Finite Group Databasebeta

← C2×#22572688 #31734404

Subgroups — C2×#22572688 #31734404

Order 17152.

1942 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×#16864092C211yesmaximal, characteristic
2#22572688C2116yesmaximal, direct product factor
3C2×#16863802C211yesmaximal, characteristic, complemented
4C2×#16863729C211yesmaximal, characteristic, complemented
5C2×#16863714C211yesmaximal, characteristic, complemented
6C2×#16863734C211yesmaximal, characteristic, complemented
7C2×#16863709C211yesmaximal, characteristic, complemented
8C2×#16863703C211yesmaximal, characteristic, complemented
9C2×#16863673C211yesmaximal, characteristic, complemented
10C2×#16863644C211yesmaximal, characteristic, complemented
11C2×#16863627C211yesmaximal, characteristic, complemented
12C2×#16863494C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic, complemented
14C2×#16863436C211yesmaximal, characteristic, complemented
15C22×#14523976C211yesmaximal, characteristic, complemented
16C2×#554×C67C211yesmaximal, characteristic, complemented
17C22×#11761615C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19C23×C67⋊C8C2211yescharacteristic
20#16864092—24no—
21#16864092C2218yes—
22C2×#14524038—21no—
23C2×#14524035C2211yescharacteristic
24C2×#14524025—21no—
25C2×#14524017C2211yescharacteristic
26C2×#14524017C2211yescharacteristic
27C2×#14524015—21no—
28C2×C4×D268C2211yescharacteristic
29C2×(C22⋊D67)⋊C4—21no—
30C2×#14524002C2211yescharacteristic
31C22×C4⋊Dic67C2211yescharacteristic
32#16863802C2218yescomplemented
33#16863734C2218yescomplemented
34#16863729C2218yescomplemented
35#16863714C2218yescomplemented
36#16863709C2218yescomplemented
37#16863703C2218yescomplemented
38#16863673C2218yescomplemented
39#16863644C2218yescomplemented
40#16863627C2218yescomplemented
41#16863494C2218yescomplemented
42#16863468C2218yescomplemented
43#16863436C2218yescomplemented
44C2×#14523976C2211yescharacteristic
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523976C2211yescharacteristic
49C2×#14523976C2211yescharacteristic
50C2×#14523976C2218yescomplemented
51C2×#14523974C2211yescharacteristic
52C2×#14523974C2211yescharacteristic
53C2×#14523974C2211yescharacteristic
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523967C2211yescharacteristic
57C2×#14523967C2211yescharacteristic
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
77C22×D268C2311yescharacteristic
78C22×C22⋊D67—21no—
79C22×C22⋊D67—21no—
80C23×Dic67—21no—
81C22×C4×D67—21no—
82C2×#11761615—24no—
83C2×#11761615C2314yes—
84C2×#11761612—24no—
85C2×#11761612C2314yes—
86C22×C67⋊C8—24no—
87C22×C67⋊C8C2311yescharacteristic
88C22×C67⋊C8C2311yescharacteristic
89C22×C67⋊C8C2311yescharacteristic
90C22×C67⋊C8C2314yes—
91C22×C67⋊C8C2311yescharacteristic
92#14524038—28no—
93#14524035—22no—
94#14524035C2314yes—
95#14524025—28no—
96#14524017—22no—
97#14524017—22no—
98#14524017C2314yes—
99#14524017C2314yes—
100#14524015—28no—
101C4×D268—22no—
102C4×D268C2314yes—
103(C22⋊D67)⋊C4—28no—
104#14524002—22no—
105#14524002C2314yes—
106C2×C4⋊Dic67—22no—
107C2×C4⋊Dic67—21no—
108C2×C4⋊Dic67C2314yes—
109C2×C4⋊Dic67C2311yescharacteristic
110C2×C4⋊Dic67C2311yescharacteristic
111C2×C4⋊Dic67C2311yescharacteristic
112C2×Dic67⋊C4—21no—
113C2×Dic67⋊C4—21no—
114C2×C22⋊Dic67—21no—
115C2×(C2×D67)⋊C4—21no—
116C2×(C2×D67)⋊C4—21no—
117C2×(C2×D67)⋊C4—21no—
118C2×C4×Dic67—21no—
119#14523976C2314yes—
120#14523976C2314yes—
121#14523976C2314yes—
122#14523976C2314yes—
123#14523976C2314yes—
124#14523976C2314yes—
125#14523974C2314yes—
126#14523974C2314yes—
127#14523974C2314yes—
128C4⋊(C67⋊C8)C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523967C2314yes—
132#14523963C2314yes—
133#14523963C2314yes—
134#14523963C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137#14523954C2314yes—
138C22×Q8×C67—21no—
139C22×Q8×C67C2311yescharacteristic
140C22×D4×C67D411yescharacteristic
141C23×C4×C67—21no—
142C23×C4×C67—21no—
143C23×C4×C67C2311yescharacteristic
144C23×C4×C67C2311yescharacteristic
145C4⋊Q8×C67—22no—
146C4⋊Q8×C67C2314yes—
147#125×C67—28no—
148C22⋊Q8×C67—22no—
149C22⋊Q8×C67—22no—
150C22⋊Q8×C67—28no—
151C22⋊Q8×C67—28no—
152C22⋊Q8×C67C2314yes—
153C22⋊Q8×C67C2314yes—
154C4×Q8×C67—22no—
155C4×Q8×C67C2314yes—
156C4×D4×C67—28no—
157C4×D4×C67D414yes—
158C4×D4×C67C2314yes—
159C2×C4⋊C4×C67—21no—
160C2×C4⋊C4×C67—21no—
161C2×C4⋊C4×C67—22no—
162C2×C4⋊C4×C67—22no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2314yes—
172C2×C4⋊C4×C67C2314yes—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67D411yescharacteristic
176C2×C22⋊C4×C67D411yescharacteristic
177C2×C42×C67—21no—
178C2×C42×C67C2311yescharacteristic
179C23×D67—21no—
180C2×D268—22no—
181C2×D268—22no—
182C2×D268—21no—
183C2×D268C2412yes—
184C2×C22⋊D67—24no—
185C2×C22⋊D67—24no—
186C2×C22⋊D67—44no—
187C2×C22⋊D67—82no—
188C22×Dic67—21no—
189C22×Dic67—21no—
190C22×Dic67—21no—
191C22×Dic67—24no—
192C22×Dic67—82no—
193C2×C4×D67—24no—
194C2×C4×D67—82no—
195#11761615—28no—
196#11761612—28no—
197C2×C67⋊C8—22no—
198C2×C67⋊C8—22no—
199C2×C67⋊C8—22no—
200C2×C67⋊C8—28no—
201C2×C67⋊C8#4114yes—
202C2×C67⋊C8C2412yes—
203C2×C67⋊C8C2412yes—
204C2×C67⋊C8C2412yes—
205C2×C67⋊C8C2412yes—
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67—24no—
209C4⋊Dic67—21no—
210C4⋊Dic67C2412yes—
211C4⋊Dic67C2412yes—
212C4⋊Dic67C2412yes—
213Dic67⋊C4—24no—
214Dic67⋊C4—24no—
215C22⋊Dic67—24no—
216(C2×D67)⋊C4—24no—
217(C2×D67)⋊C4—24no—
218(C2×D67)⋊C4—24no—
219C4×Dic67—24no—
220C24×C67C2×D411yescharacteristic
221C24×C67C2×D411yescharacteristic
222C2×Q8×C67—21no—
223C2×Q8×C67—24no—
224C2×Q8×C67—22no—
225C2×Q8×C67—22no—
226C2×Q8×C67—82no—
227C2×Q8×C67C2412yes—
228C2×D4×C67—24no—
229C2×D4×C67C2×D414yes—
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—21no—
238C22×C4×C67—24no—
239C22×C4×C67—24no—
240C22×C4×C67—82no—
241C22×C4×C67—82no—
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D411yescharacteristic
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D412yes—
247C22×C4×C67C2×D412yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2412yes—
250C22×C4×C67C2411yescharacteristic
251C4⋊C4×C67—21no—
252C4⋊C4×C67—24no—
253C4⋊C4×C67—24no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—24no—
257C4⋊C4×C67—24no—
258C4⋊C4×C67—24no—
259C4⋊C4×C67—24no—
260C4⋊C4×C67C2×D414yes—
261C4⋊C4×C67C2412yes—
262C4⋊C4×C67C2412yes—
263C4⋊C4×C67C2412yes—
264C22⋊C4×C67—24no—
265C22⋊C4×C67—24no—
266C22⋊C4×C67C2×D414yes—
267C22⋊C4×C67C2×D414yes—
268C42×C67—24no—
269C42×C67C2×D412yes—
270C42×C67C2412yes—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67#13714yes—
277C23×C67C22×D412yes—
278C23×C67C22×D412yes—
279C23×C67C22×D411yescharacteristic
280C22×D67—22no—
281C22×D67—42no—
282C22×D67—42no—
283C22×D67—42no—
284Q8×C67—22no—
285Q8×C67—22no—
286Q8×C67—42no—
287Q8×C67—84no—
288D4×C67—28no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—24no—
294C2×C4×C67—24no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—42no—
304C2×C4×C67—42no—
305C2×C4×C67—42no—
306C2×C4×C67—42no—
307C2×C4×C67—84no—
308C2×C4×C67—84no—
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×C672−1+412yes—
316C2×C4×C67C2511yescharacteristic
317C22⋊D67—48no—
318C22⋊D67—84no—
319C2×Dic67—22no—
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—42no—
323C2×Dic67—42no—
324C2×Dic67—42no—
325C2×Dic67—84no—
326D268—22no—
327D268—22no—
328D268—42no—
329C4×D67—84no—
330C67⋊C8—22no—
331C67⋊C8—22no—
332C67⋊C8—22no—
333C67⋊C8C2×#4114yes—
334C22×C67—28no—
335C22×C67—22no—
336C22×C67—22no—
337C22×C67—22no—
338C22×C67—22no—
339C22×C67—22no—
340C22×C67—44no—
341C22×C67#54712yes—
342C22×C67C2×#13714yes—
343C22×C67C2×#13712yes—
344C22×C67#57612yes—
345C22×C67C23×D411yescharacteristic
346C2×D67—42no—
347C2×D67—42no—
348C2×D67—42no—
349C2×D67—84no—
350C4×C67—22no—
351C4×C67—22no—
352C4×C67—22no—
353C4×C67—22no—
354C4×C67—42no—
355C4×C67—42no—
356C4×C67—42no—
357C4×C67—42no—
358C4×C67#54712yes—
359C4×C67C22×#4111yescharacteristic
360C4×C67C2×2−1+411yescharacteristic
361Dic67—42no—
362Dic67—42no—
363Dic67—42no—
364C2×#3346—671nomaximal, Sylow
365C2×C67—24no—
366C2×C67—42no—
367C2×C67#334614yescomplemented
368C2×C67C2×#54711yescharacteristic
369C2×C67C22×#13711yescharacteristic
370C2×C67C2×#57611yescharacteristic
371D67—82no—
372C2×#554D6711yescharacteristic, complemented
373C2×#553—671no—
374#3346—6716no—
375C2×#501—671no—
376C2×#484—671no—
377C2×#481—671no—
378C2×#485—671no—
379C2×#480—671no—
380C2×#479—671no—
381C2×#474—671no—
382C2×#468—671no—
383C2×#465—671no—
384C2×#440—671no—
385C2×#435—671no—
386C2×#428—671no—
387C22×#107—671no—
388C67C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—671no—
390C22×M16—671no—
391C23×C8—671no—
392#554—24no—
393#554C2×D6718yescomplemented
394#553—678no—
395#553—1344no—
396C2×C4⋊Q8C2×D6711yescharacteristic
397C2×#126—1341no—
398C2×#125—21no—
399C2×#125—671no—
400C2×#123—1341no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8C2×D6711yescharacteristic
404C2×C22⋊Q8C2×D6711yescharacteristic
405C2×#121—671no—
406C2×#121—671no—
407C2×#121—1341no—
408C2×C4×Q8C2×D6711yescharacteristic
409C2×C4×D4—21no—
410C2×C4×D4—671no—
411C2×C4×D4—1341no—
412C2×C4×D4C2×D6711yescharacteristic
413C2×#117—671no—
414C22×C4⋊C4—671no—
415C22×C4⋊C4C2×D6711yescharacteristic
416C22×C4⋊C4C2×D6711yescharacteristic
417#501—678no—
418#485—678no—
419#484—678no—
420#481—678no—
421#480—678no—
422#479—678no—
423#474—678no—
424#468—678no—
425#465—678no—
426#440—678no—
427#435—678no—
428#428—678no—
429C2×#107—671no—
430C2×#107—671no—
431C2×#107—671no—
432C2×#107—671no—
433C2×#107—678no—
434C2×#107—671no—
435C2×#107—671no—
436C2×#106—671no—
437C2×#106—671no—
438C2×#106—671no—
439C2×C4⋊C8—671no—
440C2×#103—671no—
441C2×#103—671no—
442C2×#103—671no—
443C2×#102—671no—
444C2×#102—671no—
445C2×#102—671no—
446C2×C22⋊C8—671no—
447C2×C22⋊C8—671no—
448C2×#97—671no—
449C22×Q8—21no—
450C22×Q8C22×D6711yescharacteristic
451C22×D4—671no—
452C22×D4—1341no—
453C22×D4—1341no—
454C22×D4C22⋊D6711yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—1341no—
458C23×C4—1341no—
459C23×C4C22×D6711yescharacteristic
460C23×C4C22×D6711yescharacteristic
461C2×SD16—674no—
462C2×SD16—1344no—
463C2×M16—674no—
464C2×M16—1344no—
465C22×C8—671no—
466C22×C8—671no—
467C22×C8—674no—
468C22×C8—671no—
469C22×C8—671no—
470C22×C8—1344no—
471C4⋊Q8—22no—
472C4⋊Q8C22×D6714yes—
473#126—1348no—
474#125—28no—
475#125—674no—
476#125—1342no—
477#123—1348no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8C22×D6714yes—
483C22⋊Q8C22×D6714yes—
484#121—674no—
485#121—674no—
486#121—1348no—
487#121—1342no—
488#121—1342no—
489C4×Q8—22no—
490C4×Q8C22×D6714yes—
491C4×D4—28no—
492C4×D4—674no—
493C4×D4—1348no—
494C4×D4—1342no—
495C4×D4C22⋊D6714yes—
496C4×D4C22×D6714yes—
497#117—674no—
498#117—1342no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—671no—
508C2×C4⋊C4—671no—
509C2×C4⋊C4—674no—
510C2×C4⋊C4—671no—
511C2×C4⋊C4—1341no—
512C2×C4⋊C4—1342no—
513C2×C4⋊C4—1341no—
514C2×C4⋊C4—1341no—
515C2×C4⋊C4C22⋊D6711yescharacteristic
516C2×C4⋊C4C22×D6711yescharacteristic
517C2×C4⋊C4C22×D6711yescharacteristic
518C2×C4⋊C4C22×D6711yescharacteristic
519C2×C4⋊C4C22×D6714yes—
520C2×C4⋊C4C22×D6714yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1341no—
524C2×C22⋊C4—1341no—
525C2×C22⋊C4—1341no—
526C2×C22⋊C4—1341no—
527C2×C22⋊C4C22⋊D6711yescharacteristic
528C2×C22⋊C4C22⋊D6711yescharacteristic
529C2×C42—21no—
530C2×C42—1341no—
531C2×C42C22×D6711yescharacteristic
532#107—674no—
533#107—674no—
534#107—674no—
535#107—674no—
536#107—674no—
537#107—674no—
538#106—674no—
539#106—674no—
540#106—674no—
541C4⋊C8—674no—
542#103—674no—
543#103—674no—
544#103—674no—
545#102—674no—
546#102—674no—
547#102—674no—
548C22⋊C8—674no—
549C22⋊C8—674no—
550#97—674no—
551C24—1341no—
552C24C2×C22⋊D6711yescharacteristic
553C24C2×C22⋊D6711yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C23×D6712yes—
560C2×D4—24no—
561C2×D4—2684no—
562C2×D4—5362no—
563C2×D4—672no—
564C2×D4—1344no—
565C2×D4—1344no—
566C2×D4—1341no—
567C2×D4—1342no—
568C2×D4—1342no—
569C2×D4C2×C22⋊D6714yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—5362no—
583C22×C4—5362no—
584C22×C4—1341no—
585C22×C4—1341no—
586C22×C4—1341no—
587C22×C4—1344no—
588C22×C4—1344no—
589C22×C4C2×C22⋊D6712yes—
590C22×C4C2×C22⋊D6712yes—
591C22×C4C2×C22⋊D6711yescharacteristic
592C22×C4C2×C22⋊D6711yescharacteristic
593C22×C4C2×C22⋊D6711yescharacteristic
594C22×C4C2×C22⋊D6711yescharacteristic
595C22×C4C23×D6712yes—
596C22×C4C23×D6712yes—
597C22×C4C23×D6711yescharacteristic
598SD16—1348no—
599M16—1348no—
600C2×C8—674no—
601C2×C8—672no—
602C2×C8—672no—
603C2×C8—672no—
604C2×C8—672no—
605C2×C8—1348no—
606C2×C8—1342no—
607C2×C8—1342no—
608C2×C8—1342no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—672no—
619C4⋊C4—672no—
620C4⋊C4—672no—
621C4⋊C4—1341no—
622C4⋊C4—1341no—
623C4⋊C4—1344no—
624C4⋊C4—1341no—
625C4⋊C4—1344no—
626C4⋊C4—1344no—
627C4⋊C4C2×C22⋊D6714yes—
628C4⋊C4C23×D6712yes—
629C4⋊C4C23×D6712yes—
630C4⋊C4C23×D6712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1344no—
634C22⋊C4—1344no—
635C22⋊C4—1344no—
636C22⋊C4—1344no—
637C22⋊C4C2×C22⋊D6714yes—
638C22⋊C4C2×C22⋊D6714yes—
639C42—24no—
640C42—1344no—
641C42C2×C22⋊D6712yes—
642C42C23×D6712yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—2682no—
649C23—2682no—
650C23—2682no—
651C23—1342no—
652C23#1452407414yes—
653C23C22×C22⋊D6712yes—
654C23C22×C22⋊D6712yes—
655C23C22×C22⋊D6711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—2688no—
662D4—2682no—
663D4—5364no—
664D4—1342no—
665D4—1342no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—2682no—
687C2×C4—2682no—
688C2×C4—2682no—
689C2×C4—5364no—
690C2×C4—5364no—
691C2×C4—1342no—
692C2×C4—1342no—
693C2×C4—1342no—
694C2×C4C22×C22⋊D6712yes—
695C2×C4C22×C22⋊D6712yes—
696C2×C4C22×C22⋊D6712yes—
697C2×C4C22×C22⋊D6712yes—
698C2×C4C22×C22⋊D6711yescharacteristic
699C2×C4#41×D6712yes—
700C2×C4#1452409012yes—
701C2×C4C24×D6711yescharacteristic
702C8—674no—
703C8—1342no—
704C8—1342no—
705C8—1342no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—2682no—
714C22—2682no—
715C22—2682no—
716C22—5364no—
717C22#1686404512yes—
718C22C2×#1452407414yes—
719C22C2×#1452407412yes—
720C22#1686419912yes—
721C22C23×C22⋊D6711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—2682no—
731C4—2682no—
732C4—2682no—
733C4#1686404512yes—
734C4C2×#41×D6711yescharacteristic
735C4C2×#1452409011yescharacteristic
736C2—24no—
737C2—42no—
738C2—5362no—
739C2#2257268814yesdirect product factor
740C2C2×#1686404511yescharacteristic
741C2C22×#1452407411yescharacteristic
742C2C2×#1686419911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#554×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864092C2
hypercenterC2×#554D67
hypocenterC67C2×#3346
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. #22572688C2direct (N × H)
3. C2×#16863802C2semidirect
4. C2×#16863729C2semidirect
5. C2×#16863714C2semidirect
6. C2×#16863734C2semidirect
7. C2×#16863709C2semidirect
8. C2×#16863703C2semidirect
9. C2×#16863673C2semidirect
10. C2×#16863644C2semidirect
11. C2×#16863627C2semidirect
12. C2×#16863494C2semidirect
13. C2×#16863468C2semidirect
14. C2×#16863436C2semidirect
15. C22×#14523976C2semidirect
16. C2×#554×C67C2semidirect
32. #16863802C22semidirect
33. #16863734C22semidirect
34. #16863729C22semidirect
35. #16863714C22semidirect
36. #16863709C22semidirect
37. #16863703C22semidirect
38. #16863673C22semidirect
39. #16863644C22semidirect
40. #16863627C22semidirect
41. #16863494C22semidirect
42. #16863468C22semidirect
43. #16863436C22semidirect
50. C2×#14523976C22semidirect
65. #554×C67C22semidirect
367. C2×C67#3346semidirect
372. C2×#554D67semidirect
388. C67C2×#3346semidirect
393. #554C2×D67semidirect
739. C2#22572688direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640922
#225726882
C2×#168638022
C2×#168637292
C2×#168637142
C2×#168637342
C2×#168637092
C2×#168637032
C2×#168636732
C2×#168636442
C2×#168636272
C2×#168634942
C2×#168634682
C2×#168634362
C22×#145239762
C2×#554×C672
C2×#334667