Finite Group Databasebeta

← C2×#22570877 #31725699

Subgroups — C2×#22570877 #31725699

Order 17152.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864017C211yesmaximal, characteristic
2C2×#16864008C211yesmaximal, characteristic, complemented
3#22570877C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863790C211yesmaximal, characteristic, complemented
6C2×#16863751C211yesmaximal, characteristic, complemented
7C2×#16863747C211yesmaximal, characteristic, complemented
8C2×#16863654C211yesmaximal, characteristic, complemented
9C2×#16863642C211yesmaximal, characteristic
10C2×#16863637C211yesmaximal, characteristic, complemented
11C2×#16863625C211yesmaximal, characteristic
12C2×#16863504C211yesmaximal, characteristic, complemented
13C2×#16863498C211yesmaximal, characteristic, complemented
14C2×C4×Dic268C211yesmaximal, characteristic, complemented
15C2×C4×#11761617C211yesmaximal, characteristic, complemented
16C2×#405×C67C211yesmaximal, characteristic, complemented
17C22×Dic268C2211yescharacteristic
18C22×Dic268C2211yescharacteristic
19C22×#11761617C2211yescharacteristic
20C22×#11761617C2211yescharacteristic
21#16864017—24no—
22#16864017C2218yes—
23#16864008—24no—
24#16864008C2218yescomplemented
25C2×#14524043C2211yescharacteristic
26C2×#14524043C2211yescharacteristic
27C2×#14524038—21no—
28C2×#14524036—21no—
29C2×#14524036—21no—
30C2×#14524035C2211yescharacteristic
31C2×#14524033—21no—
32C2×#14524033—21no—
33C2×#14524031C2211yescharacteristic
34C2×#14524029—21no—
35C2×#14524025—21no—
36C2×#14524022C2211yescharacteristic
37C2×#14524022C2211yescharacteristic
38C2×#14524022C2211yescharacteristic
39C2×#14524021—21no—
40C2×#14524017C2211yescharacteristic
41C2×C4×Dic134C2211yescharacteristic
42C2×C4×Dic134C2211yescharacteristic
43C2×C4×Dic134C2211yescharacteristic
44C2×C4×D268C2211yescharacteristic
45#16863805C2218yescomplemented
46#16863790C2218yescomplemented
47#16863751C2218yescomplemented
48#16863747C2218yescomplemented
49#16863654C2218yescomplemented
50#16863642C2218yes—
51#16863637C2218yescomplemented
52#16863625C2218yes—
53#16863504C2218yescomplemented
54#16863498C2218yescomplemented
55C4×Dic268C2218yescomplemented
56C4×#11761617C2218yescomplemented
57C2×#14523977C2211yescharacteristic
58C2×#14523977C2211yescharacteristic
59C2×#14523975C2211yescharacteristic
60C2×#14523975C2211yescharacteristic
61C2×#14523968C2211yescharacteristic
62C2×#14523968C2211yescharacteristic
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523968C2211yescharacteristic
66C2×#14523968C2211yescharacteristic
67C2×#14523965C2211yescharacteristic
68C2×#14523965C2211yescharacteristic
69C22×M16×C67C2211yescharacteristic
70C23×C8×C67C2211yescharacteristic
71C2×#117×C67C2211yescharacteristic
72#405×C67C2218yescomplemented
73C2×#97×C67C2211yescharacteristic
74C2×#97×C67C2211yescharacteristic
75C2×C4×C8×C67C2211yescharacteristic
76C2×C4×C8×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C22×Dic134C2311yescharacteristic
80C22×Dic134C2311yescharacteristic
81C22×D268C2311yescharacteristic
82C22×C22⋊D67—21no—
83C22×C4×D67—21no—
84C2×Dic268—24no—
85C2×Dic268—24no—
86C2×Dic268C2314yes—
87C2×Dic268C2314yes—
88C2×#11761617—24no—
89C2×#11761617—24no—
90C2×#11761617C2314yes—
91C2×#11761617C2314yes—
92#14524043—22no—
93#14524043—22no—
94#14524043C2314yes—
95#14524043C2314yes—
96#14524038—28no—
97#14524036—28no—
98#14524036—28no—
99#14524035—22no—
100#14524035C2314yes—
101#14524033—28no—
102#14524033—28no—
103#14524031—22no—
104#14524031C2314yes—
105#14524029—28no—
106#14524025—28no—
107#14524022—22no—
108#14524022—22no—
109#14524022—22no—
110#14524022C2314yes—
111#14524022C2314yes—
112#14524022C2314yes—
113#14524021—28no—
114#14524017—22no—
115#14524017C2314yes—
116C4×Dic134—22no—
117C4×Dic134—22no—
118C4×Dic134—22no—
119C4×Dic134C2314yes—
120C4×Dic134C2314yes—
121C4×Dic134C2314yes—
122C4×D268—22no—
123C4×D268C2314yes—
124C2×C4⋊Dic67—21no—
125C2×C4⋊Dic67—21no—
126C2×C4⋊Dic67—21no—
127C2×C4⋊Dic67C2311yescharacteristic
128C2×C4⋊Dic67C2311yescharacteristic
129C2×C4⋊Dic67C2311yescharacteristic
130C2×C4⋊Dic67C2311yescharacteristic
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4—21no—
133C2×Dic67⋊C4—21no—
134C2×Dic67⋊C4—21no—
135C2×Dic67⋊C4—21no—
136C2×Dic67⋊C4—21no—
137C2×Dic67⋊C4—21no—
138C2×Dic67⋊C4—21no—
139C2×C22⋊Dic67—21no—
140C2×C22⋊Dic67—21no—
141C2×C22⋊Dic67—21no—
142C2×(C2×D67)⋊C4—21no—
143C2×(C2×D67)⋊C4—21no—
144C2×(C2×D67)⋊C4—21no—
145C2×(C2×D67)⋊C4—21no—
146C2×C4×Dic67—21no—
147C2×C4×Dic67—21no—
148C2×C4×Dic67—21no—
149#14523977C2314yes—
150#14523977C2314yes—
151#14523975C2314yes—
152#14523975C2314yes—
153#14523968C2314yes—
154#14523968C2314yes—
155#14523968C2314yes—
156#14523968C2314yes—
157#14523968C2314yes—
158#14523968C2314yes—
159#14523965C2314yes—
160#14523965C2314yes—
161C23×C4×C67C2311yescharacteristic
162C2×M16×C67—24no—
163C2×M16×C67C2314yes—
164C22×C8×C67—24no—
165C22×C8×C67C2314yes—
166C22×C8×C67C2311yescharacteristic
167C22×C8×C67C2311yescharacteristic
168C22×C8×C67C2311yescharacteristic
169C22×C8×C67C2311yescharacteristic
170#117×C67D414yes—
171#117×C67C2314yes—
172C2×C4⋊C4×C67D411yescharacteristic
173C2×C4⋊C4×C67D411yescharacteristic
174C2×C22⋊C4×C67D411yescharacteristic
175C2×C22⋊C4×C67D411yescharacteristic
176C2×C42×C67C2311yescharacteristic
177C2×C42×C67C2311yescharacteristic
178#97×C67C2314yes—
179#97×C67C2314yes—
180C4×C8×C67C2314yes—
181C4×C8×C67C2314yes—
182C23×D67—21no—
183C2×Dic134—22no—
184C2×Dic134—22no—
185C2×Dic134—22no—
186C2×Dic134—22no—
187C2×Dic134—22no—
188C2×Dic134—22no—
189C2×Dic134—21no—
190C2×Dic134—21no—
191C2×Dic134—21no—
192C2×Dic134—24no—
193C2×Dic134—82no—
194C2×Dic134C2412yes—
195C2×Dic134C2412yes—
196C2×Dic134C2412yes—
197C2×D268—22no—
198C2×D268—22no—
199C2×D268—21no—
200C2×D268C2412yes—
201C2×C22⋊D67—24no—
202C2×C22⋊D67—82no—
203C22×Dic67—21no—
204C22×Dic67—21no—
205C22×Dic67—21no—
206C22×Dic67—21no—
207C22×Dic67—21no—
208C22×Dic67—21no—
209C22×Dic67—21no—
210C2×C4×D67—24no—
211C2×C4×D67—82no—
212Dic268—28no—
213Dic268—28no—
214#11761617—28no—
215#11761617—28no—
216C4⋊Dic67—24no—
217C4⋊Dic67—24no—
218C4⋊Dic67—24no—
219C4⋊Dic67—21no—
220C4⋊Dic67—21no—
221C4⋊Dic67—21no—
222C4⋊Dic67—21no—
223C4⋊Dic67C2412yes—
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⋊C4—24no—
234Dic67⋊C4—24no—
235C22⋊Dic67—24no—
236C22⋊Dic67—24no—
237C22⋊Dic67—24no—
238(C2×D67)⋊C4—24no—
239(C2×D67)⋊C4—24no—
240(C2×D67)⋊C4—24no—
241(C2×D67)⋊C4—24no—
242C4×Dic67—24no—
243C4×Dic67—24no—
244C4×Dic67—24no—
245C24×C67C2×D411yescharacteristic
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×D411yescharacteristic
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2×D412yes—
254C22×C4×C67C2412yes—
255C22×C4×C67C2411yescharacteristic
256M16×C67—28no—
257C2×C8×C67—22no—
258C2×C8×C67—22no—
259C2×C8×C67—28no—
260C2×C8×C67#4114yes—
261C2×C8×C67#4114yes—
262C2×C8×C67C2412yes—
263C2×C8×C67C2412yes—
264C2×C8×C67C2412yes—
265C2×C8×C67C2412yes—
266C4⋊C4×C67C2×D414yes—
267C4⋊C4×C67C2×D414yes—
268C22⋊C4×C67C2×D414yes—
269C22⋊C4×C67C2×D414yes—
270C42×C67C2×D412yes—
271C42×C67C2×D412yes—
272C42×C67C2412yes—
273C42×C67C2412yes—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67C22×D412yes—
278C23×C67C22×D411yescharacteristic
279C22×D67—22no—
280C22×D67—42no—
281C22×D67—42no—
282C22×D67—42no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—24no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67C22×D412yes—
292C2×C4×C67C22×D412yes—
293C2×C4×C67C22×D412yes—
294C2×C4×C67C22×D412yes—
295C2×C4×C67C22×D412yes—
296C2×C4×C67C22×D411yescharacteristic
297C2×C4×C67C2×#4112yes—
298C2×C4×C67C2×#4112yes—
299C2×C4×C67C2511yescharacteristic
300C22⋊D67—84no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—42no—
309C2×Dic67—42no—
310C2×Dic67—42no—
311C2×Dic67—42no—
312C2×Dic67—42no—
313C2×Dic67—42no—
314C2×Dic67—42no—
315D268—22no—
316D268—22no—
317D268—42no—
318C4×D67—84no—
319Dic134—22no—
320Dic134—22no—
321Dic134—22no—
322Dic134—22no—
323Dic134—22no—
324Dic134—22no—
325Dic134—42no—
326Dic134—42no—
327Dic134—42no—
328Dic134—84no—
329C8×C67—22no—
330C8×C67—22no—
331C8×C67C2×#4114yes—
332C8×C67C2×#4114yes—
333C22×C67—22no—
334C22×C67—22no—
335C22×C67—22no—
336C22×C67—44no—
337C22×C67#53212yes—
338C22×C67#57712yes—
339C22×C67#57812yes—
340C22×C67C23×D411yescharacteristic
341C2×D67—42no—
342C2×D67—42no—
343C2×D67—42no—
344C2×D67—84no—
345C4×C67—22no—
346C4×C67—22no—
347C4×C67—22no—
348C4×C67—22no—
349C4×C67—22no—
350C4×C67#53212yes—
351C4×C67C22×#4111yescharacteristic
352C4×C67C22×#4111yescharacteristic
353Dic67—42no—
354Dic67—42no—
355Dic67—42no—
356Dic67—42no—
357Dic67—42no—
358Dic67—42no—
359Dic67—42no—
360C2×#3178—671nomaximal, Sylow
361C2×C67—42no—
362C2×C67#317814yescomplemented
363C2×C67C2×#53211yescharacteristic
364C2×C67C2×#57711yescharacteristic
365C2×C67C2×#57811yescharacteristic
366D67—82no—
367C2×#542—671no—
368C2×#541—671no—
369#3178—6716no—
370C2×#501—671no—
371C2×#497—671no—
372C2×#488—671no—
373C2×#487—671no—
374C2×#470—671no—
375C2×#468—671no—
376C2×#467—671no—
377C2×#465—671no—
378C2×#441—671no—
379C2×#440—671no—
380C2×C4×Q16—671no—
381C2×C4×SD16—671no—
382C2×#405D6711yescharacteristic, complemented
383C67C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16—671no—
385C22×Q16—671no—
386C22×SD16—671no—
387C22×SD16—671no—
388C22×M16C2×D6711yescharacteristic
389C23×C8C2×D6711yescharacteristic
390#542—678no—
391#542—1344no—
392#541—678no—
393#541—1344no—
394C2×C4⋊Q8—671no—
395C2×C4⋊Q8—671no—
396C2×#126—1341no—
397C2×#126—1341no—
398C2×#126—1341no—
399C2×#125—671no—
400C2×#125—1341no—
401C2×#125—1341no—
402C2×#124—671no—
403C2×#124—1341no—
404C2×#123—1341no—
405C2×C22⋊Q8—671no—
406C2×C22⋊Q8—671no—
407C2×C22⋊Q8—671no—
408C2×C22⋊Q8—1341no—
409C2×#121—671no—
410C2×C4×Q8—671no—
411C2×C4×Q8—671no—
412C2×C4×Q8—671no—
413C2×C4×D4—671no—
414C2×#117C2×D6711yescharacteristic
415#501—678no—
416#497—678no—
417#488—678no—
418#487—678no—
419#470—678no—
420#468—678no—
421#467—678no—
422#465—678no—
423#441—678no—
424#440—678no—
425C4×Q16—678no—
426C4×SD16—678no—
427C2×#107—671no—
428C2×#107—671no—
429C2×#106—671no—
430C2×#106—671no—
431C2×#103—671no—
432C2×#103—671no—
433C2×#103—671no—
434C2×#103—671no—
435C2×#103—671no—
436C2×#103—671no—
437C2×#102—671no—
438C2×#102—671no—
439#405C2×D6718yescomplemented
440C2×#97C2×D6711yescharacteristic
441C2×#97C2×D6711yescharacteristic
442C2×C4×C8C2×D6711yescharacteristic
443C2×C4×C8C2×D6711yescharacteristic
444C22×Q8—671no—
445C22×Q8—671no—
446C22×Q8—671no—
447C22×Q8—1341no—
448C22×D4—671no—
449C22×D4—1341no—
450C23×C4—1341no—
451C23×C4C22×D6711yescharacteristic
452C2×Q16—674no—
453C2×Q16—674no—
454C2×Q16—1344no—
455C2×Q16—1344no—
456C2×SD16—674no—
457C2×SD16—674no—
458C2×SD16—1344no—
459C2×SD16—1344no—
460C2×M16—24no—
461C2×M16C22×D6714yes—
462C22×C8—24no—
463C22×C8C22×D6711yescharacteristic
464C22×C8C22×D6714yes—
465C22×C8C22×D6711yescharacteristic
466C22×C8C22×D6711yescharacteristic
467C22×C8C22×D6711yescharacteristic
468C4⋊Q8—674no—
469C4⋊Q8—674no—
470C4⋊Q8—1342no—
471C4⋊Q8—1342no—
472#126—1348no—
473#126—1348no—
474#126—1348no—
475#125—674no—
476#125—1348no—
477#125—1348no—
478#125—1342no—
479#124—674no—
480#124—1348no—
481#124—1342no—
482#123—1348no—
483C22⋊Q8—674no—
484C22⋊Q8—674no—
485C22⋊Q8—674no—
486C22⋊Q8—1342no—
487C22⋊Q8—1342no—
488C22⋊Q8—1342no—
489C22⋊Q8—1348no—
490#121—674no—
491#121—1342no—
492C4×Q8—674no—
493C4×Q8—674no—
494C4×Q8—674no—
495C4×Q8—1342no—
496C4×Q8—1342no—
497C4×Q8—1342no—
498C4×D4—674no—
499C4×D4—1342no—
500#117D26814yes—
501#117C22×D6714yes—
502C2×C4⋊C4—671no—
503C2×C4⋊C4—671no—
504C2×C4⋊C4—671no—
505C2×C4⋊C4—671no—
506C2×C4⋊C4—1341no—
507C2×C4⋊C4—1341no—
508C2×C4⋊C4—1341no—
509C2×C4⋊C4—1341no—
510C2×C4⋊C4—1341no—
511C2×C4⋊C4—1341no—
512C2×C4⋊C4—1341no—
513C2×C4⋊C4—1341no—
514C2×C4⋊C4—1341no—
515C2×C4⋊C4—1341no—
516C2×C4⋊C4—1341no—
517C2×C4⋊C4D26811yescharacteristic
518C2×C4⋊C4D26811yescharacteristic
519C2×C22⋊C4—1341no—
520C2×C22⋊C4—1341no—
521C2×C22⋊C4—1341no—
522C2×C22⋊C4—1341no—
523C2×C22⋊C4—1341no—
524C2×C22⋊C4—1341no—
525C2×C22⋊C4—1341no—
526C2×C22⋊C4D26811yescharacteristic
527C2×C22⋊C4D26811yescharacteristic
528C2×C42—1341no—
529C2×C42—1341no—
530C2×C42—1341no—
531C2×C42C22×D6711yescharacteristic
532C2×C42C22×D6711yescharacteristic
533#107—674no—
534#107—674no—
535#106—674no—
536#106—674no—
537#103—674no—
538#103—674no—
539#103—674no—
540#103—674no—
541#103—674no—
542#103—674no—
543#102—674no—
544#102—674no—
545#97C22×D6714yes—
546#97C22×D6714yes—
547C4×C8C22×D6714yes—
548C4×C8C22×D6714yes—
549C24—1341no—
550C24C2×D26811yescharacteristic
551C2×Q8—5362no—
552C2×Q8—672no—
553C2×Q8—672no—
554C2×Q8—672no—
555C2×Q8—1342no—
556C2×Q8—1342no—
557C2×Q8—1342no—
558C2×Q8—1342no—
559C2×Q8—1342no—
560C2×Q8—1342no—
561C2×Q8—1341no—
562C2×Q8—1341no—
563C2×Q8—1341no—
564C2×Q8—1344no—
565C2×D4—5362no—
566C2×D4—672no—
567C2×D4—1344no—
568C2×D4—1341no—
569C2×D4—1342no—
570C2×D4—1342no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—5362no—
574C22×C4—1341no—
575C22×C4—1341no—
576C22×C4—1341no—
577C22×C4—1341no—
578C22×C4—1341no—
579C22×C4—1341no—
580C22×C4—1341no—
581C22×C4—1344no—
582C22×C4C2×D26812yes—
583C22×C4C2×D26811yescharacteristic
584C22×C4C2×D26811yescharacteristic
585C22×C4C2×D26811yescharacteristic
586C22×C4C2×D26811yescharacteristic
587C22×C4C2×D26811yescharacteristic
588C22×C4C23×D6712yes—
589C22×C4C23×D6711yescharacteristic
590Q16—1348no—
591Q16—1348no—
592SD16—1348no—
593SD16—1348no—
594M16—28no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—28no—
598C2×C8#1176162814yes—
599C2×C8#1176162814yes—
600C2×C8C23×D6712yes—
601C2×C8C23×D6712yes—
602C2×C8C23×D6712yes—
603C2×C8C23×D6712yes—
604C4⋊C4—672no—
605C4⋊C4—672no—
606C4⋊C4—672no—
607C4⋊C4—672no—
608C4⋊C4—1341no—
609C4⋊C4—1341no—
610C4⋊C4—1341no—
611C4⋊C4—1341no—
612C4⋊C4—1344no—
613C4⋊C4—1344no—
614C4⋊C4—1344no—
615C4⋊C4—1344no—
616C4⋊C4—1344no—
617C4⋊C4—1344no—
618C4⋊C4—1344no—
619C4⋊C4—1344no—
620C4⋊C4—1344no—
621C4⋊C4—1344no—
622C4⋊C4—1344no—
623C4⋊C4C2×D26814yes—
624C4⋊C4C2×D26814yes—
625C22⋊C4—1344no—
626C22⋊C4—1344no—
627C22⋊C4—1344no—
628C22⋊C4—1344no—
629C22⋊C4—1344no—
630C22⋊C4—1344no—
631C22⋊C4—1344no—
632C22⋊C4C2×D26814yes—
633C22⋊C4C2×D26814yes—
634C42—1344no—
635C42—1344no—
636C42—1344no—
637C42C2×D26812yes—
638C42C2×D26812yes—
639C42C23×D6712yes—
640C42C23×D6712yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—2682no—
645C23—2682no—
646C23—2682no—
647C23—1342no—
648C23C22×D26812yes—
649C23C22×D26811yescharacteristic
650Q8—2682no—
651Q8—2682no—
652Q8—2682no—
653Q8—5364no—
654Q8—1342no—
655Q8—1342no—
656Q8—1342no—
657Q8—1342no—
658Q8—1342no—
659Q8—1342no—
660D4—2682no—
661D4—5364no—
662D4—1342no—
663D4—1342no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—2682no—
673C2×C4—2682no—
674C2×C4—2682no—
675C2×C4—2682no—
676C2×C4—2682no—
677C2×C4—2682no—
678C2×C4—2682no—
679C2×C4—5364no—
680C2×C4—1342no—
681C2×C4—1342no—
682C2×C4—1342no—
683C2×C4—1342no—
684C2×C4—1342no—
685C2×C4—1342no—
686C2×C4—1342no—
687C2×C4C22×D26812yes—
688C2×C4C22×D26812yes—
689C2×C4C22×D26812yes—
690C2×C4C22×D26812yes—
691C2×C4C22×D26812yes—
692C2×C4C22×D26811yescharacteristic
693C2×C4C2×#1176162812yes—
694C2×C4C2×#1176162812yes—
695C2×C4C24×D6711yescharacteristic
696C8—22no—
697C8—22no—
698C8C2×#1176162814yes—
699C8C2×#1176162814yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—2682no—
705C22—2682no—
706C22—2682no—
707C22—5364no—
708C22#1686394612yes—
709C22#1686420812yes—
710C22#1686421312yes—
711C22C23×D26811yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—2682no—
718C4—2682no—
719C4—2682no—
720C4—2682no—
721C4—2682no—
722C4—2682no—
723C4—2682no—
724C4#1686394612yes—
725C4C22×#1176162811yescharacteristic
726C4C22×#1176162811yescharacteristic
727C2—42no—
728C2—5362no—
729C2#2257087714yesdirect product factor
730C2C2×#1686394611yescharacteristic
731C2C2×#1686420811yescharacteristic
732C2C2×#1686421311yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#405×C67C2
socleC23×C67C22×D4
prime radicalC2×#14524017C22
hypercenterC2×#405D67
hypocenterC67C2×#3178
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#16864008C2semidirect
3. #22570877C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863790C2semidirect
6. C2×#16863751C2semidirect
7. C2×#16863747C2semidirect
8. C2×#16863654C2semidirect
10. C2×#16863637C2semidirect
12. C2×#16863504C2semidirect
13. C2×#16863498C2semidirect
14. C2×C4×Dic268C2semidirect
15. C2×C4×#11761617C2semidirect
16. C2×#405×C67C2semidirect
24. #16864008C22semidirect
45. #16863805C22semidirect
46. #16863790C22semidirect
47. #16863751C22semidirect
48. #16863747C22semidirect
49. #16863654C22semidirect
51. #16863637C22semidirect
53. #16863504C22semidirect
54. #16863498C22semidirect
55. C4×Dic268C22semidirect
56. C4×#11761617C22semidirect
72. #405×C67C22semidirect
362. C2×C67#3178semidirect
382. C2×#405D67semidirect
383. C67C2×#3178semidirect
439. #405C2×D67semidirect
729. C2#22570877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640172
C2×#168640082
#225708772
C2×#168638052
C2×#168637902
C2×#168637512
C2×#168637472
C2×#168636542
C2×#168636422
C2×#168636372
C2×#168636252
C2×#168635042
C2×#168634982
C2×C4×Dic2682
C2×C4×#117616172
C2×#405×C672
C2×#317867