Finite Group Databasebeta

← C67×#26154 #30705405

Subgroups — C67×#26154 #30705405

Order 17152.

846 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C67C211yesmaximal, characteristic, complemented
2C2×#428×C67C211yesmaximal, characteristic, complemented
3C67×#2415C211yesmaximal, characteristic
4C67×#2352C211yesmaximal, characteristic
5C67×#2097C211yesmaximal, characteristic, complemented
6C67×#2085C211yesmaximal, characteristic, complemented
7C67×#2076C211yesmaximal, characteristic, complemented
8C67×#2035C211yesmaximal, characteristic, complemented
9C67×#1928C211yesmaximal, characteristic, complemented
10C67×#1920C211yesmaximal, characteristic, complemented
11C67×#1894C211yesmaximal, characteristic, complemented
12C67×#1872C211yesmaximal, characteristic, complemented
13C67×#1870C211yesmaximal, characteristic
14C67×#1854C211yesmaximal, characteristic, complemented
15C67×#1854C211yesmaximal, characteristic, complemented
16C22×M16×C67C2211yescharacteristic
17C2×C22⋊Q8×C67C2211yescharacteristic
18C2×C22⋊Q8×C67C2211yescharacteristic
19C2×C4×D4×C67C2211yescharacteristic
20C2×#117×C67C2211yescharacteristic
21C2×#117×C67C2211yescharacteristic
22C22×C4⋊C4×C67C2211yescharacteristic
23#485×C67—24no—
24#428×C67—24no—
25C2×#107×C67C2211yescharacteristic
26C2×#107×C67C2211yescharacteristic
27C2×#107×C67C2211yescharacteristic
28C2×#106×C67C2211yescharacteristic
29C2×#106×C67C2211yescharacteristic
30C2×#106×C67C2211yescharacteristic
31C2×#103×C67C2211yescharacteristic
32C2×#103×C67C2211yescharacteristic
33C2×#103×C67C2211yescharacteristic
34C2×#103×C67C2211yescharacteristic
35C2×C22⋊C8×C67C2211yescharacteristic
36C2×C22⋊C8×C67C2211yescharacteristic
37C2×C22⋊C8×C67C2211yescharacteristic
38#397×C67—21no—
39#394×C67—21no—
40#391×C67C2211yescharacteristic
41#389×C67—21no—
42#389×C67C2211yescharacteristic
43#388×C67—21no—
44#388×C67—21no—
45#387×C67—21no—
46#386×C67—21no—
47#382×C67C2211yescharacteristic
48#380×C67C2211yescharacteristic
49#380×C67C2211yescharacteristic
50#380×C67C2211yescharacteristic
51C4×C4⋊C4×C67C2211yescharacteristic
52C4×C22⋊C4×C67—21no—
53#340×C67C2211yescharacteristic
54#340×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#336×C67C2211yescharacteristic
60#336×C67C2211yescharacteristic
61C22×Q8×C67C2311yescharacteristic
62C22×D4×C67D411yescharacteristic
63C23×C4×C67—21no—
64C23×C4×C67C2311yescharacteristic
65C23×C4×C67C2311yescharacteristic
66C2×M16×C67—22no—
67C2×M16×C67—22no—
68C2×M16×C67—22no—
69C22×C8×C67C2311yescharacteristic
70C22×C8×C67C2311yescharacteristic
71C22×C8×C67C2311yescharacteristic
72C22×C8×C67C2311yescharacteristic
73C22⋊Q8×C67—22no—
74C22⋊Q8×C67—22no—
75C22⋊Q8×C67—22no—
76C22⋊Q8×C67—41no—
77C4×D4×C67—22no—
78C4×D4×C67—22no—
79#117×C67—22no—
80#117×C67—22no—
81#117×C67—41no—
82#117×C67—41no—
83C2×C4⋊C4×C67—22no—
84C2×C4⋊C4×C67—21no—
85C2×C4⋊C4×C67—21no—
86C2×C4⋊C4×C67—21no—
87C2×C4⋊C4×C67—21no—
88C2×C4⋊C4×C67—41no—
89C2×C4⋊C4×C67D411yescharacteristic
90C2×C4⋊C4×C67C2311yescharacteristic
91C2×C4⋊C4×C67C2311yescharacteristic
92C2×C4⋊C4×C67C2311yescharacteristic
93C2×C4⋊C4×C67C2311yescharacteristic
94C2×C4⋊C4×C67C2311yescharacteristic
95C2×C4⋊C4×C67C2311yescharacteristic
96C2×C4⋊C4×C67C2311yescharacteristic
97C2×C22⋊C4×C67—21no—
98C2×C22⋊C4×C67—21no—
99C2×C22⋊C4×C67—21no—
100C2×C22⋊C4×C67—21no—
101C2×C22⋊C4×C67—21no—
102C2×C22⋊C4×C67—21no—
103C2×C22⋊C4×C67—21no—
104C2×C22⋊C4×C67D411yescharacteristic
105C2×C22⋊C4×C67D411yescharacteristic
106C2×C42×C67—21no—
107C2×C42×C67—21no—
108C2×C42×C67—21no—
109C2×C42×C67C2311yescharacteristic
110#107×C67—22no—
111#107×C67—22no—
112#107×C67—22no—
113#106×C67—22no—
114#106×C67—41no—
115#106×C67D414yescomplemented
116#103×C67—22no—
117#103×C67—22no—
118#103×C67—22no—
119#103×C67—41no—
120C22⋊C8×C67—22no—
121C22⋊C8×C67—22no—
122C22⋊C8×C67—22no—
123#95×C67—21no—
124#95×C67—21no—
125#95×C67—21no—
126#95×C67—21no—
127#95×C67—21no—
128#95×C67—21no—
129#95×C67—21no—
130#95×C67—21no—
131#95×C67—21no—
132C24×C67C2×D411yescharacteristic
133C24×C67C2×D411yescharacteristic
134C2×Q8×C67—21no—
135C2×Q8×C67—21no—
136C2×Q8×C67—21no—
137C2×Q8×C67—21no—
138C2×Q8×C67—21no—
139C2×Q8×C67—21no—
140C2×D4×C67—22no—
141C2×D4×C67—41no—
142C2×D4×C67—41no—
143C22×C4×C67—21no—
144C22×C4×C67—21no—
145C22×C4×C67—21no—
146C22×C4×C67—21no—
147C22×C4×C67—21no—
148C22×C4×C67—21no—
149C22×C4×C67—21no—
150C22×C4×C67—21no—
151C22×C4×C67—21no—
152C22×C4×C67—21no—
153C22×C4×C67—21no—
154C22×C4×C67—21no—
155C22×C4×C67—21no—
156C22×C4×C67—21no—
157C22×C4×C67—21no—
158C22×C4×C67—21no—
159C22×C4×C67—21no—
160C22×C4×C67—21no—
161C22×C4×C67—42no—
162C22×C4×C67—42no—
163C22×C4×C67—81no—
164C22×C4×C67C2×D411yescharacteristic
165C22×C4×C67C2×D411yescharacteristic
166C22×C4×C67C2×D411yescharacteristic
167C22×C4×C67C2×D411yescharacteristic
168C22×C4×C67#4112yes—
169C22×C4×C67#4112yes—
170C22×C4×C67C2411yescharacteristic
171M16×C67—28no—
172C2×C8×C67—21no—
173C2×C8×C67—21no—
174C2×C8×C67—21no—
175C2×C8×C67—21no—
176C2×C8×C67—21no—
177C2×C8×C67—21no—
178C2×C8×C67—21no—
179C2×C8×C67—21no—
180C2×C8×C67—21no—
181C2×C8×C67—21no—
182C2×C8×C67C2×D412yes—
183C2×C8×C67#4112yes—
184C4⋊C4×C67—22no—
185C4⋊C4×C67—21no—
186C4⋊C4×C67—21no—
187C4⋊C4×C67—21no—
188C4⋊C4×C67—21no—
189C4⋊C4×C67—21no—
190C4⋊C4×C67—21no—
191C4⋊C4×C67—21no—
192C4⋊C4×C67—21no—
193C4⋊C4×C67—21no—
194C4⋊C4×C67—21no—
195C4⋊C4×C67—21no—
196C4⋊C4×C67—21no—
197C4⋊C4×C67—42no—
198C4⋊C4×C67—42no—
199C4⋊C4×C67—42no—
200C4⋊C4×C67—42no—
201C4⋊C4×C67C2×D412yes—
202C4⋊C4×C67C2×D412yes—
203C22⋊C4×C67—22no—
204C22⋊C4×C67—22no—
205C22⋊C4×C67—42no—
206C22⋊C4×C67—42no—
207C22⋊C4×C67—42no—
208C22⋊C4×C67—42no—
209C22⋊C4×C67—42no—
210C22⋊C4×C67—42no—
211C22⋊C4×C67—81no—
212C42×C67—21no—
213C42×C67—21no—
214C42×C67—42no—
215C42×C67—42no—
216C42×C67—81no—
217C23×C67—21no—
218C23×C67—21no—
219C23×C67—21no—
220C23×C67—21no—
221C23×C67—21no—
222C23×C67—21no—
223C23×C67—21no—
224C23×C67—21no—
225C23×C67—21no—
226C23×C67—21no—
227C23×C67—21no—
228C23×C67—21no—
229C23×C67—21no—
230C23×C67#12312yes—
231C23×C67C22×D411yescharacteristic
232Q8×C67—41no—
233Q8×C67—41no—
234Q8×C67—41no—
235Q8×C67—41no—
236D4×C67—44no—
237C2×C4×C67—21no—
238C2×C4×C67—21no—
239C2×C4×C67—22no—
240C2×C4×C67—22no—
241C2×C4×C67—22no—
242C2×C4×C67—22no—
243C2×C4×C67—21no—
244C2×C4×C67—21no—
245C2×C4×C67—21no—
246C2×C4×C67—21no—
247C2×C4×C67—22no—
248C2×C4×C67—22no—
249C2×C4×C67—21no—
250C2×C4×C67—21no—
251C2×C4×C67—21no—
252C2×C4×C67—21no—
253C2×C4×C67—21no—
254C2×C4×C67—41no—
255C2×C4×C67—41no—
256C2×C4×C67—41no—
257C2×C4×C67—41no—
258C2×C4×C67—41no—
259C2×C4×C67—41no—
260C2×C4×C67—41no—
261C2×C4×C67—41no—
262C2×C4×C67—41no—
263C2×C4×C67—41no—
264C2×C4×C67—41no—
265C2×C4×C67—41no—
266C2×C4×C67—41no—
267C2×C4×C67—41no—
268C2×C4×C67—41no—
269C2×C4×C67—41no—
270C2×C4×C67—41no—
271C2×C4×C67—41no—
272C2×C4×C67—41no—
273C2×C4×C67—41no—
274C2×C4×C67—41no—
275C2×C4×C67—41no—
276C2×C4×C67—41no—
277C2×C4×C67—41no—
278C2×C4×C67—41no—
279C2×C4×C67—41no—
280C2×C4×C67—84no—
281C2×C4×C67#12312yes—
282C2×C4×C67C22×D411yescharacteristic
283C2×C4×C67C2×#4111yescharacteristic
284C2×C4×C67C2×#4111yescharacteristic
285C2×C4×C67C2×#4111yescharacteristic
286C2×C4×C67H(5,𝔽2)11yescharacteristic
287C2×C4×C672−1+411yescharacteristic
288C8×C67—22no—
289C8×C67—22no—
290C8×C67—41no—
291C8×C67—41no—
292C22×C67—22no—
293C22×C67—22no—
294C22×C67—22no—
295C22×C67—41no—
296C22×C67—41no—
297C22×C67—41no—
298C22×C67—41no—
299C22×C67—41no—
300C22×C67—41no—
301C22×C67—41no—
302C22×C67—41no—
303C22×C67—41no—
304C22×C67—41no—
305C22×C67—41no—
306C22×C67C2×#12311yescharacteristic
307C22×C67D4211yescharacteristic
308C22×C67#54711yescharacteristic
309C22×C67#57511yescharacteristic
310C22×C67#57511yescharacteristic
311C22×C67#57711yescharacteristic
312C22×C67#57811yescharacteristic
313C4×C67—22no—
314C4×C67—41no—
315C4×C67—41no—
316C4×C67—41no—
317C4×C67—42no—
318C4×C67—42no—
319C4×C67—81no—
320C4×C67—81no—
321C4×C67—81no—
322C4×C67—81no—
323C4×C67—81no—
324C4×C67—81no—
325C4×C67#52511yescharacteristic
326C4×C67#53911yescharacteristic
327C4×C67#54811yescharacteristic
328C4×C67#55311yescharacteristic
329#26154C6711yesmaximal, characteristic, direct product factor, Sylow
330C2×C67—42no—
331C2×C67—81no—
332C2×C67#244311yescharacteristic
333C2×C67#309311yescharacteristic
334C2×C67#309711yescharacteristic
335C2×C67#326911yescharacteristic
336C2×C67#327511yescharacteristic
337C2×C67#335011yescharacteristic
338C2×C67#335211yescharacteristic
339C2×#485C2×C6711yescharacteristic, complemented
340C2×#428C2×C6711yescharacteristic, complemented
341#2415C2×C6711yescharacteristic
342#2352C2×C6711yescharacteristic
343#2097C2×C6711yescharacteristic, complemented
344#2085C2×C6711yescharacteristic, complemented
345#2076C2×C6711yescharacteristic, complemented
346#2035C2×C6711yescharacteristic, complemented
347#1928C2×C6711yescharacteristic, complemented
348#1920C2×C6711yescharacteristic, complemented
349#1894C2×C6711yescharacteristic, complemented
350#1872C2×C6711yescharacteristic, complemented
351#1870C2×C6711yescharacteristic
352#1854C2×C6711yescharacteristic, complemented
353#1854C2×C6711yescharacteristic, complemented
354C67#2615411yescharacteristic, direct product factor, Sylow
355C22×M16C22×C6711yescharacteristic
356C2×C22⋊Q8C22×C6711yescharacteristic
357C2×C22⋊Q8C22×C6711yescharacteristic
358C2×C4×D4C22×C6711yescharacteristic
359C2×#117C22×C6711yescharacteristic
360C2×#117C22×C6711yescharacteristic
361C22×C4⋊C4C22×C6711yescharacteristic
362#485—24no—
363#428—24no—
364C2×#107C22×C6711yescharacteristic
365C2×#107C22×C6711yescharacteristic
366C2×#107C22×C6711yescharacteristic
367C2×#106C22×C6711yescharacteristic
368C2×#106C22×C6711yescharacteristic
369C2×#106C22×C6711yescharacteristic
370C2×#103C22×C6711yescharacteristic
371C2×#103C22×C6711yescharacteristic
372C2×#103C22×C6711yescharacteristic
373C2×#103C22×C6711yescharacteristic
374C2×C22⋊C8C22×C6711yescharacteristic
375C2×C22⋊C8C22×C6711yescharacteristic
376C2×C22⋊C8C22×C6711yescharacteristic
377#397—21no—
378#394—21no—
379#391C22×C6711yescharacteristic
380#389—21no—
381#389C22×C6711yescharacteristic
382#388—21no—
383#388—21no—
384#387—21no—
385#386—21no—
386#382C22×C6711yescharacteristic
387#380C22×C6711yescharacteristic
388#380C22×C6711yescharacteristic
389#380C22×C6711yescharacteristic
390C4×C4⋊C4C22×C6711yescharacteristic
391C4×C22⋊C4—21no—
392#340C22×C6711yescharacteristic
393#340C22×C6711yescharacteristic
394#340C22×C6711yescharacteristic
395#340C22×C6711yescharacteristic
396#340C22×C6711yescharacteristic
397#340C22×C6711yescharacteristic
398#336C22×C6711yescharacteristic
399#336C22×C6711yescharacteristic
400C22×Q8C23×C6711yescharacteristic
401C22×D4D4×C6711yescharacteristic
402C23×C4—21no—
403C23×C4C23×C6711yescharacteristic
404C23×C4C23×C6711yescharacteristic
405C2×M16—22no—
406C2×M16—22no—
407C2×M16—22no—
408C22×C8C23×C6711yescharacteristic
409C22×C8C23×C6711yescharacteristic
410C22×C8C23×C6711yescharacteristic
411C22×C8C23×C6711yescharacteristic
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—41no—
416C4×D4—22no—
417C4×D4—22no—
418#117—22no—
419#117—22no—
420#117—41no—
421#117—41no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4D4×C6711yescharacteristic
429C2×C4⋊C4C23×C6711yescharacteristic
430C2×C4⋊C4C23×C6711yescharacteristic
431C2×C4⋊C4C23×C6711yescharacteristic
432C2×C4⋊C4C23×C6711yescharacteristic
433C2×C4⋊C4C23×C6711yescharacteristic
434C2×C4⋊C4C23×C6711yescharacteristic
435C2×C4⋊C4C23×C6711yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4D4×C6711yescharacteristic
444C2×C22⋊C4D4×C6711yescharacteristic
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42C23×C6711yescharacteristic
449#107—22no—
450#107—22no—
451#107—22no—
452#106—22no—
453#106—41no—
454#106D4×C6714yescomplemented
455#103—22no—
456#103—22no—
457#103—22no—
458#103—41no—
459C22⋊C8—22no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471C24C2×D4×C6711yescharacteristic
472C24C2×D4×C6711yescharacteristic
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×D4—22no—
480C2×D4—41no—
481C2×D4—41no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—81no—
503C22×C4C2×D4×C6711yescharacteristic
504C22×C4C2×D4×C6711yescharacteristic
505C22×C4C2×D4×C6711yescharacteristic
506C22×C4C2×D4×C6711yescharacteristic
507C22×C4#41×C6712yes—
508C22×C4#41×C6712yes—
509C22×C4C24×C6711yescharacteristic
510M16—28no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8C2×D4×C6712yes—
522C2×C8#41×C6712yes—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4C2×D4×C6712yes—
541C4⋊C4C2×D4×C6712yes—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—42no—
555C42—81no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23#123×C6712yes—
570C23C22×D4×C6711yescharacteristic
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—41no—
575D4—44no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—84no—
620C2×C4#123×C6712yes—
621C2×C4C22×D4×C6711yescharacteristic
622C2×C4C2×#41×C6711yescharacteristic
623C2×C4C2×#41×C6711yescharacteristic
624C2×C4C2×#41×C6711yescharacteristic
625C2×C4H(5,𝔽2)×C6711yescharacteristic
626C2×C42−1+4×C6711yescharacteristic
627C8—22no—
628C8—22no—
629C8—41no—
630C8—41no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C2×#123×C6711yescharacteristic
646C22D42×C6711yescharacteristic
647C22#547×C6711yescharacteristic
648C22#575×C6711yescharacteristic
649C22#575×C6711yescharacteristic
650C22#577×C6711yescharacteristic
651C22#578×C6711yescharacteristic
652C4—22no—
653C4—42no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4#525×C6711yescharacteristic
665C4#539×C6711yescharacteristic
666C4#548×C6711yescharacteristic
667C4#553×C6711yescharacteristic
668C2—42no—
669C2—81no—
670C2C67×#244311yescharacteristic
671C2C67×#309311yescharacteristic
672C2C67×#309711yescharacteristic
673C2C67×#326911yescharacteristic
674C2C67×#327511yescharacteristic
675C2C67×#335011yescharacteristic
676C2C67×#335211yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC22×D4×C67D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C67C2semidirect
2. C2×#428×C67C2semidirect
5. C67×#2097C2semidirect
6. C67×#2085C2semidirect
7. C67×#2076C2semidirect
8. C67×#2035C2semidirect
9. C67×#1928C2semidirect
10. C67×#1920C2semidirect
11. C67×#1894C2semidirect
12. C67×#1872C2semidirect
14. C67×#1854C2semidirect
15. C67×#1854C2semidirect
115. #106×C67D4semidirect
329. #26154C67direct (N × H)
339. C2×#485C2×C67semidirect
340. C2×#428C2×C67semidirect
343. #2097C2×C67semidirect
344. #2085C2×C67semidirect
345. #2076C2×C67semidirect
346. #2035C2×C67semidirect
347. #1928C2×C67semidirect
348. #1920C2×C67semidirect
349. #1894C2×C67semidirect
350. #1872C2×C67semidirect
352. #1854C2×C67semidirect
353. #1854C2×C67semidirect
354. C67#26154direct (N × H)
454. #106D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C672
C2×#428×C672
C67×#24152
C67×#23522
C67×#20972
C67×#20852
C67×#20762
C67×#20352
C67×#19282
C67×#19202
C67×#18942
C67×#18722
C67×#18702
C67×#18542
#2615467