Finite Group Databasebeta

← C67×#25174 #30704425

Subgroups — C67×#25174 #30704425

Order 17152.

1234 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C67C211yesmaximal, characteristic, complemented
2C2×#449×C67C211yesmaximal, characteristic, complemented
3C2×#449×C67C211yesmaximal, characteristic, complemented
4C2×#442×C67C211yesmaximal, characteristic, complemented
5C67×#2428C211yesmaximal, characteristic, complemented
6C67×#2339C211yesmaximal, characteristic, complemented
7C67×#2066C211yesmaximal, characteristic, complemented
8C67×#2034C211yesmaximal, characteristic, complemented
9C67×#2033C211yesmaximal, characteristic, complemented
10C67×#2014C211yesmaximal, characteristic, complemented
11C67×#1973C211yesmaximal, characteristic, complemented
12C67×#1924C211yesmaximal, characteristic, complemented
13C67×#1879C211yesmaximal, characteristic, complemented
14C67×#1877C211yesmaximal, characteristic, complemented
15C67×#1862C211yesmaximal, 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×D4×C67C2211yescharacteristic
26C2×C4×D4×C67C2211yescharacteristic
27C2×C4×D4×C67C2211yescharacteristic
28#459×C67—24no—
29#449×C67—24no—
30#449×C67—24no—
31#442×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#391×C67C2211yescharacteristic
49#391×C67C2211yescharacteristic
50#390×C67C2211yescharacteristic
51#389×C67C2211yescharacteristic
52#386×C67—21no—
53#386×C67—21no—
54#386×C67—21no—
55#381×C67—21no—
56#380×C67C2211yescharacteristic
57C4×C22⋊C4×C67C2211yescharacteristic
58C2×#95×C67—21no—
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×C67—21no—
81C23×C4×C67—21no—
82C23×C4×C67C2311yescharacteristic
83C2×SD16×C67—22no—
84C2×SD16×C67—22no—
85C2×SD16×C67—22no—
86C2×SD16×C67—22no—
87C2×SD16×C67—41no—
88C2×SD16×C67—41no—
89C2×D8×C67—22no—
90C2×D8×C67—22no—
91C2×D8×C67—22no—
92C2×D8×C67—22no—
93C2×D8×C67—22no—
94C2×D8×C67D414yescomplemented
95C22×C8×C67C2311yescharacteristic
96C22×C8×C67C2311yescharacteristic
97C22×C8×C67C2311yescharacteristic
98C22×C8×C67C2311yescharacteristic
99#127×C67—22no—
100#127×C67—41no—
101#121×C67—22no—
102#121×C67—22no—
103#121×C67—44no—
104#121×C67—41no—
105#121×C67—41no—
106C4×D4×C67—22no—
107C4×D4×C67—22no—
108C4×D4×C67—22no—
109C4×D4×C67—41no—
110C4×D4×C67—41no—
111C4×D4×C67—41no—
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×C67D411yescharacteristic
126C2×C22⋊C4×C67D411yescharacteristic
127C2×C42×C67C2311yescharacteristic
128C2×C42×C67C2311yescharacteristic
129#107×C67—41no—
130#106×C67—22no—
131C4⋊C8×C67—22no—
132#103×C67—22no—
133#103×C67—22no—
134#102×C67—22no—
135#102×C67—22no—
136#102×C67—22no—
137#102×C67—22no—
138#102×C67—41no—
139#102×C67D414yescomplemented
140C22⋊C8×C67—22no—
141C22⋊C8×C67—22no—
142#97×C67—22no—
143#95×C67—21no—
144#95×C67—21no—
145#95×C67—21no—
146#95×C67—21no—
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×C67—21no—
163C2×Q8×C67—21no—
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—42no—
181C2×D4×C67—42no—
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—81no—
191C2×D4×C67—81no—
192C2×D4×C67—81no—
193C2×D4×C67—81no—
194C2×D4×C67C2×D412yes—
195C2×D4×C67C2×D412yes—
196C2×D4×C67C2×D412yes—
197C2×D4×C67#4112yes—
198C22×C4×C67—24no—
199C22×C4×C67—21no—
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—42no—
215C22×C4×C67—42no—
216C22×C4×C67—42no—
217C22×C4×C67—42no—
218C22×C4×C67—81no—
219C22×C4×C67—81no—
220C22×C4×C67—81no—
221C22×C4×C67C2×D411yescharacteristic
222C22×C4×C67C2×D411yescharacteristic
223C22×C4×C67C2×D411yescharacteristic
224C22×C4×C67C2×D411yescharacteristic
225C22×C4×C67C2×D411yescharacteristic
226C22×C4×C67C2411yescharacteristic
227SD16×C67—44no—
228SD16×C67—44no—
229D8×C67—28no—
230D8×C67—44no—
231C2×C8×C67—21no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C2×C8×C67—21no—
235C2×C8×C67—21no—
236C2×C8×C67—21no—
237C2×C8×C67—21no—
238C2×C8×C67—21no—
239C2×C8×C67—21no—
240C2×C8×C67—21no—
241C2×C8×C67C2×D412yes—
242C2×C8×C67C2×D412yes—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—21no—
245C4⋊C4×C67—21no—
246C4⋊C4×C67—21no—
247C4⋊C4×C67—21no—
248C4⋊C4×C67—21no—
249C4⋊C4×C67—21no—
250C4⋊C4×C67—42no—
251C4⋊C4×C67C2×D412yes—
252C22⋊C4×C67—22no—
253C22⋊C4×C67—41no—
254C22⋊C4×C67—42no—
255C22⋊C4×C67—42no—
256C22⋊C4×C67—42no—
257C22⋊C4×C67—42no—
258C22⋊C4×C67—42no—
259C22⋊C4×C67—42no—
260C22⋊C4×C67—81no—
261C22⋊C4×C67—81no—
262C42×C67—21no—
263C42×C67—21no—
264C42×C67—21no—
265C42×C67—21no—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—21no—
270C23×C67—22no—
271C23×C67—21no—
272C23×C67—21no—
273C23×C67—21no—
274C23×C67—21no—
275C23×C67—21no—
276C23×C67—21no—
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—41no—
298Q8×C67—41no—
299D4×C67—22no—
300D4×C67—22no—
301D4×C67—22no—
302D4×C67—22no—
303D4×C67—22no—
304D4×C67—48no—
305D4×C67—41no—
306D4×C67—41no—
307D4×C67—41no—
308D4×C67—41no—
309D4×C67—41no—
310D4×C67—41no—
311D4×C67—84no—
312D4×C67—84no—
313D4×C67—84no—
314D4×C67—84no—
315D4×C67#12114yescomplemented
316C2×C4×C67—21no—
317C2×C4×C67—21no—
318C2×C4×C67—21no—
319C2×C4×C67—22no—
320C2×C4×C67—21no—
321C2×C4×C67—21no—
322C2×C4×C67—21no—
323C2×C4×C67—22no—
324C2×C4×C67—21no—
325C2×C4×C67—21no—
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—48no—
333C2×C4×C67—41no—
334C2×C4×C67—41no—
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×C67—84no—
352C2×C4×C67—84no—
353C2×C4×C67AGL(1,ℤ/8)12yes—
354C2×C4×C67C22×D411yescharacteristic
355C2×C4×C67C22×D411yescharacteristic
356C2×C4×C67C2×#4111yescharacteristic
357C2×C4×C67C2×#4111yescharacteristic
358C2×C4×C67H(5,𝔽2)11yescharacteristic
359C2×C4×C67H(5,𝔽2)11yescharacteristic
360C8×C67—22no—
361C8×C67—22no—
362C8×C67—41no—
363C8×C67—41no—
364C22×C67—24no—
365C22×C67—42no—
366C22×C67—42no—
367C22×C67—42no—
368C22×C67—42no—
369C22×C67—42no—
370C22×C67—42no—
371C22×C67—41no—
372C22×C67—41no—
373C22×C67—41no—
374C22×C67—42no—
375C22×C67—41no—
376C22×C67—42no—
377C22×C67—42no—
378C22×C67—41no—
379C22×C67—41no—
380C22×C67—41no—
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—81no—
391C22×C67—81no—
392C22×C67#52511yescharacteristic
393C22×C67D4211yescharacteristic
394C22×C67D4211yescharacteristic
395C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C67#57511yescharacteristic
397C22×C67#57611yescharacteristic
398C22×C67#57711yescharacteristic
399C4×C67—22no—
400C4×C67—41no—
401C4×C67—42no—
402C4×C67—41no—
403C4×C67—41no—
404C4×C67—41no—
405C4×C67—42no—
406C4×C67—81no—
407C4×C67—81no—
408C4×C67—81no—
409C4×C67C2×#12111yescharacteristic
410C4×C67#53811yescharacteristic
411C4×C67#54611yescharacteristic
412C4×C67#54611yescharacteristic
413#25174C6711yesmaximal, characteristic, direct product factor, Sylow
414C2×C67—44no—
415C2×C67—81no—
416C2×C67—82no—
417C2×C67—161no—
418C2×C67#242411yescharacteristic
419C2×C67#311511yescharacteristic
420C2×C67#311911yescharacteristic
421C2×C67#326411yescharacteristic
422C2×C67#326711yescharacteristic
423C2×C67#326811yescharacteristic
424C2×C67#327211yescharacteristic
425C2×#459C2×C6711yescharacteristic, complemented
426C2×#449C2×C6711yescharacteristic, complemented
427C2×#449C2×C6711yescharacteristic, complemented
428C2×#442C2×C6711yescharacteristic, complemented
429#2428C2×C6711yescharacteristic, complemented
430#2339C2×C6711yescharacteristic, complemented
431#2066C2×C6711yescharacteristic, complemented
432#2034C2×C6711yescharacteristic, complemented
433#2033C2×C6711yescharacteristic, complemented
434#2014C2×C6711yescharacteristic, complemented
435#1973C2×C6711yescharacteristic, complemented
436#1924C2×C6711yescharacteristic, complemented
437#1879C2×C6711yescharacteristic, complemented
438#1877C2×C6711yescharacteristic, complemented
439#1862C2×C6711yescharacteristic, complemented
440C67#2517411yescharacteristic, direct product factor, Sylow
441C22×#41C22×C6711yescharacteristic
442C22×SD16C22×C6711yescharacteristic
443C22×SD16C22×C6711yescharacteristic
444C22×D8C22×C6711yescharacteristic
445C22×D8C22×C6711yescharacteristic
446C2×#127C22×C6711yescharacteristic
447C2×#121—21no—
448C2×#121C22×C6711yescharacteristic
449C2×#121C22×C6711yescharacteristic
450C2×C4×D4C22×C6711yescharacteristic
451C2×C4×D4C22×C6711yescharacteristic
452C2×C4×D4C22×C6711yescharacteristic
453#459—24no—
454#449—24no—
455#449—24no—
456#442—24no—
457C2×#107C22×C6711yescharacteristic
458C2×#106C22×C6711yescharacteristic
459C2×C4⋊C8C22×C6711yescharacteristic
460C2×#103C22×C6711yescharacteristic
461C2×#103C22×C6711yescharacteristic
462C2×#102C22×C6711yescharacteristic
463C2×#102C22×C6711yescharacteristic
464C2×#102C22×C6711yescharacteristic
465C2×#102C22×C6711yescharacteristic
466C2×#102C22×C6711yescharacteristic
467C2×#102C22×C6711yescharacteristic
468C2×C22⋊C8C22×C6711yescharacteristic
469C2×C22⋊C8C22×C6711yescharacteristic
470C2×#97C22×C6711yescharacteristic
471#394—21no—
472#392—21no—
473#391C22×C6711yescharacteristic
474#391C22×C6711yescharacteristic
475#390C22×C6711yescharacteristic
476#389C22×C6711yescharacteristic
477#386—21no—
478#386—21no—
479#386—21no—
480#381—21no—
481#380C22×C6711yescharacteristic
482C4×C22⋊C4C22×C6711yescharacteristic
483C2×#95—21no—
484#340C22×C6711yescharacteristic
485#340C22×C6711yescharacteristic
486#336C22×C6711yescharacteristic
487#336C22×C6711yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C6711yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C6711yescharacteristic
501C22×D4C23×C6711yescharacteristic
502C22×D4C23×C6711yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C6711yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C6714yescomplemented
520C22×C8C23×C6711yescharacteristic
521C22×C8C23×C6711yescharacteristic
522C22×C8C23×C6711yescharacteristic
523C22×C8C23×C6711yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C6711yescharacteristic
539C2×C4⋊C4C23×C6711yescharacteristic
540C2×C4⋊C4C23×C6711yescharacteristic
541C2×C4⋊C4C23×C6711yescharacteristic
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×C42C23×C6711yescharacteristic
553C2×C42C23×C6711yescharacteristic
554#107—41no—
555#106—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C6714yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567#97—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C6711yescharacteristic
575#95D4×C6711yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C6711yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C6712yes—
590C2×D4—24no—
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×D4C2×D4×C6712yes—
621C2×D4C2×D4×C6712yes—
622C2×D4#41×C6712yes—
623C22×C4—24no—
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—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C6711yescharacteristic
647C22×C4C2×D4×C6711yescharacteristic
648C22×C4C2×D4×C6711yescharacteristic
649C22×C4C2×D4×C6711yescharacteristic
650C22×C4C2×D4×C6711yescharacteristic
651C22×C4C24×C6711yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C6712yes—
667C2×C8C2×D4×C6712yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C6712yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
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—
717C23—41no—
718C23—41no—
719C23C22×D4×C6711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C6714yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
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—41no—
774C2×C4—41no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4AGL(1,ℤ/8)×C6712yes—
779C2×C4C22×D4×C6711yescharacteristic
780C2×C4C22×D4×C6711yescharacteristic
781C2×C4C2×#41×C6711yescharacteristic
782C2×C4C2×#41×C6711yescharacteristic
783C2×C4H(5,𝔽2)×C6711yescharacteristic
784C2×C4H(5,𝔽2)×C6711yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22#525×C6711yescharacteristic
818C22D42×C6711yescharacteristic
819C22D42×C6711yescharacteristic
820C22C2×AGL(1,ℤ/8)×C6711yescharacteristic
821C22#575×C6711yescharacteristic
822C22#576×C6711yescharacteristic
823C22#577×C6711yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C6711yescharacteristic
835C4#538×C6711yescharacteristic
836C4#546×C6711yescharacteristic
837C4#546×C6711yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C67×#242411yescharacteristic
843C2C67×#311511yescharacteristic
844C2C67×#311911yescharacteristic
845C2C67×#326411yescharacteristic
846C2C67×#326711yescharacteristic
847C2C67×#326811yescharacteristic
848C2C67×#327211yescharacteristic
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×#459×C67C2semidirect
2. C2×#449×C67C2semidirect
3. C2×#449×C67C2semidirect
4. C2×#442×C67C2semidirect
5. C67×#2428C2semidirect
6. C67×#2339C2semidirect
7. C67×#2066C2semidirect
8. C67×#2034C2semidirect
9. C67×#2033C2semidirect
10. C67×#2014C2semidirect
11. C67×#1973C2semidirect
12. C67×#1924C2semidirect
13. C67×#1879C2semidirect
14. C67×#1877C2semidirect
15. C67×#1862C2semidirect
94. C2×D8×C67D4semidirect
139. #102×C67D4semidirect
315. D4×C67#121semidirect
413. #25174C67direct (N × H)
425. C2×#459C2×C67semidirect
426. C2×#449C2×C67semidirect
427. C2×#449C2×C67semidirect
428. C2×#442C2×C67semidirect
429. #2428C2×C67semidirect
430. #2339C2×C67semidirect
431. #2066C2×C67semidirect
432. #2034C2×C67semidirect
433. #2033C2×C67semidirect
434. #2014C2×C67semidirect
435. #1973C2×C67semidirect
436. #1924C2×C67semidirect
437. #1879C2×C67semidirect
438. #1877C2×C67semidirect
439. #1862C2×C67semidirect
440. C67#25174direct (N × H)
519. C2×D8D4×C67semidirect
564. #102D4×C67semidirect
740. D4#121×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C672
C2×#449×C672
C2×#442×C672
C67×#24282
C67×#23392
C67×#20662
C67×#20342
C67×#20332
C67×#20142
C67×#19732
C67×#19242
C67×#18792
C67×#18772
C67×#18622
#2517467