Finite Group Databasebeta

← C2×#22570057 #31723409

Subgroups — C2×#22570057 #31723409

Order 17152.

2094 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×#16864023C211yesmaximal, characteristic, complemented
2C2×#16863878C211yesmaximal, characteristic
3#22570057C2116yesmaximal, direct product factor
4C2×#16863703C211yesmaximal, characteristic, complemented
5C2×#16863701C211yesmaximal, characteristic, complemented
6C2×#16863689C211yesmaximal, characteristic, complemented
7C2×#16863699C211yesmaximal, characteristic, complemented
8C2×#16863697C211yesmaximal, characteristic, complemented
9C2×#16863675C211yesmaximal, characteristic, complemented
10C2×#16863673C211yesmaximal, characteristic, complemented
11C2×#16863437C211yesmaximal, characteristic, complemented
12C2×#107×D67C211yesmaximal, characteristic, complemented
13C2×#16863421C211yesmaximal, characteristic, complemented
14C2×#16863396C211yesmaximal, characteristic
15C2×#16863391C211yesmaximal, characteristic
16C2×#477×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×#11761611C2211yescharacteristic
19C22×C8×D67C2211yescharacteristic
20#16864023—24no—
21#16864023C2218yescomplemented
22C2×#14524042C2211yescharacteristic
23C2×#14524041—21no—
24C2×#14524035C2211yescharacteristic
25C2×#14524034C2211yescharacteristic
26C2×#14524033—21no—
27C2×#14524021—21no—
28C2×#14524019—21no—
29#16863878—24no—
30#16863878C2218yes—
31C2×Q8×Dic67C2211yescharacteristic
32C2×C4×D268—21no—
33C2×C4×D268C2211yescharacteristic
34C2×#14524005—21no—
35C2×#14524005C2211yescharacteristic
36C2×#14524001C2211yescharacteristic
37C2×#14524000—21no—
38C2×#14524000C2211yescharacteristic
39C2×C4⋊C4×D67—21no—
40C2×C4⋊C4×D67C2211yescharacteristic
41C2×C4⋊C4×D67C2211yescharacteristic
42#16863703C2218yescomplemented
43#16863701C2218yescomplemented
44#16863699C2218yescomplemented
45#16863697C2218yescomplemented
46#16863689C2218yescomplemented
47#16863675C2218yescomplemented
48#16863673C2218yescomplemented
49#16863437C2218yescomplemented
50C2×#14523977C2211yescharacteristic
51C2×#14523976C2211yescharacteristic
52C2×#14523976C2211yescharacteristic
53C2×#14523976C2211yescharacteristic
54#107×D67C2218yescomplemented
55C2×#14523975C2211yescharacteristic
56C2×#14523974C2211yescharacteristic
57#16863421C2218yescomplemented
58C2×C4⋊(C67⋊C8)C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C2×Dic67⋊C8C2211yescharacteristic
61#16863396C2218yes—
62#16863391C2218yes—
63C2×#14523967C2211yescharacteristic
64C2×#14523967C2211yescharacteristic
65C2×#14523965C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523963C2211yescharacteristic
68C2×#14523963C2211yescharacteristic
69C2×C4⋊Q8×C67C2211yescharacteristic
70C2×C4×Q8×C67C2211yescharacteristic
71#477×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic
73C2×#107×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×D268—21no—
83C22×D268C2311yescharacteristic
84C22×C4×D67—21no—
85C22×C4×D67—21no—
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88C22×C4×D67—21no—
89C22×C4×D67C2311yescharacteristic
90C2×#11761611—24no—
91C2×#11761611C2314yes—
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94C2×C8×D67—24no—
95C2×C8×D67C2314yes—
96#14524042—22no—
97#14524042C2314yes—
98#14524041—28no—
99#14524035—22no—
100#14524035C2314yes—
101#14524034—22no—
102#14524034C2314yes—
103#14524033—28no—
104#14524021—28no—
105#14524019—28no—
106Q8×Dic67—22no—
107Q8×Dic67C2314yes—
108C4×D268—28no—
109C4×D268—22no—
110C4×D268C2314yes—
111#14524005—28no—
112#14524005—22no—
113#14524005C2314yes—
114#14524001—22no—
115#14524001C2314yes—
116#14524000—28no—
117#14524000D414yes—
118#14524000C2314yes—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4D411yescharacteristic
131C2×Dic67⋊C4D411yescharacteristic
132C4⋊C4×D67—22no—
133C4⋊C4×D67—22no—
134C4⋊C4×D67—28no—
135C4⋊C4×D67C2314yes—
136C4⋊C4×D67C2314yes—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×(C2×D67)⋊C4D411yescharacteristic
141C2×(C2×D67)⋊C4D411yescharacteristic
142C2×C4×Dic67—21no—
143C2×C4×Dic67—21no—
144C2×C4×Dic67C2311yescharacteristic
145#14523977C2314yes—
146#14523976C2314yes—
147#14523976C2314yes—
148#14523976C2314yes—
149#14523975C2314yes—
150#14523974C2314yes—
151C4⋊(C67⋊C8)C2314yes—
152Dic67⋊C8C2314yes—
153Dic67⋊C8C2314yes—
154#14523967C2314yes—
155#14523967C2314yes—
156#14523965C2314yes—
157#14523965C2314yes—
158#14523963C2314yes—
159#14523963C2314yes—
160C22×Q8×C67—21no—
161C22×Q8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163C22×C8×C67C2311yescharacteristic
164C4⋊Q8×C67—22no—
165C4⋊Q8×C67C2314yes—
166C4×Q8×C67—22no—
167C4×Q8×C67C2314yes—
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#107×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—82no—
187C2×D268—28no—
188C2×D268—24no—
189C2×D268—21no—
190C2×D268—22no—
191C2×D268C2×Q814yes—
192C2×D268C2412yes—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67C2×D411yescharacteristic
197C22×Dic67C2×D411yescharacteristic
198C22×Dic67C2×D411yescharacteristic
199C2×C4×D67—28no—
200C2×C4×D67—24no—
201C2×C4×D67—24no—
202C2×C4×D67—24no—
203C2×C4×D67—24no—
204C2×C4×D67—24no—
205C2×C4×D67—82no—
206C2×C4×D67—82no—
207C2×C4×D67—82no—
208C2×C4×D67—82no—
209C2×C4×D67C2×D412yes—
210C2×C4×D67C2×Q814yes—
211C2×C4×D67#4114yes—
212C2×C4×D67C2412yes—
213#11761611—28no—
214C2×C67⋊C8—22no—
215C2×C67⋊C8—22no—
216C2×C67⋊C8C2412yes—
217C2×C67⋊C8C2412yes—
218C8×D67—28no—
219C4⋊Dic67—21no—
220C4⋊Dic67—21no—
221C4⋊Dic67—21no—
222C4⋊Dic67—24no—
223C4⋊Dic67—24no—
224C4⋊Dic67C2412yes—
225C4⋊Dic67C2412yes—
226C4⋊Dic67C2412yes—
227Dic67⋊C4—24no—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231Dic67⋊C4—24no—
232Dic67⋊C4—24no—
233Dic67⋊C4C2×D414yes—
234Dic67⋊C4C2×D414yes—
235(C2×D67)⋊C4—24no—
236(C2×D67)⋊C4—24no—
237(C2×D67)⋊C4—24no—
238(C2×D67)⋊C4C2×D414yes—
239(C2×D67)⋊C4C2×D414yes—
240C4×Dic67—24no—
241C4×Dic67—24no—
242C4×Dic67C2×D412yes—
243C4×Dic67C2412yes—
244C2×Q8×C67—21no—
245C2×Q8×C67—24no—
246C2×Q8×C67—22no—
247C2×Q8×C67—82no—
248C2×Q8×C67C2×Q814yes—
249C2×Q8×C67C2412yes—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67—21no—
253C22×C4×C67—21no—
254C22×C4×C67C2×D411yescharacteristic
255C22×C4×C67C2×D411yescharacteristic
256C22×C4×C67C2411yescharacteristic
257C2×C8×C67—22no—
258C2×C8×C67—22no—
259C2×C8×C67C2412yes—
260C2×C8×C67C2412yes—
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×C67—84no—
284Q8×C67C22×Q814yes—
285C2×C4×C67—24no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—42no—
293C2×C4×C67—42no—
294C2×C4×C67—42no—
295C2×C4×C67C22×D412yes—
296C2×C4×C67C22×D412yes—
297C2×C4×C67C22×D411yescharacteristic
298C2×C4×C67C22×Q812yes—
299C2×C4×C67C2×#4112yes—
300C2×C4×C67C2511yescharacteristic
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—42no—
307C2×Dic67—42no—
308C2×Dic67—42no—
309C2×Dic67C22⋊Q814yes—
310C2×Dic67C22×D412yes—
311C2×Dic67C22×D412yes—
312C2×Dic67C22×D412yes—
313D268—216no—
314D268—24no—
315D268—22no—
316D268C22×Q814yes—
317C4×D67—216no—
318C4×D67—84no—
319C4×D67—84no—
320C4×D67—84no—
321C4×D67—84no—
322C4×D67C22⋊Q818yes—
323C4×D67C22×Q814yes—
324C4×D67C2×#4114yes—
325Dic134—84no—
326C8×C67—22no—
327C8×C67—22no—
328C67⋊C8—22no—
329C67⋊C8—22no—
330C22×C67C2×C22⋊Q812yes—
331C22×C67#57612yes—
332C22×C67#57812yes—
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—22no—
353Dic67—42no—
354Dic67—42no—
355Dic67—42no—
356Dic67C2×C22⋊Q814yes—
357C2×#3083—671nomaximal, Sylow
358C2×C67#308314yescomplemented
359C2×C67C22×C22⋊Q811yescharacteristic
360C2×C67C2×#57611yescharacteristic
361C2×C67C2×#57811yescharacteristic
362D67—24no—
363D67—44no—
364C2×#544—671no—
365C2×#520—671no—
366#3083—6716no—
367C2×#479—671no—
368C2×#479—671no—
369C2×#477—671no—
370C2×#477D6711yescharacteristic, complemented
371C2×#478—671no—
372C2×#478—671no—
373C2×#474—671no—
374C2×#474—671no—
375C2×#428—671no—
376C22×#107—671no—
377C2×#424—671no—
378C2×#417—671no—
379C2×#416—671no—
380C67C2×#308311yescharacteristic, complemented, Sylow
381C22×#41—671no—
382C22×M16—671no—
383C23×C8—671no—
384#544—678no—
385#544—1344no—
386C2×C4⋊Q8—671no—
387C2×C4⋊Q8—1341no—
388C2×C4⋊Q8C2×D6711yescharacteristic
389C2×#125—671no—
390C2×#125—671no—
391C2×#125—1341no—
392C2×C22⋊Q8—1341no—
393C2×C22⋊Q8—1341no—
394#520—678no—
395#520—1344no—
396C2×C4×Q8—671no—
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—1341no—
405C22×C4⋊C4—671no—
406C22×C4⋊C4—671no—
407C22×C4⋊C4—1341no—
408#479—678no—
409#479—678no—
410#478—678no—
411#478—678no—
412#477—678no—
413#477C2×D6718yescomplemented
414#474—678no—
415#474—678no—
416#428—678no—
417C2×#107—671no—
418C2×#107—671no—
419C2×#107—671no—
420C2×#107—671no—
421C2×#107—678no—
422C2×#107C2×D6711yescharacteristic
423C2×#107C2×D6711yescharacteristic
424C2×#106—671no—
425C2×#106—671no—
426#424—678no—
427C2×C4⋊C8—671no—
428C2×C4⋊C8—671no—
429C2×C4⋊C8—671no—
430C2×C4⋊C8C2×D6711yescharacteristic
431#417—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—21no—
446C22×Q8—1341no—
447C22×Q8C22×D6711yescharacteristic
448C22×D4—671no—
449C22×D4—1341no—
450C23×C4—671no—
451C23×C4—1341no—
452C23×C4—1341no—
453C23×C4—1341no—
454C23×C4—1341no—
455C23×C4—1341no—
456C2×M16—674no—
457C2×M16—1344no—
458C22×C8—671no—
459C22×C8—671no—
460C22×C8—674no—
461C22×C8—1344no—
462C22×C8C22×D6711yescharacteristic
463C22×C8C22×D6711yescharacteristic
464C4⋊Q8—22no—
465C4⋊Q8—674no—
466C4⋊Q8—1342no—
467C4⋊Q8—1348no—
468C4⋊Q8C22×D6714yes—
469#125—674no—
470#125—674no—
471#125—1342no—
472#125—1348no—
473#125—1342no—
474C22⋊Q8—1348no—
475C22⋊Q8—1348no—
476C4×Q8—22no—
477C4×Q8—674no—
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—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—671no—
496C2×C4⋊C4—671no—
497C2×C4⋊C4—671no—
498C2×C4⋊C4—674no—
499C2×C4⋊C4—674no—
500C2×C4⋊C4—1348no—
501C2×C4⋊C4—1342no—
502C2×C4⋊C4—1342no—
503C2×C4⋊C4—1341no—
504C2×C4⋊C4—1341no—
505C2×C4⋊C4—1341no—
506C2×C4⋊C4—1341no—
507C2×C4⋊C4—1341no—
508C2×C4⋊C4—1341no—
509C2×C4⋊C4—1341no—
510C2×C4⋊C4—1341no—
511C2×C4⋊C4C22×D6711yescharacteristic
512C2×C4⋊C4C22×D6711yescharacteristic
513C2×C4⋊C4C22×D6711yescharacteristic
514C2×C22⋊C4—671no—
515C2×C22⋊C4—671no—
516C2×C22⋊C4—1341no—
517C2×C22⋊C4—1341no—
518C2×C22⋊C4—1341no—
519C2×C42—21no—
520C2×C42—671no—
521C2×C42—1341no—
522C2×C42—1341no—
523C2×C42C22×D6711yescharacteristic
524#107—674no—
525#107—674no—
526#107—674no—
527#107—674no—
528#107C22×D6714yes—
529#107C22×D6714yes—
530#106—674no—
531#106—674no—
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—24no—
551C2×Q8—22no—
552C2×Q8—82no—
553C2×Q8—5362no—
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—5362no—
568C22×C4—5362no—
569C22×C4—5362no—
570C22×C4—5362no—
571C22×C4—671no—
572C22×C4—672no—
573C22×C4—674no—
574C22×C4—674no—
575C22×C4—672no—
576C22×C4—671no—
577C22×C4—671no—
578C22×C4—1344no—
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
590M16—1348no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—672no—
594C2×C8—672no—
595C2×C8—1348no—
596C2×C8—1342no—
597C2×C8—1342no—
598C2×C8C23×D6712yes—
599C2×C8C23×D6712yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—674no—
606C4⋊C4—674no—
607C4⋊C4—672no—
608C4⋊C4—672no—
609C4⋊C4—672no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4—1344no—
613C4⋊C4—1344no—
614C4⋊C4—1344no—
615C4⋊C4—1344no—
616C4⋊C4—1341no—
617C4⋊C4—1341no—
618C4⋊C4—1341no—
619C4⋊C4—1344no—
620C4⋊C4—1344no—
621C4⋊C4C23×D6712yes—
622C4⋊C4C23×D6712yes—
623C4⋊C4C23×D6712yes—
624C22⋊C4—674no—
625C22⋊C4—674no—
626C22⋊C4—1344no—
627C22⋊C4—1344no—
628C22⋊C4—1344no—
629C42—24no—
630C42—672no—
631C42—672no—
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—84no—
648Q8—5364no—
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—2682no—
665C2×C4—2682no—
666C2×C4—2682no—
667C2×C4—5364no—
668C2×C4—5364no—
669C2×C4—5364no—
670C2×C4—5364no—
671C2×C4—674no—
672C2×C4—672no—
673C2×C4—678no—
674C2×C4—674no—
675C2×C4—674no—
676C2×C4—672no—
677C2×C4—672no—
678C2×C4—13416no—
679C2×C4—1342no—
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#1686420012yes—
704C22#1686420912yes—
705C22C22×D4×D6711yescharacteristic
706C4—22no—
707C4—24no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—2682no—
713C4—2682no—
714C4—2682no—
715C4—674no—
716C4—1342no—
717C4—1342no—
718C4C22⋊Q8×D6712yes—
719C4C22×Q8×D6711yescharacteristic
720C4C2×#41×D6711yescharacteristic
721C2—2684no—
722C2—1344no—
723C2#2257005714yesdirect product factor
724C2C2×C22⋊Q8×D6711yescharacteristic
725C2C2×#1686420011yescharacteristic
726C2C2×#1686420911yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#477×C67C2
socleC23×C67C22×D4
prime radicalC22×#11761629C22
hypercenterC2×#477D67
hypocenterC67C2×#3083
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#16864023C2semidirect
3. #22570057C2direct (N × H)
4. C2×#16863703C2semidirect
5. C2×#16863701C2semidirect
6. C2×#16863689C2semidirect
7. C2×#16863699C2semidirect
8. C2×#16863697C2semidirect
9. C2×#16863675C2semidirect
10. C2×#16863673C2semidirect
11. C2×#16863437C2semidirect
12. C2×#107×D67C2semidirect
13. C2×#16863421C2semidirect
16. C2×#477×C67C2semidirect
21. #16864023C22semidirect
42. #16863703C22semidirect
43. #16863701C22semidirect
44. #16863699C22semidirect
45. #16863697C22semidirect
46. #16863689C22semidirect
47. #16863675C22semidirect
48. #16863673C22semidirect
49. #16863437C22semidirect
54. #107×D67C22semidirect
57. #16863421C22semidirect
71. #477×C67C22semidirect
79. C2×#11761629Q8semidirect
184. #11761629C2×Q8semidirect
358. C2×C67#3083semidirect
370. C2×#477D67semidirect
380. C67C2×#3083semidirect
413. #477C2×D67semidirect
723. C2#22570057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640232
C2×#168638782
#225700572
C2×#168637032
C2×#168637012
C2×#168636892
C2×#168636992
C2×#168636972
C2×#168636752
C2×#168636732
C2×#168634372
C2×#107×D672
C2×#168634212
C2×#168633962
C2×#168633912
C2×#477×C672
C2×#308367