋊C8×C67C2314yes—
178C22⋊C8×C67C2314yes—
179C22⋊C8×C67C2314yes—
180C22⋊C8×C67C2314yes—
181C23×D67C22×C411yescharacteristic
182C23×D67C22×C411yescharacteristic
183#11761628—48no—
184#11761628—44no—
185#11761628—44no—
186C2×Dic134—42no—
187C2×Dic134C22×C414yes—
188C2×D268—42no—
189C2×D268C22×C414yes—
190C2×C22⋊D67—24no—
191C2×C22⋊D67—24no—
192C2×C22⋊D67—42no—
193C2×C22⋊D67—42no—
194C2×C22⋊D67—42no—
195C2×C22⋊D67—42no—
196C2×C22⋊D67C22×C414yes—
197C2×C22⋊D67C22×C414yes—
198C2×C22⋊D67C22×C414yes—
199C2×C22⋊D67C22×C414yes—
200C2×C22⋊D67C22×C414yes—
201C2×C22⋊D67C22×C414yes—
202C22×Dic67—24no—
203C22×Dic67—42no—
204C22×Dic67C22×C411yescharacteristic
205C22×Dic67C22×C411yescharacteristic
206C22×Dic67C22×C411yescharacteristic
207C22×Dic67C22×C414yes—
208C22×Dic67C22×C411yescharacteristic
209C22×Dic67C22×C411yescharacteristic
210C22×Dic67C22×C414yes—
211C22×Dic67C22×C411yescharacteristic
212C2×C4×D67—22no—
213C2×C4×D67—22no—
214C2×C4×D67—22no—
215C2×C4×D67—22no—
216C2×C4×D67C22×C412yes—
217C2×C4×D67C22×C412yes—
218C2×C4×D67C2412yes—
219C2×C4×D67C2412yes—
220#11761612—44no—
221#11761611—44no—
222#11761611—44no—
223C2×C67⋊C8—22no—
224C2×C67⋊C8—22no—
225C2×C67⋊C8—22no—
226C2×C67⋊C8—22no—
227C2×C67⋊C8—44no—
228C2×C67⋊C8C2412yes—
229C2×C67⋊C8C2412yes—
230C2×C67⋊C8C2412yes—
231C2×C67⋊C8C2412yes—
232C8×D67—44no—
233C8×D67—44no—
234Dic67⋊C4C22×C414yes—
235Dic67⋊C4C22×C414yes—
236Dic67⋊C4C22×C414yes—
237Dic67⋊C4C22×C414yes—
238C22⋊Dic67C22×C414yes—
239C22⋊Dic67C22×C414yes—
240C22⋊Dic67C22×C414yes—
241C22⋊Dic67C22×C414yes—
242(C2×D67)⋊C4C22×C414yes—
243(C2×D67)⋊C4C22×C414yes—
244(C2×D67)⋊C4C22×C414yes—
245(C2×D67)⋊C4C22×C414yes—
246C4×Dic67C22×C412yes—
247C4×Dic67C22×C412yes—
248C4×Dic67C22×C414yes—
249C4×Dic67C22×C414yes—
250C4×Dic67C2412yes—
251C4×Dic67C2412yes—
252C24×C67C22×C411yescharacteristic
253C24×C67C22×C411yescharacteristic
254C24×C67C22×C411yescharacteristic
255#41×C67—48no—
256#41×C67—44no—
257#41×C67—44no—
258C2×Q8×C67—42no—
259C2×Q8×C67C22×C414yes—
260C2×D4×C67—42no—
261C2×D4×C67—42no—
262C2×D4×C67—42no—
263C2×D4×C67C22×C414yes—
264C2×D4×C67C22×C414yes—
265C2×D4×C67C22×C414yes—
266C22×C4×C67—22no—
267C22×C4×C67—22no—
268C22×C4×C67—22no—
269C22×C4×C67—22no—
270C22×C4×C67—22no—
271C22×C4×C67—22no—
272C22×C4×C67C22×C411yescharacteristic
273C22×C4×C67C22×C411yescharacteristic
274C22×C4×C67C22×C411yescharacteristic
275C22×C4×C67C22×C412yes—
276C22×C4×C67C22×C412yes—
277C22×C4×C67C22×C412yes—
278C22×C4×C67C2412yes—
279C22×C4×C67C2412yes—
280C22×C4×C67C2412yes—
281C22×C4×C67C2411yescharacteristic
282M16×C67—44no—
283C2×C8×C67—22no—
284C2×C8×C67—22no—
285C2×C8×C67—22no—
286C2×C8×C67—22no—
287C2×C8×C67—44no—
288C2×C8×C67C2412yes—
289C2×C8×C67C2412yes—
290C2×C8×C67C2412yes—
291C2×C8×C67C2412yes—
292C23×C67—22no—
293C23×C67—22no—
294C23×C67—22no—
295C23×C67—22no—
296C23×C67—22no—
297C23×C67—22no—
298C23×C67—22no—
299C23×C67—22no—
300C23×C67—22no—
301C23×C67C23×C412yes—
302C23×C67C23×C412yes—
303C23×C67C23×C412yes—
304C23×C67C23×C411yescharacteristic
305C22×D67—22no—
306C22×D67—22no—
307C22×D67—22no—
308C22×D67—22no—
309C22×D67—22no—
310C22×D67—22no—
311C22×D67C23×C412yes—
312C22×D67C23×C412yes—
313Q8×C67—44no—
314D4×C67—44no—
315D4×C67—44no—
316D4×C67—44no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—24no—
321C2×C4×C67—24no—
322C2×C4×C67—24no—
323C2×C4×C67—22no—
324C2×C4×C67—22no—
325C2×C4×C67—22no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—22no—
329C2×C4×C67C23×C412yes—
330C2×C4×C67C23×C412yes—
331C2×C4×C67C23×C412yes—
332C2×C4×C67C23×C411yescharacteristic
333C2×C4×C67H(5,𝔽2)12yes—
334C2×C4×C67H(5,𝔽2)12yes—
335C2×C4×C67C2511yescharacteristic
336C22⋊D67—28no—
337C22⋊D67—28no—
338C22⋊D67—44no—
339C22⋊D67—44no—
340C22⋊D67—44no—
341C22⋊D67—44no—
342C2×Dic67—22no—
343C2×Dic67—22no—
344C2×Dic67—22no—
345C2×Dic67—22no—
346C2×Dic67—22no—
347C2×Dic67—28no—
348C2×Dic67—44no—
349C2×Dic67#13114yes—
350C2×Dic67C23×C412yes—
351C2×Dic67C23×C412yes—
352C2×Dic67C23×C412yes—
353C2×Dic67C23×C412yes—
354C2×Dic67C23×C412yes—
355C2×Dic67C23×C412yes—
356D268—44no—
357C4×D67—24no—
358C4×D67—24no—
359C4×D67—22no—
360C4×D67—22no—
361C4×D67—22no—
362C4×D67—22no—
363Dic134—44no—
364C8×C67—22no—
365C8×C67—22no—
366C8×C67—22no—
367C8×C67—22no—
368C67⋊C8—22no—
369C67⋊C8—22no—
370C67⋊C8—22no—
371C67⋊C8—22no—
372C22×C67—22no—
373C22×C67—22no—
374C22×C67—22no—
375C22×C67—22no—
376C22×C67—22no—
377C22×C67—22no—
378C22×C67—22no—
379C22×C67—22no—
380C22×C67—22no—
381C22×C67—44no—
382C22×C67—44no—
383C22×C67—44no—
384C22×C67#51812yes—
385C22×C67C2×#13112yes—
386C22×C67#56812yes—
387C22×C67C24×C411yescharacteristic
388C2×D67—22no—
389C2×D67—22no—
390C2×D67—22no—
391C2×D67—22no—
392C2×D67—22no—
393C2×D67—22no—
394C2×D67—44no—
395C2×D67—44no—
396C4×C67—22no—
397C4×C67—22no—
398C4×C67—22no—
399C4×C67#51812yes—
400C4×C67C2×H(5,𝔽2)11yescharacteristic
401C4×C67C2×H(5,𝔽2)11yescharacteristic
402Dic67—22no—
403Dic67—22no—
404Dic67—22no—
405Dic67—22no—
406Dic67—22no—
407Dic67C2×#13114yes—
408C2×#2981—671nomaximal, Sylow
409C2×C67—42no—
410C2×C67—42no—
411C2×C67—42no—
412C2×C67#298114yescomplemented
413C2×C67C2×#51811yescharacteristic
414C2×C67C22×#13111yescharacteristic
415C2×C67C2×#56811yescharacteristic
416D67—42no—
417D67—42no—
418C2×#532—671no—
419#2981—6716no—
420C2×#436—671no—
421C2×#436—671no—
422C2×#435—671no—
423C2×#435—671no—
424C2×#435—671no—
425C2×#435—671no—
426C2×C8×D4—671no—
427C2×C8×D4—671no—
428C2×#432—671no—
429C2×#431—671no—
430C2×#408—671no—
431C2×#408—671no—
432C2×#408—671no—
433C2×#408D6711yescharacteristic, complemented
434C67C2×#298111yescharacteristic, complemented, Sylow
435C22×#41—671no—
436C22×#41C2×D6711yescharacteristic
437C22×M16—671no—
438C22×M16—671no—
439C22×M16—671no—
440C22×M16C2×D6711yescharacteristic
441C23×C8—671no—
442C23×C8—671no—
443C23×C8—671no—
444C23×C8C2×D6711yescharacteristic
445#532—678no—
446#532—678no—
447C2×C4⋊Q8—671no—
448C2×#127—671no—
449C2×#124—671no—
450C2×#124—671no—
451C2×#121—671no—
452C2×#121—671no—
453C2×#121—671no—
454C2×#121—671no—
455C2×C4×D4—671no—
456C2×C4×D4—671no—
457C2×C4×D4—671no—
458C2×C4×D4—671no—
459C22×C42—671no—
460#436—678no—
461#436—678no—
462#435—678no—
463#435—678no—
464#435—678no—
465#435—678no—
466C8×D4—678no—
467C8×D4—678no—
468#432—678no—
469#431—678no—
470C2×C4⋊C8—671no—
471C2×C4⋊C8—671no—
472C2×C4⋊C8—671no—
473C2×C4⋊C8—671no—
474#408—678no—
475#408—678no—
476#408—678no—
477#408C2×D6718yescomplemented
478C2×C22⋊C8—671no—
479C2×C22⋊C8—671no—
480C2×C22⋊C8—671no—
481C2×C22⋊C8—671no—
482C2×C22⋊C8—671no—
483C2×C22⋊C8—671no—
484C2×C22⋊C8—671no—
485C2×C22⋊C8—671no—
486C2×C22⋊C8C2×D6711yescharacteristic
487C2×C22⋊C8C2×D6711yescharacteristic
488C2×C22⋊C8C2×D6711yescharacteristic
489C2×C22⋊C8C2×D6711yescharacteristic
490C2×#97—671no—
491C2×#97—671no—
492C2×C4×C8—671no—
493C2×C4×C8—671no—
494C2×#41—42no—
495C2×#41—42no—
496C2×#41—2682no—
497C2×#41—2682no—
498C2×#41—674no—
499C2×#41—674no—
500C2×#41C4×D6714yes—
501C2×#41C22×D6714yes—
502C22×Q8—671no—
503C22×Q8C4×D6711yescharacteristic
504C22×D4—671no—
505C22×D4—671no—
506C22×D4—671no—
507C22×D4—671no—
508C22×D4—671no—
509C22×D4—671no—
510C22×D4—671no—
511C22×D4C4×D6711yescharacteristic
512C22×D4C4×D6711yescharacteristic
513C22×D4C4×D6711yescharacteristic
514C23×C4—671no—
515C23×C4—671no—
516C23×C4—671no—
517C23×C4—671no—
518C23×C4C22×D6711yescharacteristic
519C23×C4C22×D6711yescharacteristic
520C23×C4C22×D6711yescharacteristic
521C2×M16—42no—
522C2×M16—2682no—
523C2×M16—2682no—
524C2×M16—2682no—
525C2×M16—674no—
526C2×M16—674no—
527C2×M16—674no—
528C2×M16C22×D6714yes—
529C22×C8—42no—
530C22×C8—2682no—
531C22×C8—2682no—
532C22×C8—2682no—
533C22×C8—674no—
534C22×C8—674no—
535C22×C8—674no—
536C22×C8—671no—
537C22×C8—671no—
538C22×C8—671no—
539C22×C8—671no—
540C22×C8C22×D6711yescharacteristic
541C22×C8C22×D6711yescharacteristic
542C22×C8C22×D6711yescharacteristic
543C22×C8C22×D6711yescharacteristic
544C22×C8C22×D6714yes—
545C4⋊Q8—678no—
546#127—678no—
547#124—678no—
548#124—678no—
549#121—678no—
550#121—678no—
551#121—678no—
552#121—678no—
553C4×D4—674no—
554C4×D4—674no—
555C4×D4—674no—
556C4×D4—674no—
557C4×D4—674no—
558C4×D4—674no—
559C4×D4—674no—
560C4×D4—674no—
561C2×C4⋊C4—671no—
562C2×C4⋊C4—671no—
563C2×C4⋊C4—671no—
564C2×C4⋊C4—671no—
565C2×C22⋊C4—671no—
566C2×C22⋊C4—671no—
567C2×C22⋊C4—671no—
568C2×C22⋊C4—671no—
569C2×C22⋊C4—671no—
570C2×C22⋊C4—671no—
571C2×C22⋊C4—671no—
572C2×C22⋊C4—671no—
573C2×C42—671no—
574C2×C42—671no—
575C2×C42—674no—
576C2×C42—674no—
577C2×C42—671no—
578C2×C42—671no—
579C4⋊C8—674no—
580C4⋊C8—674no—
581C4⋊C8—674no—
582C4⋊C8—674no—
583C22⋊C8—674no—
584C22⋊C8—674no—
585C22⋊C8—674no—
586C22⋊C8—674no—
587C22⋊C8—674no—
588C22⋊C8—674no—
589C22⋊C8—674no—
590C22⋊C8—674no—
591C22⋊C8C22×D6714yes—
592C22⋊C8C22×D6714yes—
593C22⋊C8C22×D6714yes—
594C22⋊C8C22×D6714yes—
595#97—674no—
596#97—674no—
597C4×C8—674no—
598C4×C8—674no—
599C24—671no—
600C24—671no—
601C24C2×C4×D6711yescharacteristic
602C24C2×C4×D6711yescharacteristic
603C24C2×C4×D6711yescharacteristic
604#41—48no—
605#41—44no—
606#41—44no—
607#41—2688no—
608#41—2684no—
609#41—2684no—
610C2×Q8—42no—
611C2×Q8—2682no—
612C2×Q8—674no—
613C2×Q8C2×C4×D6714yes—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—2682no—
618C2×D4—2682no—
619C2×D4—2682no—
620C2×D4—2682no—
621C2×D4—2682no—
622C2×D4—674no—
623C2×D4—674no—
624C2×D4—674no—
625C2×D4—674no—
626C2×D4—674no—
627C2×D4—674no—
628C2×D4—674no—
629C2×D4—1344no—
630C2×D4—1344no—
631C2×D4C2×C4×D6714yes—
632C2×D4C2×C4×D6714yes—
633C2×D4C2×C4×D6714yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—2682no—
641C22×C4—674no—
642C22×C4—671no—
643C22×C4—671no—
644C22×C4—671no—
645C22×C4—671no—
646C22×C4—674no—
647C22×C4—671no—
648C22×C4—671no—
649C22×C4—672no—
650C22×C4—672no—
651C22×C4—672no—
652C22×C4—672no—
653C22×C4—1344no—
654C22×C4—1342no—
655C22×C4—1342no—
656C22×C4—1342no—
657C22×C4—1342no—
658C22×C4C2×C4×D6711yescharacteristic
659C22×C4C2×C4×D6712yes—
660C22×C4C2×C4×D6711yescharacteristic
661C22×C4C2×C4×D6711yescharacteristic
662C22×C4C2×C4×D6712yes—
663C22×C4C2×C4×D6712yes—
664C22×C4C23×D6712yes—
665C22×C4C23×D6712yes—
666C22×C4C23×D6712yes—
667C22×C4C23×D6711yescharacteristic
668M16—44no—
669M16—2684no—
670M16—2684no—
671M16—2684no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—2684no—
678C2×C8—2684no—
679C2×C8—2684no—
680C2×C8—672no—
681C2×C8—672no—
682C2×C8—672no—
683C2×C8—672no—
684C2×C8—1342no—
685C2×C8—1342no—
686C2×C8—1342no—
687C2×C8—1342no—
688C2×C8C23×D6712yes—
689C2×C8C23×D6712yes—
690C2×C8C23×D6712yes—
691C2×C8C23×D6712yes—
692C4⋊C4—674no—
693C4⋊C4—674no—
694C4⋊C4—674no—
695C4⋊C4—674no—
696C22⋊C4—674no—
697C22⋊C4—674no—
698C22⋊C4—674no—
699C22⋊C4—674no—
700C22⋊C4—674no—
701C22⋊C4—674no—
702C22⋊C4—674no—
703C22⋊C4—674no—
704C42—672no—
705C42—672no—
706C42—674no—
707C42—674no—
708C42—672no—
709C42—672no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—672no—
720C23—672no—
721C23—1342no—
722C23—1342no—
723C23—1342no—
724C23—1342no—
725C23—1342no—
726C23—1342no—
727C23C22×C4×D6712yes—
728C23C22×C4×D6712yes—
729C23C22×C4×D6712yes—
730C23C22×C4×D6711yescharacteristic
731Q8—44no—
732Q8—2684no—
733D4—44no—
734D4—44no—
735D4—44no—
736D4—2684no—
737D4—2684no—
738D4—2684no—
739D4—2684no—
740D4—2684no—
741D4—1348no—
742D4—1348no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—2684no—
756C2×C4—674no—
757C2×C4—672no—
758C2×C4—672no—
759C2×C4—672no—
760C2×C4—672no—
761C2×C4—672no—
762C2×C4—672no—
763C2×C4—1348no—
764C2×C4—1342no—
765C2×C4—1342no—
766C2×C4—1342no—
767C2×C4—1342no—
768C2×C4—1342no—
769C2×C4—1344no—
770C2×C4—1344no—
771C2×C4—1342no—
772C2×C4—1342no—
773C2×C4—1342no—
774C2×C4—1342no—
775C2×C4C22×C4×D6712yes—
776C2×C4C22×C4×D6712yes—
777C2×C4C22×C4×D6712yes—
778C2×C4C22×C4×D6711yescharacteristic
779C2×C4#1452408812yes—
780C2×C4#1452408812yes—
781C2×C4C24×D6711yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—1342no—
787C8—1342no—
788C8—1342no—
789C8—1342no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—2684no—
803C22—2684no—
804C22—1342no—
805C22—1342no—
806C22—1342no—
807C22—1342no—
808C22—1342no—
809C22—1342no—
810C22#1686386912yes—
811C22#131×D6712yes—
812C22#1686416112yes—
813C22C23×C4×D6711yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—674no—
818C4—1342no—
819C4—1342no—
820C4—1342no—
821C4—1342no—
822C4—1342no—
823C4#1686386912yes—
824C4C2×#1452408811yescharacteristic
825C4C2×#1452408811yescharacteristic
826C2—42no—
827C2—42no—
828C2—42no—
829C2—2682no—
830C2—2682no—
831C2#2256928214yesdirect product factor
832C2C2×#1686386911yescharacteristic
833C2C2×#131×D6711yescharacteristic
834C2C2×#1686416111yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#408×C67C2
socleC23×C67C23×C4
prime radicalC2×#16863942C2
cosocleC2×C4×C67C25
hypercenterC2×#408D67
hypocenterC67C2×#2981
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #22569282C2direct (N × H)
3. C2×#16863472C2semidirect
4. C2×#16863471C2semidirect
5. C2×#16863470C2semidirect
6. C2×#16863467C2semidirect
7. C2×#16863465C2semidirect
8. C2×#16863464C2semidirect
9. C2×C8×C22⋊D67C2semidirect
10. C2×(C22⋊D67)⋊C8C2semidirect
11. C2×#16863450C2semidirect
12. C2×#16863446C2semidirect
13. C2×#16863363C2semidirect
14. C2×#16863361C2semidirect
15. C2×#16863361C2semidirect
16. C2×#408×C67C2semidirect
39. #16863472C22semidirect
40. #16863471C22semidirect
41. #16863470C22semidirect
42. #16863467C22semidirect
43. #16863465C22semidirect
44. #16863464C22semidirect
45. C8×C22⋊D67C22semidirect
46. (C22⋊D67)⋊C8C22semidirect
47. #16863450C22semidirect
48. #16863446C22semidirect
53. #16863363C22semidirect
54. #16863361C22semidirect
55. #16863361C22semidirect
71. #408×C67C22semidirect
412. C2×C67#2981semidirect
433. C2×#408D67semidirect
434. C67C2×#2981semidirect
477. #408C2×D67semidirect
831. C2#22569282direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639422
#225692822
C2×#168634722
C2×#168634712
C2×#168634702
C2×#168634672
C2×#168634652
C2×#168634642
C2×C8×C22⋊D672
C2×(C22⋊D67)⋊C82
C2×#168634502
C2×#168634462
C2×#168633632
C2×#168633612
C2×#408×C672
C2×#298167