Finite Group Databasebeta

← C2×C4×#14524025 #31014265

Subgroups — C2×C4×#14524025 #31014265

Order 17152.

4070 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524025C211yesmaximal, characteristic
2C22×C4×C22⋊D67C211yesmaximal, characteristic
3C22×C42×D67C211yesmaximal, characteristic, complemented
4C4×#14524025C2116yesmaximal, direct product factor
5C2×#16863290C211yesmaximal, characteristic, complemented
6C2×#16863289C211yesmaximal, characteristic, complemented
7C2×#16863279C211yesmaximal, characteristic, complemented
8C2×#16863278C211yesmaximal, characteristic, complemented
9C2×#16863272C211yesmaximal, characteristic
10C2×#16863270C211yesmaximal, characteristic, complemented
11C2×#16863258C211yesmaximal, characteristic, complemented
12C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×C4⋊Dic67C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic67C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
17C23×C22⋊D67C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C2×#14524025C4116yesdirect product factor
22C2×#14524025C2218yes—
23C2×C4×C22⋊D67—28no—
24C2×C4×C22⋊D67C2218yes—
25C22×C4⋊Dic67C2211yescharacteristic
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×C4×Dic67C2211yescharacteristic
37C22×C4×Dic67C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39C22×C4×Dic67C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C2×C42×D67—28no—
42C2×C42×D67C2218yescomplemented
43#16863290C2218yescomplemented
44#16863289C2218yescomplemented
45#16863279C2218yescomplemented
46#16863278C2218yescomplemented
47#16863272C2218yes—
48#16863270C2218yescomplemented
49#16863258C2218yescomplemented
50C4×Dic67⋊C4C2218yescomplemented
51C4×C4⋊Dic67C2218yescomplemented
52C4×(C2×D67)⋊C4C2218yescomplemented
53C4×C22⋊Dic67C2218yescomplemented
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
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×C22⋊D67—24no—
72C22×C22⋊D67—24no—
73C22×C22⋊D67C2×C418yes—
74C22×C22⋊D67C2314yes—
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C22×C4×D67—24no—
83C22×C4×D67—24no—
84C22×C4×D67—24no—
85C22×C4×D67—24no—
86C22×C4×D67—24no—
87C22×C4×D67—24no—
88C22×C4×D67—24no—
89C22×C4×D67C2×C418yescomplemented
90C22×C4×D67D418yes—
91C22×C4×D67C2314yes—
92C22×C4×D67C2314yes—
93C22×C4×D67C2314yes—
94#14524025C2×C4164yesdirect product factor
95C4×C22⋊D67—232no—
96C2×C4⋊Dic67—24no—
97C2×C4⋊Dic67C2×C418yescomplemented
98C2×C4⋊Dic67C2314yes—
99C2×C4⋊Dic67C2314yes—
100C2×Dic67⋊C4—24no—
101C2×Dic67⋊C4—24no—
102C2×Dic67⋊C4C2×C418yescomplemented
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C2×C22⋊Dic67—24no—
107C2×C22⋊Dic67—24no—
108C2×C22⋊Dic67C2×C418yescomplemented
109C2×C22⋊Dic67C2314yes—
110C2×C22⋊Dic67C2314yes—
111C2×C22⋊Dic67C2314yes—
112C2×(C2×D67)⋊C4—24no—
113C2×(C2×D67)⋊C4—24no—
114C2×(C2×D67)⋊C4C2×C418yescomplemented
115C2×(C2×D67)⋊C4C2314yes—
116C2×(C2×D67)⋊C4C2314yes—
117C2×(C2×D67)⋊C4C2314yes—
118C2×C4×Dic67—24no—
119C2×C4×Dic67—24no—
120C2×C4×Dic67—24no—
121C2×C4×Dic67—24no—
122C2×C4×Dic67—24no—
123C2×C4×Dic67C2314yes—
124C2×C4×Dic67C2314yes—
125C2×C4×Dic67C2314yes—
126C2×C4×Dic67C2314yes—
127C2×C4×Dic67C2314yes—
128C42×D67—232no—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
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×D67C22×C414yes—
163C23×D67C2×D414yes—
164C23×D67#4114yes—
165C23×D67C2412yes—
166C2×C22⋊D67—232no—
167C2×C22⋊D67—28no—
168C2×C22⋊D67—28no—
169C2×C22⋊D67C22×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×Dic67—22no—
186C22×Dic67C22×C414yes—
187C22×Dic67C22×C414yes—
188C22×Dic67C22×C414yes—
189C22×Dic67C2×D414yes—
190C22×Dic67#4114yes—
191C22×Dic67C2412yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C22×Dic67C2412yes—
195C22×Dic67C2412yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C2×C4×D67—232no—
199C2×C4×D67—232no—
200C2×C4×D67—28no—
201C2×C4×D67—28no—
202C2×C4×D67—28no—
203C2×C4×D67—232no—
204C2×C4×D67—28no—
205C2×C4×D67—28no—
206C2×C4×D67—28no—
207C2×C4×D67—28no—
208C2×C4×D67C22×C4116yescomplemented
209C2×C4×D67C2×D4116yes—
210C4⋊Dic67—28no—
211C4⋊Dic67C22×C4116yescomplemented
212Dic67⋊C4—28no—
213Dic67⋊C4—28no—
214Dic67⋊C4C22×C4116yescomplemented
215C22⋊Dic67—28no—
216C22⋊Dic67—28no—
217C22⋊Dic67C22×C4116yescomplemented
218(C2×D67)⋊C4—28no—
219(C2×D67)⋊C4—28no—
220(C2×D67)⋊C4C22×C4116yescomplemented
221C4×Dic67—28no—
222C4×Dic67—28no—
223C4×Dic67—28no—
224C4×Dic67—28no—
225C4×Dic67—28no—
226C24×C67—22no—
227C24×C67—22no—
228C24×C67—22no—
229C24×C67—22no—
230C24×C67—22no—
231C24×C67—22no—
232C24×C67C22×C414yes—
233C24×C67C2412yes—
234C24×C67C2411yescharacteristic
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—22no—
247C22×C4×C67—28no—
248C22×C4×C67—28no—
249C22×C4×C67—28no—
250C22×C4×C67—416no—
251C22×C4×C67C22×C414yes—
252C22×C4×C67C22×C414yes—
253C22×C4×C67C2×D414yes—
254C22×C4×C67#4114yes—
255C22×C4×C67#4114yes—
256C22×C4×C67#4114yes—
257C22×C4×C67C2412yes—
258C22×C4×C67C2412yes—
259C22×C4×C67C2412yes—
260C22×C4×C67C2412yes—
261C22×C4×C67C2412yes—
262C22×C4×C67C2412yes—
263C22⋊C4×C67—28no—
264C22⋊C4×C67C22×C4116yescomplemented
265C42×C67—28no—
266C42×C67—28no—
267C23×C67—28no—
268C23×C67—28no—
269C23×C67—28no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—44no—
277C23×C67—44no—
278C23×C67—44no—
279C23×C67—44no—
280C23×C67C23×C414yes—
281C23×C67C23×C412yes—
282C23×C67C22×D412yes—
283C23×C67C2×#4112yes—
284C23×C67C2×#4112yes—
285C23×C67C2×#4112yes—
286C23×C67C2×#4112yes—
287C23×C67C2×#4112yes—
288C23×C67C2511yescharacteristic
289C22×D67—28no—
290C22×D67—28no—
291C22×D67—28no—
292C22×D67—28no—
293C22×D67—28no—
294C22×D67—28no—
295C22×D67—22no—
296C22×D67—22no—
297C22×D67—22no—
298C22×D67—22no—
299C22×D67C4×D4116yes—
300C22×D67C23×C414yes—
301C22×D67C22×D414yes—
302C22×D67C2×#4114yes—
303C2×C4×C67—28no—
304C2×C4×C67—28no—
305C2×C4×C67—28no—
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—22no—
318C2×C4×C67—44no—
319C2×C4×C67—44no—
320C2×C4×C67—416no—
321C2×C4×C67#123116yescomplemented
322C2×C4×C67C23×C414yes—
323C2×C4×C67C23×C414yes—
324C2×C4×C67C22×D414yes—
325C2×C4×C67C2×#4114yes—
326C2×C4×C67C2×#4114yes—
327C2×C4×C67C2×#4114yes—
328C22⋊D67—232no—
329C2×Dic67—28no—
330C2×Dic67—28no—
331C2×Dic67—28no—
332C2×Dic67—28no—
333C2×Dic67—28no—
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—22no—
347C2×Dic67—22no—
348C2×Dic67—22no—
349C2×Dic67—22no—
350C2×Dic67—44no—
351C2×Dic67—44no—
352C2×Dic67C23×C414yes—
353C2×Dic67C23×C414yes—
354C2×Dic67C23×C414yes—
355C2×Dic67C22×D414yes—
356C2×Dic67C2×#4114yes—
357C4×D67—232no—
358C4×D67—232no—
359C4×D67—232no—
360C22×C67—24no—
361C22×C67—24no—
362C22×C67—24no—
363C22×C67—42no—
364C22×C67—42no—
365C22×C67—42no—
366C22×C67—42no—
367C22×C67—416no—
368C22×C67C2×C4×D414yes—
369C22×C67C4×#4114yes—
370C22×C67C4×#4114yes—
371C22×C67C2×#12314yes—
372C22×C67#52514yes—
373C22×C67#52914yes—
374C22×C67#52914yes—
375C22×C67C24×C411yescharacteristic
376C22×C67C23×D411yescharacteristic
377C22×C67C22×#4111yescharacteristic
378C22×C67C22×#4111yescharacteristic
379C22×C67C22×#4111yescharacteristic
380C22×C67C22×#4111yescharacteristic
381C22×C67C22×#4111yescharacteristic
382C2×D67—24no—
383C2×D67—24no—
384C2×D67—24no—
385C2×D67—24no—
386C2×D67—24no—
387C2×D67—24no—
388C2×D67—232no—
389C2×D67C2×C4×D418yes—
390C4×C67—24no—
391C4×C67—24no—
392C4×C67—24no—
393C4×C67—42no—
394C4×C67—42no—
395C4×C67C2×#12318yescomplemented
396Dic67—24no—
397Dic67—24no—
398Dic67—24no—
399Dic67—24no—
400Dic67—24no—
401Dic67—42no—
402Dic67—42no—
403C2×C4×#123—671nomaximal, Sylow
404C2×C67—44no—
405C2×C67C4×#12318yescomplemented
406C2×C67C22×C4×D411yescharacteristic
407C2×C67C2×C4×#4111yescharacteristic
408C2×C67C2×C4×#4111yescharacteristic
409C2×C67C22×#12311yescharacteristic
410C2×C67C2×#52511yescharacteristic
411C2×C67C2×#52911yescharacteristic
412C2×C67C2×#52911yescharacteristic
413D67—28no—
414C22×#123—671no—
415C22×C4×D4—671no—
416C23×C42—671no—
417C4×#123—6716no—
418C2×#388—671no—
419C2×#388—671no—
420C2×#387—671no—
421C2×#387—671no—
422C2×#386—671no—
423C2×#385—671no—
424C2×#381—671no—
425C2×C4×C4⋊C4—671no—
426C2×C4×C4⋊C4—671no—
427C2×C4×C22⋊C4—671no—
428C2×C4×C22⋊C4—671no—
429C2×C4×C22⋊C4D6711yescharacteristic, complemented
430C67C2×C4×#12311yescharacteristic, complemented, Sylow
431C23×D4—671no—
432C24×C4—671no—
433C24×C4—671no—
434C24×C4—671no—
435C24×C4C2×D6711yescharacteristic
436C2×#123—6716no—
437C2×#123—678no—
438C2×C4×D4—678no—
439C2×C4×D4—1348no—
440C22×C4⋊C4—671no—
441C22×C4⋊C4—671no—
442C22×C4⋊C4—671no—
443C22×C4⋊C4—671no—
444C22×C4⋊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—678no—
459C22×C42—1348no—
460C22×C42C2×D6711yescharacteristic
461C22×C42C2×D6711yescharacteristic
462#388—678no—
463#388—678no—
464#387—678no—
465#387—678no—
466#386—678no—
467#385—678no—
468#381—678no—
469C4×C4⋊C4—678no—
470C4×C4⋊C4—678no—
471C4×C22⋊C4—678no—
472C4×C22⋊C4—678no—
473C4×C22⋊C4C2×D6718yescomplemented
474C2×#95—671no—
475C2×#95—671no—
476C2×#95—671no—
477C2×#95—671no—
478C2×#95—671no—
479C2×#95—671no—
480C2×#95—671no—
481C2×#95—671no—
482C2×#95C2×D6711yescharacteristic
483C2×#95C2×D6711yescharacteristic
484C25—671no—
485C25C22×D6711yescharacteristic
486C22×D4—678no—
487C22×D4—674no—
488C22×D4—1344no—
489C22×D4—1344no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—671no—
494C23×C4—671no—
495C23×C4—671no—
496C23×C4—671no—
497C23×C4—671no—
498C23×C4—678no—
499C23×C4—678no—
500C23×C4—674no—
501C23×C4—674no—
502C23×C4—671no—
503C23×C4—671no—
504C23×C4—674no—
505C23×C4—1344no—
506C23×C4—1344no—
507C23×C4—1344no—
508C23×C4—1344no—
509C23×C4—1344no—
510C23×C4—1344no—
511C23×C4—1344no—
512C23×C4C22×D6711yescharacteristic
513C23×C4C22×D6711yescharacteristic
514C23×C4C22×D6714yes—
515C23×C4C22×D6711yescharacteristic
516C23×C4C22×D6711yescharacteristic
517C23×C4C22×D6711yescharacteristic
518C23×C4C22×D6711yescharacteristic
519#123—6764no—
520C4×D4—13432no—
521C2×C4⋊C4—678no—
522C2×C4⋊C4—678no—
523C2×C4⋊C4—674no—
524C2×C4⋊C4—674no—
525C2×C4⋊C4—674no—
526C2×C4⋊C4—674no—
527C2×C4⋊C4—674no—
528C2×C4⋊C4—1344no—
529C2×C4⋊C4—1344no—
530C2×C4⋊C4—1344no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—678no—
533C2×C22⋊C4—674no—
534C2×C22⋊C4—678no—
535C2×C22⋊C4—674no—
536C2×C22⋊C4—674no—
537C2×C22⋊C4—674no—
538C2×C22⋊C4—674no—
539C2×C22⋊C4—674no—
540C2×C22⋊C4—1344no—
541C2×C22⋊C4—1344no—
542C2×C22⋊C4—1344no—
543C2×C22⋊C4—1344no—
544C2×C22⋊C4C4×D6718yescomplemented
545C2×C22⋊C4C22×D6714yes—
546C2×C22⋊C4C22×D6714yes—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—674no—
550C2×C42—674no—
551C2×C42—674no—
552C2×C42—674no—
553C2×C42—674no—
554C2×C42—13432no—
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#95—674no—
569#95—674no—
570#95C22×D6714yes—
571#95C22×D6714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—674no—
579C24—674no—
580C24—674no—
581C24—672no—
582C24—1342no—
583C24—1342no—
584C24—1342no—
585C24—1342no—
586C24C2×C4×D6714yes—
587C24C23×D6712yes—
588C24C23×D6711yescharacteristic
589C2×D4—6716no—
590C2×D4—1348no—
591C2×D4—13432no—
592C2×D4—1348no—
593C22×C4—22no—
594C22×C4—22no—
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—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—416no—
609C22×C4—674no—
610C22×C4—674no—
611C22×C4—674no—
612C22×C4—674no—
613C22×C4—674no—
614C22×C4—672no—
615C22×C4—672no—
616C22×C4—672no—
617C22×C4—672no—
618C22×C4—672no—
619C22×C4—6716no—
620C22×C4—6716no—
621C22×C4—672no—
622C22×C4—672no—
623C22×C4—1348no—
624C22×C4—1348no—
625C22×C4—1348no—
626C22×C4—13432no—
627C22×C4—1348no—
628C22×C4—13432no—
629C22×C4—1342no—
630C22×C4—1342no—
631C22×C4—1342no—
632C22×C4—1342no—
633C22×C4—1342no—
634C22×C4—1342no—
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×C4—1342no—
644C22×C4—1342no—
645C22×C4—13432no—
646C22×C4—1348no—
647C22×C4—1348no—
648C22×C4—1348no—
649C22×C4C2×C4×D6714yes—
650C22×C4C2×C4×D6714yes—
651C22×C4D4×D6714yes—
652C22×C4#1176162714yes—
653C22×C4#1176162814yes—
654C22×C4#1176162814yes—
655C22×C4C23×D6712yes—
656C22×C4C23×D6712yes—
657C22×C4C23×D6712yes—
658C22×C4C23×D6712yes—
659C22×C4C23×D6712yes—
660C22×C4C23×D6712yes—
661C4⋊C4—6716no—
662C4⋊C4—6716no—
663C4⋊C4—1348no—
664C4⋊C4—1348no—
665C4⋊C4—1348no—
666C22⋊C4—28no—
667C22⋊C4—6716no—
668C22⋊C4—6716no—
669C22⋊C4—1348no—
670C22⋊C4—1348no—
671C22⋊C4—1348no—
672C22⋊C4—1348no—
673C22⋊C4C2×C4×D67116yescomplemented
674C42—28no—
675C42—28no—
676C42—1348no—
677C42—1348no—
678C42—1348no—
679C42—1348no—
680C42—1348no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—6716no—
695C23—674no—
696C23—674no—
697C23—674no—
698C23—1348no—
699C23—1348no—
700C23—1348no—
701C23—1348no—
702C23—1348no—
703C23—1348no—
704C23—1342no—
705C23—1342no—
706C23—1342no—
707C23—1342no—
708C23C22×C4×D6714yes—
709C23C22×C4×D6712yes—
710C23C2×D4×D6712yes—
711C23#41×D6712yes—
712C23#41×D6712yes—
713C23C2×#1176162712yes—
714C23C2×#1176162812yes—
715C23C2×#1176162812yes—
716C23C24×D6711yescharacteristic
717D4—13432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
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—22no—
732C2×C4—22no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—416no—
736C2×C4—2684no—
737C2×C4—2684no—
738C2×C4—674no—
739C2×C4—674no—
740C2×C4—674no—
741C2×C4—674no—
742C2×C4—674no—
743C2×C4—13432no—
744C2×C4—13432no—
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—1348no—
756C2×C4—1342no—
757C2×C4—1342no—
758C2×C4—1342no—
759C2×C4—1342no—
760C2×C4—1342no—
761C2×C4—1342no—
762C2×C4—1342no—
763C2×C4—1342no—
764C2×C4—1342no—
765C2×C4—1342no—
766C2×C4—13432no—
767C2×C4#14524025116yesdirect product factor
768C2×C4C22×C4×D6714yes—
769C2×C4C22×C4×D6714yes—
770C2×C4C2×D4×D6714yes—
771C2×C4C2×#1176162714yes—
772C2×C4C2×#1176162814yes—
773C2×C4C2×#1176162814yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—416no—
782C22—678no—
783C22—1344no—
784C22—1344no—
785C22—1344no—
786C22—1344no—
787C22—1344no—
788C22—1344no—
789C22—13432no—
790C22C4×D4×D6714yes—
791C22C4×#1176162714yes—
792C22C4×#1176162814yes—
793C22C2×#1452402514yes—
794C22#1686390514yes—
795C22#1686392414yes—
796C22#1686392814yes—
797C22C23×C4×D6711yescharacteristic
798C22C22×D4×D6711yescharacteristic
799C22C2×#41×D6711yescharacteristic
800C22C2×#41×D6711yescharacteristic
801C22C22×#1176162711yescharacteristic
802C22C22×#1176162811yescharacteristic
803C22C22×#1176162811yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—2682no—
810C4—2682no—
811C4—1344no—
812C4—1344no—
813C4—1344no—
814C4—1344no—
815C4—1344no—
816C4C2×#1452402518yesdirect product factor
817C2—44no—
818C2—1348no—
819C2C4×#1452402518yesdirect product factor
820C2C2×C4×D4×D6711yescharacteristic
821C2C2×C4×#1176162711yescharacteristic
822C2C2×C4×#1176162811yescharacteristic
823C2C22×#1452402511yescharacteristic
824C2C2×#1686390511yescharacteristic
825C2C2×#1686392411yescharacteristic
826C2C2×#1686392811yescharacteristic
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×#123
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
3. C22×C42×D67C2semidirect
4. C4×#14524025C2direct (N × H)
5. C2×#16863290C2semidirect
6. C2×#16863289C2semidirect
7. C2×#16863279C2semidirect
8. C2×#16863278C2semidirect
10. C2×#16863270C2semidirect
11. C2×#16863258C2semidirect
12. C2×C4×Dic67⋊C4C2semidirect
13. C2×C4×C4⋊Dic67C2semidirect
14. C2×C4×(C2×D67)⋊C4C2semidirect
15. C2×C4×C22⋊Dic67C2semidirect
16. C2×C4×C22⋊C4×C67C2semidirect
21. C2×#14524025C4direct (N × H)
42. C2×C42×D67C22semidirect
43. #16863290C22semidirect
44. #16863289C22semidirect
45. #16863279C22semidirect
46. #16863278C22semidirect
48. #16863270C22semidirect
49. #16863258C22semidirect
50. C4×Dic67⋊C4C22semidirect
51. C4×C4⋊Dic67C22semidirect
52. C4×(C2×D67)⋊C4C22semidirect
53. C4×C22⋊Dic67C22semidirect
67. C4×C22⋊C4×C67C22semidirect
89. C22×C4×D67C2×C4semidirect
94. #14524025C2×C4direct (N × H)
97. C2×C4⋊Dic67C2×C4semidirect
102. C2×Dic67⋊C4C2×C4semidirect
108. C2×C22⋊Dic67C2×C4semidirect
114. C2×(C2×D67)⋊C4C2×C4semidirect
149. C2×C22⋊C4×C67C2×C4semidirect
208. C2×C4×D67C22×C4semidirect
211. C4⋊Dic67C22×C4semidirect
214. Dic67⋊C4C22×C4semidirect
217. C22⋊Dic67C22×C4semidirect
220. (C2×D67)⋊C4C22×C4semidirect
264. C22⋊C4×C67C22×C4semidirect
321. C2×C4×C67#123semidirect
395. C4×C67C2×#123semidirect
405. C2×C67C4×#123semidirect
429. C2×C4×C22⋊C4D67semidirect
430. C67C2×C4×#123semidirect
473. C4×C22⋊C4C2×D67semidirect
544. C2×C22⋊C4C4×D67semidirect
673. C22⋊C4C2×C4×D67semidirect
767. C2×C4#14524025direct (N × H)
816. C4C2×#14524025direct (N × H)
819. C2C4×#14524025direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240252
C22×C4×C22⋊D672
C22×C42×D672
C4×#145240252
C2×#168632902
C2×#168632892
C2×#168632792
C2×#168632782
C2×#168632722
C2×#168632702
C2×#168632582
C2×C4×Dic67⋊C42
C2×C4×C4⋊Dic672
C2×C4×(C2×D67)⋊C42
C2×C4×C22⋊Dic672
C2×C4×C22⋊C4×C672
C2×C4×#12367