Finite Group Databasebeta

← C67×#61008 #30740259

Subgroups — C67×#61008 #30740259

Order 17152.

1712 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3511C211yesmaximal, characteristic
2C67×#3509C211yesmaximal, characteristic, complemented
3C67×#3258C214yesmaximal, complemented
4C67×#3231C211yesmaximal, characteristic, complemented
5C67×#3230C211yesmaximal, characteristic, complemented
6C67×#3229C211yesmaximal, characteristic, complemented
7C67×#3228C211yesmaximal, characteristic, complemented
8C67×#3210C211yesmaximal, characteristic, complemented
9C67×#3210C211yesmaximal, characteristic, complemented
10C67×#3209C211yesmaximal, characteristic, complemented
11C67×#3206C211yesmaximal, characteristic, complemented
12C67×#3201C214yesmaximal, complemented
13C67×#3185C211yesmaximal, characteristic, complemented
14C67×#3182C211yesmaximal, characteristic, complemented
15C67×#3170C211yesmaximal, characteristic, complemented
16C67×#3167C211yesmaximal, characteristic, complemented
17C67×#3121C214yesmaximal, complemented
18C67×#3120C214yesmaximal, complemented
19C67×#2922C211yesmaximal, characteristic, complemented
20#557×C67—21no—
21#557×C67—21no—
22#556×C67—21no—
23#556×C67—21no—
24#556×C67—21no—
25#555×C67—21no—
26#554×C67—21no—
27#553×C67—21no—
28#553×C67—21no—
29#552×C67—21no—
30#552×C67—21no—
31#552×C67—21no—
32#552×C67—21no—
33#548×C67—21no—
34#548×C67—21no—
35#547×C67—21no—
36#542×C67C2212yes—
37#542×C67C2212yes—
38#541×C67C2212yes—
39#541×C67C2212yes—
40#537×C67C2212yes—
41#536×C67C2212yes—
42#533×C67C2211yescharacteristic
43#533×C67C2211yescharacteristic
44#533×C67C2211yescharacteristic
45#533×C67C2211yescharacteristic
46#533×C67C2211yescharacteristic
47#533×C67C2211yescharacteristic
48#533×C67C2211yescharacteristic
49#532×C67C2211yescharacteristic
50#532×C67C2211yescharacteristic
51#532×C67C2211yescharacteristic
52C2×C4⋊Q8×C67C2211yescharacteristic
53C2×C4⋊Q8×C67C2211yescharacteristic
54#520×C67C2212yes—
55#519×C67C2212yes—
56C4×#41×C67C2211yescharacteristic
57#500×C67C2211yescharacteristic
58#500×C67C2211yescharacteristic
59#498×C67C2211yescharacteristic
60#498×C67C2211yescharacteristic
61#494×C67C2211yescharacteristic
62#494×C67C2211yescharacteristic
63#492×C67C2211yescharacteristic
64#492×C67C2211yescharacteristic
65#487×C67C2211yescharacteristic
66#487×C67C2211yescharacteristic
67#487×C67C2211yescharacteristic
68#487×C67C2211yescharacteristic
69#487×C67C2211yescharacteristic
70#487×C67C2211yescharacteristic
71#486×C67C2211yescharacteristic
72#486×C67C2211yescharacteristic
73#485×C67C2214yes—
74#484×C67C2214yes—
75#483×C67C2214yes—
76#482×C67C2214yes—
77#479×C67C2214yes—
78#478×C67C2214yes—
79#477×C67C2214yes—
80#475×C67C2214yes—
81#470×C67C2214yes—
82#468×C67C2214yes—
83#467×C67C2214yes—
84#465×C67C2214yes—
85#464×C67C2214yes—
86#464×C67C2214yes—
87#462×C67C2214yes—
88#461×C67C2214yes—
89#452×C67C2214yes—
90#452×C67C2214yes—
91#451×C67C2214yes—
92#448×C67C2214yes—
93#441×C67C2214yes—
94#440×C67C2214yes—
95C4×Q16×C67C2214yes—
96C4×SD16×C67C2214yes—
97#433×C67C2212yes—
98#433×C67C2212yes—
99#431×C67C2211yescharacteristic
100#431×C67C2211yescharacteristic
101#431×C67C2211yescharacteristic
102#431×C67C2211yescharacteristic
103#424×C67C2212yes—
104#408×C67C2212yes—
105C4×M16×C67C2211yescharacteristic
106C2×C4×C8×C67C2211yescharacteristic
107C2×#41×C67—21no—
108C2×#41×C67—21no—
109C2×#41×C67C2312yes—
110C2×#41×C67C2311yescharacteristic
111C22×Q8×C67—21no—
112C22×Q8×C67C2312yes—
113C2×Q16×C67C2314yes—
114C2×Q16×C67C2314yes—
115C2×SD16×C67C2314yes—
116C2×SD16×C67C2314yes—
117C2×M16×C67C2312yes—
118C22×C8×C67C2312yes—
119C4⋊Q8×C67—22no—
120C4⋊Q8×C67—21no—
121C4⋊Q8×C67—21no—
122C4⋊Q8×C67—21no—
123C4⋊Q8×C67—21no—
124C4⋊Q8×C67C2312yes—
125C4⋊Q8×C67C2311yescharacteristic
126C4⋊Q8×C67C2311yescharacteristic
127C4⋊Q8×C67C2311yescharacteristic
128C4⋊Q8×C67C2312yes—
129C4⋊Q8×C67C2311yescharacteristic
130C4⋊Q8×C67C2311yescharacteristic
131C4⋊Q8×C67C2311yescharacteristic
132C4⋊Q8×C67C2311yescharacteristic
133#127×C67C2311yescharacteristic
134#126×C67—22no—
135#126×C67—22no—
136#126×C67—22no—
137#126×C67—22no—
138#126×C67—22no—
139#126×C67—22no—
140#125×C67—22no—
141#125×C67—22no—
142#125×C67—22no—
143#125×C67—22no—
144#125×C67—21no—
145#125×C67—21no—
146#125×C67—21no—
147#125×C67—21no—
148#125×C67—21no—
149#125×C67—21no—
150#125×C67C2312yes—
151#124×C67—22no—
152#124×C67—22no—
153#124×C67—22no—
154#124×C67—21no—
155#124×C67—21no—
156#124×C67C2312yes—
157#123×C67—22no—
158#123×C67—22no—
159#123×C67—22no—
160#123×C67—22no—
161C22⋊Q8×C67—22no—
162C22⋊Q8×C67—21no—
163C22⋊Q8×C67—21no—
164C22⋊Q8×C67—21no—
165C22⋊Q8×C67—21no—
166C22⋊Q8×C67—21no—
167C22⋊Q8×C67—21no—
168C22⋊Q8×C67—21no—
169C22⋊Q8×C67—21no—
170C22⋊Q8×C67—22no—
171C22⋊Q8×C67—22no—
172C22⋊Q8×C67C2312yes—
173C22⋊Q8×C67C2312yes—
174C22⋊Q8×C67C2312yes—
175C22⋊Q8×C67C2312yes—
176C22⋊Q8×C67C2312yes—
177C22⋊Q8×C67C2312yes—
178#121×C67—22no—
179#121×C67—22no—
180#121×C67—22no—
181#121×C67—21no—
182#121×C67—21no—
183#121×C67—21no—
184#121×C67—21no—
185#121×C67C2312yes—
186#121×C67C2312yes—
187C4×Q8×C67—22no—
188C4×Q8×C67—22no—
189C4×Q8×C67—21no—
190C4×Q8×C67—21no—
191C4×Q8×C67—21no—
192C4×Q8×C67—21no—
193C4×Q8×C67—21no—
194C4×Q8×C67—21no—
195C4×Q8×C67—21no—
196C4×Q8×C67—21no—
197C4×Q8×C67D411yescharacteristic
198C4×Q8×C67D411yescharacteristic
199C4×Q8×C67C2312yes—
200C4×Q8×C67C2312yes—
201C4×Q8×C67C2312yes—
202C4×Q8×C67C2312yes—
203C4×Q8×C67C2312yes—
204C4×Q8×C67C2312yes—
205C4×D4×C67—22no—
206C4×D4×C67—22no—
207C4×D4×C67—21no—
208C4×D4×C67—21no—
209C4×D4×C67—21no—
210C4×D4×C67—21no—
211C4×D4×C67D411yescharacteristic
212C4×D4×C67D411yescharacteristic
213C4×D4×C67D411yescharacteristic
214C4×D4×C67D411yescharacteristic
215C4×D4×C67D411yescharacteristic
216C4×D4×C67D411yescharacteristic
217C4×D4×C67C2312yes—
218C4×D4×C67C2312yes—
219#117×C67—21no—
220#117×C67—21no—
221#117×C67—21no—
222#117×C67—21no—
223#117×C67—21no—
224#117×C67—21no—
225#117×C67—22no—
226#117×C67—22no—
227#117×C67—22no—
228#117×C67C2312yes—
229#117×C67C2311yescharacteristic
230#117×C67C2311yescharacteristic
231#117×C67C2311yescharacteristic
232C2×C4⋊C4×C67—21no—
233C2×C4⋊C4×C67—21no—
234C2×C4⋊C4×C67—21no—
235C2×C4⋊C4×C67—22no—
236C2×C4⋊C4×C67C2312yes—
237C2×C42×C67C2311yescharacteristic
238C2×C42×C67C2311yescharacteristic
239C2×C42×C67C2311yescharacteristic
240#107×C67C2314yes—
241#107×C67C2314yes—
242#106×C67C2314yes—
243#106×C67C2314yes—
244C4⋊C8×C67C2312yes—
245C4⋊C8×C67C2312yes—
246C4⋊C8×C67C2312yes—
247C4⋊C8×C67C2312yes—
248#103×C67C2314yes—
249#103×C67C2314yes—
250#103×C67C2314yes—
251#103×C67C2314yes—
252#103×C67C2314yes—
253#103×C67C2314yes—
254#102×C67C2314yes—
255#102×C67C2314yes—
256C22⋊C8×C67C2312yes—
257C22⋊C8×C67C2312yes—
258C22⋊C8×C67C2312yes—
259C22⋊C8×C67C2312yes—
260#97×C67C2312yes—
261C4×C8×C67C2311yescharacteristic
262C4×C8×C67C2311yescharacteristic
263C4×C8×C67C2311yescharacteristic
264C4×C8×C67C2311yescharacteristic
265C4×C8×C67C2312yes—
266#41×C67—42no—
267#41×C67—44no—
268#41×C67—82no—
269#41×C67—82no—
270C2×Q8×C67—21no—
271C2×Q8×C67—21no—
272C2×Q8×C67—22no—
273C2×Q8×C67—21no—
274C2×Q8×C67—21no—
275C2×Q8×C67—22no—
276C2×Q8×C67—44no—
277C2×Q8×C67—82no—
278C2×Q8×C67C2×D411yescharacteristic
279C2×Q8×C67C2412yes—
280C2×Q8×C67C2412yes—
281C2×Q8×C67C2412yes—
282C2×D4×C67—22no—
283C2×D4×C67—22no—
284C2×D4×C67—22no—
285C2×D4×C67—21no—
286C2×D4×C67—21no—
287C2×D4×C67C2×D411yescharacteristic
288C2×D4×C67C2×D411yescharacteristic
289C2×D4×C67C2×D411yescharacteristic
290C2×D4×C67C2412yes—
291C22×C4×C67—22no—
292C22×C4×C67—22no—
293C22×C4×C67—22no—
294C22×C4×C67—22no—
295C22×C4×C67—22no—
296C22×C4×C67C2×D411yescharacteristic
297C22×C4×C67C2×D411yescharacteristic
298C22×C4×C67C2×D411yescharacteristic
299C22×C4×C67C2×D411yescharacteristic
300C22×C4×C67C2×D411yescharacteristic
301C22×C4×C67C2×D411yescharacteristic
302C22×C4×C67C2411yescharacteristic
303C22×C4×C67C2411yescharacteristic
304C22×C4×C67C2411yescharacteristic
305Q16×C67—44no—
306Q16×C67—44no—
307SD16×C67—44no—
308SD16×C67—44no—
309M16×C67—42no—
310C2×C8×C67—42no—
311C2×C8×C67C2412yes—
312C2×C8×C67C2412yes—
313C2×C8×C67C2412yes—
314C2×C8×C67C2412yes—
315C4⋊C4×C67—22no—
316C4⋊C4×C67—21no—
317C4⋊C4×C67—21no—
318C4⋊C4×C67—21no—
319C4⋊C4×C67—21no—
320C4⋊C4×C67—21no—
321C4⋊C4×C67—21no—
322C4⋊C4×C67—22no—
323C4⋊C4×C67—22no—
324C4⋊C4×C67—22no—
325C4⋊C4×C67—22no—
326C4⋊C4×C67—22no—
327C4⋊C4×C67—21no—
328C4⋊C4×C67—21no—
329C4⋊C4×C67—21no—
330C4⋊C4×C67—22no—
331C4⋊C4×C67—22no—
332C4⋊C4×C67—22no—
333C4⋊C4×C67—22no—
334C4⋊C4×C67—21no—
335C4⋊C4×C67—22no—
336C4⋊C4×C67—22no—
337C4⋊C4×C67—22no—
338C4⋊C4×C67—22no—
339C4⋊C4×C67—22no—
340C4⋊C4×C67—22no—
341C4⋊C4×C67—22no—
342C4⋊C4×C67—22no—
343C4⋊C4×C67C2×D411yescharacteristic
344C4⋊C4×C67C2×D411yescharacteristic
345C4⋊C4×C67C2×D411yescharacteristic
346C4⋊C4×C67C2×D411yescharacteristic
347C4⋊C4×C67C2×D411yescharacteristic
348C4⋊C4×C67C2×D411yescharacteristic
349C4⋊C4×C67C2412yes—
350C4⋊C4×C67C2412yes—
351C4⋊C4×C67C2412yes—
352C4⋊C4×C67C2412yes—
353C22⋊C4×C67—22no—
354C22⋊C4×C67—22no—
355C22⋊C4×C67—22no—
356C22⋊C4×C67—22no—
357C22⋊C4×C67—22no—
358C22⋊C4×C67—22no—
359C22⋊C4×C67—22no—
360C22⋊C4×C67—22no—
361C22⋊C4×C67—22no—
362C22⋊C4×C67—22no—
363C22⋊C4×C67—22no—
364C22⋊C4×C67—22no—
365C22⋊C4×C67—22no—
366C22⋊C4×C67C2×D411yescharacteristic
367C22⋊C4×C67C2×D411yescharacteristic
368C22⋊C4×C67C2×D411yescharacteristic
369C22⋊C4×C67C2×D411yescharacteristic
370C22⋊C4×C67C2×D411yescharacteristic
371C22⋊C4×C67C2×D411yescharacteristic
372C42×C67—22no—
373C42×C67—22no—
374C42×C67—22no—
375C42×C67—22no—
376C42×C67—22no—
377C42×C67—22no—
378C42×C67—22no—
379C42×C67C2×D411yescharacteristic
380C42×C67C2×D411yescharacteristic
381C42×C67C2×D411yescharacteristic
382C42×C67C2×D411yescharacteristic
383C42×C67C2×D411yescharacteristic
384C42×C67C2×D411yescharacteristic
385C42×C67C2411yescharacteristic
386C42×C67C2411yescharacteristic
387C42×C67C2411yescharacteristic
388C42×C67C2411yescharacteristic
389C23×C67—22no—
390C23×C67C22×D411yescharacteristic
391C23×C67C22×D411yescharacteristic
392C23×C67C22×D411yescharacteristic
393Q8×C67—24no—
394Q8×C67—24no—
395Q8×C67—24no—
396Q8×C67—41no—
397Q8×C67—44no—
398Q8×C67—42no—
399Q8×C67—42no—
400Q8×C67—42no—
401Q8×C67—42no—
402Q8×C67—82no—
403D4×C67—24no—
404D4×C67—41no—
405D4×C67—41no—
406D4×C67—41no—
407D4×C67—44no—
408D4×C67—42no—
409D4×C67—42no—
410D4×C67—82no—
411D4×C67—82no—
412C2×C4×C67—22no—
413C2×C4×C67—22no—
414C2×C4×C67—22no—
415C2×C4×C67—22no—
416C2×C4×C67—22no—
417C2×C4×C67—22no—
418C2×C4×C67—22no—
419C2×C4×C67—22no—
420C2×C4×C67—22no—
421C2×C4×C67—22no—
422C2×C4×C67—22no—
423C2×C4×C67—22no—
424C2×C4×C67—22no—
425C2×C4×C67—22no—
426C2×C4×C67—22no—
427C2×C4×C67—22no—
428C2×C4×C67—44no—
429C2×C4×C67—44no—
430C2×C4×C67—82no—
431C2×C4×C67—82no—
432C2×C4×C67—82no—
433C2×C4×C67C22×D411yescharacteristic
434C2×C4×C67C22×D411yescharacteristic
435C2×C4×C67C22×D411yescharacteristic
436C2×C4×C67C22×D411yescharacteristic
437C2×C4×C67C22×D411yescharacteristic
438C2×C4×C67C22×D411yescharacteristic
439C2×C4×C67C22×D411yescharacteristic
440C2×C4×C67C22×D411yescharacteristic
441C2×C4×C67C22×D411yescharacteristic
442C2×C4×C67C22×D411yescharacteristic
443C2×C4×C67C22×D411yescharacteristic
444C2×C4×C67C2511yescharacteristic
445C8×C67—22no—
446C8×C67—22no—
447C8×C67—22no—
448C8×C67—22no—
449C22×C67—21no—
450C22×C67—21no—
451C22×C67—21no—
452C22×C67—21no—
453C22×C67—21no—
454C22×C67—21no—
455C22×C67—21no—
456C22×C67—21no—
457C22×C67—21no—
458C22×C67—42no—
459C22×C67—42no—
460C22×C67—42no—
461C22×C67C23×D411yescharacteristic
462C4×C67—21no—
463C4×C67—21no—
464C4×C67—21no—
465C4×C67—21no—
466C4×C67—21no—
467C4×C67—21no—
468C4×C67—21no—
469C4×C67—21no—
470C4×C67—21no—
471C4×C67—42no—
472C4×C67—42no—
473C4×C67—42no—
474C4×C67—42no—
475C4×C67—42no—
476C4×C67—42no—
477C4×C67—42no—
478C4×C67#57712yes—
479C4×C67#57812yes—
480C4×C67#58512yes—
481#61008C6711yesmaximal, characteristic, direct product factor, Sylow
482C2×C67—41no—
483C2×C67—41no—
484C2×C67—41no—
485C2×C67—82no—
486C2×C67#344911yescharacteristic
487C2×C67C2×#57711yescharacteristic
488C2×C67C2×#57811yescharacteristic
489#3511C2×C6711yescharacteristic
490#3509C2×C6711yescharacteristic, complemented
491#3258C2×C6714yescomplemented
492#3231C2×C6711yescharacteristic, complemented
493#3230C2×C6711yescharacteristic, complemented
494#3229C2×C6711yescharacteristic, complemented
495#3228C2×C6711yescharacteristic, complemented
496#3210C2×C6711yescharacteristic, complemented
497#3210C2×C6711yescharacteristic, complemented
498#3209C2×C6711yescharacteristic, complemented
499#3206C2×C6711yescharacteristic, complemented
500#3201C2×C6714yescomplemented
501#3185C2×C6711yescharacteristic, complemented
502#3182C2×C6711yescharacteristic, complemented
503#3170C2×C6711yescharacteristic, complemented
504#3167C2×C6711yescharacteristic, complemented
505#3121C2×C6714yescomplemented
506#3120C2×C6714yescomplemented
507#2922C2×C6711yescharacteristic, complemented
508C67#6100811yescharacteristic, direct product factor, Sylow
509#557—21no—
510#557—21no—
511#556—21no—
512#556—21no—
513#556—21no—
514#555—21no—
515#554—21no—
516#553—21no—
517#553—21no—
518#552—21no—
519#552—21no—
520#552—21no—
521#552—21no—
522#548—21no—
523#548—21no—
524#547—21no—
525#542C22×C6712yes—
526#542C22×C6712yes—
527#541C22×C6712yes—
528#541C22×C6712yes—
529#537C22×C6712yes—
530#536C22×C6712yes—
531#533C22×C6711yescharacteristic
532#533C22×C6711yescharacteristic
533#533C22×C6711yescharacteristic
534#533C22×C6711yescharacteristic
535#533C22×C6711yescharacteristic
536#533C22×C6711yescharacteristic
537#533C22×C6711yescharacteristic
538#532C22×C6711yescharacteristic
539#532C22×C6711yescharacteristic
540#532C22×C6711yescharacteristic
541C2×C4⋊Q8C22×C6711yescharacteristic
542C2×C4⋊Q8C22×C6711yescharacteristic
543#520C22×C6712yes—
544#519C22×C6712yes—
545C4×#41C22×C6711yescharacteristic
546#500C22×C6711yescharacteristic
547#500C22×C6711yescharacteristic
548#498C22×C6711yescharacteristic
549#498C22×C6711yescharacteristic
550#494C22×C6711yescharacteristic
551#494C22×C6711yescharacteristic
552#492C22×C6711yescharacteristic
553#492C22×C6711yescharacteristic
554#487C22×C6711yescharacteristic
555#487C22×C6711yescharacteristic
556#487C22×C6711yescharacteristic
557#487C22×C6711yescharacteristic
558#487C22×C6711yescharacteristic
559#487C22×C6711yescharacteristic
560#486C22×C6711yescharacteristic
561#486C22×C6711yescharacteristic
562#485C22×C6714yes—
563#484C22×C6714yes—
564#483C22×C6714yes—
565#482C22×C6714yes—
566#479C22×C6714yes—
567#478C22×C6714yes—
568#477C22×C6714yes—
569#475C22×C6714yes—
570#470C22×C6714yes—
571#468C22×C6714yes—
572#467C22×C6714yes—
573#465C22×C6714yes—
574#464C22×C6714yes—
575#464C22×C6714yes—
576#462C22×C6714yes—
577#461C22×C6714yes—
578#452C22×C6714yes—
579#452C22×C6714yes—
580#451C22×C6714yes—
581#448C22×C6714yes—
582#441C22×C6714yes—
583#440C22×C6714yes—
584C4×Q16C22×C6714yes—
585C4×SD16C22×C6714yes—
586#433C22×C6712yes—
587#433C22×C6712yes—
588#431C22×C6711yescharacteristic
589#431C22×C6711yescharacteristic
590#431C22×C6711yescharacteristic
591#431C22×C6711yescharacteristic
592#424C22×C6712yes—
593#408C22×C6712yes—
594C4×M16C22×C6711yescharacteristic
595C2×C4×C8C22×C6711yescharacteristic
596C2×#41—21no—
597C2×#41—21no—
598C2×#41C23×C6712yes—
599C2×#41C23×C6711yescharacteristic
600C22×Q8—21no—
601C22×Q8C23×C6712yes—
602C2×Q16C23×C6714yes—
603C2×Q16C23×C6714yes—
604C2×SD16C23×C6714yes—
605C2×SD16C23×C6714yes—
606C2×M16C23×C6712yes—
607C22×C8C23×C6712yes—
608C4⋊Q8—22no—
609C4⋊Q8—21no—
610C4⋊Q8—21no—
611C4⋊Q8—21no—
612C4⋊Q8—21no—
613C4⋊Q8C23×C6711yescharacteristic
614C4⋊Q8C23×C6711yescharacteristic
615C4⋊Q8C23×C6712yes—
616C4⋊Q8C23×C6711yescharacteristic
617C4⋊Q8C23×C6711yescharacteristic
618C4⋊Q8C23×C6711yescharacteristic
619C4⋊Q8C23×C6712yes—
620C4⋊Q8C23×C6711yescharacteristic
621C4⋊Q8C23×C6711yescharacteristic
622#127C23×C6711yescharacteristic
623#126—22no—
624#126—22no—
625#126—22no—
626#126—22no—
627#126—22no—
628#126—22no—
629#125—22no—
630#125—22no—
631#125—22no—
632#125—22no—
633#125—21no—
634#125—21no—
635#125—21no—
636#125—21no—
637#125—21no—
638#125—21no—
639#125C23×C6712yes—
640#124—22no—
641#124—22no—
642#124—22no—
643#124—21no—
644#124—21no—
645#124C23×C6712yes—
646#123—22no—
647#123—22no—
648#123—22no—
649#123—22no—
650C22⋊Q8—22no—
651C22⋊Q8—21no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658C22⋊Q8—21no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8C23×C6712yes—
662C22⋊Q8C23×C6712yes—
663C22⋊Q8C23×C6712yes—
664C22⋊Q8C23×C6712yes—
665C22⋊Q8C23×C6712yes—
666C22⋊Q8C23×C6712yes—
667#121—22no—
668#121—22no—
669#121—22no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121C23×C6712yes—
675#121C23×C6712yes—
676C4×Q8—22no—
677C4×Q8—22no—
678C4×Q8—21no—
679C4×Q8—21no—
680C4×Q8—21no—
681C4×Q8—21no—
682C4×Q8—21no—
683C4×Q8—21no—
684C4×Q8—21no—
685C4×Q8—21no—
686C4×Q8D4×C6711yescharacteristic
687C4×Q8D4×C6711yescharacteristic
688C4×Q8C23×C6712yes—
689C4×Q8C23×C6712yes—
690C4×Q8C23×C6712yes—
691C4×Q8C23×C6712yes—
692C4×Q8C23×C6712yes—
693C4×Q8C23×C6712yes—
694C4×D4—22no—
695C4×D4—22no—
696C4×D4—21no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4D4×C6711yescharacteristic
701C4×D4D4×C6711yescharacteristic
702C4×D4D4×C6711yescharacteristic
703C4×D4D4×C6711yescharacteristic
704C4×D4D4×C6711yescharacteristic
705C4×D4D4×C6711yescharacteristic
706C4×D4C23×C6712yes—
707C4×D4C23×C6712yes—
708#117—21no—
709#117—21no—
710#117—21no—
711#117—21no—
712#117—21no—
713#117—21no—
714#117—22no—
715#117—22no—
716#117—22no—
717#117C23×C6712yes—
718#117C23×C6711yescharacteristic
719#117C23×C6711yescharacteristic
720#117C23×C6711yescharacteristic
721C2×C4⋊C4—21no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C6712yes—
726C2×C42C23×C6711yescharacteristic
727C2×C42C23×C6711yescharacteristic
728C2×C42C23×C6711yescharacteristic
729#107C23×C6714yes—
730#107C23×C6714yes—
731#106C23×C6714yes—
732#106C23×C6714yes—
733C4⋊C8C23×C6712yes—
734C4⋊C8C23×C6712yes—
735C4⋊C8C23×C6712yes—
736C4⋊C8C23×C6712yes—
737#103C23×C6714yes—
738#103C23×C6714yes—
739#103C23×C6714yes—
740#103C23×C6714yes—
741#103C23×C6714yes—
742#103C23×C6714yes—
743#102C23×C6714yes—
744#102C23×C6714yes—
745C22⋊C8C23×C6712yes—
746C22⋊C8C23×C6712yes—
747C22⋊C8C23×C6712yes—
748C22⋊C8C23×C6712yes—
749#97C23×C6712yes—
750C4×C8C23×C6711yescharacteristic
751C4×C8C23×C6711yescharacteristic
752C4×C8C23×C6712yes—
753C4×C8C23×C6711yescharacteristic
754C4×C8C23×C6711yescharacteristic
755#41—42no—
756#41—44no—
757#41—82no—
758#41—82no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—22no—
765C2×Q8—44no—
766C2×Q8—82no—
767C2×Q8C2×D4×C6711yescharacteristic
768C2×Q8C24×C6712yes—
769C2×Q8C24×C6712yes—
770C2×Q8C24×C6712yes—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4C2×D4×C6711yescharacteristic
777C2×D4C2×D4×C6711yescharacteristic
778C2×D4C2×D4×C6711yescharacteristic
779C2×D4C24×C6712yes—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4C2×D4×C6711yescharacteristic
786C22×C4C2×D4×C6711yescharacteristic
787C22×C4C2×D4×C6711yescharacteristic
788C22×C4C2×D4×C6711yescharacteristic
789C22×C4C2×D4×C6711yescharacteristic
790C22×C4C2×D4×C6711yescharacteristic
791C22×C4C24×C6711yescharacteristic
792C22×C4C24×C6711yescharacteristic
793C22×C4C24×C6711yescharacteristic
794Q16—44no—
795Q16—44no—
796SD16—44no—
797SD16—44no—
798M16—42no—
799C2×C8—42no—
800C2×C8C24×C6712yes—
801C2×C8C24×C6712yes—
802C2×C8C24×C6712yes—
803C2×C8C24×C6712yes—
804C4⋊C4—22no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—21no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4C2×D4×C6711yescharacteristic
833C4⋊C4C2×D4×C6711yescharacteristic
834C4⋊C4C2×D4×C6711yescharacteristic
835C4⋊C4C2×D4×C6711yescharacteristic
836C4⋊C4C2×D4×C6711yescharacteristic
837C4⋊C4C2×D4×C6711yescharacteristic
838C4⋊C4C24×C6712yes—
839C4⋊C4C24×C6712yes—
840C4⋊C4C24×C6712yes—
841C4⋊C4C24×C6712yes—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—22no—
848C22⋊C4—22no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4C2×D4×C6711yescharacteristic
856C22⋊C4C2×D4×C6711yescharacteristic
857C22⋊C4C2×D4×C6711yescharacteristic
858C22⋊C4C2×D4×C6711yescharacteristic
859C22⋊C4C2×D4×C6711yescharacteristic
860C22⋊C4C2×D4×C6711yescharacteristic
861C42—22no—
862C42—22no—
863C42—22no—
864C42—22no—
865C42—22no—
866C42—22no—
867C42—22no—
868C42C2×D4×C6711yescharacteristic
869C42C2×D4×C6711yescharacteristic
870C42C2×D4×C6711yescharacteristic
871C42C2×D4×C6711yescharacteristic
872C42C2×D4×C6711yescharacteristic
873C42C2×D4×C6711yescharacteristic
874C42C24×C6711yescharacteristic
875C42C24×C6711yescharacteristic
876C42C24×C6711yescharacteristic
877C42C24×C6711yescharacteristic
878C23—22no—
879C23C22×D4×C6711yescharacteristic
880C23C22×D4×C6711yescharacteristic
881C23C22×D4×C6711yescharacteristic
882Q8—24no—
883Q8—24no—
884Q8—24no—
885Q8—41no—
886Q8—44no—
887Q8—42no—
888Q8—42no—
889Q8—42no—
890Q8—42no—
891Q8—82no—
892D4—24no—
893D4—41no—
894D4—41no—
895D4—41no—
896D4—44no—
897D4—42no—
898D4—42no—
899D4—82no—
900D4—82no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—82no—
920C2×C4—82no—
921C2×C4—82no—
922C2×C4C22×D4×C6711yescharacteristic
923C2×C4C22×D4×C6711yescharacteristic
924C2×C4C22×D4×C6711yescharacteristic
925C2×C4C22×D4×C6711yescharacteristic
926C2×C4C22×D4×C6711yescharacteristic
927C2×C4C22×D4×C6711yescharacteristic
928C2×C4C22×D4×C6711yescharacteristic
929C2×C4C22×D4×C6711yescharacteristic
930C2×C4C22×D4×C6711yescharacteristic
931C2×C4C22×D4×C6711yescharacteristic
932C2×C4C22×D4×C6711yescharacteristic
933C2×C4C25×C6711yescharacteristic
934C8—22no—
935C8—22no—
936C8—22no—
937C8—22no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—21no—
946C22—21no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22C23×D4×C6711yescharacteristic
951C4—21no—
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4#577×C6712yes—
968C4#578×C6712yes—
969C4#585×C6712yes—
970C2—41no—
971C2—41no—
972C2—41no—
973C2—82no—
974C2C67×#344911yescharacteristic
975C2C2×#577×C6711yescharacteristic
976C2C2×#578×C6711yescharacteristic
subgroupG/H
center, socleC22×C67C23×D4
commutator, Frattini, cosocleC2×C4C25×C67
prime radicalC67×#3511C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C67 ◁ C4×#41×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C67×#3509C2semidirect
3. C67×#3258C2semidirect
4. C67×#3231C2semidirect
5. C67×#3230C2semidirect
6. C67×#3229C2semidirect
7. C67×#3228C2semidirect
8. C67×#3210C2semidirect
9. C67×#3210C2semidirect
10. C67×#3209C2semidirect
11. C67×#3206C2semidirect
12. C67×#3201C2semidirect
13. C67×#3185C2semidirect
14. C67×#3182C2semidirect
15. C67×#3170C2semidirect
16. C67×#3167C2semidirect
17. C67×#3121C2semidirect
18. C67×#3120C2semidirect
19. C67×#2922C2semidirect
481. #61008C67direct (N × H)
490. #3509C2×C67semidirect
491. #3258C2×C67semidirect
492. #3231C2×C67semidirect
493. #3230C2×C67semidirect
494. #3229C2×C67semidirect
495. #3228C2×C67semidirect
496. #3210C2×C67semidirect
497. #3210C2×C67semidirect
498. #3209C2×C67semidirect
499. #3206C2×C67semidirect
500. #3201C2×C67semidirect
501. #3185C2×C67semidirect
502. #3182C2×C67semidirect
503. #3170C2×C67semidirect
504. #3167C2×C67semidirect
505. #3121C2×C67semidirect
506. #3120C2×C67semidirect
507. #2922C2×C67semidirect
508. C67#61008direct (N × H)

Maximal subgroups

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

subgroupindex
C67×#35112
C67×#35092
C67×#32582
C67×#32312
C67×#32302
C67×#32292
C67×#32282
C67×#32102
C67×#32092
C67×#32062
C67×#32012
C67×#31852
C67×#31822
C67×#31702
C67×#31672
C67×#31212
C67×#31202
C67×#29222
#6100867