Finite Group Databasebeta

← C2×#22570417 #31724088

Subgroups — C2×#22570417 #31724088

Order 17152.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863876C211yesmaximal, characteristic
2#22570417C2116yesmaximal, direct product factor
3C2×#16863729C211yesmaximal, characteristic, complemented
4C2×#16863724C211yesmaximal, characteristic, complemented
5C2×#16863700C211yesmaximal, characteristic, complemented
6C2×#16863693C211yesmaximal, characteristic, complemented
7C2×#16863603C211yesmaximal, characteristic, complemented
8C2×#16863598C211yesmaximal, characteristic, complemented
9C2×#16863556C211yesmaximal, characteristic
10C2×#16863556C211yesmaximal, characteristic
11C2×#16863501C211yesmaximal, characteristic, complemented
12C2×#16863494C211yesmaximal, characteristic, complemented
13C2×C4×#11761618C211yesmaximal, characteristic, complemented
14C2×C4×#11761615C211yesmaximal, characteristic, complemented
15C2×#16863457C211yesmaximal, characteristic, complemented
16C2×#541×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2211yescharacteristic
18C22×#11761618C2211yescharacteristic
19C22×#11761618C2211yescharacteristic
20C22×#11761615C2211yescharacteristic
21C22×#11761615C2211yescharacteristic
22#16863876—24no—
23#16863876C2218yes—
24C2×C4×Dic134C2211yescharacteristic
25C2×C4×Dic134C2211yescharacteristic
26C2×C4×D268C2211yescharacteristic
27C2×C4×D268C2211yescharacteristic
28C2×(C22⋊D67)⋊C4—21no—
29C2×(C22⋊D67)⋊C4—21no—
30C2×#14524001—21no—
31C22×C4⋊Dic67C2211yescharacteristic
32C2×C4⋊C4×D67—21no—
33#16863729C2218yescomplemented
34#16863724C2218yescomplemented
35#16863700C2218yescomplemented
36#16863693C2218yescomplemented
37#16863603C2218yescomplemented
38#16863598C2218yescomplemented
39#16863556C2218yes—
40#16863556C2218yes—
41#16863501C2218yescomplemented
42#16863494C2218yescomplemented
43C4×#11761618C2218yescomplemented
44C4×#11761615C2218yescomplemented
45#16863457C2218yescomplemented
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×C4⋊(C67⋊C8)C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523967C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523966C2211yescharacteristic
57C2×#14523966C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#541×C67—24no—
65#541×C67C2218yescomplemented
66C2×C4⋊Q8×C67C2211yescharacteristic
67C2×#126×C67—21no—
68C2×#126×C67—21no—
69C2×#125×C67—21no—
70C2×#125×C67—21no—
71C2×#125×C67C2211yescharacteristic
72C2×C22⋊Q8×C67C2211yescharacteristic
73C2×C22⋊Q8×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×C4×Q8×C67C2211yescharacteristic
76C2×#117×C67C2211yescharacteristic
77C2×#11761628—24no—
78C2×#11761628—24no—
79C2×#11761628—22no—
80C2×#11761628C2314yes—
81C22×Dic134C2311yescharacteristic
82C22×D268C2311yescharacteristic
83C22×C22⋊D67—21no—
84C23×Dic67—21no—
85C22×C4×D67—21no—
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88C2×#11761618—24no—
89C2×#11761618—24no—
90C2×#11761618C2314yes—
91C2×#11761618C2314yes—
92C2×#11761615—24no—
93C2×#11761615—24no—
94C2×#11761615C2314yes—
95C2×#11761615C2314yes—
96C22×C67⋊C8C2311yescharacteristic
97C22×C67⋊C8C2311yescharacteristic
98C22×C67⋊C8C2311yescharacteristic
99C22×C67⋊C8C2311yescharacteristic
100C4×Dic134—22no—
101C4×Dic134—22no—
102C4×Dic134C2314yes—
103C4×Dic134C2314yes—
104C4×D268—22no—
105C4×D268—22no—
106C4×D268C2314yes—
107C4×D268C2314yes—
108(C22⋊D67)⋊C4—28no—
109(C22⋊D67)⋊C4—28no—
110#14524001—28no—
111C2×C4⋊Dic67—21no—
112C2×C4⋊Dic67—22no—
113C2×C4⋊Dic67C2311yescharacteristic
114C2×C4⋊Dic67C2311yescharacteristic
115C2×C4⋊Dic67C2314yes—
116C2×Dic67⋊C4—21no—
117C2×Dic67⋊C4—21no—
118C4⋊C4×D67—28no—
119C2×(C2×D67)⋊C4—21no—
120C2×(C2×D67)⋊C4—21no—
121C2×C4×Dic67—21no—
122C2×C4×Dic67—21no—
123#14523976C2314yes—
124#14523976C2314yes—
125#14523974C2314yes—
126#14523974C2314yes—
127C4⋊(C67⋊C8)C2314yes—
128C4⋊(C67⋊C8)C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523967C2314yes—
132#14523967C2314yes—
133#14523966C2314yes—
134#14523966C2314yes—
135#14523963C2314yes—
136#14523963C2314yes—
137C22⋊(C67⋊C8)C2314yes—
138C22⋊(C67⋊C8)C2314yes—
139#14523954C2314yes—
140C4×C67⋊C8C2314yes—
141C22×Q8×C67C2311yescharacteristic
142C22×Q8×C67C2311yescharacteristic
143C23×C4×C67C2311yescharacteristic
144C4⋊Q8×C67—22no—
145C4⋊Q8×C67C2314yes—
146#126×C67—28no—
147#126×C67—28no—
148#125×C67—28no—
149#125×C67—28no—
150#125×C67—22no—
151#125×C67C2314yes—
152C22⋊Q8×C67—22no—
153C22⋊Q8×C67—22no—
154C22⋊Q8×C67C2314yes—
155C22⋊Q8×C67C2314yes—
156C4×Q8×C67—22no—
157C4×Q8×C67—22no—
158C4×Q8×C67C2314yes—
159C4×Q8×C67C2314yes—
160#117×C67D414yes—
161#117×C67C2314yes—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67—21no—
170C2×C4⋊C4×C67D411yescharacteristic
171C2×C4⋊C4×C67D411yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C4⋊C4×C67C2311yescharacteristic
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C22⋊C4×C67D411yescharacteristic
177C2×C22⋊C4×C67D411yescharacteristic
178C2×C42×C67—21no—
179C2×C42×C67—21no—
180C2×C42×C67C2311yescharacteristic
181C2×C42×C67C2311yescharacteristic
182C23×D67—21no—
183#11761628—216no—
184#11761628—28no—
185#11761628—28no—
186C2×Dic134—21no—
187C2×Dic134—22no—
188C2×Dic134#4114yes—
189C2×Dic134C2412yes—
190C2×D268—21no—
191C2×D268—22no—
192C2×D268#4114yes—
193C2×D268C2412yes—
194C2×C22⋊D67—28no—
195C2×C22⋊D67—24no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C22×Dic67—21no—
199C22×Dic67—24no—
200C22×Dic67—82no—
201C2×C4×D67—28no—
202C2×C4×D67—24no—
203C2×C4×D67—24no—
204C2×C4×D67—24no—
205C2×C4×D67—82no—
206C2×C4×D67—82no—
207#11761618—28no—
208#11761618—28no—
209#11761615—28no—
210#11761615—28no—
211C2×C67⋊C8—22no—
212C2×C67⋊C8—22no—
213C2×C67⋊C8—22no—
214C2×C67⋊C8—22no—
215C2×C67⋊C8C2412yes—
216C2×C67⋊C8C2412yes—
217C2×C67⋊C8C2412yes—
218C2×C67⋊C8C2412yes—
219C4⋊Dic67—24no—
220C4⋊Dic67—21no—
221C4⋊Dic67—21no—
222C4⋊Dic67C2412yes—
223C4⋊Dic67C2412yes—
224Dic67⋊C4—24no—
225Dic67⋊C4—24no—
226(C2×D67)⋊C4—24no—
227(C2×D67)⋊C4—24no—
228C4×Dic67—24no—
229C4×Dic67—24no—
230C24×C67C2×D411yescharacteristic
231C2×Q8×C67—21no—
232C2×Q8×C67—21no—
233C2×Q8×C67—22no—
234C2×Q8×C67—22no—
235C2×Q8×C67—22no—
236C2×Q8×C67—22no—
237C2×Q8×C67C2412yes—
238C2×Q8×C67C2412yes—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D412yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2411yescharacteristic
253C4⋊C4×C67—24no—
254C4⋊C4×C67—24no—
255C4⋊C4×C67—24no—
256C4⋊C4×C67—24no—
257C4⋊C4×C67—24no—
258C4⋊C4×C67—24no—
259C4⋊C4×C67—24no—
260C4⋊C4×C67—24no—
261C4⋊C4×C67—21no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67C2×D414yes—
264C4⋊C4×C67C2×D414yes—
265C4⋊C4×C67C2412yes—
266C4⋊C4×C67C2412yes—
267C22⋊C4×C67—24no—
268C22⋊C4×C67—24no—
269C22⋊C4×C67C2×D414yes—
270C22⋊C4×C67C2×D414yes—
271C42×C67—24no—
272C42×C67—24no—
273C42×C67C2×D412yes—
274C42×C67C2×D412yes—
275C42×C67C2412yes—
276C42×C67C2412yes—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67—22no—
280C23×C67C22×D412yes—
281C23×C67C22×D411yescharacteristic
282C22×D67—24no—
283C22×D67—22no—
284C22×D67—42no—
285C22×D67—42no—
286Q8×C67—22no—
287Q8×C67—22no—
288Q8×C67—22no—
289Q8×C67—22no—
290Q8×C67—42no—
291Q8×C67—42no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—24no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—42no—
305C2×C4×C67—42no—
306C2×C4×C67—42no—
307C2×C4×C67—42no—
308C2×C4×C67C22×D412yes—
309C2×C4×C67C22×D412yes—
310C2×C4×C67C22×D412yes—
311C2×C4×C67C22×D412yes—
312C2×C4×C67C22×D412yes—
313C2×C4×C67C22×D411yescharacteristic
314C2×C4×C67C2×#4112yes—
315C2×C4×C67C2×#4112yes—
316C2×C4×C67C2511yescharacteristic
317C22⋊D67—216no—
318C2×Dic67—24no—
319C2×Dic67—22no—
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—42no—
323C2×Dic67—42no—
324C2×Dic67—84no—
325D268—24no—
326D268—22no—
327D268C2×#4114yes—
328C4×D67—216no—
329C4×D67—84no—
330C4×D67—84no—
331Dic134—24no—
332Dic134—22no—
333Dic134C2×#4114yes—
334C67⋊C8—22no—
335C67⋊C8—22no—
336C67⋊C8—22no—
337C67⋊C8—22no—
338C22×C67—22no—
339C22×C67—22no—
340C22×C67—22no—
341C22×C67—44no—
342C22×C67#52512yes—
343C22×C67#57712yes—
344C22×C67#57812yes—
345C22×C67C23×D411yescharacteristic
346C2×D67—24no—
347C2×D67—48no—
348C2×D67—42no—
349C2×D67—42no—
350C4×C67—22no—
351C4×C67—22no—
352C4×C67—22no—
353C4×C67—22no—
354C4×C67—22no—
355C4×C67—42no—
356C4×C67—42no—
357C4×C67—42no—
358C4×C67—42no—
359C4×C67#52512yes—
360C4×C67C22×#4111yescharacteristic
361C4×C67C22×#4111yescharacteristic
362Dic67—24no—
363Dic67—42no—
364Dic67—42no—
365C2×#3120—671nomaximal, Sylow
366C2×C67—42no—
367C2×C67#312014yescomplemented
368C2×C67C2×#52511yescharacteristic
369C2×C67C2×#57711yescharacteristic
370C2×C67C2×#57811yescharacteristic
371D67—44no—
372C2×#541D6711yescharacteristic, complemented
373C2×#520—671no—
374#3120—6716no—
375C2×#484—671no—
376C2×#483—671no—
377C2×#479—671no—
378C2×#478—671no—
379C2×#462—671no—
380C2×#461—671no—
381C2×#452—671no—
382C2×#452—671no—
383C2×#441—671no—
384C2×#440—671no—
385C2×C4×Q16—671no—
386C2×C4×SD16—671no—
387C2×#433—671no—
388C67C2×#312011yescharacteristic, complemented, Sylow
389C22×#41—671no—
390C22×Q16—671no—
391C22×Q16—671no—
392C22×SD16—671no—
393C22×SD16—671no—
394#541—24no—
395#541C2×D6718yescomplemented
396C2×C4⋊Q8C2×D6711yescharacteristic
397C2×#126—21no—
398C2×#126—21no—
399C2×#125—21no—
400C2×#125—21no—
401C2×#125C2×D6711yescharacteristic
402C2×C22⋊Q8C2×D6711yescharacteristic
403C2×C22⋊Q8C2×D6711yescharacteristic
404#520—678no—
405#520—1344no—
406C2×C4×Q8—671no—
407C2×C4×Q8—671no—
408C2×C4×Q8C2×D6711yescharacteristic
409C2×C4×Q8C2×D6711yescharacteristic
410C2×C4×D4—671no—
411C2×C4×D4—671no—
412C2×C4×D4—1341no—
413C2×C4×D4—1341no—
414C2×#117—1341no—
415C2×#117C2×D6711yescharacteristic
416C22×C4⋊C4—671no—
417C22×C4⋊C4—1341no—
418#484—678no—
419#483—678no—
420#479—678no—
421#478—678no—
422#462—678no—
423#461—678no—
424#452—678no—
425#452—678no—
426#441—678no—
427#440—678no—
428C4×Q16—678no—
429C4×SD16—678no—
430#433—678no—
431C2×#107—671no—
432C2×#107—671no—
433C2×#106—671no—
434C2×#106—671no—
435C2×C4⋊C8—671no—
436C2×C4⋊C8—671no—
437C2×#103—671no—
438C2×#103—671no—
439C2×#103—671no—
440C2×#103—671no—
441C2×#103—671no—
442C2×#103—671no—
443C2×#102—671no—
444C2×#102—671no—
445C2×C22⋊C8—671no—
446C2×C22⋊C8—671no—
447C2×#97—671no—
448C2×C4×C8—671no—
449C2×#41—674no—
450C2×#41—1344no—
451C2×#41—1344no—
452C2×#41—1342no—
453C22×Q8—671no—
454C22×Q8C22×D6711yescharacteristic
455C22×Q8C22×D6711yescharacteristic
456C22×D4—671no—
457C22×D4—1341no—
458C23×C4—1341no—
459C23×C4—1341no—
460C23×C4—1341no—
461C23×C4—1341no—
462C23×C4C22×D6711yescharacteristic
463C2×Q16—674no—
464C2×Q16—674no—
465C2×Q16—1344no—
466C2×Q16—1344no—
467C2×SD16—674no—
468C2×SD16—674no—
469C2×SD16—1344no—
470C2×SD16—1344no—
471C22×C8—671no—
472C22×C8—671no—
473C22×C8—671no—
474C22×C8—671no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D6714yes—
477#126—28no—
478#126—28no—
479#125—28no—
480#125—28no—
481#125—22no—
482#125C22×D6714yes—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8C22×D6714yes—
486C22⋊Q8C22×D6714yes—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—674no—
490C4×Q8—674no—
491C4×Q8—1342no—
492C4×Q8—1342no—
493C4×Q8C22×D6714yes—
494C4×Q8C22×D6714yes—
495C4×D4—674no—
496C4×D4—674no—
497C4×D4—1348no—
498C4×D4—1348no—
499C4×D4—1342no—
500C4×D4—1342no—
501#117—1348no—
502#117C22⋊D6714yes—
503#117C22×D6714yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—671no—
513C2×C4⋊C4—671no—
514C2×C4⋊C4—674no—
515C2×C4⋊C4—1341no—
516C2×C4⋊C4—1342no—
517C2×C4⋊C4—1341no—
518C2×C4⋊C4—1341no—
519C2×C4⋊C4—1348no—
520C2×C4⋊C4C22⋊D6711yescharacteristic
521C2×C4⋊C4C22⋊D6711yescharacteristic
522C2×C4⋊C4C22×D6711yescharacteristic
523C2×C4⋊C4C22×D6711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—1341no—
527C2×C22⋊C4—1341no—
528C2×C22⋊C4C22⋊D6711yescharacteristic
529C2×C22⋊C4C22⋊D6711yescharacteristic
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—1341no—
533C2×C42—1341no—
534C2×C42C22×D6711yescharacteristic
535C2×C42C22×D6711yescharacteristic
536#107—674no—
537#107—674no—
538#106—674no—
539#106—674no—
540C4⋊C8—674no—
541C4⋊C8—674no—
542#103—674no—
543#103—674no—
544#103—674no—
545#103—674no—
546#103—674no—
547#103—674no—
548#102—674no—
549#102—674no—
550C22⋊C8—674no—
551C22⋊C8—674no—
552#97—674no—
553C4×C8—674no—
554C24—1341no—
555C24C2×C22⋊D6711yescharacteristic
556#41—1348no—
557#41—1348no—
558#41—13416no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—674no—
566C2×Q8—672no—
567C2×Q8—1341no—
568C2×Q8—1342no—
569C2×Q8C23×D6712yes—
570C2×Q8C23×D6712yes—
571C2×D4—674no—
572C2×D4—672no—
573C2×D4—1348no—
574C2×D4—1344no—
575C2×D4—1341no—
576C2×D4—1342no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—5362no—
584C22×C4—5362no—
585C22×C4—5362no—
586C22×C4—1348no—
587C22×C4—1341no—
588C22×C4—1341no—
589C22×C4—1344no—
590C22×C4—1344no—
591C22×C4—1344no—
592C22×C4—1341no—
593C22×C4—1344no—
594C22×C4C2×C22⋊D6712yes—
595C22×C4C2×C22⋊D6711yescharacteristic
596C22×C4C2×C22⋊D6711yescharacteristic
597C22×C4C2×C22⋊D6711yescharacteristic
598C22×C4C2×C22⋊D6711yescharacteristic
599C22×C4C2×C22⋊D6711yescharacteristic
600C22×C4C23×D6712yes—
601C22×C4C23×D6711yescharacteristic
602Q16—1348no—
603Q16—1348no—
604SD16—1348no—
605SD16—1348no—
606C2×C8—672no—
607C2×C8—672no—
608C2×C8—672no—
609C2×C8—672no—
610C2×C8—1342no—
611C2×C8—1342no—
612C2×C8—1342no—
613C2×C8—1342no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—672no—
625C4⋊C4—672no—
626C4⋊C4—1344no—
627C4⋊C4—1341no—
628C4⋊C4—1341no—
629C4⋊C4—1344no—
630C4⋊C4—1344no—
631C4⋊C4C2×C22⋊D6714yes—
632C4⋊C4C2×C22⋊D6714yes—
633C4⋊C4C23×D6712yes—
634C4⋊C4C23×D6712yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—1344no—
638C22⋊C4—1344no—
639C22⋊C4C2×C22⋊D6714yes—
640C22⋊C4C2×C22⋊D6714yes—
641C42—24no—
642C42—24no—
643C42—1344no—
644C42—1344no—
645C42C2×C22⋊D6712yes—
646C42C2×C22⋊D6712yes—
647C42C23×D6712yes—
648C42C23×D6712yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2682no—
653C23—2682no—
654C23—1344no—
655C23—1342no—
656C23C22×C22⋊D6712yes—
657C23C22×C22⋊D6711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—674no—
665Q8—1344no—
666Q8—1342no—
667D4—674no—
668D4—13416no—
669D4—1344no—
670D4—1342no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—2682no—
688C2×C4—2682no—
689C2×C4—5364no—
690C2×C4—5364no—
691C2×C4—5364no—
692C2×C4—13416no—
693C2×C4—1342no—
694C2×C4—1342no—
695C2×C4—1344no—
696C2×C4—1342no—
697C2×C4C22×C22⋊D6712yes—
698C2×C4C22×C22⋊D6712yes—
699C2×C4C22×C22⋊D6712yes—
700C2×C4C22×C22⋊D6712yes—
701C2×C4C22×C22⋊D6712yes—
702C2×C4C22×C22⋊D6711yescharacteristic
703C2×C4#41×D6712yes—
704C2×C4#41×D6712yes—
705C2×C4C24×D6711yescharacteristic
706C8—1342no—
707C8—1342no—
708C8—1342no—
709C8—1342no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—2682no—
715C22—2682no—
716C22—2688no—
717C22—1344no—
718C22#1686390312yes—
719C22#1686420412yes—
720C22#1686421112yes—
721C22C23×C22⋊D6711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—2682no—
732C4—2682no—
733C4—1344no—
734C4#1686390312yes—
735C4C2×#41×D6711yescharacteristic
736C4C2×#41×D6711yescharacteristic
737C2—42no—
738C2—2684no—
739C2#2257041714yesdirect product factor
740C2C2×#1686390311yescharacteristic
741C2C2×#1686420411yescharacteristic
742C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#541×C67C2
socleC23×C67C22×D4
prime radicalC22×#11761628C22
hypercenterC2×#541D67
hypocenterC67C2×#3120
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #22570417C2direct (N × H)
3. C2×#16863729C2semidirect
4. C2×#16863724C2semidirect
5. C2×#16863700C2semidirect
6. C2×#16863693C2semidirect
7. C2×#16863603C2semidirect
8. C2×#16863598C2semidirect
11. C2×#16863501C2semidirect
12. C2×#16863494C2semidirect
13. C2×C4×#11761618C2semidirect
14. C2×C4×#11761615C2semidirect
15. C2×#16863457C2semidirect
16. C2×#541×C67C2semidirect
33. #16863729C22semidirect
34. #16863724C22semidirect
35. #16863700C22semidirect
36. #16863693C22semidirect
37. #16863603C22semidirect
38. #16863598C22semidirect
41. #16863501C22semidirect
42. #16863494C22semidirect
43. C4×#11761618C22semidirect
44. C4×#11761615C22semidirect
45. #16863457C22semidirect
65. #541×C67C22semidirect
367. C2×C67#3120semidirect
372. C2×#541D67semidirect
388. C67C2×#3120semidirect
395. #541C2×D67semidirect
739. C2#22570417direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168638762
#225704172
C2×#168637292
C2×#168637242
C2×#168637002
C2×#168636932
C2×#168636032
C2×#168635982
C2×#168635562
C2×#168635012
C2×#168634942
C2×C4×#117616182
C2×C4×#117616152
C2×#168634572
C2×#541×C672
C2×#312067