Finite Group Databasebeta

← C2×#22572696 #31734412

Subgroups — C2×#22572696 #31734412

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×#16864103C211yesmaximal, characteristic, complemented
2C2×#16864092C211yesmaximal, characteristic
3#22572696C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863732C211yesmaximal, characteristic, complemented
6C2×#16863715C211yesmaximal, characteristic, complemented
7C2×#16863738C211yesmaximal, characteristic, complemented
8C2×#16863710C211yesmaximal, characteristic, complemented
9C2×#16863704C211yesmaximal, characteristic, complemented
10C2×#16863677C211yesmaximal, characteristic, complemented
11C2×#16863642C211yesmaximal, characteristic, complemented
12C2×#16863625C211yesmaximal, characteristic, complemented
13C2×#16863498C211yesmaximal, characteristic, complemented
14C2×#16863438C211yesmaximal, characteristic, complemented
15C22×#14523977C211yesmaximal, characteristic, complemented
16C2×#435×C67C211yesmaximal, characteristic, complemented
17C22×#11761617C2211yescharacteristic
18#16864103—24no—
19#16864103C2218yescomplemented
20#16864092—24no—
21#16864092C2218yes—
22C2×#14524043C2211yescharacteristic
23C2×#14524038—21no—
24C2×#14524035C2211yescharacteristic
25C2×#14524034—21no—
26C2×#14524025—21no—
27C2×#14524022C2211yescharacteristic
28C2×#14524022C2211yescharacteristic
29C2×#14524020—21no—
30C2×#14524020—21no—
31C2×#14524017C2211yescharacteristic
32C2×#14524017C2211yescharacteristic
33C2×#14524015—21no—
34C2×C4×Dic134C2211yescharacteristic
35C2×C4×D268C2211yescharacteristic
36C2×D4×Dic67—21no—
37C2×(C22⋊D67)⋊C4—21no—
38C2×#14524002C2211yescharacteristic
39C22×C4⋊Dic67C2211yescharacteristic
40C22×C4⋊Dic67C2211yescharacteristic
41C22×C4⋊Dic67C2211yescharacteristic
42#16863805C2218yescomplemented
43#16863738C2218yescomplemented
44#16863732C2218yescomplemented
45#16863715C2218yescomplemented
46#16863710C2218yescomplemented
47#16863704C2218yescomplemented
48#16863677C2218yescomplemented
49#16863642C2218yescomplemented
50#16863625C2218yescomplemented
51#16863498C2218yescomplemented
52#16863438C2218yescomplemented
53C2×#14523977C2211yescharacteristic
54C2×#14523977C2211yescharacteristic
55C2×#14523977C2211yescharacteristic
56C2×#14523977C2211yescharacteristic
57C2×#14523977C2211yescharacteristic
58C2×#14523977C2211yescharacteristic
59C2×#14523977C2218yescomplemented
60C2×#14523975C2211yescharacteristic
61C2×#14523975C2211yescharacteristic
62C2×#14523975C2211yescharacteristic
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523968C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523965C2211yescharacteristic
68C2×#14523965C2211yescharacteristic
69C22×M16×C67C2211yescharacteristic
70C23×C8×C67C2211yescharacteristic
71C2×C4×D4×C67C2211yescharacteristic
72#435×C67C2218yescomplemented
73C2×C4⋊C8×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C22⋊C8×C67C2211yescharacteristic
76C2×#97×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C22×D268C2311yescharacteristic
80C22×C22⋊D67—21no—
81C22×C22⋊D67—21no—
82C23×Dic67—21no—
83C23×Dic67—21no—
84C23×Dic67—21no—
85C22×C4×D67—21no—
86C2×#11761617—24no—
87C2×#11761617C2314yes—
88#14524043—22no—
89#14524043C2314yes—
90#14524038—28no—
91#14524035—22no—
92#14524035C2314yes—
93#14524034—28no—
94#14524025—28no—
95#14524022—22no—
96#14524022—22no—
97#14524022C2314yes—
98#14524022C2314yes—
99#14524020—28no—
100#14524020—28no—
101#14524017—22no—
102#14524017—22no—
103#14524017C2314yes—
104#14524017C2314yes—
105#14524015—28no—
106C4×Dic134—22no—
107C4×Dic134C2314yes—
108C4×D268—22no—
109C4×D268C2314yes—
110D4×Dic67—28no—
111(C22⋊D67)⋊C4—28no—
112#14524002—22no—
113#14524002C2314yes—
114C2×C4⋊Dic67—22no—
115C2×C4⋊Dic67—22no—
116C2×C4⋊Dic67—22no—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67C2314yes—
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2314yes—
124C2×C4⋊Dic67C2314yes—
125C2×C4⋊Dic67C2311yescharacteristic
126C2×C4⋊Dic67C2311yescharacteristic
127C2×C4⋊Dic67C2311yescharacteristic
128C2×C4⋊Dic67C2311yescharacteristic
129C2×C4⋊Dic67C2311yescharacteristic
130C2×Dic67⋊C4—21no—
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4—21no—
133C2×Dic67⋊C4—21no—
134C2×Dic67⋊C4—21no—
135C2×C22⋊Dic67—21no—
136C2×C22⋊Dic67—21no—
137C2×C22⋊Dic67—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×(C2×D67)⋊C4—21no—
141C2×C4×Dic67—21no—
142C2×C4×Dic67—21no—
143#14523977C2314yes—
144#14523977C2314yes—
145#14523977C2314yes—
146#14523977C2314yes—
147#14523977C2314yes—
148#14523977C2314yes—
149#14523975C2314yes—
150#14523975C2314yes—
151#14523975C2314yes—
152#14523968C2314yes—
153#14523968C2314yes—
154#14523968C2314yes—
155#14523965C2314yes—
156#14523965C2314yes—
157#14523965C2314yes—
158C22×D4×C67D411yescharacteristic
159C23×C4×C67C2311yescharacteristic
160C23×C4×C67C2311yescharacteristic
161C2×M16×C67—24no—
162C2×M16×C67C2314yes—
163C22×C8×C67—24no—
164C22×C8×C67C2314yes—
165C22×C8×C67C2311yescharacteristic
166C22×C8×C67C2311yescharacteristic
167C22×C8×C67C2311yescharacteristic
168C22×C8×C67C2311yescharacteristic
169C4×D4×C67D414yes—
170C4×D4×C67C2314yes—
171C2×C4⋊C4×C67D411yescharacteristic
172C2×C22⋊C4×C67D411yescharacteristic
173C2×C22⋊C4×C67D411yescharacteristic
174C2×C42×C67C2311yescharacteristic
175C4⋊C8×C67C2314yes—
176C22⋊C8×C67C2314yes—
177C22⋊C8×C67C2314yes—
178#97×C67C2314yes—
179C23×D67—21no—
180C2×Dic134—22no—
181C2×Dic134—22no—
182C2×Dic134—21no—
183C2×Dic134—24no—
184C2×Dic134—82no—
185C2×Dic134C2412yes—
186C2×D268—22no—
187C2×D268—22no—
188C2×D268—21no—
189C2×D268C2412yes—
190C2×C22⋊D67—24no—
191C2×C22⋊D67—24no—
192C2×C22⋊D67—44no—
193C2×C22⋊D67—82no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C22×Dic67—21no—
199C22×Dic67—21no—
200C22×Dic67—21no—
201C22×Dic67—24no—
202C22×Dic67—24no—
203C22×Dic67—24no—
204C22×Dic67—82no—
205C22×Dic67—82no—
206C22×Dic67—82no—
207C2×C4×D67—24no—
208C2×C4×D67—82no—
209#11761617—28no—
210C4⋊Dic67—21no—
211C4⋊Dic67—21no—
212C4⋊Dic67—21no—
213C4⋊Dic67—24no—
214C4⋊Dic67—24no—
215C4⋊Dic67—21no—
216C4⋊Dic67—21no—
217C4⋊Dic67—24no—
218C4⋊Dic67—24no—
219C4⋊Dic67—21no—
220C4⋊Dic67C2412yes—
221C4⋊Dic67C2412yes—
222C4⋊Dic67C2412yes—
223C4⋊Dic67C2412yes—
224C4⋊Dic67C2412yes—
225C4⋊Dic67C2412yes—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231C22⋊Dic67—24no—
232C22⋊Dic67—24no—
233C22⋊Dic67—24no—
234(C2×D67)⋊C4—24no—
235(C2×D67)⋊C4—24no—
236(C2×D67)⋊C4—24no—
237C4×Dic67—24no—
238C4×Dic67—24no—
239C24×C67C2×D411yescharacteristic
240C24×C67C2×D411yescharacteristic
241C2×D4×C67—24no—
242C2×D4×C67C2×D414yes—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67—22no—
246C22×C4×C67—22no—
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×D412yes—
252C22×C4×C67C2×D412yes—
253C22×C4×C67C2412yes—
254C22×C4×C67C2412yes—
255C22×C4×C67C2411yescharacteristic
256M16×C67—28no—
257C2×C8×C67—22no—
258C2×C8×C67—22no—
259C2×C8×C67—22no—
260C2×C8×C67—28no—
261C2×C8×C67#4114yes—
262C2×C8×C67C2412yes—
263C2×C8×C67C2412yes—
264C2×C8×C67C2412yes—
265C2×C8×C67C2412yes—
266C4⋊C4×C67C2×D414yes—
267C22⋊C4×C67C2×D414yes—
268C22⋊C4×C67C2×D414yes—
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—
284D4×C67—28no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—24no—
290C2×C4×C67—24no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67C22×D412yes—
296C2×C4×C67C22×D412yes—
297C2×C4×C67C22×D412yes—
298C2×C4×C67C22×D412yes—
299C2×C4×C67C22×D411yescharacteristic
300C2×C4×C67C2×#4112yes—
301C2×C4×C672−1+412yes—
302C2×C4×C67C2511yescharacteristic
303C22⋊D67—48no—
304C22⋊D67—84no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—22no—
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—42no—
313C2×Dic67—42no—
314C2×Dic67—42no—
315C2×Dic67—42no—
316C2×Dic67—42no—
317C2×Dic67—42no—
318C2×Dic67—42no—
319C2×Dic67—84no—
320C2×Dic67—84no—
321C2×Dic67—84no—
322D268—22no—
323D268—22no—
324D268—42no—
325C4×D67—84no—
326Dic134—22no—
327Dic134—22no—
328Dic134—42no—
329Dic134—84no—
330C8×C67—22no—
331C8×C67—22no—
332C8×C67—22no—
333C8×C67C2×#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#54712yes—
355C4×C67C22×#4111yescharacteristic
356C4×C67C2×2−1+411yescharacteristic
357Dic67—42no—
358Dic67—42no—
359Dic67—42no—
360Dic67—42no—
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×#554—671no—
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×#435D6711yescharacteristic, complemented
386C2×#428—671no—
387C22×#107—671no—
388C67C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—671no—
390C22×M16C2×D6711yescharacteristic
391C23×C8C2×D6711yescharacteristic
392#554—678no—
393#554—1344no—
394#553—678no—
395#553—1344no—
396C2×C4⋊Q8—671no—
397C2×#126—1341no—
398C2×#125—671no—
399C2×#125—1341no—
400C2×#123—1341no—
401C2×C22⋊Q8—671no—
402C2×C22⋊Q8—671no—
403C2×C22⋊Q8—1341no—
404C2×C22⋊Q8—1341no—
405C2×#121—671no—
406C2×#121—671no—
407C2×#121—1341no—
408C2×C4×Q8—671no—
409C2×C4×D4—671no—
410C2×C4×D4—1341no—
411C2×C4×D4—1341no—
412C2×C4×D4C2×D6711yescharacteristic
413C2×#117—671no—
414C22×C4⋊C4—671no—
415C22×C4⋊C4—671no—
416C22×C4⋊C4—671no—
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#435C2×D6718yescomplemented
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⋊C8C2×D6711yescharacteristic
440C2×#103—671no—
441C2×#103—671no—
442C2×#103—671no—
443C2×#102—671no—
444C2×#102—671no—
445C2×#102—671no—
446C2×C22⋊C8C2×D6711yescharacteristic
447C2×C22⋊C8C2×D6711yescharacteristic
448C2×#97C2×D6711yescharacteristic
449C22×Q8—671no—
450C22×Q8—1341no—
451C22×D4—671no—
452C22×D4—1341no—
453C22×D4—1341no—
454C22×D4D26811yescharacteristic
455C23×C4—1341no—
456C23×C4—1341no—
457C23×C4—1341no—
458C23×C4—1341no—
459C23×C4C22×D6711yescharacteristic
460C23×C4C22×D6711yescharacteristic
461C2×SD16—674no—
462C2×SD16—1344no—
463C2×M16—24no—
464C2×M16C22×D6714yes—
465C22×C8—24no—
466C22×C8C22×D6711yescharacteristic
467C22×C8C22×D6714yes—
468C22×C8C22×D6711yescharacteristic
469C22×C8C22×D6711yescharacteristic
470C22×C8C22×D6711yescharacteristic
471C4⋊Q8—674no—
472C4⋊Q8—1342no—
473#126—1348no—
474#125—674no—
475#125—1348no—
476#125—1342no—
477#123—1348no—
478C22⋊Q8—674no—
479C22⋊Q8—674no—
480C22⋊Q8—1342no—
481C22⋊Q8—1342no—
482C22⋊Q8—1348no—
483C22⋊Q8—1348no—
484#121—674no—
485#121—674no—
486#121—1348no—
487#121—1342no—
488#121—1342no—
489C4×Q8—674no—
490C4×Q8—1342no—
491C4×D4—674no—
492C4×D4—1348no—
493C4×D4—1348no—
494C4×D4—1342no—
495C4×D4D26814yes—
496C4×D4C22×D6714yes—
497#117—674no—
498#117—1342no—
499C2×C4⋊C4—671no—
500C2×C4⋊C4—671no—
501C2×C4⋊C4—671no—
502C2×C4⋊C4—671no—
503C2×C4⋊C4—671no—
504C2×C4⋊C4—674no—
505C2×C4⋊C4—674no—
506C2×C4⋊C4—674no—
507C2×C4⋊C4—671no—
508C2×C4⋊C4—1341no—
509C2×C4⋊C4—1341no—
510C2×C4⋊C4—1341no—
511C2×C4⋊C4—1342no—
512C2×C4⋊C4—1342no—
513C2×C4⋊C4—1342no—
514C2×C4⋊C4—1341no—
515C2×C4⋊C4—1341no—
516C2×C4⋊C4—1341no—
517C2×C4⋊C4—1341no—
518C2×C4⋊C4—1341no—
519C2×C4⋊C4—1341no—
520C2×C4⋊C4D26811yescharacteristic
521C2×C22⋊C4—1341no—
522C2×C22⋊C4—1341no—
523C2×C22⋊C4—1341no—
524C2×C22⋊C4—1341no—
525C2×C22⋊C4—1341no—
526C2×C22⋊C4—1341no—
527C2×C22⋊C4D26811yescharacteristic
528C2×C22⋊C4D26811yescharacteristic
529C2×C42—1341no—
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⋊C8C22×D6714yes—
542#103—674no—
543#103—674no—
544#103—674no—
545#102—674no—
546#102—674no—
547#102—674no—
548C22⋊C8C22×D6714yes—
549C22⋊C8C22×D6714yes—
550#97C22×D6714yes—
551C24—1341no—
552C24C2×D26811yescharacteristic
553C24C2×D26811yescharacteristic
554C2×Q8—5362no—
555C2×Q8—672no—
556C2×Q8—1342no—
557C2×Q8—1342no—
558C2×Q8—1341no—
559C2×Q8—1344no—
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×D26814yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—5362no—
575C22×C4—5362no—
576C22×C4—5362no—
577C22×C4—5362no—
578C22×C4—1341no—
579C22×C4—1341no—
580C22×C4—1341no—
581C22×C4—1341no—
582C22×C4—1341no—
583C22×C4—1341no—
584C22×C4—1341no—
585C22×C4—1344no—
586C22×C4—1344no—
587C22×C4—1344no—
588C22×C4—1344no—
589C22×C4C2×D26812yes—
590C22×C4C2×D26812yes—
591C22×C4C2×D26811yescharacteristic
592C22×C4C2×D26811yescharacteristic
593C22×C4C2×D26811yescharacteristic
594C22×C4C2×D26811yescharacteristic
595C22×C4C23×D6712yes—
596C22×C4C23×D6712yes—
597C22×C4C23×D6711yescharacteristic
598SD16—1348no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#1176162714yes—
605C2×C8C23×D6712yes—
606C2×C8C23×D6712yes—
607C2×C8C23×D6712yes—
608C2×C8C23×D6712yes—
609C4⋊C4—672no—
610C4⋊C4—672no—
611C4⋊C4—672no—
612C4⋊C4—672no—
613C4⋊C4—672no—
614C4⋊C4—672no—
615C4⋊C4—1341no—
616C4⋊C4—1341no—
617C4⋊C4—1341no—
618C4⋊C4—1344no—
619C4⋊C4—1344no—
620C4⋊C4—1341no—
621C4⋊C4—1341no—
622C4⋊C4—1344no—
623C4⋊C4—1341no—
624C4⋊C4—1344no—
625C4⋊C4—1344no—
626C4⋊C4—1344no—
627C4⋊C4—1344no—
628C4⋊C4—1344no—
629C4⋊C4—1344no—
630C4⋊C4C2×D26814yes—
631C22⋊C4—1344no—
632C22⋊C4—1344no—
633C22⋊C4—1344no—
634C22⋊C4—1344no—
635C22⋊C4—1344no—
636C22⋊C4—1344no—
637C22⋊C4C2×D26814yes—
638C22⋊C4C2×D26814yes—
639C42—1344no—
640C42—1344no—
641C42C2×D26812yes—
642C42C23×D6712yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—2682no—
649C23—2682no—
650C23—2682no—
651C23—1342no—
652C23#1452407614yes—
653C23C22×D26812yes—
654C23C22×D26812yes—
655C23C22×D26811yescharacteristic
656Q8—2682no—
657Q8—5364no—
658Q8—1342no—
659Q8—1342no—
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—2682no—
677C2×C4—2682no—
678C2×C4—2682no—
679C2×C4—2682no—
680C2×C4—2682no—
681C2×C4—2682no—
682C2×C4—2682no—
683C2×C4—5364no—
684C2×C4—5364no—
685C2×C4—5364no—
686C2×C4—5364no—
687C2×C4—1342no—
688C2×C4—1342no—
689C2×C4—1342no—
690C2×C4—1342no—
691C2×C4—1342no—
692C2×C4—1342no—
693C2×C4—1342no—
694C2×C4C22×D26812yes—
695C2×C4C22×D26812yes—
696C2×C4C22×D26812yes—
697C2×C4C22×D26812yes—
698C2×C4C22×D26811yescharacteristic
699C2×C4C2×#1176162712yes—
700C2×C4#1452409012yes—
701C2×C4C24×D6711yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#1176162714yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—2682no—
714C22—2682no—
715C22—2682no—
716C22—5364no—
717C22#1686405012yes—
718C22C2×#1452407614yes—
719C22C2×#1452407612yes—
720C22#1686420112yes—
721C22C23×D26811yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—2682no—
727C4—2682no—
728C4—2682no—
729C4—2682no—
730C4—2682no—
731C4—2682no—
732C4—2682no—
733C4#1686405012yes—
734C4C22×#1176162711yescharacteristic
735C4C2×#1452409011yescharacteristic
736C2—24no—
737C2—42no—
738C2—5362no—
739C2#2257269614yesdirect product factor
740C2C2×#1686405011yescharacteristic
741C2C22×#1452407611yescharacteristic
742C2C2×#1686420111yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#435×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864092C2
hypercenterC2×#435D67
hypocenterC67C2×#3346
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16864103C2semidirect
3. #22572696C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863732C2semidirect
6. C2×#16863715C2semidirect
7. C2×#16863738C2semidirect
8. C2×#16863710C2semidirect
9. C2×#16863704C2semidirect
10. C2×#16863677C2semidirect
11. C2×#16863642C2semidirect
12. C2×#16863625C2semidirect
13. C2×#16863498C2semidirect
14. C2×#16863438C2semidirect
15. C22×#14523977C2semidirect
16. C2×#435×C67C2semidirect
19. #16864103C22semidirect
42. #16863805C22semidirect
43. #16863738C22semidirect
44. #16863732C22semidirect
45. #16863715C22semidirect
46. #16863710C22semidirect
47. #16863704C22semidirect
48. #16863677C22semidirect
49. #16863642C22semidirect
50. #16863625C22semidirect
51. #16863498C22semidirect
52. #16863438C22semidirect
59. C2×#14523977C22semidirect
72. #435×C67C22semidirect
367. C2×C67#3346semidirect
385. C2×#435D67semidirect
388. C67C2×#3346semidirect
427. #435C2×D67semidirect
739. C2#22572696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641032
C2×#168640922
#225726962
C2×#168638052
C2×#168637322
C2×#168637152
C2×#168637382
C2×#168637102
C2×#168637042
C2×#168636772
C2×#168636422
C2×#168636252
C2×#168634982
C2×#168634382
C22×#145239772
C2×#435×C672
C2×#334667