Finite Group Databasebeta

← C2×#22572314 #31732415

Subgroups — C2×#22572314 #31732415

Order 17152.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864055C211yesmaximal, characteristic
2#22572314C2116yesmaximal, direct product factor
3C2×#16863758C211yesmaximal, characteristic, complemented
4C2×#16863714C211yesmaximal, characteristic, complemented
5C2×#16863726C211yesmaximal, characteristic, complemented
6C2×#16863678C211yesmaximal, characteristic, complemented
7C2×#16863652C211yesmaximal, characteristic, complemented
8C2×#16863627C211yesmaximal, characteristic, complemented
9C2×#16863618C211yesmaximal, characteristic, complemented
10C2×#16863556C211yesmaximal, characteristic, complemented
11C2×#16863551C211yesmaximal, characteristic, complemented
12C2×#16863501C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic, complemented
14C2×#16863395C211yesmaximal, characteristic, complemented
15C22×#14523966C211yesmaximal, characteristic, complemented
16C2×#554×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2211yescharacteristic
18C23×Dic134C2211yescharacteristic
19C22×#11761618C2211yescharacteristic
20C22×#11761618C2211yescharacteristic
21C22×#11761615C2211yescharacteristic
22C22×#11761612C2211yescharacteristic
23C23×C67⋊C8C2211yescharacteristic
24#16864055—24no—
25#16864055C2218yes—
26C2×#14524031C2211yescharacteristic
27C2×#14524029—21no—
28C2×#14524022C2211yescharacteristic
29C2×#14524021—21no—
30C2×#14524017C2211yescharacteristic
31C2×#14524015—21no—
32C2×C4×Dic134C2211yescharacteristic
33C2×(C22⋊D67)⋊C4—21no—
34#16863758C2218yescomplemented
35#16863726C2218yescomplemented
36#16863714C2218yescomplemented
37#16863678C2218yescomplemented
38#16863652C2218yescomplemented
39#16863627C2218yescomplemented
40#16863618C2218yescomplemented
41#16863556C2218yescomplemented
42#16863551C2218yescomplemented
43#16863501C2218yescomplemented
44#16863468C2218yescomplemented
45C2×#14523974C2211yescharacteristic
46C2×#14523974C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49#16863395C2218yescomplemented
50C2×#14523967C2211yescharacteristic
51C2×#14523966C2211yescharacteristic
52C2×#14523966C2211yescharacteristic
53C2×#14523966C2211yescharacteristic
54C2×#14523966C2211yescharacteristic
55C2×#14523966C2211yescharacteristic
56C2×#14523966C2211yescharacteristic
57C2×#14523966C2218yescomplemented
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×#14523963C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64#554×C67—24no—
65#554×C67C2218yescomplemented
66C2×C4⋊Q8×C67C2211yescharacteristic
67C2×#125×C67—21no—
68C2×C22⋊Q8×C67—21no—
69C2×C22⋊Q8×C67—21no—
70C2×C22⋊Q8×C67C2211yescharacteristic
71C2×C22⋊Q8×C67C2211yescharacteristic
72C2×C4×Q8×C67C2211yescharacteristic
73C2×C4×D4×C67—21no—
74C2×C4×D4×C67C2211yescharacteristic
75C22×C4⋊C4×C67C2211yescharacteristic
76C22×C4⋊C4×C67C2211yescharacteristic
77C2×#11761628—24no—
78C2×#11761628—22no—
79C2×#11761628—42no—
80C2×#11761628C2314yes—
81C22×Dic134—24no—
82C22×Dic134—22no—
83C22×Dic134—21no—
84C22×Dic134—42no—
85C22×Dic134C2311yescharacteristic
86C22×Dic134C2314yes—
87C22×Dic134C2311yescharacteristic
88C22×D268C2311yescharacteristic
89C22×C22⋊D67—21no—
90C22×C22⋊D67—21no—
91C23×Dic67—21no—
92C22×C4×D67—21no—
93C2×#11761618—24no—
94C2×#11761618—42no—
95C2×#11761618C2314yes—
96C2×#11761618C2314yes—
97C2×#11761615—42no—
98C2×#11761615C2314yes—
99C2×#11761612—42no—
100C2×#11761612C2314yes—
101C22×C67⋊C8—42no—
102C22×C67⋊C8C2311yescharacteristic
103C22×C67⋊C8C2311yescharacteristic
104C22×C67⋊C8C2311yescharacteristic
105C22×C67⋊C8C2311yescharacteristic
106C22×C67⋊C8C2314yes—
107#14524031—22no—
108#14524031C2314yes—
109#14524029—28no—
110#14524022—22no—
111#14524022C2314yes—
112#14524021—28no—
113#14524017—22no—
114#14524017C2314yes—
115#14524015—28no—
116C4×Dic134—22no—
117C4×Dic134C2314yes—
118(C22⋊D67)⋊C4—28no—
119C2×C4⋊Dic67C2311yescharacteristic
120C2×Dic67⋊C4—21no—
121C2×Dic67⋊C4—21no—
122C2×C22⋊Dic67—21no—
123C2×(C2×D67)⋊C4—21no—
124C2×(C2×D67)⋊C4—21no—
125C2×(C2×D67)⋊C4—21no—
126C2×C4×Dic67—21no—
127#14523974C2314yes—
128#14523974C2314yes—
129#14523974C2314yes—
130C4⋊(C67⋊C8)C2314yes—
131#14523967C2314yes—
132#14523966C2314yes—
133#14523966C2314yes—
134#14523966C2314yes—
135#14523966C2314yes—
136#14523966C2314yes—
137#14523966C2314yes—
138#14523963C2314yes—
139#14523963C2314yes—
140#14523963C2314yes—
141C22⋊(C67⋊C8)C2314yes—
142C22⋊(C67⋊C8)C2314yes—
143#14523954C2314yes—
144C22×Q8×C67—21no—
145C22×Q8×C67C2311yescharacteristic
146C22×D4×C67D411yescharacteristic
147C23×C4×C67—21no—
148C23×C4×C67—21no—
149C23×C4×C67C2311yescharacteristic
150C23×C4×C67C2311yescharacteristic
151C4⋊Q8×C67—22no—
152C4⋊Q8×C67C2314yes—
153#125×C67—28no—
154C22⋊Q8×C67—22no—
155C22⋊Q8×C67—22no—
156C22⋊Q8×C67—28no—
157C22⋊Q8×C67—28no—
158C22⋊Q8×C67C2314yes—
159C22⋊Q8×C67C2314yes—
160C4×Q8×C67—22no—
161C4×Q8×C67C2314yes—
162C4×D4×C67—28no—
163C4×D4×C67D414yes—
164C4×D4×C67C2314yes—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—22no—
168C2×C4⋊C4×C67—22no—
169C2×C4⋊C4×C67—21no—
170C2×C4⋊C4×C67—21no—
171C2×C4⋊C4×C67—21no—
172C2×C4⋊C4×C67—21no—
173C2×C4⋊C4×C67D411yescharacteristic
174C2×C4⋊C4×C67C2311yescharacteristic
175C2×C4⋊C4×C67C2311yescharacteristic
176C2×C4⋊C4×C67C2311yescharacteristic
177C2×C4⋊C4×C67C2314yes—
178C2×C4⋊C4×C67C2314yes—
179C2×C22⋊C4×C67—21no—
180C2×C22⋊C4×C67—21no—
181C2×C22⋊C4×C67D411yescharacteristic
182C2×C22⋊C4×C67D411yescharacteristic
183C2×C42×C67—21no—
184C2×C42×C67C2311yescharacteristic
185C23×D67—21no—
186#11761628—28no—
187#11761628—44no—
188#11761628—48no—
189C2×Dic134—21no—
190C2×Dic134—22no—
191C2×Dic134—22no—
192C2×Dic134—22no—
193C2×Dic134—28no—
194C2×Dic134—24no—
195C2×Dic134—21no—
196C2×Dic134—44no—
197C2×Dic134—48no—
198C2×Dic134—44no—
199C2×Dic134#4114yes—
200C2×Dic134C2412yes—
201C2×Dic134C2412yes—
202C2×D268—22no—
203C2×D268—22no—
204C2×D268—21no—
205C2×D268C2412yes—
206C2×C22⋊D67—24no—
207C2×C22⋊D67—24no—
208C2×C22⋊D67—44no—
209C2×C22⋊D67—44no—
210C22×Dic67—21no—
211C22×Dic67—21no—
212C22×Dic67—21no—
213C22×Dic67—24no—
214C22×Dic67—44no—
215C2×C4×D67—24no—
216C2×C4×D67—44no—
217#11761618—28no—
218#11761618—44no—
219#11761615—44no—
220#11761612—44no—
221C2×C67⋊C8—22no—
222C2×C67⋊C8—22no—
223C2×C67⋊C8—22no—
224C2×C67⋊C8—22no—
225C2×C67⋊C8—44no—
226C2×C67⋊C8C2412yes—
227C2×C67⋊C8C2412yes—
228C2×C67⋊C8C2412yes—
229C2×C67⋊C8C2412yes—
230C4⋊Dic67—21no—
231C4⋊Dic67C2412yes—
232Dic67⋊C4—24no—
233Dic67⋊C4—24no—
234C22⋊Dic67—24no—
235(C2×D67)⋊C4—24no—
236(C2×D67)⋊C4—24no—
237(C2×D67)⋊C4—24no—
238C4×Dic67—24no—
239C24×C67C2×D411yescharacteristic
240C24×C67C2×D411yescharacteristic
241C2×Q8×C67—21no—
242C2×Q8×C67—24no—
243C2×Q8×C67—22no—
244C2×Q8×C67—22no—
245C2×Q8×C67—82no—
246C2×Q8×C67C2412yes—
247C2×D4×C67—24no—
248C2×D4×C67C2×D414yes—
249C22×C4×C67—22no—
250C22×C4×C67—22no—
251C22×C4×C67—22no—
252C22×C4×C67—22no—
253C22×C4×C67—21no—
254C22×C4×C67—21no—
255C22×C4×C67—21no—
256C22×C4×C67—21no—
257C22×C4×C67—24no—
258C22×C4×C67—24no—
259C22×C4×C67—82no—
260C22×C4×C67—82no—
261C22×C4×C67C2×D411yescharacteristic
262C22×C4×C67C2×D411yescharacteristic
263C22×C4×C67C2×D411yescharacteristic
264C22×C4×C67C2×D411yescharacteristic
265C22×C4×C67C2×D412yes—
266C22×C4×C67C2×D412yes—
267C22×C4×C67C2412yes—
268C22×C4×C67C2412yes—
269C22×C4×C67C2411yescharacteristic
270C4⋊C4×C67—21no—
271C4⋊C4×C67—24no—
272C4⋊C4×C67—24no—
273C4⋊C4×C67—21no—
274C4⋊C4×C67—21no—
275C4⋊C4×C67—24no—
276C4⋊C4×C67—24no—
277C4⋊C4×C67—24no—
278C4⋊C4×C67—24no—
279C4⋊C4×C67C2×D414yes—
280C4⋊C4×C67C2412yes—
281C4⋊C4×C67C2412yes—
282C4⋊C4×C67C2412yes—
283C22⋊C4×C67—24no—
284C22⋊C4×C67—24no—
285C22⋊C4×C67C2×D414yes—
286C22⋊C4×C67C2×D414yes—
287C42×C67—24no—
288C42×C67C2×D412yes—
289C42×C67C2412yes—
290C23×C67—22no—
291C23×C67—22no—
292C23×C67—22no—
293C23×C67—22no—
294C23×C67—22no—
295C23×C67#13714yes—
296C23×C67C22×D412yes—
297C23×C67C22×D412yes—
298C23×C67C22×D411yescharacteristic
299C22×D67—22no—
300C22×D67—42no—
301C22×D67—42no—
302C22×D67—42no—
303Q8×C67—22no—
304Q8×C67—22no—
305Q8×C67—42no—
306Q8×C67—84no—
307D4×C67—28no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—24no—
313C2×C4×C67—24no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—42no—
323C2×C4×C67—42no—
324C2×C4×C67—42no—
325C2×C4×C67—42no—
326C2×C4×C67—84no—
327C2×C4×C67—84no—
328C2×C4×C67C22×D412yes—
329C2×C4×C67C22×D412yes—
330C2×C4×C67C22×D412yes—
331C2×C4×C67C22×D412yes—
332C2×C4×C67C22×D411yescharacteristic
333C2×C4×C67C2×#4112yes—
334C2×C4×C67H(5,𝔽2)12yes—
335C2×C4×C67C2511yescharacteristic
336C22⋊D67—48no—
337C22⋊D67—48no—
338C2×Dic67—24no—
339C2×Dic67—22no—
340C2×Dic67—22no—
341C2×Dic67—22no—
342C2×Dic67—48no—
343C2×Dic67—42no—
344C2×Dic67—42no—
345D268—22no—
346D268—22no—
347D268—42no—
348C4×D67—48no—
349Dic134—24no—
350Dic134—22no—
351Dic134—22no—
352Dic134—22no—
353Dic134—48no—
354Dic134—42no—
355Dic134C2×#4114yes—
356C67⋊C8—22no—
357C67⋊C8—22no—
358C67⋊C8—22no—
359C67⋊C8—22no—
360C22×C67—22no—
361C22×C67—28no—
362C22×C67—22no—
363C22×C67—22no—
364C22×C67—22no—
365C22×C67—22no—
366C22×C67—44no—
367C22×C67#54612yes—
368C22×C67C2×#13714yes—
369C22×C67C2×#13712yes—
370C22×C67#57712yes—
371C22×C67C23×D411yescharacteristic
372C2×D67—42no—
373C2×D67—42no—
374C2×D67—42no—
375C2×D67—84no—
376C4×C67—22no—
377C4×C67—22no—
378C4×C67—22no—
379C4×C67—22no—
380C4×C67—42no—
381C4×C67—42no—
382C4×C67—42no—
383C4×C67—42no—
384C4×C67#54612yes—
385C4×C67C22×#4111yescharacteristic
386C4×C67C2×H(5,𝔽2)11yescharacteristic
387Dic67—24no—
388Dic67—42no—
389Dic67—42no—
390C2×#3316—671nomaximal, Sylow
391C2×C67—24no—
392C2×C67—42no—
393C2×C67#331614yescomplemented
394C2×C67C2×#54611yescharacteristic
395C2×C67C22×#13711yescharacteristic
396C2×C67C2×#57711yescharacteristic
397D67—82no—
398C2×#554D6711yescharacteristic, complemented
399C2×#548—671no—
400#3316—6716no—
401C2×#489—671no—
402C2×#481—671no—
403C2×#483—671no—
404C2×#475—671no—
405C2×#470—671no—
406C2×#465—671no—
407C2×#464—671no—
408C2×#452—671no—
409C2×#451—671no—
410C2×#441—671no—
411C2×#435—671no—
412C2×#417—671no—
413C22×#103—671no—
414C67C2×#331611yescharacteristic, complemented, Sylow
415C22×#41—671no—
416C23×Q8—671no—
417C22×Q16—671no—
418C22×Q16—671no—
419C22×SD16—671no—
420C22×M16—671no—
421C23×C8—671no—
422#554—24no—
423#554C2×D6718yescomplemented
424#548—678no—
425#548—1344no—
426C2×C4⋊Q8C2×D6711yescharacteristic
427C2×#125—21no—
428C2×#124—671no—
429C2×#124—1341no—
430C2×C22⋊Q8—21no—
431C2×C22⋊Q8—21no—
432C2×C22⋊Q8—671no—
433C2×C22⋊Q8—1341no—
434C2×C22⋊Q8C2×D6711yescharacteristic
435C2×C22⋊Q8C2×D6711yescharacteristic
436C2×#121—671no—
437C2×#121—1341no—
438C2×C4×Q8—671no—
439C2×C4×Q8C2×D6711yescharacteristic
440C2×C4×D4—21no—
441C2×C4×D4—1341no—
442C2×C4×D4C2×D6711yescharacteristic
443C22×C4⋊C4C2×D6711yescharacteristic
444C22×C4⋊C4C2×D6711yescharacteristic
445#489—678no—
446#483—678no—
447#481—678no—
448#475—678no—
449#470—678no—
450#465—678no—
451#464—678no—
452#452—678no—
453#451—678no—
454#441—678no—
455#435—678no—
456C2×#106—671no—
457C2×#106—671no—
458C2×#106—671no—
459C2×C4⋊C8—671no—
460#417—678no—
461C2×#103—671no—
462C2×#103—671no—
463C2×#103—671no—
464C2×#103—671no—
465C2×#103—671no—
466C2×#103—671no—
467C2×#103—671no—
468C2×#103—678no—
469C2×#102—671no—
470C2×#102—671no—
471C2×#102—671no—
472C2×C22⋊C8—671no—
473C2×C22⋊C8—671no—
474C2×#97—671no—
475C2×#41—2682no—
476C2×#41—674no—
477C2×#41—1344no—
478C2×#41—1342no—
479C22×Q8—21no—
480C22×Q8—2682no—
481C22×Q8—674no—
482C22×Q8—671no—
483C22×Q8—671no—
484C22×Q8—1344no—
485C22×Q8—1341no—
486C22×Q8—1342no—
487C22×Q8C22×D6711yescharacteristic
488C22×D4—671no—
489C22×D4—1341no—
490C22×D4—1341no—
491C22×D4C22⋊D6711yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1341no—
495C23×C4—1341no—
496C23×C4C22×D6711yescharacteristic
497C23×C4C22×D6711yescharacteristic
498C2×Q16—2682no—
499C2×Q16—674no—
500C2×Q16—674no—
501C2×Q16—1344no—
502C2×SD16—2682no—
503C2×SD16—674no—
504C2×M16—2682no—
505C2×M16—674no—
506C22×C8—2682no—
507C22×C8—674no—
508C22×C8—671no—
509C22×C8—671no—
510C22×C8—671no—
511C22×C8—671no—
512C4⋊Q8—22no—
513C4⋊Q8C22×D6714yes—
514#125—28no—
515#124—674no—
516#124—1348no—
517#124—1342no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522C22⋊Q8—674no—
523C22⋊Q8—1342no—
524C22⋊Q8—1348no—
525C22⋊Q8C22×D6714yes—
526C22⋊Q8C22×D6714yes—
527#121—674no—
528#121—1348no—
529#121—1342no—
530C4×Q8—22no—
531C4×Q8—674no—
532C4×Q8—1342no—
533C4×Q8C22×D6714yes—
534C4×D4—28no—
535C4×D4—1348no—
536C4×D4C22⋊D6714yes—
537C4×D4C22×D6714yes—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—671no—
547C2×C4⋊C4—1341no—
548C2×C4⋊C4—1341no—
549C2×C4⋊C4C22⋊D6711yescharacteristic
550C2×C4⋊C4C22×D6711yescharacteristic
551C2×C4⋊C4C22×D6711yescharacteristic
552C2×C4⋊C4C22×D6711yescharacteristic
553C2×C4⋊C4C22×D6714yes—
554C2×C4⋊C4C22×D6714yes—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—1341no—
558C2×C22⋊C4—1341no—
559C2×C22⋊C4—1341no—
560C2×C22⋊C4—1341no—
561C2×C22⋊C4C22⋊D6711yescharacteristic
562C2×C22⋊C4C22⋊D6711yescharacteristic
563C2×C42—21no—
564C2×C42—1341no—
565C2×C42C22×D6711yescharacteristic
566#106—674no—
567#106—674no—
568#106—674no—
569C4⋊C8—674no—
570#103—674no—
571#103—674no—
572#103—674no—
573#103—674no—
574#103—674no—
575#103—674no—
576#103—674no—
577#102—674no—
578#102—674no—
579#102—674no—
580C22⋊C8—674no—
581C22⋊C8—674no—
582#97—674no—
583C24—1341no—
584C24C2×C22⋊D6711yescharacteristic
585C24C2×C22⋊D6711yescharacteristic
586#41—2688no—
587#41—2684no—
588#41—1348no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—82no—
594C2×Q8—2688no—
595C2×Q8—2684no—
596C2×Q8—2684no—
597C2×Q8—674no—
598C2×Q8—672no—
599C2×Q8—672no—
600C2×Q8—1348no—
601C2×Q8—1342no—
602C2×Q8—1342no—
603C2×Q8—1341no—
604C2×Q8—1344no—
605C2×Q8—1341no—
606C2×Q8—1342no—
607C2×Q8C23×D6712yes—
608C2×D4—24no—
609C2×D4—2684no—
610C2×D4—2684no—
611C2×D4—672no—
612C2×D4—1344no—
613C2×D4—1344no—
614C2×D4—1341no—
615C2×D4—1342no—
616C2×D4—1342no—
617C2×D4C2×C22⋊D6714yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—82no—
630C22×C4—2684no—
631C22×C4—2684no—
632C22×C4—1344no—
633C22×C4—1341no—
634C22×C4—1341no—
635C22×C4—1344no—
636C22×C4—1341no—
637C22×C4C2×C22⋊D6712yes—
638C22×C4C2×C22⋊D6712yes—
639C22×C4C2×C22⋊D6711yescharacteristic
640C22×C4C2×C22⋊D6711yescharacteristic
641C22×C4C2×C22⋊D6711yescharacteristic
642C22×C4C2×C22⋊D6711yescharacteristic
643C22×C4C23×D6712yes—
644C22×C4C23×D6712yes—
645C22×C4C23×D6711yescharacteristic
646Q16—2684no—
647Q16—1348no—
648SD16—2684no—
649M16—2684no—
650C2×C8—2684no—
651C2×C8—672no—
652C2×C8—672no—
653C2×C8—672no—
654C2×C8—672no—
655C2×C8—1342no—
656C2×C8—1342no—
657C2×C8—1342no—
658C2×C8—1342no—
659C4⋊C4—21no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—672no—
669C4⋊C4—1341no—
670C4⋊C4—1344no—
671C4⋊C4—1344no—
672C4⋊C4C2×C22⋊D6714yes—
673C4⋊C4C23×D6712yes—
674C4⋊C4C23×D6712yes—
675C4⋊C4C23×D6712yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—1344no—
679C22⋊C4—1344no—
680C22⋊C4—1344no—
681C22⋊C4—1344no—
682C22⋊C4C2×C22⋊D6714yes—
683C22⋊C4C2×C22⋊D6714yes—
684C42—24no—
685C42—1344no—
686C42C2×C22⋊D6712yes—
687C42C23×D6712yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—2682no—
694C23—2682no—
695C23—2682no—
696C23—1342no—
697C23#1452407414yes—
698C23C22×C22⋊D6712yes—
699C23C22×C22⋊D6712yes—
700C23C22×C22⋊D6711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—84no—
705Q8—2688no—
706Q8—2682no—
707Q8—674no—
708Q8—1342no—
709Q8—1342no—
710Q8—1344no—
711Q8—1342no—
712D4—28no—
713D4—2688no—
714D4—2688no—
715D4—2682no—
716D4—1342no—
717D4—1342no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—2688no—
739C2×C4—2682no—
740C2×C4—2682no—
741C2×C4—2688no—
742C2×C4—1342no—
743C2×C4—1342no—
744C2×C4—1344no—
745C2×C4—1342no—
746C2×C4C22×C22⋊D6712yes—
747C2×C4C22×C22⋊D6712yes—
748C2×C4C22×C22⋊D6712yes—
749C2×C4C22×C22⋊D6712yes—
750C2×C4C22×C22⋊D6711yescharacteristic
751C2×C4#41×D6712yes—
752C2×C4#1452408912yes—
753C2×C4C24×D6711yescharacteristic
754C8—1342no—
755C8—1342no—
756C8—1342no—
757C8—1342no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—2682no—
766C22—2682no—
767C22—2682no—
768C22—5364no—
769C22#1686403412yes—
770C22C2×#1452407414yes—
771C22C2×#1452407412yes—
772C22#1686420712yes—
773C22C23×C22⋊D6711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2682no—
783C4—2682no—
784C4—1344no—
785C4#1686403412yes—
786C4C2×#41×D6711yescharacteristic
787C4C2×#1452408911yescharacteristic
788C2—24no—
789C2—42no—
790C2—5362no—
791C2#2257231414yesdirect product factor
792C2C2×#1686403411yescharacteristic
793C2C22×#1452407411yescharacteristic
794C2C2×#1686420711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#554×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864055C2
hypercenterC2×#554D67
hypocenterC67C2×#3316
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #22572314C2direct (N × H)
3. C2×#16863758C2semidirect
4. C2×#16863714C2semidirect
5. C2×#16863726C2semidirect
6. C2×#16863678C2semidirect
7. C2×#16863652C2semidirect
8. C2×#16863627C2semidirect
9. C2×#16863618C2semidirect
10. C2×#16863556C2semidirect
11. C2×#16863551C2semidirect
12. C2×#16863501C2semidirect
13. C2×#16863468C2semidirect
14. C2×#16863395C2semidirect
15. C22×#14523966C2semidirect
16. C2×#554×C67C2semidirect
34. #16863758C22semidirect
35. #16863726C22semidirect
36. #16863714C22semidirect
37. #16863678C22semidirect
38. #16863652C22semidirect
39. #16863627C22semidirect
40. #16863618C22semidirect
41. #16863556C22semidirect
42. #16863551C22semidirect
43. #16863501C22semidirect
44. #16863468C22semidirect
49. #16863395C22semidirect
57. C2×#14523966C22semidirect
65. #554×C67C22semidirect
393. C2×C67#3316semidirect
398. C2×#554D67semidirect
414. C67C2×#3316semidirect
423. #554C2×D67semidirect
791. C2#22572314direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640552
#225723142
C2×#168637582
C2×#168637142
C2×#168637262
C2×#168636782
C2×#168636522
C2×#168636272
C2×#168636182
C2×#168635562
C2×#168635512
C2×#168635012
C2×#168634682
C2×#168633952
C22×#145239662
C2×#554×C672
C2×#331667