Finite Group Databasebeta

← C2×#22569996 #31723331

Subgroups — C2×#22569996 #31723331

Order 17152.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863952C211yesmaximal, characteristic, complemented
2C2×C4×#11761629C211yesmaximal, characteristic
3#22569996C2116yesmaximal, direct product factor
4C2×#16863703C211yesmaximal, characteristic, complemented
5C2×#16863689C211yesmaximal, characteristic, complemented
6C2×#16863679C211yesmaximal, characteristic, complemented
7C2×#16863697C211yesmaximal, characteristic, complemented
8C2×#16863693C211yesmaximal, characteristic, complemented
9C2×#16863685C211yesmaximal, characteristic, complemented
10C2×#16863675C211yesmaximal, characteristic, complemented
11C2×#16863433C211yesmaximal, characteristic, complemented
12C2×#16863431C211yesmaximal, characteristic, complemented
13C2×C4⋊C8×D67C211yesmaximal, characteristic, complemented
14C2×#16863391C211yesmaximal, characteristic
15C2×#16863391C211yesmaximal, characteristic
16C2×#479×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×C8×D67C2211yescharacteristic
19C22×C8×D67C2211yescharacteristic
20#16863952—24no—
21#16863952C2218yescomplemented
22C2×#14524042C2211yescharacteristic
23C2×#14524042C2211yescharacteristic
24C2×#14524035C2211yescharacteristic
25C2×#14524021—21no—
26C2×#14524021—21no—
27C4×#11761629—24no—
28C4×#11761629C2218yes—
29C2×Q8×Dic67C2211yescharacteristic
30C2×#14524008—21no—
31C2×#14524008—21no—
32C2×C4×D268—21no—
33C2×C4×D268C2211yescharacteristic
34C2×#14524005—21no—
35C2×#14524005C2211yescharacteristic
36C2×#14524001—21no—
37C2×#14524001C2211yescharacteristic
38C2×#14524001C2211yescharacteristic
39C2×#14524001C2211yescharacteristic
40C2×C42×D67—21no—
41C2×C42×D67C2211yescharacteristic
42#16863703C2218yescomplemented
43#16863697C2218yescomplemented
44#16863693C2218yescomplemented
45#16863689C2218yescomplemented
46#16863685C2218yescomplemented
47#16863679C2218yescomplemented
48#16863675C2218yescomplemented
49#16863433C2218yescomplemented
50#16863431C2218yescomplemented
51C2×#14523977C2211yescharacteristic
52C2×#14523976C2211yescharacteristic
53C2×#14523976C2211yescharacteristic
54C2×#14523975C2211yescharacteristic
55C2×#14523974C2211yescharacteristic
56C2×#14523974C2211yescharacteristic
57C2×C4⋊(C67⋊C8)C2211yescharacteristic
58C2×Dic67⋊C8C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C4⋊C8×D67C2218yescomplemented
61#16863391C2218yes—
62#16863391C2218yes—
63C2×#14523967C2211yescharacteristic
64C2×#14523967C2211yescharacteristic
65C2×#14523965C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523963C2211yescharacteristic
68C2×#14523963C2211yescharacteristic
69C2×#125×C67C2211yescharacteristic
70C2×C4×Q8×C67C2211yescharacteristic
71#479×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic
73C2×#106×C67C2211yescharacteristic
74C2×C4⋊C8×C67C2211yescharacteristic
75C2×#103×C67C2211yescharacteristic
76C2×#103×C67C2211yescharacteristic
77C2×#11761629—22no—
78C2×#11761629—24no—
79C2×#11761629Q818yescomplemented
80C2×#11761629C2314yes—
81C22×Dic134—21no—
82C22×Dic134—21no—
83C22×D268—21no—
84C22×D268C2311yescharacteristic
85C22×C4×D67—21no—
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88C22×C4×D67D411yescharacteristic
89C22×C4×D67D411yescharacteristic
90C22×C4×D67C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93C2×C8×D67—24no—
94C2×C8×D67—24no—
95C2×C8×D67C2314yes—
96C2×C8×D67C2314yes—
97#14524042—22no—
98#14524042—22no—
99#14524042C2314yes—
100#14524042C2314yes—
101#14524035—22no—
102#14524035C2314yes—
103#14524021—28no—
104#14524021—28no—
105Q8×Dic67—22no—
106Q8×Dic67C2314yes—
107#14524008—28no—
108#14524008—28no—
109C4×D268—28no—
110C4×D268—22no—
111C4×D268C2314yes—
112#14524005—28no—
113#14524005—22no—
114#14524005C2314yes—
115#14524001—22no—
116#14524001—22no—
117#14524001—22no—
118#14524001—28no—
119#14524001C2314yes—
120#14524001C2314yes—
121#14524001C2314yes—
122C2×C4⋊Dic67—21no—
123C2×C4⋊Dic67C2311yescharacteristic
124C2×C4⋊Dic67C2311yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×(C2×D67)⋊C4—21no—
131C2×(C2×D67)⋊C4—21no—
132C2×(C2×D67)⋊C4—21no—
133C2×(C2×D67)⋊C4—21no—
134C2×(C2×D67)⋊C4—21no—
135C2×C4×Dic67—21no—
136C2×C4×Dic67—21no—
137C2×C4×Dic67—21no—
138C2×C4×Dic67—21no—
139C2×C4×Dic67D411yescharacteristic
140C2×C4×Dic67D411yescharacteristic
141C2×C4×Dic67C2311yescharacteristic
142C42×D67—28no—
143C42×D67D414yes—
144C42×D67C2314yes—
145#14523977C2314yes—
146#14523976C2314yes—
147#14523976C2314yes—
148#14523975C2314yes—
149#14523974C2314yes—
150#14523974C2314yes—
151C4⋊(C67⋊C8)C2314yes—
152Dic67⋊C8C2314yes—
153Dic67⋊C8C2314yes—
154#14523967C2314yes—
155#14523967C2314yes—
156#14523965C2314yes—
157#14523965C2314yes—
158#14523963C2314yes—
159#14523963C2314yes—
160C22×Q8×C67C2311yescharacteristic
161C22×C8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163#125×C67—22no—
164#125×C67C2314yes—
165C4×Q8×C67—22no—
166C4×Q8×C67C2314yes—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67—21no—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C42×C67—21no—
174C2×C42×C67C2311yescharacteristic
175#107×C67C2314yes—
176#106×C67C2314yes—
177C4⋊C8×C67C2314yes—
178#103×C67C2314yes—
179#103×C67C2314yes—
180C23×D67—21no—
181C23×D67C2×D411yescharacteristic
182#11761629—216no—
183#11761629—28no—
184#11761629C2×Q8116yescomplemented
185C2×Dic134—24no—
186C2×Dic134—24no—
187C2×Dic134—44no—
188C2×Dic134—44no—
189C2×D268—28no—
190C2×D268—24no—
191C2×D268—21no—
192C2×D268—22no—
193C2×D268C2×Q814yes—
194C2×D268C2412yes—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C22×Dic67C2×D411yescharacteristic
199C22×Dic67C2×D411yescharacteristic
200C22×Dic67C2×D411yescharacteristic
201C2×C4×D67—28no—
202C2×C4×D67—24no—
203C2×C4×D67—24no—
204C2×C4×D67—24no—
205C2×C4×D67—24no—
206C2×C4×D67—42no—
207C2×C4×D67—44no—
208C2×C4×D67—44no—
209C2×C4×D67C2×D414yes—
210C2×C4×D67C2×D414yes—
211C2×C4×D67C2×D412yes—
212C2×C4×D67C2×Q814yes—
213C2×C4×D67#4114yes—
214C2×C4×D67C2412yes—
215C2×C67⋊C8—22no—
216C2×C67⋊C8—22no—
217C2×C67⋊C8C2412yes—
218C2×C67⋊C8C2412yes—
219C8×D67—28no—
220C8×D67—28no—
221C4⋊Dic67—21no—
222C4⋊Dic67—21no—
223C4⋊Dic67—21no—
224C4⋊Dic67—24no—
225C4⋊Dic67C2412yes—
226C4⋊Dic67C2412yes—
227C4⋊Dic67C2412yes—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231Dic67⋊C4—24no—
232(C2×D67)⋊C4—24no—
233(C2×D67)⋊C4—24no—
234(C2×D67)⋊C4—24no—
235(C2×D67)⋊C4—24no—
236(C2×D67)⋊C4—24no—
237C4×Dic67—24no—
238C4×Dic67—24no—
239C4×Dic67—24no—
240C4×Dic67—24no—
241C4×Dic67C2×D414yes—
242C4×Dic67C2×D412yes—
243C4×Dic67C2×D414yes—
244C4×Dic67C2412yes—
245C2×Q8×C67—21no—
246C2×Q8×C67—22no—
247C2×Q8×C67C2×Q814yes—
248C2×Q8×C67C2412yes—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67—21no—
253C22×C4×C67C2×D411yescharacteristic
254C22×C4×C67C2×D411yescharacteristic
255C22×C4×C67C2411yescharacteristic
256C2×C8×C67—22no—
257C2×C8×C67—22no—
258C2×C8×C67C2412yes—
259C2×C8×C67C2412yes—
260C4⋊C4×C67—24no—
261C4⋊C4×C67—24no—
262C4⋊C4×C67—24no—
263C4⋊C4×C67—21no—
264C4⋊C4×C67—21no—
265C4⋊C4×C67—21no—
266C4⋊C4×C67C2412yes—
267C4⋊C4×C67C2412yes—
268C4⋊C4×C67C2412yes—
269C42×C67—24no—
270C42×C67C2×D412yes—
271C42×C67C2412yes—
272C23×C67C22×D411yescharacteristic
273C22×D67—22no—
274C22×D67—22no—
275C22×D67—24no—
276C22×D67—22no—
277C22×D67—42no—
278C22×D67—42no—
279C22×D67C22⋊Q814yes—
280C22×D67C22×D412yes—
281Q8×C67—24no—
282Q8×C67—22no—
283Q8×C67C22×Q814yes—
284C2×C4×C67—24no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—42no—
292C2×C4×C67—42no—
293C2×C4×C67—42no—
294C2×C4×C67C22×D412yes—
295C2×C4×C67C22×D412yes—
296C2×C4×C67C22×D411yescharacteristic
297C2×C4×C67C22×Q812yes—
298C2×C4×C67C2×#4112yes—
299C2×C4×C67C2511yescharacteristic
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—42no—
305C2×Dic67—42no—
306C2×Dic67—42no—
307C2×Dic67C22⋊Q814yes—
308C2×Dic67#13514yes—
309C2×Dic67C22×D412yes—
310C2×Dic67C22×D412yes—
311C2×Dic67C22×D412yes—
312D268—216no—
313D268—24no—
314D268—22no—
315D268C22×Q814yes—
316C4×D67—216no—
317C4×D67—28no—
318C4×D67—44no—
319C4×D67—48no—
320C4×D67—48no—
321C4×D67C22⋊Q818yes—
322C4×D67C22×Q814yes—
323C4×D67C2×#4114yes—
324Dic134—48no—
325Dic134—48no—
326C8×C67—22no—
327C8×C67—22no—
328C67⋊C8—22no—
329C67⋊C8—22no—
330C22×C67C2×C22⋊Q812yes—
331C22×C67C2×#13512yes—
332C22×C67#57512yes—
333C22×C67C23×D411yescharacteristic
334C2×D67—28no—
335C2×D67—22no—
336C2×D67—22no—
337C2×D67—24no—
338C2×D67—48no—
339C2×D67—42no—
340C2×D67—42no—
341C2×D67C2×C22⋊Q814yes—
342C4×C67—24no—
343C4×C67—22no—
344C4×C67—22no—
345C4×C67—42no—
346C4×C67—42no—
347C4×C67—42no—
348C4×C67C2×C22⋊Q812yes—
349C4×C67C23×Q811yescharacteristic
350C4×C67C22×#4111yescharacteristic
351Dic67—22no—
352Dic67—42no—
353Dic67—42no—
354Dic67—42no—
355Dic67C2×C22⋊Q814yes—
356Dic67C2×#13514yes—
357C2×#3076—671nomaximal, Sylow
358C2×C67#307614yescomplemented
359C2×C67C22×C22⋊Q811yescharacteristic
360C2×C67C22×#13511yescharacteristic
361C2×C67C2×#57511yescharacteristic
362D67—24no—
363D67—44no—
364C2×#533—671no—
365C2×C4×#41—671no—
366#3076—6716no—
367C2×#479—671no—
368C2×#479D6711yescharacteristic, complemented
369C2×#477—671no—
370C2×#475—671no—
371C2×#478—671no—
372C2×#478—671no—
373C2×#476—671no—
374C2×#474—671no—
375C2×#427—671no—
376C2×#427—671no—
377C22×C4⋊C8—671no—
378C2×#416—671no—
379C2×#416—671no—
380C67C2×#307611yescharacteristic, complemented, Sylow
381C22×#41—671no—
382C23×C8—671no—
383C23×C8—671no—
384#533—678no—
385#533—1344no—
386C2×C4⋊Q8—671no—
387C2×C4⋊Q8—671no—
388C2×#125—671no—
389C2×#125C2×D6711yescharacteristic
390C2×C22⋊Q8—1341no—
391C2×C22⋊Q8—1341no—
392C4×#41—678no—
393C4×#41—1344no—
394C2×C4×Q8—671no—
395C2×C4×Q8—1341no—
396C2×C4×Q8—1341no—
397C2×C4×Q8C2×D6711yescharacteristic
398C2×C4×D4—671no—
399C2×C4×D4—671no—
400C2×C4×D4—1341no—
401C2×C4×D4—1341no—
402C2×#117—671no—
403C2×#117—671no—
404C2×#117—671no—
405C2×#117—1341no—
406C22×C42—671no—
407C22×C42—1341no—
408#479—678no—
409#479C2×D6718yescomplemented
410#478—678no—
411#478—678no—
412#477—678no—
413#476—678no—
414#475—678no—
415#474—678no—
416#427—678no—
417#427—678no—
418C2×#107—671no—
419C2×#107—671no—
420C2×#107—671no—
421C2×#107C2×D6711yescharacteristic
422C2×#106—671no—
423C2×#106—671no—
424C2×#106—671no—
425C2×#106C2×D6711yescharacteristic
426C2×C4⋊C8—671no—
427C2×C4⋊C8—671no—
428C2×C4⋊C8—671no—
429C2×C4⋊C8—678no—
430C2×C4⋊C8C2×D6711yescharacteristic
431#416—678no—
432#416—678no—
433C2×#103—671no—
434C2×#103—671no—
435C2×#103C2×D6711yescharacteristic
436C2×#103C2×D6711yescharacteristic
437C2×#102—671no—
438C2×#102—671no—
439C2×#102—671no—
440C2×#102—671no—
441C2×#41—678no—
442C2×#41—674no—
443C2×#41—1342no—
444C2×#41—1344no—
445C22×Q8—1341no—
446C22×Q8—1341no—
447C22×Q8C22×D6711yescharacteristic
448C22×D4—671no—
449C22×D4—1341no—
450C23×C4—671no—
451C23×C4—671no—
452C23×C4—671no—
453C23×C4—1341no—
454C23×C4—1341no—
455C23×C4—1341no—
456C22×C8—671no—
457C22×C8—671no—
458C22×C8—674no—
459C22×C8—674no—
460C22×C8—1344no—
461C22×C8—1344no—
462C22×C8C22×D6711yescharacteristic
463C22×C8C22×D6711yescharacteristic
464C4⋊Q8—674no—
465C4⋊Q8—674no—
466C4⋊Q8—1342no—
467C4⋊Q8—1342no—
468#125—22no—
469#125—674no—
470#125—1342no—
471#125C22×D6714yes—
472C22⋊Q8—1348no—
473C22⋊Q8—1348no—
474C4×Q8—22no—
475C4×Q8—674no—
476C4×Q8—1348no—
477C4×Q8—1348no—
478C4×Q8—1342no—
479C4×Q8C22×D6714yes—
480C4×D4—674no—
481C4×D4—674no—
482C4×D4—1348no—
483C4×D4—1342no—
484C4×D4—1348no—
485C4×D4—1342no—
486#117—674no—
487#117—674no—
488#117—674no—
489#117—1348no—
490#117—1342no—
491#117—1342no—
492#117—1342no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—671no—
497C2×C4⋊C4—671no—
498C2×C4⋊C4—671no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4—1341no—
504C2×C4⋊C4C22×D6711yescharacteristic
505C2×C4⋊C4C22×D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C22⋊C4—1341no—
508C2×C22⋊C4—1341no—
509C2×C22⋊C4—1341no—
510C2×C22⋊C4—1341no—
511C2×C22⋊C4—1341no—
512C2×C42—21no—
513C2×C42—671no—
514C2×C42—671no—
515C2×C42—671no—
516C2×C42—674no—
517C2×C42—674no—
518C2×C42—1348no—
519C2×C42—1341no—
520C2×C42—1341no—
521C2×C42—1341no—
522C2×C42—1341no—
523C2×C42C22×D6711yescharacteristic
524#107—674no—
525#107—674no—
526#107—674no—
527#107C22×D6714yes—
528#106—674no—
529#106—674no—
530#106—674no—
531#106C22×D6714yes—
532C4⋊C8—674no—
533C4⋊C8—674no—
534C4⋊C8—674no—
535C4⋊C8C22×D6714yes—
536#103—674no—
537#103—674no—
538#103C22×D6714yes—
539#103C22×D6714yes—
540#102—674no—
541#102—674no—
542#102—674no—
543#102—674no—
544C24—671no—
545C24—1341no—
546#41—6716no—
547#41—13416no—
548#41—1348no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—2684no—
552C2×Q8—2684no—
553C2×Q8—1344no—
554C2×Q8—1344no—
555C2×Q8Q8×D6714yes—
556C2×Q8C23×D6712yes—
557C2×D4—674no—
558C2×D4—672no—
559C2×D4—1344no—
560C2×D4—1348no—
561C2×D4—1341no—
562C2×D4—1342no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—2684no—
568C22×C4—2682no—
569C22×C4—2684no—
570C22×C4—674no—
571C22×C4—671no—
572C22×C4—671no—
573C22×C4—672no—
574C22×C4—674no—
575C22×C4—674no—
576C22×C4—672no—
577C22×C4—671no—
578C22×C4—674no—
579C22×C4—1344no—
580C22×C4—1344no—
581C22×C4—1344no—
582C22×C4—1348no—
583C22×C4—1341no—
584C22×C4—1341no—
585C22×C4—1341no—
586C22×C4—1344no—
587C22×C4D4×D6711yescharacteristic
588C22×C4D4×D6711yescharacteristic
589C22×C4C23×D6711yescharacteristic
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—672no—
593C2×C8—672no—
594C2×C8—1348no—
595C2×C8—1348no—
596C2×C8—1342no—
597C2×C8—1342no—
598C2×C8C23×D6712yes—
599C2×C8C23×D6712yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—672no—
607C4⋊C4—672no—
608C4⋊C4—672no—
609C4⋊C4—1344no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4—1341no—
613C4⋊C4—1341no—
614C4⋊C4—1341no—
615C4⋊C4—1344no—
616C4⋊C4—1344no—
617C4⋊C4C23×D6712yes—
618C4⋊C4C23×D6712yes—
619C4⋊C4C23×D6712yes—
620C22⋊C4—1344no—
621C22⋊C4—1344no—
622C22⋊C4—1344no—
623C22⋊C4—1344no—
624C22⋊C4—1344no—
625C42—24no—
626C42—674no—
627C42—674no—
628C42—672no—
629C42—672no—
630C42—1344no—
631C42—1344no—
632C42—1344no—
633C42—1344no—
634C42D4×D6712yes—
635C42C23×D6712yes—
636C23—2682no—
637C23—2682no—
638C23—674no—
639C23—672no—
640C23—1344no—
641C23—1342no—
642C23—1342no—
643C23—1342no—
644C23C2×D4×D6711yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—2688no—
648Q8—2688no—
649Q8C2×Q8×D6714yes—
650D4—674no—
651D4—13416no—
652D4—1344no—
653D4—1342no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—2688no—
665C2×C4—2684no—
666C2×C4—2688no—
667C2×C4—2682no—
668C2×C4—2682no—
669C2×C4—2682no—
670C2×C4—674no—
671C2×C4—674no—
672C2×C4—672no—
673C2×C4—672no—
674C2×C4—678no—
675C2×C4—674no—
676C2×C4—674no—
677C2×C4—672no—
678C2×C4—1348no—
679C2×C4—13416no—
680C2×C4—1342no—
681C2×C4—1342no—
682C2×C4—1342no—
683C2×C4—1342no—
684C2×C4C2×D4×D6712yes—
685C2×C4C2×D4×D6712yes—
686C2×C4C2×D4×D6711yescharacteristic
687C2×C4C2×Q8×D6712yes—
688C2×C4#41×D6712yes—
689C2×C4C24×D6711yescharacteristic
690C8—22no—
691C8—22no—
692C8—1342no—
693C8—1342no—
694C22—2688no—
695C22—2682no—
696C22—2682no—
697C22—674no—
698C22—1344no—
699C22—1348no—
700C22—1342no—
701C22—1342no—
702C22C22⋊Q8×D6712yes—
703C22#135×D6712yes—
704C22#1686419512yes—
705C22C22×D4×D6711yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—2682no—
713C4—2682no—
714C4—2682no—
715C4—674no—
716C4—674no—
717C4—1342no—
718C4C22⋊Q8×D6712yes—
719C4C22×Q8×D6711yescharacteristic
720C4C2×#41×D6711yescharacteristic
721C2—2684no—
722C2—1344no—
723C2#2256999614yesdirect product factor
724C2C2×C22⋊Q8×D6711yescharacteristic
725C2C2×#135×D6711yescharacteristic
726C2C2×#1686419511yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#479×C67C2
socleC23×C67C22×D4
prime radicalC22×#11761629C22
hypercenterC2×#479D67
hypocenterC67C2×#3076
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#16863952C2semidirect
3. #22569996C2direct (N × H)
4. C2×#16863703C2semidirect
5. C2×#16863689C2semidirect
6. C2×#16863679C2semidirect
7. C2×#16863697C2semidirect
8. C2×#16863693C2semidirect
9. C2×#16863685C2semidirect
10. C2×#16863675C2semidirect
11. C2×#16863433C2semidirect
12. C2×#16863431C2semidirect
13. C2×C4⋊C8×D67C2semidirect
16. C2×#479×C67C2semidirect
21. #16863952C22semidirect
42. #16863703C22semidirect
43. #16863697C22semidirect
44. #16863693C22semidirect
45. #16863689C22semidirect
46. #16863685C22semidirect
47. #16863679C22semidirect
48. #16863675C22semidirect
49. #16863433C22semidirect
50. #16863431C22semidirect
60. C4⋊C8×D67C22semidirect
71. #479×C67C22semidirect
79. C2×#11761629Q8semidirect
184. #11761629C2×Q8semidirect
358. C2×C67#3076semidirect
368. C2×#479D67semidirect
380. C67C2×#3076semidirect
409. #479C2×D67semidirect
723. C2#22569996direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639522
C2×C4×#117616292
#225699962
C2×#168637032
C2×#168636892
C2×#168636792
C2×#168636972
C2×#168636932
C2×#168636852
C2×#168636752
C2×#168634332
C2×#168634312
C2×C4⋊C8×D672
C2×#168633912
C2×#479×C672
C2×#307667