Finite Group Databasebeta

← C2×#22563148 #31015169

Subgroups — C2×#22563148 #31015169

Order 17152.

3374 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524005C211yesmaximal, characteristic
2#22563148C2116yesmaximal, direct product factor
3C2×#16863288C211yesmaximal, characteristic, complemented
4C2×#16863286C211yesmaximal, characteristic, complemented
5C2×#16863282C211yesmaximal, characteristic, complemented
6C2×#16863274C211yesmaximal, characteristic
7C2×#16863274C211yesmaximal, characteristic
8C2×#16863263C211yesmaximal, characteristic, complemented
9C2×#16863258C211yesmaximal, characteristic, complemented
10C2×#16863253C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
13C2×#16863243C211yesmaximal, characteristic, complemented
14C2×#16863241C211yesmaximal, characteristic, complemented
15C2×#95×D67C211yesmaximal, characteristic, complemented
16C2×#387×C67C211yesmaximal, characteristic, complemented
17C23×D268C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C23×C4×D67C2211yescharacteristic
22C2×#14524005C4116yescomplemented
23C2×#14524005C2218yes—
24C22×C4⋊Dic67C2211yescharacteristic
25C22×(C2×D67)⋊C4C2211yescharacteristic
26C22×(C2×D67)⋊C4C2211yescharacteristic
27C22×(C2×D67)⋊C4C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×(C2×D67)⋊C4C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34C22×C4×Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37#16863288C2218yescomplemented
38#16863286C2218yescomplemented
39#16863282C2218yescomplemented
40#16863274C2218yes—
41#16863274C2218yes—
42#16863263C2218yescomplemented
43#16863258C2218yescomplemented
44#16863253C2218yescomplemented
45C4×(C2×D67)⋊C4C2218yescomplemented
46C4×(C2×D67)⋊C4C2218yescomplemented
47#16863243C2218yescomplemented
48#16863241C2218yescomplemented
49C2×C67⋊#95C2211yescharacteristic
50C2×C67⋊#95C2211yescharacteristic
51C2×C67⋊#95C2211yescharacteristic
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59#95×D67C2218yescomplemented
60C22×C4⋊C4×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C42×C67C2211yescharacteristic
63#387×C67C2218yescomplemented
64C2×#95×C67C2211yescharacteristic
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C24×D67C2311yescharacteristic
69C24×D67C2311yescharacteristic
70C22×D268—24no—
71C22×D268—24no—
72C22×D268C2×C418yes—
73C22×D268C2314yes—
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C22×C4×D67—24no—
81C22×C4×D67—24no—
82C22×C4×D67—24no—
83C22×C4×D67—24no—
84C22×C4×D67—42no—
85C22×C4×D67—42no—
86C22×C4×D67—42no—
87C22×C4×D67—42no—
88C22×C4×D67—42no—
89C22×C4×D67—42no—
90C22×C4×D67C2×C418yes—
91C22×C4×D67C2×C418yescomplemented
92C22×C4×D67C2314yes—
93C22×C4×D67C2314yes—
94C22×C4×D67C2314yes—
95C22×C4×D67C2314yes—
96#14524005C2×C4164yescomplemented
97C2×C4⋊Dic67—42no—
98C2×C4⋊Dic67C2314yes—
99C2×(C2×D67)⋊C4—24no—
100C2×(C2×D67)⋊C4—24no—
101C2×(C2×D67)⋊C4—24no—
102C2×(C2×D67)⋊C4—24no—
103C2×(C2×D67)⋊C4—42no—
104C2×(C2×D67)⋊C4—42no—
105C2×(C2×D67)⋊C4C2×C418yes—
106C2×(C2×D67)⋊C4C2×C418yescomplemented
107C2×(C2×D67)⋊C4C2314yes—
108C2×(C2×D67)⋊C4C2314yes—
109C2×(C2×D67)⋊C4C2314yes—
110C2×(C2×D67)⋊C4C2314yes—
111C2×(C2×D67)⋊C4C2314yes—
112C2×(C2×D67)⋊C4C2314yes—
113C2×(C2×D67)⋊C4C2314yes—
114C2×(C2×D67)⋊C4C2314yes—
115C2×C4×Dic67—24no—
116C2×C4×Dic67—24no—
117C2×C4×Dic67—42no—
118C2×C4×Dic67C2×C418yescomplemented
119C2×C4×Dic67C2314yes—
120C2×C4×Dic67C2314yes—
121C2×C4×Dic67C2314yes—
122C2×C4×Dic67C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C23×C4×C67C2311yescharacteristic
138C23×C4×C67C2311yescharacteristic
139C23×C4×C67C2311yescharacteristic
140C2×C4⋊C4×C67—42no—
141C2×C4⋊C4×C67C2×C418yescomplemented
142C2×C4⋊C4×C67C2314yes—
143C2×C4⋊C4×C67C2314yes—
144C2×C42×C67—42no—
145C2×C42×C67C2314yes—
146#95×C67C2314yes—
147#95×C67C2314yes—
148#95×C67C2314yes—
149#95×C67C2314yes—
150C23×D67—22no—
151C23×D67—22no—
152C23×D67—22no—
153C23×D67—22no—
154C23×D67—22no—
155C23×D67—22no—
156C23×D67—22no—
157C23×D67—22no—
158C23×D67—22no—
159C23×D67—22no—
160C23×D67C22×C414yes—
161C23×D67C22×C414yes—
162C23×D67#4114yes—
163C23×D67#4114yes—
164C23×D67C2412yes—
165C23×D67C2412yes—
166C2×D268—232no—
167C2×D268—28no—
168C2×D268—28no—
169C2×D268C22×C4116yes—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—22no—
173C22×Dic67—22no—
174C22×Dic67—22no—
175C22×Dic67—22no—
176C22×Dic67—22no—
177C22×Dic67—22no—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67—22no—
181C22×Dic67—22no—
182C22×Dic67—22no—
183C22×Dic67—22no—
184C22×Dic67—22no—
185C22×Dic67C22×C414yes—
186C22×Dic67C22×C414yes—
187C22×Dic67#4114yes—
188C22×Dic67C2412yes—
189C22×Dic67C2412yes—
190C22×Dic67C2412yes—
191C22×Dic67C2412yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C2×C4×D67—28no—
195C2×C4×D67—28no—
196C2×C4×D67—28no—
197C2×C4×D67—28no—
198C2×C4×D67—416no—
199C2×C4×D67—416no—
200C2×C4×D67—44no—
201C2×C4×D67—44no—
202C2×C4×D67—44no—
203C2×C4×D67—44no—
204C2×C4×D67—44no—
205C2×C4×D67—44no—
206C2×C4×D67—416no—
207C2×C4×D67—416no—
208C2×C4×D67C22×C4116yes—
209C2×C4×D67C22×C4116yescomplemented
210C4⋊Dic67—44no—
211(C2×D67)⋊C4—28no—
212(C2×D67)⋊C4—28no—
213(C2×D67)⋊C4—28no—
214(C2×D67)⋊C4—28no—
215(C2×D67)⋊C4—44no—
216(C2×D67)⋊C4—44no—
217(C2×D67)⋊C4C22×C4116yes—
218(C2×D67)⋊C4C22×C4116yescomplemented
219C4×Dic67—28no—
220C4×Dic67—28no—
221C4×Dic67—44no—
222C4×Dic67C22×C4116yescomplemented
223C24×C67C2411yescharacteristic
224C22×C4×C67—22no—
225C22×C4×C67—22no—
226C22×C4×C67—22no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—22no—
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67—22no—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67C22×C414yes—
242C22×C4×C67C22×C414yes—
243C22×C4×C67C22×C414yes—
244C22×C4×C67#4114yes—
245C22×C4×C67C2412yes—
246C22×C4×C67C2412yes—
247C22×C4×C67C2412yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2412yes—
250C22×C4×C67C2412yes—
251C22×C4×C67C2412yes—
252C4⋊C4×C67—44no—
253C4⋊C4×C67C22×C4116yescomplemented
254C42×C67—44no—
255C23×C67C23×C412yes—
256C23×C67C2×#4112yes—
257C23×C67C2×#4112yes—
258C23×C67C2×#4112yes—
259C23×C67C2×#4112yes—
260C23×C67H(5,𝔽2)12yes—
261C23×C67H(5,𝔽2)12yes—
262C23×C67C2511yescharacteristic
263C22×D67—28no—
264C22×D67—28no—
265C22×D67—28no—
266C22×D67—28no—
267C22×D67—28no—
268C22×D67—28no—
269C22×D67—22no—
270C22×D67—22no—
271C22×D67—22no—
272C22×D67—22no—
273C22×D67—28no—
274C22×D67—28no—
275C22×D67—28no—
276C22×D67—22no—
277C22×D67—22no—
278C22×D67—22no—
279C22×D67—22no—
280C22×D67—22no—
281C22×D67—22no—
282C22×D67—44no—
283C22×D67—44no—
284C22×D67—44no—
285C22×D67—44no—
286C22×D67#117116yes—
287C22×D67C23×C414yes—
288C22×D67C23×C414yes—
289C22×D67C2×#4114yes—
290C22×D67C2×#4114yes—
291C2×C4×C67—28no—
292C2×C4×C67—28no—
293C2×C4×C67—28no—
294C2×C4×C67—28no—
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—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—44no—
313C2×C4×C67—44no—
314C2×C4×C67—44no—
315C2×C4×C67C23×C414yes—
316C2×C4×C67C23×C414yes—
317C2×C4×C67C23×C414yes—
318C2×C4×C67C2×#4114yes—
319C2×Dic67—28no—
320C2×Dic67—28no—
321C2×Dic67—28no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—22no—
328C2×Dic67—22no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—44no—
338C2×Dic67—44no—
339C2×Dic67—44no—
340C2×Dic67C23×C414yes—
341C2×Dic67C23×C414yes—
342C2×Dic67C2×#4114yes—
343D268—232no—
344C4×D67—416no—
345C4×D67—416no—
346C4×D67—416no—
347C4×D67—416no—
348C22×C67C2×#11714yes—
349C22×C67C4×#4114yes—
350C22×C67#51814yes—
351C22×C67#55114yes—
352C22×C67#55114yes—
353C22×C67#55314yes—
354C22×C67#55314yes—
355C22×C67C24×C411yescharacteristic
356C22×C67C22×#4111yescharacteristic
357C22×C67C22×#4111yescharacteristic
358C22×C67C22×#4111yescharacteristic
359C22×C67C22×#4111yescharacteristic
360C22×C67C2×H(5,𝔽2)11yescharacteristic
361C22×C67C2×H(5,𝔽2)11yescharacteristic
362C2×D67—232no—
363C2×D67—24no—
364C2×D67—24no—
365C2×D67—24no—
366C2×D67—24no—
367C2×D67—24no—
368C2×D67—24no—
369C2×D67—24no—
370C2×D67—24no—
371C2×D67—24no—
372C2×D67—416no—
373C2×D67—42no—
374C2×D67—42no—
375C2×D67—42no—
376C2×D67—42no—
377C2×D67C2×#11718yes—
378C4×C67—24no—
379C4×C67—24no—
380C4×C67—24no—
381C4×C67—24no—
382C4×C67—42no—
383C4×C67—42no—
384C4×C67—42no—
385Dic67—24no—
386Dic67—24no—
387Dic67—24no—
388Dic67—42no—
389Dic67—42no—
390Dic67—42no—
391C2×#2353—671nomaximal, Sylow
392C2×C67#235318yescomplemented
393C2×C67C22×#11711yescharacteristic
394C2×C67C2×C4×#4111yescharacteristic
395C2×C67C2×#51811yescharacteristic
396C2×C67C2×#55111yescharacteristic
397C2×C67C2×#55111yescharacteristic
398C2×C67C2×#55311yescharacteristic
399C2×C67C2×#55311yescharacteristic
400D67—28no—
401D67—44no—
402C22×C4×D4—671no—
403#2353—6716no—
404C2×#388—671no—
405C2×#388—671no—
406C2×#387—671no—
407C2×#387D6711yescharacteristic, complemented
408C2×#386—671no—
409C2×#386—671no—
410C2×#383—671no—
411C2×#381—671no—
412C2×#380—671no—
413C2×C4×C22⋊C4—671no—
414C2×C4×C22⋊C4—671no—
415C2×C4×C22⋊C4—671no—
416C2×#376—671no—
417C22×#95—671no—
418C67C2×#235311yescharacteristic, complemented, Sylow
419C23×D4—671no—
420C24×C4—671no—
421C24×C4—671no—
422C24×C4—671no—
423C24×C4—671no—
424C2×C4×D4—6716no—
425C2×C4×D4—678no—
426C22×C4⋊C4—671no—
427C22×C4⋊C4C2×D6711yescharacteristic
428C22×C4⋊C4C2×D6711yescharacteristic
429C22×C22⋊C4—671no—
430C22×C22⋊C4—671no—
431C22×C22⋊C4—671no—
432C22×C22⋊C4—671no—
433C22×C22⋊C4—671no—
434C22×C22⋊C4—671no—
435C22×C22⋊C4—671no—
436C22×C22⋊C4—671no—
437C22×C42—671no—
438C22×C42—671no—
439C22×C42—671no—
440C22×C42—671no—
441C22×C42C2×D6711yescharacteristic
442#388—678no—
443#388—678no—
444#387—678no—
445#387C2×D6718yescomplemented
446#386—678no—
447#386—678no—
448#383—678no—
449#381—678no—
450#380—678no—
451C4×C22⋊C4—678no—
452C4×C22⋊C4—678no—
453C4×C22⋊C4—678no—
454#376—678no—
455C2×#95—671no—
456C2×#95—671no—
457C2×#95—671no—
458C2×#95—671no—
459C2×#95—671no—
460C2×#95—671no—
461C2×#95—671no—
462C2×#95—671no—
463C2×#95—671no—
464C2×#95—671no—
465C2×#95—678no—
466C2×#95C2×D6711yescharacteristic
467C2×#95C2×D6711yescharacteristic
468C2×#95C2×D6711yescharacteristic
469C2×#95C2×D6711yescharacteristic
470C25—671no—
471C25—671no—
472C22×D4—678no—
473C22×D4—674no—
474C22×D4—1344no—
475C22×D4—1344no—
476C23×C4—2682no—
477C23×C4—2682no—
478C23×C4—2682no—
479C23×C4—2682no—
480C23×C4—2682no—
481C23×C4—2682no—
482C23×C4—678no—
483C23×C4—678no—
484C23×C4—674no—
485C23×C4—674no—
486C23×C4—674no—
487C23×C4—674no—
488C23×C4—671no—
489C23×C4—671no—
490C23×C4—671no—
491C23×C4—671no—
492C23×C4—671no—
493C23×C4—671no—
494C23×C4—1344no—
495C23×C4—1344no—
496C23×C4—1344no—
497C23×C4—1344no—
498C23×C4C22×D6711yescharacteristic
499C23×C4C22×D6711yescharacteristic
500C23×C4C22×D6711yescharacteristic
501C23×C4C22×D6711yescharacteristic
502C23×C4C22×D6711yescharacteristic
503C23×C4C22×D6711yescharacteristic
504C23×C4C22×D6711yescharacteristic
505C4×D4—6764no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—2682no—
508C2×C4⋊C4—674no—
509C2×C4⋊C4C4×D6718yescomplemented
510C2×C4⋊C4C22×D6714yes—
511C2×C4⋊C4C22×D6714yes—
512C2×C22⋊C4—2682no—
513C2×C22⋊C4—2682no—
514C2×C22⋊C4—674no—
515C2×C22⋊C4—674no—
516C2×C22⋊C4—678no—
517C2×C22⋊C4—678no—
518C2×C22⋊C4—674no—
519C2×C22⋊C4—674no—
520C2×C22⋊C4—674no—
521C2×C22⋊C4—674no—
522C2×C22⋊C4—674no—
523C2×C22⋊C4—674no—
524C2×C22⋊C4—1344no—
525C2×C22⋊C4—1344no—
526C2×C22⋊C4—1344no—
527C2×C22⋊C4—1344no—
528C2×C42—42no—
529C2×C42—2682no—
530C2×C42—674no—
531C2×C42—678no—
532C2×C42—674no—
533C2×C42—674no—
534C2×C42—674no—
535C2×C42—1344no—
536C2×C42—1344no—
537C2×C42C22×D6714yes—
538#95—674no—
539#95—674no—
540#95—674no—
541#95—674no—
542#95—674no—
543#95—674no—
544#95—674no—
545#95—674no—
546#95—674no—
547#95—674no—
548#95C22×D6714yes—
549#95C22×D6714yes—
550#95C22×D6714yes—
551#95C22×D6714yes—
552C24—674no—
553C24—674no—
554C24—674no—
555C24—672no—
556C24—674no—
557C24—672no—
558C24—1342no—
559C24—1342no—
560C24—1342no—
561C24—1342no—
562C24—1342no—
563C24—1342no—
564C24—1342no—
565C24—1342no—
566C24—1342no—
567C24—1342no—
568C24C23×D6711yescharacteristic
569C2×D4—6716no—
570C2×D4—13432no—
571C2×D4—1348no—
572C2×D4—1348no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—26816no—
591C22×C4—26816no—
592C22×C4—26816no—
593C22×C4—2684no—
594C22×C4—2684no—
595C22×C4—2684no—
596C22×C4—2684no—
597C22×C4—2684no—
598C22×C4—2684no—
599C22×C4—26816no—
600C22×C4—6716no—
601C22×C4—6716no—
602C22×C4—674no—
603C22×C4—674no—
604C22×C4—674no—
605C22×C4—672no—
606C22×C4—672no—
607C22×C4—672no—
608C22×C4—672no—
609C22×C4—672no—
610C22×C4—672no—
611C22×C4—1348no—
612C22×C4—1348no—
613C22×C4—1348no—
614C22×C4—1342no—
615C22×C4—1342no—
616C22×C4—1342no—
617C22×C4—1342no—
618C22×C4—1342no—
619C22×C4—1342no—
620C22×C4—1342no—
621C22×C4—1342no—
622C22×C4—1342no—
623C22×C4—1348no—
624C22×C4—1342no—
625C22×C4—1342no—
626C22×C4—1342no—
627C22×C4—1342no—
628C22×C4—1342no—
629C22×C4—1342no—
630C22×C4C2×C4×D6714yes—
631C22×C4C2×C4×D6714yes—
632C22×C4C2×C4×D6714yes—
633C22×C4#1176162914yes—
634C22×C4C23×D6712yes—
635C22×C4C23×D6712yes—
636C22×C4C23×D6712yes—
637C22×C4C23×D6712yes—
638C22×C4C23×D6712yes—
639C22×C4C23×D6712yes—
640C22×C4C23×D6712yes—
641C4⋊C4—44no—
642C4⋊C4—2684no—
643C4⋊C4C2×C4×D67116yescomplemented
644C22⋊C4—2684no—
645C22⋊C4—2684no—
646C22⋊C4—6716no—
647C22⋊C4—6716no—
648C22⋊C4—1348no—
649C22⋊C4—1348no—
650C22⋊C4—1348no—
651C22⋊C4—1348no—
652C42—44no—
653C42—2684no—
654C42—6716no—
655C42—1348no—
656C42—1348no—
657C23—2684no—
658C23—2684no—
659C23—2684no—
660C23—2684no—
661C23—6716no—
662C23—674no—
663C23—674no—
664C23—674no—
665C23—674no—
666C23—1348no—
667C23—1348no—
668C23—1348no—
669C23—1342no—
670C23—1342no—
671C23—1342no—
672C23—1342no—
673C23—1342no—
674C23—1342no—
675C23—1348no—
676C23—1348no—
677C23—1348no—
678C23—1348no—
679C23—1348no—
680C23—1348no—
681C23—1342no—
682C23—1342no—
683C23—1342no—
684C23—1342no—
685C23C22×C4×D6712yes—
686C23#41×D6712yes—
687C23#41×D6712yes—
688C23#41×D6712yes—
689C23C2×#1176162912yes—
690C23#1452408812yes—
691C23#1452408912yes—
692C23C24×D6711yescharacteristic
693D4—13432no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—26816no—
719C2×C4—26816no—
720C2×C4—26816no—
721C2×C4—26816no—
722C2×C4—2684no—
723C2×C4—2684no—
724C2×C4—2684no—
725C2×C4—674no—
726C2×C4—674no—
727C2×C4—674no—
728C2×C4—1342no—
729C2×C4—1342no—
730C2×C4—1342no—
731C2×C4—1342no—
732C2×C4—1342no—
733C2×C4—1342no—
734C2×C4—1342no—
735C2×C4—1342no—
736C2×C4—1342no—
737C2×C4—1348no—
738C2×C4—1348no—
739C2×C4—1348no—
740C2×C4—1342no—
741C2×C4—1342no—
742C2×C4—1342no—
743C2×C4—1342no—
744C2×C4—1342no—
745C2×C4—1342no—
746C2×C4C22×C4×D6714yes—
747C2×C4C22×C4×D6714yes—
748C2×C4C22×C4×D6714yes—
749C2×C4C2×#1176162914yes—
750C22—26816no—
751C22—2682no—
752C22—2682no—
753C22—2682no—
754C22—2682no—
755C22—678no—
756C22—1344no—
757C22—1344no—
758C22—1344no—
759C22—13432no—
760C22—1344no—
761C22—1344no—
762C22—1344no—
763C22—1344no—
764C22—1344no—
765C22—1344no—
766C22#117×D6714yes—
767C22C4×#1176162914yes—
768C22#1686386814yes—
769C22#1686407114yes—
770C22#1686407314yes—
771C22#1686409114yes—
772C22#1686409914yes—
773C22C23×C4×D6711yescharacteristic
774C22C2×#41×D6711yescharacteristic
775C22C2×#41×D6711yescharacteristic
776C22C2×#41×D6711yescharacteristic
777C22C22×#1176162911yescharacteristic
778C22C2×#1452408811yescharacteristic
779C22C2×#1452408911yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—2682no—
788C4—2682no—
789C4—2682no—
790C4—1344no—
791C4—1344no—
792C4—1344no—
793C2—2684no—
794C2—1348no—
795C2#2256314818yesdirect product factor
796C2C2×#117×D6711yescharacteristic
797C2C2×C4×#1176162911yescharacteristic
798C2C2×#1686386811yescharacteristic
799C2C2×#1686407111yescharacteristic
800C2C2×#1686407311yescharacteristic
801C2C2×#1686409111yescharacteristic
802C2C2×#1686409911yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#387×C67C2
socleC24×C67C24
prime radicalC23×D268C22
cosocleC23×C67C25
hypercenterC2×#387D67
hypocenterC67C2×#2353
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #22563148C2direct (N × H)
3. C2×#16863288C2semidirect
4. C2×#16863286C2semidirect
5. C2×#16863282C2semidirect
8. C2×#16863263C2semidirect
9. C2×#16863258C2semidirect
10. C2×#16863253C2semidirect
11. C2×C4×(C2×D67)⋊C4C2semidirect
12. C2×C4×(C2×D67)⋊C4C2semidirect
13. C2×#16863243C2semidirect
14. C2×#16863241C2semidirect
15. C2×#95×D67C2semidirect
16. C2×#387×C67C2semidirect
22. C2×#14524005C4semidirect
37. #16863288C22semidirect
38. #16863286C22semidirect
39. #16863282C22semidirect
42. #16863263C22semidirect
43. #16863258C22semidirect
44. #16863253C22semidirect
45. C4×(C2×D67)⋊C4C22semidirect
46. C4×(C2×D67)⋊C4C22semidirect
47. #16863243C22semidirect
48. #16863241C22semidirect
59. #95×D67C22semidirect
63. #387×C67C22semidirect
91. C22×C4×D67C2×C4semidirect
96. #14524005C2×C4semidirect
106. C2×(C2×D67)⋊C4C2×C4semidirect
118. C2×C4×Dic67C2×C4semidirect
141. C2×C4⋊C4×C67C2×C4semidirect
209. C2×C4×D67C22×C4semidirect
218. (C2×D67)⋊C4C22×C4semidirect
222. C4×Dic67C22×C4semidirect
253. C4⋊C4×C67C22×C4semidirect
392. C2×C67#2353semidirect
407. C2×#387D67semidirect
418. C67C2×#2353semidirect
445. #387C2×D67semidirect
509. C2×C4⋊C4C4×D67semidirect
643. C4⋊C4C2×C4×D67semidirect
795. C2#22563148direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240052
#225631482
C2×#168632882
C2×#168632862
C2×#168632822
C2×#168632742
C2×#168632632
C2×#168632582
C2×#168632532
C2×C4×(C2×D67)⋊C42
C2×#168632432
C2×#168632412
C2×#95×D672
C2×#387×C672
C2×#235367