Finite Group Databasebeta

← C67×#25179 #30704430

Subgroups — C67×#25179 #30704430

Order 17152.

1206 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C67C211yesmaximal, characteristic, complemented
2C2×#449×C67C211yesmaximal, characteristic, complemented
3C2×#449×C67C211yesmaximal, characteristic, complemented
4C2×#440×C67C211yesmaximal, characteristic, complemented
5C67×#2428C211yesmaximal, characteristic, complemented
6C67×#2341C211yesmaximal, characteristic, complemented
7C67×#2067C211yesmaximal, characteristic, complemented
8C67×#2034C211yesmaximal, characteristic, complemented
9C67×#2033C211yesmaximal, characteristic, complemented
10C67×#2011C211yesmaximal, characteristic, complemented
11C67×#1972C211yesmaximal, characteristic, complemented
12C67×#1924C211yesmaximal, characteristic, complemented
13C67×#1880C211yesmaximal, characteristic, complemented
14C67×#1879C211yesmaximal, characteristic, complemented
15C67×#1865C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C22×SD16×C67C2211yescharacteristic
18C22×SD16×C67C2211yescharacteristic
19C22×D8×C67C2211yescharacteristic
20C22×D8×C67C2211yescharacteristic
21C2×#127×C67C2211yescharacteristic
22C2×#121×C67—21no—
23C2×#121×C67C2211yescharacteristic
24C2×#121×C67C2211yescharacteristic
25C2×C4×Q8×C67C2211yescharacteristic
26C2×C4×Q8×C67C2211yescharacteristic
27C2×C4×D4×C67C2211yescharacteristic
28#460×C67—24no—
29#449×C67—24no—
30#449×C67—24no—
31#440×C67—24no—
32C2×#107×C67C2211yescharacteristic
33C2×#106×C67C2211yescharacteristic
34C2×C4⋊C8×C67C2211yescharacteristic
35C2×#103×C67C2211yescharacteristic
36C2×#103×C67C2211yescharacteristic
37C2×#102×C67C2211yescharacteristic
38C2×#102×C67C2211yescharacteristic
39C2×#102×C67C2211yescharacteristic
40C2×#102×C67C2211yescharacteristic
41C2×#102×C67C2211yescharacteristic
42C2×#102×C67C2211yescharacteristic
43C2×C22⋊C8×C67C2211yescharacteristic
44C2×C22⋊C8×C67C2211yescharacteristic
45C2×#97×C67C2211yescharacteristic
46#394×C67—21no—
47#392×C67—21no—
48#390×C67—21no—
49#390×C67—21no—
50#390×C67C2211yescharacteristic
51#390×C67C2211yescharacteristic
52#390×C67C2211yescharacteristic
53#389×C67C2211yescharacteristic
54#386×C67—21no—
55#380×C67—21no—
56#380×C67C2211yescharacteristic
57C4×C22⋊C4×C67—21no—
58C4×C22⋊C4×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61#336×C67C2211yescharacteristic
62#336×C67C2211yescharacteristic
63C2×#41×C67—22no—
64C2×#41×C67—22no—
65C2×#41×C67—22no—
66C2×#41×C67—22no—
67C2×#41×C67—41no—
68C2×#41×C67—41no—
69C22×Q8×C67C2311yescharacteristic
70C22×D4×C67—21no—
71C22×D4×C67—21no—
72C22×D4×C67—21no—
73C22×D4×C67—21no—
74C22×D4×C67—21no—
75C22×D4×C67C2311yescharacteristic
76C22×D4×C67C2311yescharacteristic
77C22×D4×C67C2311yescharacteristic
78C23×C4×C67—21no—
79C23×C4×C67—21no—
80C23×C4×C67C2311yescharacteristic
81C2×SD16×C67—22no—
82C2×SD16×C67—22no—
83C2×SD16×C67—22no—
84C2×SD16×C67—22no—
85C2×SD16×C67—22no—
86C2×SD16×C67D414yescomplemented
87C2×D8×C67—22no—
88C2×D8×C67—22no—
89C2×D8×C67—22no—
90C2×D8×C67—22no—
91C2×D8×C67—41no—
92C2×D8×C67—41no—
93C22×C8×C67C2311yescharacteristic
94C22×C8×C67C2311yescharacteristic
95C22×C8×C67C2311yescharacteristic
96C22×C8×C67C2311yescharacteristic
97#127×C67—22no—
98#127×C67—41no—
99#121×C67—22no—
100#121×C67—22no—
101#121×C67—44no—
102#121×C67—41no—
103#121×C67—41no—
104C4×Q8×C67—22no—
105C4×Q8×C67—22no—
106C4×Q8×C67—41no—
107C4×Q8×C67—41no—
108C4×D4×C67—22no—
109C4×D4×C67—41no—
110C2×C4⋊C4×C67—21no—
111C2×C4⋊C4×C67—21no—
112C2×C4⋊C4×C67—21no—
113C2×C4⋊C4×C67C2311yescharacteristic
114C2×C4⋊C4×C67C2311yescharacteristic
115C2×C4⋊C4×C67C2311yescharacteristic
116C2×C4⋊C4×C67C2311yescharacteristic
117C2×C22⋊C4×C67—21no—
118C2×C22⋊C4×C67—21no—
119C2×C22⋊C4×C67—21no—
120C2×C22⋊C4×C67—21no—
121C2×C22⋊C4×C67—21no—
122C2×C22⋊C4×C67—21no—
123C2×C22⋊C4×C67—21no—
124C2×C22⋊C4×C67—21no—
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—21no—
127C2×C22⋊C4×C67D411yescharacteristic
128C2×C22⋊C4×C67D411yescharacteristic
129C2×C42×C67—21no—
130C2×C42×C67—21no—
131C2×C42×C67C2311yescharacteristic
132C2×C42×C67C2311yescharacteristic
133#107×C67—22no—
134#106×C67—41no—
135C4⋊C8×C67—22no—
136#103×C67—22no—
137#103×C67D414yescomplemented
138#102×C67—22no—
139#102×C67—22no—
140#102×C67—22no—
141#102×C67—22no—
142#102×C67—22no—
143#102×C67—41no—
144C22⋊C8×C67—22no—
145C22⋊C8×C67—22no—
146#97×C67—22no—
147#95×C67—21no—
148#95×C67—21no—
149#95×C67D411yescharacteristic
150#95×C67D411yescharacteristic
151C24×C67—21no—
152C24×C67—21no—
153C24×C67—21no—
154C24×C67C2×D411yescharacteristic
155#41×C67—44no—
156#41×C67—44no—
157#41×C67—44no—
158#41×C67—44no—
159C2×Q8×C67—21no—
160C2×Q8×C67—21no—
161C2×Q8×C67—21no—
162C2×Q8×C67C2×D412yes—
163C2×Q8×C67C2×D412yes—
164C2×Q8×C67#4112yes—
165C2×D4×C67—24no—
166C2×D4×C67—21no—
167C2×D4×C67—21no—
168C2×D4×C67—21no—
169C2×D4×C67—21no—
170C2×D4×C67—21no—
171C2×D4×C67—21no—
172C2×D4×C67—21no—
173C2×D4×C67—21no—
174C2×D4×C67—21no—
175C2×D4×C67—21no—
176C2×D4×C67—21no—
177C2×D4×C67—21no—
178C2×D4×C67—21no—
179C2×D4×C67—21no—
180C2×D4×C67—21no—
181C2×D4×C67—21no—
182C2×D4×C67—42no—
183C2×D4×C67—42no—
184C2×D4×C67—42no—
185C2×D4×C67—42no—
186C2×D4×C67—42no—
187C2×D4×C67—42no—
188C2×D4×C67—42no—
189C2×D4×C67—42no—
190C2×D4×C67—42no—
191C2×D4×C67—42no—
192C2×D4×C67—81no—
193C2×D4×C67—81no—
194C2×D4×C67—81no—
195C2×D4×C67—81no—
196C2×D4×C67C2×D412yes—
197C2×D4×C67#4112yes—
198C22×C4×C67—21no—
199C22×C4×C67—24no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—21no—
203C22×C4×C67—21no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
208C22×C4×C67—21no—
209C22×C4×C67—21no—
210C22×C4×C67—42no—
211C22×C4×C67—42no—
212C22×C4×C67—42no—
213C22×C4×C67—42no—
214C22×C4×C67—81no—
215C22×C4×C67C2×D411yescharacteristic
216C22×C4×C67C2×D411yescharacteristic
217C22×C4×C67C2×D411yescharacteristic
218C22×C4×C67C2×D411yescharacteristic
219C22×C4×C67C2×D411yescharacteristic
220C22×C4×C67C2411yescharacteristic
221SD16×C67—28no—
222SD16×C67—44no—
223D8×C67—44no—
224D8×C67—44no—
225C2×C8×C67—21no—
226C2×C8×C67—21no—
227C2×C8×C67—21no—
228C2×C8×C67—21no—
229C2×C8×C67—21no—
230C2×C8×C67—21no—
231C2×C8×C67—21no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C2×C8×C67—21no—
235C2×C8×C67C2×D412yes—
236C2×C8×C67C2×D412yes—
237C4⋊C4×C67—21no—
238C4⋊C4×C67—21no—
239C4⋊C4×C67—21no—
240C4⋊C4×C67—21no—
241C4⋊C4×C67—21no—
242C4⋊C4×C67—21no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—42no—
245C4⋊C4×C67—42no—
246C4⋊C4×C67—42no—
247C4⋊C4×C67C2×D412yes—
248C22⋊C4×C67—22no—
249C22⋊C4×C67—41no—
250C22⋊C4×C67—42no—
251C22⋊C4×C67—42no—
252C22⋊C4×C67—42no—
253C22⋊C4×C67—42no—
254C22⋊C4×C67—42no—
255C22⋊C4×C67—42no—
256C22⋊C4×C67—81no—
257C22⋊C4×C67—81no—
258C22⋊C4×C67—81no—
259C22⋊C4×C67—81no—
260C42×C67—21no—
261C42×C67—21no—
262C42×C67—21no—
263C42×C67—21no—
264C42×C67—42no—
265C42×C67—42no—
266C23×C67—21no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—21no—
270C23×C67—21no—
271C23×C67—21no—
272C23×C67—21no—
273C23×C67—21no—
274C23×C67—21no—
275C23×C67—41no—
276C23×C67—41no—
277C23×C67—41no—
278C23×C67—41no—
279C23×C67—41no—
280C23×C67—41no—
281C23×C67—41no—
282C23×C67—41no—
283C23×C67—41no—
284C23×C67—41no—
285C23×C67—41no—
286C23×C67—41no—
287C23×C67—41no—
288C23×C67—41no—
289C23×C67—41no—
290C23×C67—41no—
291C23×C67—41no—
292C23×C67—41no—
293C23×C67—41no—
294C23×C67C22×D411yescharacteristic
295Q8×C67—22no—
296Q8×C67—22no—
297Q8×C67—22no—
298Q8×C67#12114yescomplemented
299D4×C67—22no—
300D4×C67—22no—
301D4×C67—22no—
302D4×C67—22no—
303D4×C67—48no—
304D4×C67—41no—
305D4×C67—41no—
306D4×C67—41no—
307D4×C67—41no—
308D4×C67—41no—
309D4×C67—41no—
310D4×C67—41no—
311D4×C67—41no—
312D4×C67—84no—
313D4×C67—84no—
314D4×C67—84no—
315D4×C67—84no—
316C2×C4×C67—22no—
317C2×C4×C67—21no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—21no—
321C2×C4×C67—21no—
322C2×C4×C67—21no—
323C2×C4×C67—21no—
324C2×C4×C67—21no—
325C2×C4×C67—22no—
326C2×C4×C67—21no—
327C2×C4×C67—21no—
328C2×C4×C67—21no—
329C2×C4×C67—21no—
330C2×C4×C67—21no—
331C2×C4×C67—21no—
332C2×C4×C67—21no—
333C2×C4×C67—21no—
334C2×C4×C67—48no—
335C2×C4×C67—41no—
336C2×C4×C67—41no—
337C2×C4×C67—41no—
338C2×C4×C67—41no—
339C2×C4×C67—41no—
340C2×C4×C67—41no—
341C2×C4×C67—41no—
342C2×C4×C67—41no—
343C2×C4×C67—41no—
344C2×C4×C67—41no—
345C2×C4×C67—41no—
346C2×C4×C67—41no—
347C2×C4×C67—41no—
348C2×C4×C67—41no—
349C2×C4×C67—41no—
350C2×C4×C67—84no—
351C2×C4×C67AGL(1,ℤ/8)12yes—
352C2×C4×C67C22×D411yescharacteristic
353C2×C4×C67C22×D411yescharacteristic
354C2×C4×C67C2×#4111yescharacteristic
355C2×C4×C67C2×#4111yescharacteristic
356C2×C4×C67H(5,𝔽2)11yescharacteristic
357C2×C4×C67H(5,𝔽2)11yescharacteristic
358C8×C67—22no—
359C8×C67—22no—
360C8×C67—41no—
361C8×C67—41no—
362C22×C67—41no—
363C22×C67—42no—
364C22×C67—41no—
365C22×C67—42no—
366C22×C67—42no—
367C22×C67—41no—
368C22×C67—42no—
369C22×C67—41no—
370C22×C67—42no—
371C22×C67—42no—
372C22×C67—41no—
373C22×C67—41no—
374C22×C67—41no—
375C22×C67—81no—
376C22×C67—81no—
377C22×C67—81no—
378C22×C67—81no—
379C22×C67—81no—
380C22×C67—81no—
381C22×C67—81no—
382C22×C67—81no—
383C22×C67—81no—
384C22×C67—81no—
385C22×C67—81no—
386C22×C67—81no—
387C22×C67—81no—
388C22×C67—81no—
389C22×C67—81no—
390C22×C67#52511yescharacteristic
391C22×C67D4211yescharacteristic
392C22×C67D4211yescharacteristic
393C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C67#57511yescharacteristic
395C22×C67#57611yescharacteristic
396C22×C67#57711yescharacteristic
397C4×C67—24no—
398C4×C67—22no—
399C4×C67—41no—
400C4×C67—41no—
401C4×C67—41no—
402C4×C67—41no—
403C4×C67—42no—
404C4×C67—81no—
405C4×C67—81no—
406C4×C67—81no—
407C4×C67C2×#12111yescharacteristic
408C4×C67#53811yescharacteristic
409C4×C67#54611yescharacteristic
410C4×C67#54611yescharacteristic
411#25179C6711yesmaximal, characteristic, direct product factor, Sylow
412C2×C67—81no—
413C2×C67—82no—
414C2×C67—82no—
415C2×C67—161no—
416C2×C67#242411yescharacteristic
417C2×C67#311511yescharacteristic
418C2×C67#311911yescharacteristic
419C2×C67#326511yescharacteristic
420C2×C67#326811yescharacteristic
421C2×C67#327111yescharacteristic
422C2×C67#327411yescharacteristic
423C2×#460C2×C6711yescharacteristic, complemented
424C2×#449C2×C6711yescharacteristic, complemented
425C2×#449C2×C6711yescharacteristic, complemented
426C2×#440C2×C6711yescharacteristic, complemented
427#2428C2×C6711yescharacteristic, complemented
428#2341C2×C6711yescharacteristic, complemented
429#2067C2×C6711yescharacteristic, complemented
430#2034C2×C6711yescharacteristic, complemented
431#2033C2×C6711yescharacteristic, complemented
432#2011C2×C6711yescharacteristic, complemented
433#1972C2×C6711yescharacteristic, complemented
434#1924C2×C6711yescharacteristic, complemented
435#1880C2×C6711yescharacteristic, complemented
436#1879C2×C6711yescharacteristic, complemented
437#1865C2×C6711yescharacteristic, complemented
438C67#2517911yescharacteristic, direct product factor, Sylow
439C22×#41C22×C6711yescharacteristic
440C22×SD16C22×C6711yescharacteristic
441C22×SD16C22×C6711yescharacteristic
442C22×D8C22×C6711yescharacteristic
443C22×D8C22×C6711yescharacteristic
444C2×#127C22×C6711yescharacteristic
445C2×#121—21no—
446C2×#121C22×C6711yescharacteristic
447C2×#121C22×C6711yescharacteristic
448C2×C4×Q8C22×C6711yescharacteristic
449C2×C4×Q8C22×C6711yescharacteristic
450C2×C4×D4C22×C6711yescharacteristic
451#460—24no—
452#449—24no—
453#449—24no—
454#440—24no—
455C2×#107C22×C6711yescharacteristic
456C2×#106C22×C6711yescharacteristic
457C2×C4⋊C8C22×C6711yescharacteristic
458C2×#103C22×C6711yescharacteristic
459C2×#103C22×C6711yescharacteristic
460C2×#102C22×C6711yescharacteristic
461C2×#102C22×C6711yescharacteristic
462C2×#102C22×C6711yescharacteristic
463C2×#102C22×C6711yescharacteristic
464C2×#102C22×C6711yescharacteristic
465C2×#102C22×C6711yescharacteristic
466C2×C22⋊C8C22×C6711yescharacteristic
467C2×C22⋊C8C22×C6711yescharacteristic
468C2×#97C22×C6711yescharacteristic
469#394—21no—
470#392—21no—
471#390—21no—
472#390—21no—
473#390C22×C6711yescharacteristic
474#390C22×C6711yescharacteristic
475#390C22×C6711yescharacteristic
476#389C22×C6711yescharacteristic
477#386—21no—
478#380—21no—
479#380C22×C6711yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4C22×C6711yescharacteristic
482#340C22×C6711yescharacteristic
483#340C22×C6711yescharacteristic
484#336C22×C6711yescharacteristic
485#336C22×C6711yescharacteristic
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C6711yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C6711yescharacteristic
499C22×D4C23×C6711yescharacteristic
500C22×D4C23×C6711yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C6711yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C6714yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C6711yescharacteristic
517C22×C8C23×C6711yescharacteristic
518C22×C8C23×C6711yescharacteristic
519C22×C8C23×C6711yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C6711yescharacteristic
537C2×C4⋊C4C23×C6711yescharacteristic
538C2×C4⋊C4C23×C6711yescharacteristic
539C2×C4⋊C4C23×C6711yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C6711yescharacteristic
551C2×C22⋊C4D4×C6711yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C6711yescharacteristic
555C2×C42C23×C6711yescharacteristic
556#107—22no—
557#106—41no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C6714yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569#97—22no—
570#95—21no—
571#95—21no—
572#95D4×C6711yescharacteristic
573#95D4×C6711yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C6711yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C6712yes—
586C2×Q8C2×D4×C6712yes—
587C2×Q8#41×C6712yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C6712yes—
620C2×D4#41×C6712yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C6711yescharacteristic
639C22×C4C2×D4×C6711yescharacteristic
640C22×C4C2×D4×C6711yescharacteristic
641C22×C4C2×D4×C6711yescharacteristic
642C22×C4C2×D4×C6711yescharacteristic
643C22×C4C24×C6711yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C6712yes—
659C2×C8C2×D4×C6712yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C6712yes—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C6711yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C6714yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4AGL(1,ℤ/8)×C6712yes—
775C2×C4C22×D4×C6711yescharacteristic
776C2×C4C22×D4×C6711yescharacteristic
777C2×C4C2×#41×C6711yescharacteristic
778C2×C4C2×#41×C6711yescharacteristic
779C2×C4H(5,𝔽2)×C6711yescharacteristic
780C2×C4H(5,𝔽2)×C6711yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22#525×C6711yescharacteristic
814C22D42×C6711yescharacteristic
815C22D42×C6711yescharacteristic
816C22C2×AGL(1,ℤ/8)×C6711yescharacteristic
817C22#575×C6711yescharacteristic
818C22#576×C6711yescharacteristic
819C22#577×C6711yescharacteristic
820C4—22no—
821C4—24no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C6711yescharacteristic
831C4#538×C6711yescharacteristic
832C4#546×C6711yescharacteristic
833C4#546×C6711yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C67×#242411yescharacteristic
839C2C67×#311511yescharacteristic
840C2C67×#311911yescharacteristic
841C2C67×#326511yescharacteristic
842C2C67×#326811yescharacteristic
843C2C67×#327111yescharacteristic
844C2C67×#327411yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C4×C22⋊C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#460×C67C2semidirect
2. C2×#449×C67C2semidirect
3. C2×#449×C67C2semidirect
4. C2×#440×C67C2semidirect
5. C67×#2428C2semidirect
6. C67×#2341C2semidirect
7. C67×#2067C2semidirect
8. C67×#2034C2semidirect
9. C67×#2033C2semidirect
10. C67×#2011C2semidirect
11. C67×#1972C2semidirect
12. C67×#1924C2semidirect
13. C67×#1880C2semidirect
14. C67×#1879C2semidirect
15. C67×#1865C2semidirect
86. C2×SD16×C67D4semidirect
137. #103×C67D4semidirect
298. Q8×C67#121semidirect
411. #25179C67direct (N × H)
423. C2×#460C2×C67semidirect
424. C2×#449C2×C67semidirect
425. C2×#449C2×C67semidirect
426. C2×#440C2×C67semidirect
427. #2428C2×C67semidirect
428. #2341C2×C67semidirect
429. #2067C2×C67semidirect
430. #2034C2×C67semidirect
431. #2033C2×C67semidirect
432. #2011C2×C67semidirect
433. #1972C2×C67semidirect
434. #1924C2×C67semidirect
435. #1880C2×C67semidirect
436. #1879C2×C67semidirect
437. #1865C2×C67semidirect
438. C67#25179direct (N × H)
509. C2×SD16D4×C67semidirect
560. #103D4×C67semidirect
721. Q8#121×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C672
C2×#449×C672
C2×#440×C672
C67×#24282
C67×#23412
C67×#20672
C67×#20342
C67×#20332
C67×#20112
C67×#19722
C67×#19242
C67×#18802
C67×#18792
C67×#18652
#2517967