Finite Group Databasebeta

← C2×#22564018 #31023313

Subgroups — C2×#22564018 #31023313

Order 17152.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524022C211yesmaximal, characteristic, complemented
2C22×#14524021C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D67C211yesmaximal, characteristic
4#22564018C2116yesmaximal, direct product factor
5C2×#16863331C211yesmaximal, characteristic, complemented
6C2×#16863327C211yesmaximal, characteristic, complemented
7C2×#16863318C211yesmaximal, characteristic, complemented
8C2×#16863316C211yesmaximal, characteristic, complemented
9C2×#16863291C211yesmaximal, characteristic, complemented
10C2×#16863282C211yesmaximal, characteristic, complemented
11C2×#16863275C211yesmaximal, characteristic
12C2×#16863275C211yesmaximal, characteristic
13C2×#16863269C211yesmaximal, characteristic, complemented
14C2×#16863269C211yesmaximal, characteristic, complemented
15C2×#16863267C211yesmaximal, characteristic, complemented
16C23×C4⋊C4×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×C22⋊D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C2×#14524022—28no—
21C2×#14524022C2218yescomplemented
22C2×#14524021—28no—
23C2×#14524021C2218yescomplemented
24C2×C4×C22⋊D67—28no—
25C2×C4×C22⋊D67C2218yes—
26C22×C4⋊Dic67C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×C22⋊Dic67C2211yescharacteristic
35C22×C22⋊Dic67C2211yescharacteristic
36C22×C22⋊Dic67C2211yescharacteristic
37C22×(C2×D67)⋊C4C2211yescharacteristic
38C22×(C2×D67)⋊C4C2211yescharacteristic
39C22×(C2×D67)⋊C4C2211yescharacteristic
40C22×(C2×D67)⋊C4C2211yescharacteristic
41C22×(C2×D67)⋊C4C2211yescharacteristic
42C22×C4×Dic67C2211yescharacteristic
43#16863331C2218yescomplemented
44#16863327C2218yescomplemented
45#16863318C2218yescomplemented
46#16863316C2218yescomplemented
47#16863291C2218yescomplemented
48#16863282C2218yescomplemented
49#16863275C2218yes—
50#16863275C2218yes—
51#16863269C2218yescomplemented
52#16863269C2218yescomplemented
53#16863267C2218yescomplemented
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C2×C67⋊#95C2211yescharacteristic
62C24×C4×C67C2211yescharacteristic
63C24×C4×C67C2211yescharacteristic
64C24×C4×C67C2211yescharacteristic
65C22×C4⋊C4×C67—28no—
66C22×C4⋊C4×C67C2211yescharacteristic
67C22×C4⋊C4×C67C2211yescharacteristic
68C22×C4⋊C4×C67C2211yescharacteristic
69C22×C4⋊C4×C67C2211yescharacteristic
70C22×C4⋊C4×C67C2218yescomplemented
71C24×D67C2311yescharacteristic
72C22×Dic134—24no—
73C22×Dic134—24no—
74C22×Dic134—42no—
75C22×Dic134C2314yes—
76C22×C22⋊D67—24no—
77C22×C22⋊D67—24no—
78C22×C22⋊D67Q818yescomplemented
79C22×C22⋊D67C2314yes—
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C23×Dic67C2311yescharacteristic
87C22×C4×D67—24no—
88C22×C4×D67—24no—
89C22×C4×D67—42no—
90C22×C4×D67C2314yes—
91#14524022—232no—
92#14524021—232no—
93C4×C22⋊D67—232no—
94C2×C4⋊Dic67—24no—
95C2×C4⋊Dic67C2314yes—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4—24no—
98C2×Dic67⋊C4—24no—
99C2×Dic67⋊C4—24no—
100C2×Dic67⋊C4—24no—
101C2×Dic67⋊C4—24no—
102C2×Dic67⋊C4—42no—
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C2×Dic67⋊C4C2314yes—
107C2×Dic67⋊C4C2314yes—
108C2×Dic67⋊C4C2314yes—
109C2×Dic67⋊C4C2314yes—
110C2×C22⋊Dic67—24no—
111C2×C22⋊Dic67—24no—
112C2×C22⋊Dic67D418yes—
113C2×C22⋊Dic67C2314yes—
114C2×C22⋊Dic67C2314yes—
115C2×C22⋊Dic67C2314yes—
116C2×(C2×D67)⋊C4—24no—
117C2×(C2×D67)⋊C4—24no—
118C2×(C2×D67)⋊C4—24no—
119C2×(C2×D67)⋊C4—24no—
120C2×(C2×D67)⋊C4—42no—
121C2×(C2×D67)⋊C4C2314yes—
122C2×(C2×D67)⋊C4C2314yes—
123C2×(C2×D67)⋊C4C2314yes—
124C2×(C2×D67)⋊C4C2314yes—
125C2×(C2×D67)⋊C4C2314yes—
126C2×C4×Dic67—24no—
127C2×C4×Dic67C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C67⋊#95C2314yes—
136C25×C67C2311yescharacteristic
137C23×C4×C67—24no—
138C23×C4×C67—24no—
139C23×C4×C67—24no—
140C23×C4×C67—24no—
141C23×C4×C67—24no—
142C23×C4×C67—24no—
143C23×C4×C67—24no—
144C23×C4×C67—42no—
145C23×C4×C67—42no—
146C23×C4×C67C2311yescharacteristic
147C23×C4×C67C2311yescharacteristic
148C23×C4×C67C2314yes—
149C23×C4×C67C2314yes—
150C23×C4×C67C2314yes—
151C23×C4×C67C2311yescharacteristic
152C23×C4×C67C2311yescharacteristic
153C23×C4×C67C2311yescharacteristic
154C23×C4×C67C2311yescharacteristic
155C2×C4⋊C4×C67—24no—
156C2×C4⋊C4×C67—24no—
157C2×C4⋊C4×C67—24no—
158C2×C4⋊C4×C67—232no—
159C2×C4⋊C4×C67D418yescomplemented
160C2×C4⋊C4×C67C2314yes—
161C2×C4⋊C4×C67C2314yes—
162C2×C4⋊C4×C67C2314yes—
163C2×C4⋊C4×C67C2314yes—
164C23×D67—22no—
165C23×D67—22no—
166C23×D67—22no—
167C23×D67—22no—
168C23×D67—22no—
169C23×D67—22no—
170C23×D67C2×Q814yes—
171C23×D67C2412yes—
172C2×Dic134—28no—
173C2×Dic134—28no—
174C2×Dic134—44no—
175C2×Dic134—416no—
176C2×C22⋊D67—232no—
177C2×C22⋊D67—28no—
178C2×C22⋊D67—28no—
179C2×C22⋊D67C2×Q8116yescomplemented
180C22×Dic67—22no—
181C22×Dic67—22no—
182C22×Dic67—22no—
183C22×Dic67—22no—
184C22×Dic67—22no—
185C22×Dic67—22no—
186C22×Dic67—22no—
187C22×Dic67—22no—
188C22×Dic67—22no—
189C22×Dic67—22no—
190C22×Dic67—22no—
191C22×Dic67—22no—
192C22×Dic67—22no—
193C22×Dic67—22no—
194C22×Dic67—22no—
195C22×Dic67—22no—
196C22×Dic67—22no—
197C22×Dic67—22no—
198C22×Dic67C2×D414yes—
199C22×Dic67C2×D414yes—
200C22×Dic67C2×Q814yes—
201C22×Dic67C2412yes—
202C22×Dic67C2412yes—
203C22×Dic67C2412yes—
204C22×Dic67C2412yes—
205C22×Dic67C2412yes—
206C22×Dic67C2412yes—
207C22×Dic67C2412yes—
208C2×C4×D67—28no—
209C2×C4×D67—28no—
210C2×C4×D67—44no—
211C2×C4×D67—416no—
212C4⋊Dic67—28no—
213Dic67⋊C4—28no—
214Dic67⋊C4—28no—
215Dic67⋊C4—28no—
216Dic67⋊C4—28no—
217Dic67⋊C4—28no—
218Dic67⋊C4—28no—
219Dic67⋊C4—44no—
220C22⋊Dic67—28no—
221C22⋊Dic67—28no—
222C22⋊Dic67C2×D4116yes—
223(C2×D67)⋊C4—28no—
224(C2×D67)⋊C4—28no—
225(C2×D67)⋊C4—28no—
226(C2×D67)⋊C4—28no—
227(C2×D67)⋊C4—44no—
228C4×Dic67—28no—
229C24×C67—22no—
230C24×C67—22no—
231C24×C67—22no—
232C24×C67—22no—
233C24×C67C2×D414yes—
234C24×C67C2×Q814yes—
235C24×C67#4114yes—
236C24×C67C2412yes—
237C24×C67C2411yescharacteristic
238C22×C4×C67—232no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67—28no—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67—22no—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67—28no—
249C22×C4×C67—28no—
250C22×C4×C67—22no—
251C22×C4×C67—22no—
252C22×C4×C67—22no—
253C22×C4×C67—22no—
254C22×C4×C67—28no—
255C22×C4×C67—28no—
256C22×C4×C67—22no—
257C22×C4×C67—22no—
258C22×C4×C67—28no—
259C22×C4×C67—28no—
260C22×C4×C67—44no—
261C22×C4×C67—44no—
262C22×C4×C67—416no—
263C22×C4×C67—416no—
264C22×C4×C67C2×D414yes—
265C22×C4×C67C2×D414yes—
266C22×C4×C67C2×D414yes—
267C22×C4×C67#4114yes—
268C22×C4×C67C2412yes—
269C22×C4×C67C2412yes—
270C22×C4×C67C2412yes—
271C22×C4×C67C2412yes—
272C22×C4×C67C2412yes—
273C22×C4×C67C2412yes—
274C4⋊C4×C67—28no—
275C4⋊C4×C67—28no—
276C4⋊C4×C67—28no—
277C4⋊C4×C67C2×D4116yescomplemented
278C23×C67—28no—
279C23×C67—28no—
280C23×C67—28no—
281C23×C67—28no—
282C23×C67—28no—
283C23×C67—28no—
284C23×C67—22no—
285C23×C67—22no—
286C23×C67—22no—
287C23×C67—22no—
288C23×C67C22⋊Q8116yescomplemented
289C23×C67C22×D414yes—
290C23×C67C22×D412yes—
291C23×C67C22×D412yes—
292C23×C67C22×Q814yes—
293C23×C67C22×Q812yes—
294C23×C67C2×#4114yes—
295C23×C67C2×#4112yes—
296C23×C67C2×#4112yes—
297C23×C67H(5,𝔽2)12yes—
298C23×C672−1+412yes—
299C23×C67C2511yescharacteristic
300C22×D67—28no—
301C22×D67—28no—
302C22×D67—28no—
303C22×D67—22no—
304C22×D67—22no—
305C22×D67—22no—
306C22×D67—22no—
307C22×D67—22no—
308C22×D67—22no—
309C22×D67—44no—
310C22×D67—44no—
311C22×D67—44no—
312C22×D67—44no—
313C22×D67C22×Q814yes—
314C2×C4×C67—232no—
315C2×C4×C67—28no—
316C2×C4×C67—28no—
317C2×C4×C67—28no—
318C2×C4×C67—28no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—22no—
323C2×C4×C67—22no—
324C2×C4×C67—22no—
325C2×C4×C67—22no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—22no—
329C2×C4×C67—22no—
330C2×C4×C67—22no—
331C2×C4×C67—22no—
332C2×C4×C67—22no—
333C2×C4×C67—416no—
334C2×C4×C67—416no—
335C2×C4×C67—44no—
336C2×C4×C67—44no—
337C2×C4×C67C22×D414yes—
338C2×C4×C67C22×D414yes—
339C2×C4×C67C22×D414yes—
340C2×C4×C67C2×#4114yes—
341C22⋊D67—232no—
342C2×Dic67—28no—
343C2×Dic67—28no—
344C2×Dic67—28no—
345C2×Dic67—22no—
346C2×Dic67—22no—
347C2×Dic67—22no—
348C2×Dic67—22no—
349C2×Dic67—22no—
350C2×Dic67—22no—
351C2×Dic67—22no—
352C2×Dic67—22no—
353C2×Dic67—22no—
354C2×Dic67—22no—
355C2×Dic67—22no—
356C2×Dic67—22no—
357C2×Dic67—22no—
358C2×Dic67—22no—
359C2×Dic67—22no—
360C2×Dic67—22no—
361C2×Dic67—22no—
362C2×Dic67—22no—
363C2×Dic67—44no—
364C2×Dic67—44no—
365C2×Dic67—44no—
366C2×Dic67—44no—
367C2×Dic67C22×D414yes—
368C2×Dic67C22×D414yes—
369C2×Dic67C22×Q814yes—
370C4×D67—416no—
371Dic134—416no—
372C22×C67—24no—
373C22×C67—24no—
374C22×C67—24no—
375C22×C67—24no—
376C22×C67—24no—
377C22×C67—24no—
378C22×C67—232no—
379C22×C67C2×C22⋊Q814yes—
380C22×C67C2×C22⋊Q818yescomplemented
381C22×C67#52514yes—
382C22×C67#53914yes—
383C22×C67D4214yes—
384C22×C67#54714yes—
385C22×C67D4×Q814yes—
386C22×C67#55414yes—
387C22×C67C23×D411yescharacteristic
388C22×C67C23×D411yescharacteristic
389C22×C67C23×Q811yescharacteristic
390C22×C67C22×#4111yescharacteristic
391C22×C67C22×#4111yescharacteristic
392C22×C67C2×H(5,𝔽2)11yescharacteristic
393C22×C67C2×2−1+411yescharacteristic
394C2×D67—24no—
395C2×D67—24no—
396C2×D67—24no—
397C2×D67—42no—
398C2×D67—42no—
399C2×D67—42no—
400C2×D67—42no—
401C2×D67—416no—
402C4×C67—24no—
403C4×C67—24no—
404C4×C67—24no—
405C4×C67—24no—
406C4×C67—42no—
407C4×C67—42no—
408Dic67—24no—
409Dic67—24no—
410Dic67—24no—
411Dic67—42no—
412Dic67—42no—
413Dic67—42no—
414Dic67—42no—
415C2×#2449—671nomaximal, Sylow
416C2×C67—28no—
417C2×C67#244918yescomplemented
418C2×C67C22×C22⋊Q811yescharacteristic
419C2×C67C2×#52511yescharacteristic
420C2×C67C2×#53911yescharacteristic
421C2×C67C2×D4211yescharacteristic
422C2×C67C2×#54711yescharacteristic
423C2×C67C2×D4×Q811yescharacteristic
424C2×C67C2×#55411yescharacteristic
425D67—44no—
426C22×C22⋊Q8—671no—
427C22×C22⋊Q8—671no—
428C22×C4×D4—671no—
429C23×C4⋊C4D6711yescharacteristic, complemented
430#2449—6716no—
431C2×#399—671no—
432C2×#398—671no—
433C2×#396—671no—
434C2×#395—671no—
435C2×#389—671no—
436C2×#387—671no—
437C2×#386—671no—
438C2×#386—671no—
439C2×#385—671no—
440C2×#385—671no—
441C2×#385—671no—
442C67C2×#244911yescharacteristic, complemented, Sylow
443C23×Q8—671no—
444C23×D4—671no—
445C24×C4—671no—
446C24×C4C2×D6711yescharacteristic
447C24×C4C2×D6711yescharacteristic
448C24×C4C2×D6711yescharacteristic
449C2×C22⋊Q8—678no—
450C2×C22⋊Q8—678no—
451C2×C22⋊Q8—1348no—
452C2×C22⋊Q8—1348no—
453C2×C4×D4—678no—
454C2×C4×D4—1348no—
455C22×C4⋊C4—28no—
456C22×C4⋊C4—671no—
457C22×C4⋊C4—671no—
458C22×C4⋊C4—671no—
459C22×C4⋊C4—671no—
460C22×C4⋊C4—671no—
461C22×C4⋊C4—671no—
462C22×C4⋊C4—671no—
463C22×C4⋊C4—671no—
464C22×C4⋊C4C2×D6711yescharacteristic
465C22×C4⋊C4C2×D6711yescharacteristic
466C22×C4⋊C4C2×D6711yescharacteristic
467C22×C4⋊C4C2×D6711yescharacteristic
468C22×C4⋊C4C2×D6718yescomplemented
469C22×C22⋊C4—671no—
470C22×C22⋊C4—671no—
471C22×C22⋊C4—671no—
472C22×C22⋊C4—671no—
473C22×C22⋊C4—671no—
474C22×C22⋊C4—671no—
475C22×C22⋊C4—671no—
476C22×C22⋊C4—671no—
477C22×C42—671no—
478#399—678no—
479#398—678no—
480#396—678no—
481#395—678no—
482#389—678no—
483#387—678no—
484#386—678no—
485#386—678no—
486#385—678no—
487#385—678no—
488#385—678no—
489C2×#95—671no—
490C2×#95—671no—
491C2×#95—671no—
492C2×#95—671no—
493C2×#95—671no—
494C2×#95—671no—
495C2×#95—671no—
496C2×#95—671no—
497C25—671no—
498C25C22×D6711yescharacteristic
499C22×Q8—2682no—
500C22×Q8—674no—
501C22×Q8—1344no—
502C22×Q8—1344no—
503C22×D4—678no—
504C22×D4—674no—
505C22×D4—1344no—
506C22×D4—1344no—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—42no—
515C23×C4—42no—
516C23×C4—2682no—
517C23×C4—674no—
518C23×C4—671no—
519C23×C4—671no—
520C23×C4—671no—
521C23×C4—671no—
522C23×C4—671no—
523C23×C4—671no—
524C23×C4—671no—
525C23×C4—1344no—
526C23×C4—1344no—
527C23×C4C22×D6714yes—
528C23×C4C22×D6711yescharacteristic
529C23×C4C22×D6711yescharacteristic
530C23×C4C22×D6714yes—
531C23×C4C22×D6714yes—
532C23×C4C22×D6711yescharacteristic
533C23×C4C22×D6711yescharacteristic
534C23×C4C22×D6711yescharacteristic
535C23×C4C22×D6711yescharacteristic
536C22⋊Q8—13432no—
537C22⋊Q8—13432no—
538C4×D4—13432no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—232no—
543C2×C4⋊C4—2682no—
544C2×C4⋊C4—674no—
545C2×C4⋊C4—674no—
546C2×C4⋊C4—674no—
547C2×C4⋊C4—674no—
548C2×C4⋊C4—674no—
549C2×C4⋊C4—674no—
550C2×C4⋊C4—674no—
551C2×C4⋊C4—674no—
552C2×C4⋊C4—1344no—
553C2×C4⋊C4—1344no—
554C2×C4⋊C4—1344no—
555C2×C4⋊C4—1344no—
556C2×C4⋊C4—1344no—
557C2×C4⋊C4—1344no—
558C2×C4⋊C4—1344no—
559C2×C4⋊C4C22⋊D6718yescomplemented
560C2×C4⋊C4C22×D6714yes—
561C2×C4⋊C4C22×D6714yes—
562C2×C4⋊C4C22×D6714yes—
563C2×C4⋊C4C22×D6714yes—
564C2×C22⋊C4—2682no—
565C2×C22⋊C4—674no—
566C2×C22⋊C4—678no—
567C2×C22⋊C4—674no—
568C2×C22⋊C4—674no—
569C2×C22⋊C4—674no—
570C2×C22⋊C4—674no—
571C2×C22⋊C4—674no—
572C2×C22⋊C4—674no—
573C2×C22⋊C4—674no—
574C2×C22⋊C4—1344no—
575C2×C22⋊C4—1344no—
576C2×C22⋊C4—1344no—
577C2×C22⋊C4—1344no—
578C2×C22⋊C4—1344no—
579C2×C22⋊C4—1344no—
580C2×C42—674no—
581C2×C42—1344no—
582#95—674no—
583#95—674no—
584#95—674no—
585#95—674no—
586#95—674no—
587#95—674no—
588#95—674no—
589#95—674no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—674no—
595C24—672no—
596C24—1342no—
597C24—1342no—
598C24—1342no—
599C24—1342no—
600C24—1342no—
601C24—1342no—
602C24D4×D6714yes—
603C24Q8×D6714yes—
604C24#1176162814yes—
605C24C23×D6712yes—
606C24C23×D6711yescharacteristic
607C2×Q8—26816no—
608C2×Q8—2684no—
609C2×Q8—1348no—
610C2×Q8—1348no—
611C2×D4—6716no—
612C2×D4—13432no—
613C2×D4—1348no—
614C2×D4—1348no—
615C22×C4—232no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—28no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—28no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—416no—
640C22×C4—416no—
641C22×C4—26816no—
642C22×C4—2684no—
643C22×C4—674no—
644C22×C4—674no—
645C22×C4—674no—
646C22×C4—672no—
647C22×C4—672no—
648C22×C4—672no—
649C22×C4—672no—
650C22×C4—672no—
651C22×C4—672no—
652C22×C4—672no—
653C22×C4—1348no—
654C22×C4—1342no—
655C22×C4—1342no—
656C22×C4—1342no—
657C22×C4—1342no—
658C22×C4—1342no—
659C22×C4—1342no—
660C22×C4—1342no—
661C22×C4—1342no—
662C22×C4—1342no—
663C22×C4—1342no—
664C22×C4—1342no—
665C22×C4—1342no—
666C22×C4—1348no—
667C22×C4—1342no—
668C22×C4—1342no—
669C22×C4—1342no—
670C22×C4—1342no—
671C22×C4—1342no—
672C22×C4—1342no—
673C22×C4C2×C22⋊D6714yes—
674C22×C4C2×C22⋊D6714yes—
675C22×C4C2×C22⋊D6714yes—
676C22×C4#1176162814yes—
677C22×C4C23×D6712yes—
678C22×C4C23×D6712yes—
679C22×C4C23×D6712yes—
680C22×C4C23×D6712yes—
681C22×C4C23×D6712yes—
682C22×C4C23×D6712yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—2684no—
687C4⋊C4—1348no—
688C4⋊C4—1348no—
689C4⋊C4—1348no—
690C4⋊C4—1348no—
691C4⋊C4—1348no—
692C4⋊C4—1348no—
693C4⋊C4—1348no—
694C4⋊C4C2×C22⋊D67116yescomplemented
695C22⋊C4—2684no—
696C22⋊C4—6716no—
697C22⋊C4—1348no—
698C22⋊C4—1348no—
699C22⋊C4—1348no—
700C22⋊C4—1348no—
701C22⋊C4—1348no—
702C22⋊C4—1348no—
703C42—1348no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—28no—
714C23—2684no—
715C23—2684no—
716C23—2684no—
717C23—2684no—
718C23—674no—
719C23—1348no—
720C23—1348no—
721C23—1348no—
722C23—1342no—
723C23—1342no—
724C23—1342no—
725C23—1342no—
726C23—1342no—
727C23—1342no—
728C23#14524021116yescomplemented
729C23C2×D4×D6714yes—
730C23C2×D4×D6712yes—
731C23C22×C22⋊D6712yes—
732C23C2×Q8×D6714yes—
733C23C2×Q8×D6712yes—
734C23C2×#1176162814yes—
735C23C2×#1176162812yes—
736C23C2×#1176162812yes—
737C23#1452408812yes—
738C23#1452409112yes—
739C23C24×D6711yescharacteristic
740Q8—26816no—
741D4—13432no—
742C2×C4—232no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—416no—
762C2×C4—416no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—26816no—
766C2×C4—2684no—
767C2×C4—2684no—
768C2×C4—2684no—
769C2×C4—2684no—
770C2×C4—674no—
771C2×C4—674no—
772C2×C4—674no—
773C2×C4—1342no—
774C2×C4—1342no—
775C2×C4—1342no—
776C2×C4—1342no—
777C2×C4—1342no—
778C2×C4—1342no—
779C2×C4—1342no—
780C2×C4—1342no—
781C2×C4—1342no—
782C2×C4—1342no—
783C2×C4—1342no—
784C2×C4—1342no—
785C2×C4—1348no—
786C2×C4—1348no—
787C2×C4—1348no—
788C2×C4—1342no—
789C2×C4—1342no—
790C2×C4—1342no—
791C2×C4—1342no—
792C2×C4—1342no—
793C2×C4—1342no—
794C2×C4C22×C22⋊D6714yes—
795C2×C4C22×C22⋊D6714yes—
796C2×C4C22×C22⋊D6714yes—
797C2×C4C2×#1176162814yes—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—232no—
804C22—24no—
805C22—2682no—
806C22—2682no—
807C22—2682no—
808C22—26816no—
809C22—2682no—
810C22—1344no—
811C22—1344no—
812C22—1344no—
813C22C2×#1452402114yes—
814C22C2×#1452402118yescomplemented
815C22#1686390714yes—
816C22#1686399314yes—
817C22D4×C22⋊D6714yes—
818C22#1686404714yes—
819C22Q8×C22⋊D6714yes—
820C22#1686410114yes—
821C22C22×D4×D6711yescharacteristic
822C22C23×C22⋊D6711yescharacteristic
823C22C22×Q8×D6711yescharacteristic
824C22C22×#1176162811yescharacteristic
825C22C22×#1176162811yescharacteristic
826C22C2×#1452408811yescharacteristic
827C22C2×#1452409111yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—42no—
834C4—2682no—
835C4—2682no—
836C4—2682no—
837C4—2682no—
838C4—1344no—
839C4—1344no—
840C4—1344no—
841C2—28no—
842C2—2684no—
843C2#2256401818yesdirect product factor
844C2C22×#1452402111yescharacteristic
845C2C2×#1686390711yescharacteristic
846C2C2×#1686399311yescharacteristic
847C2C2×D4×C22⋊D6711yescharacteristic
848C2C2×#1686404711yescharacteristic
849C2C2×Q8×C22⋊D6711yescharacteristic
850C2C2×#1686410111yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC23×C4⋊C4×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
hypercenterC23×C4⋊C4D67
hypocenterC67C2×#2449
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14524022C2semidirect
2. C22×#14524021C2semidirect
4. #22564018C2direct (N × H)
5. C2×#16863331C2semidirect
6. C2×#16863327C2semidirect
7. C2×#16863318C2semidirect
8. C2×#16863316C2semidirect
9. C2×#16863291C2semidirect
10. C2×#16863282C2semidirect
13. C2×#16863269C2semidirect
14. C2×#16863269C2semidirect
15. C2×#16863267C2semidirect
16. C23×C4⋊C4×C67C2semidirect
21. C2×#14524022C22semidirect
23. C2×#14524021C22semidirect
43. #16863331C22semidirect
44. #16863327C22semidirect
45. #16863318C22semidirect
46. #16863316C22semidirect
47. #16863291C22semidirect
48. #16863282C22semidirect
51. #16863269C22semidirect
52. #16863269C22semidirect
53. #16863267C22semidirect
70. C22×C4⋊C4×C67C22semidirect
78. C22×C22⋊D67Q8semidirect
159. C2×C4⋊C4×C67D4semidirect
179. C2×C22⋊D67C2×Q8semidirect
277. C4⋊C4×C67C2×D4semidirect
288. C23×C67C22⋊Q8semidirect
380. C22×C67C2×C22⋊Q8semidirect
417. C2×C67#2449semidirect
429. C23×C4⋊C4D67semidirect
442. C67C2×#2449semidirect
468. C22×C4⋊C4C2×D67semidirect
559. C2×C4⋊C4C22⋊D67semidirect
694. C4⋊C4C2×C22⋊D67semidirect
728. C23#14524021semidirect
814. C22C2×#14524021semidirect
843. C2#22564018direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240222
C22×#145240212
C22×C4×C22⋊D672
#225640182
C2×#168633312
C2×#168633272
C2×#168633182
C2×#168633162
C2×#168632912
C2×#168632822
C2×#168632752
C2×#168632692
C2×#168632672
C23×C4⋊C4×C672
C2×#244967