Finite Group Databasebeta

← C2×C4×#14524029 #31014300

Subgroups — C2×C4×#14524029 #31014300

Order 17152.

3790 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524029C211yesmaximal, characteristic
2C22×C4×Dic134C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D67C211yesmaximal, characteristic
4C4×#14524029C2116yesmaximal, direct product factor
5C2×#16863300C211yesmaximal, characteristic, complemented
6C2×#16863296C211yesmaximal, characteristic
7C2×#16863289C211yesmaximal, characteristic, complemented
8C2×#16863288C211yesmaximal, characteristic, complemented
9C2×#16863285C211yesmaximal, characteristic, complemented
10C2×#16863284C211yesmaximal, characteristic, complemented
11C2×#16863260C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic67C211yesmaximal, characteristic, complemented
15C2×C42×Dic67C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×C22⋊D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C2×#14524029C4116yesdirect product factor
21C2×#14524029C2218yes—
22C2×C4×Dic134—28no—
23C2×C4×Dic134C2218yescomplemented
24C2×C4×C22⋊D67—28no—
25C2×C4×C22⋊D67C2218yes—
26C22×C4⋊Dic67C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×C22⋊Dic67C2211yescharacteristic
31C22×C22⋊Dic67C2211yescharacteristic
32C22×C22⋊Dic67C2211yescharacteristic
33C22×(C2×D67)⋊C4C2211yescharacteristic
34C22×(C2×D67)⋊C4C2211yescharacteristic
35C22×(C2×D67)⋊C4C2211yescharacteristic
36C22×(C2×D67)⋊C4C2211yescharacteristic
37C22×(C2×D67)⋊C4C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39C22×C4×Dic67C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42C22×C4×Dic67C2211yescharacteristic
43C22×C4×Dic67C2211yescharacteristic
44C22×C4×Dic67C2211yescharacteristic
45#16863300C2218yescomplemented
46#16863296C2218yes—
47#16863289C2218yescomplemented
48#16863288C2218yescomplemented
49#16863285C2218yescomplemented
50#16863284C2218yescomplemented
51#16863260C2218yescomplemented
52C4×(C2×D67)⋊C4C2218yescomplemented
53C4×(C2×D67)⋊C4C2218yescomplemented
54C4×C22⋊Dic67C2218yescomplemented
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C42×Dic67C2218yescomplemented
62C24×C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65C22×C42×C67C2211yescharacteristic
66C22×C42×C67C2211yescharacteristic
67C4×C22⋊C4×C67C2218yescomplemented
68C2×#95×C67C2211yescharacteristic
69C2×#95×C67C2211yescharacteristic
70C24×D67C2311yescharacteristic
71C22×Dic134—24no—
72C22×Dic134—24no—
73C22×Dic134C2×C418yescomplemented
74C22×Dic134C2314yes—
75C22×C22⋊D67—24no—
76C22×C22⋊D67—24no—
77C22×C22⋊D67C2×C418yes—
78C22×C22⋊D67C2314yes—
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C22×C4×D67—24no—
87C22×C4×D67—24no—
88C22×C4×D67—24no—
89C22×C4×D67C2314yes—
90#14524029C2×C4164yesdirect product factor
91C4×Dic134—232no—
92C4×C22⋊D67—232no—
93C2×C4⋊Dic67—24no—
94C2×C4⋊Dic67C2314yes—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4—24no—
98C2×Dic67⋊C4C2314yes—
99C2×Dic67⋊C4C2314yes—
100C2×Dic67⋊C4C2314yes—
101C2×C22⋊Dic67—24no—
102C2×C22⋊Dic67—24no—
103C2×C22⋊Dic67C2×C418yescomplemented
104C2×C22⋊Dic67C2314yes—
105C2×C22⋊Dic67C2314yes—
106C2×C22⋊Dic67C2314yes—
107C2×(C2×D67)⋊C4—24no—
108C2×(C2×D67)⋊C4—24no—
109C2×(C2×D67)⋊C4—24no—
110C2×(C2×D67)⋊C4C2×C418yescomplemented
111C2×(C2×D67)⋊C4C2×C418yescomplemented
112C2×(C2×D67)⋊C4C2314yes—
113C2×(C2×D67)⋊C4C2314yes—
114C2×(C2×D67)⋊C4C2314yes—
115C2×(C2×D67)⋊C4C2314yes—
116C2×(C2×D67)⋊C4C2314yes—
117C2×C4×Dic67—24no—
118C2×C4×Dic67—24no—
119C2×C4×Dic67—24no—
120C2×C4×Dic67—24no—
121C2×C4×Dic67—24no—
122C2×C4×Dic67C2×C418yescomplemented
123C2×C4×Dic67D418yes—
124C2×C4×Dic67C2314yes—
125C2×C4×Dic67C2314yes—
126C2×C4×Dic67C2314yes—
127C2×C4×Dic67C2314yes—
128C2×C4×Dic67C2314yes—
129C2×C4×Dic67C2314yes—
130C2×C4×Dic67C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C67⋊#95C2314yes—
136C67⋊#95C2314yes—
137C25×C67C2311yescharacteristic
138C23×C4×C67—24no—
139C23×C4×C67—24no—
140C23×C4×C67—24no—
141C23×C4×C67C2311yescharacteristic
142C23×C4×C67C2311yescharacteristic
143C23×C4×C67C2314yes—
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146C23×C4×C67C2311yescharacteristic
147C23×C4×C67C2311yescharacteristic
148C2×C22⋊C4×C67—24no—
149C2×C22⋊C4×C67C2×C418yescomplemented
150C2×C22⋊C4×C67C2314yes—
151C2×C22⋊C4×C67C2314yes—
152C2×C42×C67—24no—
153C2×C42×C67—24no—
154C2×C42×C67C2314yes—
155C2×C42×C67C2314yes—
156#95×C67C2314yes—
157#95×C67C2314yes—
158C23×D67—22no—
159C23×D67—22no—
160C23×D67—22no—
161C23×D67—22no—
162C23×D67—22no—
163C23×D67—22no—
164C23×D67C22×C414yes—
165C23×D67C2412yes—
166C2×Dic134—232no—
167C2×Dic134—28no—
168C2×Dic134—28no—
169C2×Dic134C22×C4116yescomplemented
170C2×C22⋊D67—232no—
171C2×C22⋊D67—28no—
172C2×C22⋊D67—28no—
173C2×C22⋊D67C22×C4116yes—
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×Dic67—22no—
186C22×Dic67—22no—
187C22×Dic67—22no—
188C22×Dic67C22×C414yes—
189C22×Dic67C22×C414yes—
190C22×Dic67C22×C414yes—
191C22×Dic67C2×D414yes—
192C22×Dic67C2×D414yes—
193C22×Dic67#4114yes—
194C22×Dic67#4114yes—
195C22×Dic67C2412yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C22×Dic67C2412yes—
199C22×Dic67C2412yes—
200C22×Dic67C2412yes—
201C22×Dic67C2412yes—
202C2×C4×D67—28no—
203C2×C4×D67—28no—
204C2×C4×D67—28no—
205C2×C4×D67—416no—
206C4⋊Dic67—28no—
207Dic67⋊C4—28no—
208Dic67⋊C4—28no—
209Dic67⋊C4—28no—
210C22⋊Dic67—28no—
211C22⋊Dic67—28no—
212C22⋊Dic67C22×C4116yescomplemented
213(C2×D67)⋊C4—28no—
214(C2×D67)⋊C4—28no—
215(C2×D67)⋊C4—28no—
216(C2×D67)⋊C4C22×C4116yescomplemented
217(C2×D67)⋊C4C22×C4116yescomplemented
218C4×Dic67—28no—
219C4×Dic67—28no—
220C4×Dic67—28no—
221C4×Dic67—28no—
222C4×Dic67—28no—
223C4×Dic67C22×C4116yescomplemented
224C4×Dic67C2×D4116yes—
225C24×C67—22no—
226C24×C67—22no—
227C24×C67—22no—
228C24×C67—22no—
229C24×C67—22no—
230C24×C67—22no—
231C24×C67C22×C414yes—
232C24×C67C2412yes—
233C24×C67C2411yescharacteristic
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×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67—22no—
246C22×C4×C67—28no—
247C22×C4×C67—28no—
248C22×C4×C67—28no—
249C22×C4×C67—416no—
250C22×C4×C67C22×C414yes—
251C22×C4×C67C22×C414yes—
252C22×C4×C67C2×D414yes—
253C22×C4×C67#4114yes—
254C22×C4×C67#4114yes—
255C22×C4×C67#4114yes—
256C22×C4×C67C2412yes—
257C22×C4×C67C2412yes—
258C22×C4×C67C2412yes—
259C22×C4×C67C2412yes—
260C22×C4×C67C2412yes—
261C22×C4×C67C2412yes—
262C22⋊C4×C67—28no—
263C22⋊C4×C67C22×C4116yescomplemented
264C42×C67—28no—
265C42×C67—28no—
266C23×C67—28no—
267C23×C67—28no—
268C23×C67—28no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—44no—
276C23×C67—44no—
277C23×C67—44no—
278C23×C67—44no—
279C23×C67C23×C414yes—
280C23×C67C23×C412yes—
281C23×C67C22×D412yes—
282C23×C67C2×#4112yes—
283C23×C67C2×#4112yes—
284C23×C67C2×#4112yes—
285C23×C67C2×#4112yes—
286C23×C67C2×#4112yes—
287C23×C67C2511yescharacteristic
288C22×D67—28no—
289C22×D67—28no—
290C22×D67—28no—
291C22×D67—22no—
292C22×D67—22no—
293C22×D67—22no—
294C22×D67—22no—
295C22×D67—22no—
296C22×D67—22no—
297C22×D67—44no—
298C22×D67—44no—
299C22×D67—44no—
300C22×D67—44no—
301C22×D67C23×C414yes—
302C2×C4×C67—28no—
303C2×C4×C67—28no—
304C2×C4×C67—28no—
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—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—44no—
318C2×C4×C67—44no—
319C2×C4×C67—416no—
320C2×C4×C67#124116yescomplemented
321C2×C4×C67C23×C414yes—
322C2×C4×C67C23×C414yes—
323C2×C4×C67C22×D414yes—
324C2×C4×C67C2×#4114yes—
325C2×C4×C67C2×#4114yes—
326C2×C4×C67C2×#4114yes—
327C22⋊D67—232no—
328C2×Dic67—28no—
329C2×Dic67—28no—
330C2×Dic67—28no—
331C2×Dic67—28no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—22no—
339C2×Dic67—22no—
340C2×Dic67—22no—
341C2×Dic67—22no—
342C2×Dic67—22no—
343C2×Dic67—22no—
344C2×Dic67—22no—
345C2×Dic67—22no—
346C2×Dic67—44no—
347C2×Dic67—44no—
348C2×Dic67C4×D4116yes—
349C2×Dic67C23×C414yes—
350C2×Dic67C23×C414yes—
351C2×Dic67C23×C414yes—
352C2×Dic67C22×D414yes—
353C2×Dic67C22×D414yes—
354C2×Dic67C2×#4114yes—
355C2×Dic67C2×#4114yes—
356C4×D67—416no—
357Dic134—232no—
358C22×C67—24no—
359C22×C67—24no—
360C22×C67—24no—
361C22×C67—42no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—42no—
365C22×C67—416no—
366C22×C67C2×C4×D414yes—
367C22×C67C4×#4114yes—
368C22×C67C4×#4114yes—
369C22×C67C2×#12414yes—
370C22×C67#52914yes—
371C22×C67#52914yes—
372C22×C67#53214yes—
373C22×C67C24×C411yescharacteristic
374C22×C67C23×D411yescharacteristic
375C22×C67C22×#4111yescharacteristic
376C22×C67C22×#4111yescharacteristic
377C22×C67C22×#4111yescharacteristic
378C22×C67C22×#4111yescharacteristic
379C22×C67C22×#4111yescharacteristic
380C2×D67—24no—
381C2×D67—24no—
382C2×D67—24no—
383C2×D67—42no—
384C2×D67—42no—
385C2×D67—42no—
386C2×D67—42no—
387C2×D67—416no—
388C4×C67—24no—
389C4×C67—24no—
390C4×C67—24no—
391C4×C67—42no—
392C4×C67—42no—
393C4×C67C2×#12418yescomplemented
394Dic67—24no—
395Dic67—24no—
396Dic67—24no—
397Dic67—24no—
398Dic67—42no—
399Dic67—42no—
400Dic67C2×C4×D418yes—
401C2×C4×#124—671nomaximal, Sylow
402C2×C67—44no—
403C2×C67C4×#12418yescomplemented
404C2×C67C22×C4×D411yescharacteristic
405C2×C67C2×C4×#4111yescharacteristic
406C2×C67C2×C4×#4111yescharacteristic
407C2×C67C22×#12411yescharacteristic
408C2×C67C2×#52911yescharacteristic
409C2×C67C2×#52911yescharacteristic
410C2×C67C2×#53211yescharacteristic
411D67—44no—
412C22×#124—671no—
413C22×C4×Q8—671no—
414C22×C4×D4—671no—
415C4×#124—6716no—
416C2×#391—671no—
417C2×#390—671no—
418C2×#388—671no—
419C2×#388—671no—
420C2×#388—671no—
421C2×#388—671no—
422C2×#382—671no—
423C2×C4×C22⋊C4—671no—
424C2×C4×C22⋊C4—671no—
425C2×C4×C22⋊C4—671no—
426C2×C4×C22⋊C4D6711yescharacteristic, complemented
427C2×C43—671no—
428C67C2×C4×#12411yescharacteristic, complemented, Sylow
429C23×Q8—671no—
430C23×D4—671no—
431C24×C4—671no—
432C24×C4C2×D6711yescharacteristic
433C2×#124—6716no—
434C2×#124—678no—
435C2×C4×Q8—678no—
436C2×C4×Q8—1348no—
437C2×C4×D4—678no—
438C2×C4×D4—1348no—
439C22×C4⋊C4—671no—
440C22×C4⋊C4—671no—
441C22×C4⋊C4—671no—
442C22×C4⋊C4—671no—
443C22×C22⋊C4—671no—
444C22×C22⋊C4—671no—
445C22×C22⋊C4—671no—
446C22×C22⋊C4—671no—
447C22×C22⋊C4—671no—
448C22×C22⋊C4—671no—
449C22×C22⋊C4—671no—
450C22×C22⋊C4—671no—
451C22×C22⋊C4C2×D6711yescharacteristic
452C22×C22⋊C4C2×D6711yescharacteristic
453C22×C42—671no—
454C22×C42—671no—
455C22×C42—671no—
456C22×C42—671no—
457C22×C42—671no—
458C22×C42—671no—
459C22×C42—671no—
460C22×C42C2×D6711yescharacteristic
461C22×C42C2×D6711yescharacteristic
462#391—678no—
463#390—678no—
464#388—678no—
465#388—678no—
466#388—678no—
467#388—678no—
468#382—678no—
469C4×C22⋊C4—678no—
470C4×C22⋊C4—678no—
471C4×C22⋊C4—678no—
472C4×C22⋊C4C2×D6718yescomplemented
473C2×#95—671no—
474C2×#95—671no—
475C2×#95—671no—
476C2×#95—671no—
477C2×#95—671no—
478C2×#95—671no—
479C2×#95C2×D6711yescharacteristic
480C2×#95C2×D6711yescharacteristic
481C43—678no—
482C25—671no—
483C25C22×D6711yescharacteristic
484C22×Q8—678no—
485C22×Q8—674no—
486C22×Q8—1344no—
487C22×Q8—1344no—
488C22×D4—678no—
489C22×D4—674no—
490C22×D4—1344no—
491C22×D4—1344no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—671no—
496C23×C4—671no—
497C23×C4—671no—
498C23×C4—671no—
499C23×C4—671no—
500C23×C4—671no—
501C23×C4—671no—
502C23×C4—674no—
503C23×C4—1344no—
504C23×C4—1344no—
505C23×C4—1344no—
506C23×C4C22×D6711yescharacteristic
507C23×C4C22×D6711yescharacteristic
508C23×C4C22×D6714yes—
509C23×C4C22×D6711yescharacteristic
510C23×C4C22×D6711yescharacteristic
511C23×C4C22×D6711yescharacteristic
512C23×C4C22×D6711yescharacteristic
513#124—6764no—
514C4×Q8—13432no—
515C4×D4—13432no—
516C2×C4⋊C4—674no—
517C2×C4⋊C4—674no—
518C2×C4⋊C4—674no—
519C2×C4⋊C4—674no—
520C2×C4⋊C4—1344no—
521C2×C4⋊C4—1344no—
522C2×C4⋊C4—1344no—
523C2×C4⋊C4—1344no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—678no—
526C2×C22⋊C4—674no—
527C2×C22⋊C4—678no—
528C2×C22⋊C4—678no—
529C2×C22⋊C4—674no—
530C2×C22⋊C4—674no—
531C2×C22⋊C4—674no—
532C2×C22⋊C4—674no—
533C2×C22⋊C4—674no—
534C2×C22⋊C4—674no—
535C2×C22⋊C4—674no—
536C2×C22⋊C4—1344no—
537C2×C22⋊C4—1344no—
538C2×C22⋊C4—1344no—
539C2×C22⋊C4—1344no—
540C2×C22⋊C4—1344no—
541C2×C22⋊C4C4×D6718yescomplemented
542C2×C22⋊C4C22×D6714yes—
543C2×C22⋊C4C22×D6714yes—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—678no—
547C2×C42—678no—
548C2×C42—674no—
549C2×C42—674no—
550C2×C42—674no—
551C2×C42—674no—
552C2×C42—674no—
553C2×C42—674no—
554C2×C42—674no—
555C2×C42—1344no—
556C2×C42—1344no—
557C2×C42—1344no—
558C2×C42—1344no—
559C2×C42—1344no—
560C2×C42C22×D6714yes—
561C2×C42C22×D6714yes—
562#95—674no—
563#95—674no—
564#95—674no—
565#95—674no—
566#95—674no—
567#95—674no—
568#95C22×D6714yes—
569#95C22×D6714yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—674no—
577C24—672no—
578C24—1342no—
579C24—1342no—
580C24—1342no—
581C24—1342no—
582C24—1342no—
583C24—1342no—
584C24C2×C4×D6714yes—
585C24C23×D6712yes—
586C24C23×D6711yescharacteristic
587C2×Q8—6716no—
588C2×Q8—1348no—
589C2×Q8—13432no—
590C2×Q8—1348no—
591C2×D4—6716no—
592C2×D4—1348no—
593C2×D4—13432no—
594C2×D4—1348no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—416no—
611C22×C4—26816no—
612C22×C4—674no—
613C22×C4—674no—
614C22×C4—674no—
615C22×C4—672no—
616C22×C4—674no—
617C22×C4—674no—
618C22×C4—674no—
619C22×C4—674no—
620C22×C4—672no—
621C22×C4—672no—
622C22×C4—672no—
623C22×C4—672no—
624C22×C4—672no—
625C22×C4—672no—
626C22×C4—1342no—
627C22×C4—1342no—
628C22×C4—1342no—
629C22×C4—1342no—
630C22×C4—1342no—
631C22×C4—1342no—
632C22×C4—1348no—
633C22×C4—1348no—
634C22×C4—1348no—
635C22×C4—1342no—
636C22×C4—1342no—
637C22×C4—1342no—
638C22×C4—1342no—
639C22×C4—1342no—
640C22×C4—1342no—
641C22×C4—1342no—
642C22×C4—1342no—
643C22×C4C2×C4×D6714yes—
644C22×C4C2×C4×D6714yes—
645C22×C4D4×D6714yes—
646C22×C4#1176162714yes—
647C22×C4#1176162814yes—
648C22×C4#1176162814yes—
649C22×C4C23×D6712yes—
650C22×C4C23×D6712yes—
651C22×C4C23×D6712yes—
652C22×C4C23×D6712yes—
653C22×C4C23×D6712yes—
654C22×C4C23×D6712yes—
655C4⋊C4—1348no—
656C4⋊C4—1348no—
657C4⋊C4—1348no—
658C4⋊C4—1348no—
659C22⋊C4—28no—
660C22⋊C4—6716no—
661C22⋊C4—6716no—
662C22⋊C4—6716no—
663C22⋊C4—1348no—
664C22⋊C4—1348no—
665C22⋊C4—1348no—
666C22⋊C4—1348no—
667C22⋊C4—1348no—
668C22⋊C4C2×C4×D67116yescomplemented
669C42—28no—
670C42—28no—
671C42—6716no—
672C42—6716no—
673C42—1348no—
674C42—1348no—
675C42—1348no—
676C42—1348no—
677C42—1348no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—2684no—
692C23—2684no—
693C23—2684no—
694C23—2684no—
695C23—674no—
696C23—1348no—
697C23—1348no—
698C23—1348no—
699C23—1342no—
700C23—1342no—
701C23—1342no—
702C23—1342no—
703C23—1342no—
704C23—1342no—
705C23C22×C4×D6714yes—
706C23C22×C4×D6712yes—
707C23C2×D4×D6712yes—
708C23#41×D6712yes—
709C23#41×D6712yes—
710C23C2×#1176162712yes—
711C23C2×#1176162812yes—
712C23C2×#1176162812yes—
713C23C24×D6711yescharacteristic
714Q8—13432no—
715D4—13432no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—416no—
734C2×C4—2684no—
735C2×C4—2684no—
736C2×C4—26816no—
737C2×C4—6716no—
738C2×C4—674no—
739C2×C4—674no—
740C2×C4—674no—
741C2×C4—674no—
742C2×C4—674no—
743C2×C4—674no—
744C2×C4—674no—
745C2×C4—1342no—
746C2×C4—1342no—
747C2×C4—1342no—
748C2×C4—1342no—
749C2×C4—1342no—
750C2×C4—1342no—
751C2×C4—1348no—
752C2×C4—1348no—
753C2×C4—1348no—
754C2×C4—1348no—
755C2×C4—1342no—
756C2×C4—1342no—
757C2×C4—1342no—
758C2×C4—1342no—
759C2×C4—1342no—
760C2×C4—1342no—
761C2×C4—1342no—
762C2×C4—1342no—
763C2×C4#14524029116yesdirect product factor
764C2×C4C22×C4×D6714yes—
765C2×C4C22×C4×D6714yes—
766C2×C4C2×D4×D6714yes—
767C2×C4C2×#1176162714yes—
768C2×C4C2×#1176162814yes—
769C2×C4C2×#1176162814yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—416no—
778C22—2682no—
779C22—2682no—
780C22—2682no—
781C22—2682no—
782C22—26816no—
783C22—1344no—
784C22—1344no—
785C22—1344no—
786C22C4×D4×D6714yes—
787C22C4×#1176162714yes—
788C22C4×#1176162814yes—
789C22C2×#1452402914yes—
790C22#1686392414yes—
791C22#1686392614yes—
792C22#1686394314yes—
793C22C23×C4×D6711yescharacteristic
794C22C22×D4×D6711yescharacteristic
795C22C2×#41×D6711yescharacteristic
796C22C2×#41×D6711yescharacteristic
797C22C22×#1176162711yescharacteristic
798C22C22×#1176162811yescharacteristic
799C22C22×#1176162811yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—2682no—
806C4—2682no—
807C4—678no—
808C4—1344no—
809C4—1344no—
810C4—1344no—
811C4—1344no—
812C4C2×#1452402918yesdirect product factor
813C2—44no—
814C2—2684no—
815C2C4×#1452402918yesdirect product factor
816C2C2×C4×D4×D6711yescharacteristic
817C2C2×C4×#1176162711yescharacteristic
818C2C2×C4×#1176162811yescharacteristic
819C2C22×#1452402911yescharacteristic
820C2C2×#1686392411yescharacteristic
821C2C2×#1686392611yescharacteristic
822C2C2×#1686394311yescharacteristic
subgroupG/H
centerC23×C4C22×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×C4×C22⋊C4×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
cosocleC23×C67C25
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C2×C4×#124
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic134C2semidirect
4. C4×#14524029C2direct (N × H)
5. C2×#16863300C2semidirect
7. C2×#16863289C2semidirect
8. C2×#16863288C2semidirect
9. C2×#16863285C2semidirect
10. C2×#16863284C2semidirect
11. C2×#16863260C2semidirect
12. C2×C4×(C2×D67)⋊C4C2semidirect
13. C2×C4×(C2×D67)⋊C4C2semidirect
14. C2×C4×C22⋊Dic67C2semidirect
15. C2×C42×Dic67C2semidirect
16. C2×C4×C22⋊C4×C67C2semidirect
20. C2×#14524029C4direct (N × H)
23. C2×C4×Dic134C22semidirect
45. #16863300C22semidirect
47. #16863289C22semidirect
48. #16863288C22semidirect
49. #16863285C22semidirect
50. #16863284C22semidirect
51. #16863260C22semidirect
52. C4×(C2×D67)⋊C4C22semidirect
53. C4×(C2×D67)⋊C4C22semidirect
54. C4×C22⋊Dic67C22semidirect
61. C42×Dic67C22semidirect
67. C4×C22⋊C4×C67C22semidirect
73. C22×Dic134C2×C4semidirect
90. #14524029C2×C4direct (N × H)
103. C2×C22⋊Dic67C2×C4semidirect
110. C2×(C2×D67)⋊C4C2×C4semidirect
111. C2×(C2×D67)⋊C4C2×C4semidirect
122. C2×C4×Dic67C2×C4semidirect
149. C2×C22⋊C4×C67C2×C4semidirect
169. C2×Dic134C22×C4semidirect
212. C22⋊Dic67C22×C4semidirect
216. (C2×D67)⋊C4C22×C4semidirect
217. (C2×D67)⋊C4C22×C4semidirect
223. C4×Dic67C22×C4semidirect
263. C22⋊C4×C67C22×C4semidirect
320. C2×C4×C67#124semidirect
393. C4×C67C2×#124semidirect
403. C2×C67C4×#124semidirect
426. C2×C4×C22⋊C4D67semidirect
428. C67C2×C4×#124semidirect
472. C4×C22⋊C4C2×D67semidirect
541. C2×C22⋊C4C4×D67semidirect
668. C22⋊C4C2×C4×D67semidirect
763. C2×C4#14524029direct (N × H)
812. C4C2×#14524029direct (N × H)
815. C2C4×#14524029direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240292
C22×C4×Dic1342
C22×C4×C22⋊D672
C4×#145240292
C2×#168633002
C2×#168632962
C2×#168632892
C2×#168632882
C2×#168632852
C2×#168632842
C2×#168632602
C2×C4×(C2×D67)⋊C42
C2×C4×C22⋊Dic672
C2×C42×Dic672
C2×C4×C22⋊C4×C672
C2×C4×#12467