Finite Group Databasebeta

← C67×#34291 #30713542

Subgroups — C67×#34291 #30713542

Order 17152.

2912 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C67C211yesmaximal, characteristic
2C2×#519×C67C211yesmaximal, characteristic, complemented
3C22×C4×Q8×C67C211yesmaximal, characteristic, complemented
4C67×#2365C213yesmaximal, complemented
5C67×#2362C213yesmaximal, complemented
6C67×#2360C213yesmaximal, complemented
7C67×#2352C213yesmaximal
8C67×#2351C211yesmaximal, characteristic, complemented
9Q8×C22⋊C4×C67C211yesmaximal, characteristic, complemented
10Q8×C22⋊C4×C67C211yesmaximal, characteristic, complemented
11C67×#2327C213yesmaximal, complemented
12C67×#2323C213yesmaximal, complemented
13C4×C22⋊Q8×C67C213yesmaximal, complemented
14C67×#2290C213yesmaximal
15C67×#2276C211yesmaximal, characteristic, complemented
16C23×Q8×C67C2211yescharacteristic
17C23×Q8×C67C2211yescharacteristic
18D4×Q8×C67C4116yescomplemented
19C2×C4⋊Q8×C67C2213yes—
20C2×C22⋊Q8×C67C2213yes—
21C2×C22⋊Q8×C67C2213yes—
22#519×C67—28no—
23C2×C4×Q8×C67—28no—
24C2×C4×Q8×C67C2211yescharacteristic
25C2×C4×Q8×C67C2213yes—
26C2×C4×Q8×C67C2213yes—
27C2×C4×Q8×C67C2211yescharacteristic
28C2×C4×Q8×C67C2211yescharacteristic
29C2×C4×Q8×C67C2213yes—
30C2×C4×Q8×C67C2213yes—
31C2×C4×Q8×C67C2211yescharacteristic
32C2×C4×Q8×C67C2211yescharacteristic
33C2×C4×D4×C67C2213yes—
34C2×#117×C67C2213yes—
35C2×#117×C67C2213yes—
36C22×C4⋊C4×C67C2213yes—
37C22×C42×C67C2213yes—
38#391×C67C2213yes—
39#391×C67C2213yes—
40#391×C67C2213yes—
41#391×C67C2213yes—
42#389×C67C2213yes—
43#389×C67C2213yes—
44#389×C67C2216yes—
45#388×C67C2213yes—
46#388×C67C2213yes—
47#388×C67C2216yes—
48#387×C67C2213yes—
49#387×C67C2213yes—
50#387×C67C2216yes—
51#387×C67C2216yes—
52#387×C67C2216yes—
53#386×C67C2211yescharacteristic
54#386×C67C2213yes—
55#385×C67C2213yes—
56#385×C67C2213yes—
57#382×C67C2213yes—
58#380×C67C2213yes—
59#380×C67C2213yes—
60C4×C4⋊C4×C67C2213yes—
61C4×C4⋊C4×C67C2213yes—
62C4×C4⋊C4×C67C2213yes—
63C4×C4⋊C4×C67C2213yes—
64C4×C4⋊C4×C67C2216yes—
65C4×C22⋊C4×C67C2213yes—
66C4×C22⋊C4×C67C2213yes—
67C4×C22⋊C4×C67C2216yes—
68#376×C67C2213yes—
69C22×Q8×C67—24no—
70C22×Q8×C67—24no—
71C22×Q8×C67—24no—
72C22×Q8×C67—24no—
73C22×Q8×C67C2×C418yes—
74C22×Q8×C67C2×C418yescomplemented
75C22×Q8×C67C2313yes—
76C22×Q8×C67C2313yes—
77C22×Q8×C67C2311yescharacteristic
78C22×D4×C67C2311yescharacteristic
79C23×C4×C67C2311yescharacteristic
80C23×C4×C67C2313yes—
81C23×C4×C67C2313yes—
82C23×C4×C67C2313yes—
83C4⋊Q8×C67C2×C4124yescomplemented
84C22⋊Q8×C67C2×C4124yes—
85C22⋊Q8×C67C2×C4124yescomplemented
86C4×Q8×C67—24no—
87C4×Q8×C67—24no—
88C4×Q8×C67—24no—
89C4×Q8×C67—212no—
90C4×Q8×C67—212no—
91C4×Q8×C67—212no—
92C4×Q8×C67—212no—
93C4×Q8×C67C2×C418yescomplemented
94C4×Q8×C67D418yescomplemented
95C4×D4×C67C2×C4124yes—
96#117×C67—212no—
97#117×C67—212no—
98C2×C4⋊C4×C67—212no—
99C2×C4⋊C4×C67C2313yes—
100C2×C4⋊C4×C67C2316yes—
101C2×C4⋊C4×C67C2313yes—
102C2×C4⋊C4×C67C2313yes—
103C2×C4⋊C4×C67C2313yes—
104C2×C4⋊C4×C67C2313yes—
105C2×C4⋊C4×C67C2313yes—
106C2×C4⋊C4×C67C2313yes—
107C2×C4⋊C4×C67C2313yes—
108C2×C4⋊C4×C67C2313yes—
109C2×C4⋊C4×C67C2316yes—
110C2×C4⋊C4×C67C2313yes—
111C2×C22⋊C4×C67C2311yescharacteristic
112C2×C22⋊C4×C67C2313yes—
113C2×C22⋊C4×C67C2313yes—
114C2×C22⋊C4×C67C2311yescharacteristic
115C2×C22⋊C4×C67C2311yescharacteristic
116C2×C22⋊C4×C67C2313yes—
117C2×C22⋊C4×C67C2313yes—
118C2×C22⋊C4×C67C2313yes—
119C2×C42×C67—212no—
120C2×C42×C67C2313yes—
121C2×C42×C67C2313yes—
122C2×C42×C67C2313yes—
123C2×C42×C67C2316yes—
124C2×C42×C67C2313yes—
125C2×C42×C67C2313yes—
126C2×C42×C67C2316yes—
127C2×C42×C67C2313yes—
128C2×C42×C67C2313yes—
129#95×C67C2311yescharacteristic
130#95×C67C2313yes—
131#95×C67C2313yes—
132#95×C67C2313yes—
133#95×C67C2313yes—
134#95×C67C2316yes—
135#95×C67C2316yes—
136#95×C67C2313yes—
137#95×C67C2313yes—
138#95×C67C2313yes—
139#95×C67C2311yescharacteristic
140#95×C67C2316yes—
141#95×C67C2313yes—
142C24×C67C2411yescharacteristic
143C24×C67C2411yescharacteristic
144C2×Q8×C67—232no—
145C2×Q8×C67—232no—
146C2×Q8×C67—26no—
147C2×Q8×C67—26no—
148C2×Q8×C67—26no—
149C2×Q8×C67—26no—
150C2×Q8×C67C22×C4112yes—
151C2×Q8×C67C22×C4112yes—
152C2×Q8×C67C22×C414yes—
153C2×Q8×C67C2×D414yes—
154C2×Q8×C67#4114yes—
155C2×D4×C67—22no—
156C2×D4×C67—22no—
157C2×D4×C67C22×C414yes—
158C22×C4×C67—22no—
159C22×C4×C67—22no—
160C22×C4×C67—26no—
161C22×C4×C67—26no—
162C22×C4×C67—26no—
163C22×C4×C67—26no—
164C22×C4×C67—22no—
165C22×C4×C67—26no—
166C22×C4×C67—26no—
167C22×C4×C67—43no—
168C22×C4×C67C22×C4112yes—
169C22×C4×C67C22×C4112yes—
170C22×C4×C67C2411yescharacteristic
171C22×C4×C67C2413yes—
172C22×C4×C67C2413yes—
173C22×C4×C67C2411yescharacteristic
174C22×C4×C67C2413yes—
175C22×C4×C67C2413yes—
176C22×C4×C67C2411yescharacteristic
177C22×C4×C67C2413yes—
178C22×C4×C67C2413yes—
179C22×C4×C67C2413yes—
180C22×C4×C67C2411yescharacteristic
181C22×C4×C67C2411yescharacteristic
182C22×C4×C67C2413yes—
183C4⋊C4×C67—212no—
184C4⋊C4×C67—26no—
185C4⋊C4×C67—26no—
186C4⋊C4×C67—26no—
187C4⋊C4×C67—26no—
188C4⋊C4×C67—26no—
189C4⋊C4×C67—26no—
190C4⋊C4×C67—43no—
191C4⋊C4×C67C22×C4112yes—
192C4⋊C4×C67C22×C4112yes—
193C4⋊C4×C67C22×C4124yes—
194C4⋊C4×C67C2×D4112yes—
195C22⋊C4×C67—26no—
196C22⋊C4×C67—22no—
197C22⋊C4×C67—22no—
198C22⋊C4×C67—26no—
199C22⋊C4×C67—22no—
200C22⋊C4×C67—43no—
201C22⋊C4×C67C22×C4112yes—
202C22⋊C4×C67C22×C4112yes—
203C42×C67—26no—
204C42×C67—26no—
205C42×C67—26no—
206C42×C67—212no—
207C42×C67—26no—
208C42×C67—26no—
209C42×C67—46no—
210C42×C67C22×C4112yes—
211C42×C67C2×D4112yes—
212C23×C67—21no—
213C23×C67—21no—
214C23×C67—21no—
215C23×C67—21no—
216C23×C67—21no—
217C23×C67—21no—
218C23×C67—21no—
219C23×C67—21no—
220C23×C67—21no—
221C23×C67—21no—
222C23×C67C23×C412yes—
223C23×C67C23×C412yes—
224C23×C672−1+412yes—
225C23×C672−1+412yes—
226C23×C67C2511yescharacteristic
227Q8×C67—224no—
228Q8×C67—224no—
229Q8×C67C4×D4116yes—
230D4×C67—28no—
231C2×C4×C67—28no—
232C2×C4×C67—21no—
233C2×C4×C67—23no—
234C2×C4×C67—23no—
235C2×C4×C67—23no—
236C2×C4×C67—23no—
237C2×C4×C67—23no—
238C2×C4×C67—21no—
239C2×C4×C67—21no—
240C2×C4×C67—21no—
241C2×C4×C67—23no—
242C2×C4×C67—21no—
243C2×C4×C67—21no—
244C2×C4×C67—23no—
245C2×C4×C67—23no—
246C2×C4×C67—224no—
247C2×C4×C67—224no—
248C2×C4×C67—23no—
249C2×C4×C67—21no—
250C2×C4×C67—23no—
251C2×C4×C67—21no—
252C2×C4×C67—23no—
253C2×C4×C67—23no—
254C2×C4×C67—21no—
255C2×C4×C67—23no—
256C2×C4×C67—21no—
257C2×C4×C67—21no—
258C2×C4×C67—23no—
259C2×C4×C67—23no—
260C2×C4×C67—23no—
261C2×C4×C67—23no—
262C2×C4×C67—21no—
263C2×C4×C67—412no—
264C2×C4×C67C23×C412yes—
265C2×C4×C67C23×C416yes—
266C2×C4×C67C23×C416yes—
267C2×C4×C67C23×C416yes—
268C2×C4×C67C23×C416yes—
269C2×C4×C67C22×D412yes—
270C2×C4×C67C22×D416yes—
271C2×C4×C67C22×D416yes—
272C2×C4×C67C2×#4116yes—
273C2×C4×C672−1+412yes—
274C22×C67—22no—
275C22×C67—22no—
276C22×C67—22no—
277C22×C67—22no—
278C22×C67—22no—
279C22×C67—22no—
280C22×C67—22no—
281C22×C67—22no—
282C22×C67—22no—
283C22×C67—41no—
284C22×C67—41no—
285C22×C67—41no—
286C22×C67—41no—
287C22×C67#51914yescomplemented
288C22×C67C24×C411yescharacteristic
289C22×C67C23×D411yescharacteristic
290C22×C67C22×#4111yescharacteristic
291C22×C67C2×2−1+411yescharacteristic
292C22×C67C2×2−1+411yescharacteristic
293C22×C67C2×2−1+411yescharacteristic
294C22×C67#58511yescharacteristic
295C4×C67—26no—
296C4×C67—26no—
297C4×C67—22no—
298C4×C67—26no—
299C4×C67—22no—
300C4×C67—22no—
301C4×C67—26no—
302C4×C67—43no—
303C4×C67—41no—
304C4×C67—43no—
305C4×C67—43no—
306C4×C67—41no—
307C4×C67C2×C4×D4112yes—
308#34291C6711yesmaximal, characteristic, direct product factor, Sylow
309C2×C67—24no—
310C2×C67—42no—
311C2×C67C22×C4×D411yescharacteristic
312C2×C67C2×#51911yescharacteristic
313C2×C67C4×2−1+411yescharacteristic
314C2×C67#348611yescharacteristic
315C2×C67#348911yescharacteristic
316C2×C67#351611yescharacteristic
317C2×C67#352311yescharacteristic
318C2×D4×Q8C2×C6711yescharacteristic
319C2×#519C2×C6711yescharacteristic, complemented
320C22×C4×Q8C2×C6711yescharacteristic, complemented
321#2365C2×C6713yescomplemented
322#2362C2×C6713yescomplemented
323#2360C2×C6713yescomplemented
324#2352C2×C6713yes—
325#2351C2×C6711yescharacteristic, complemented
326Q8×C22⋊C4C2×C6711yescharacteristic, complemented
327Q8×C22⋊C4C2×C6711yescharacteristic, complemented
328#2327C2×C6713yescomplemented
329#2323C2×C6713yescomplemented
330C4×C22⋊Q8C2×C6713yescomplemented
331#2290C2×C6713yes—
332#2276C2×C6711yescharacteristic, complemented
333C67#3429111yescharacteristic, direct product factor, Sylow
334C23×Q8C22×C6711yescharacteristic
335C23×Q8C22×C6711yescharacteristic
336D4×Q8C4×C67116yescomplemented
337C2×C4⋊Q8C22×C6713yes—
338C2×C22⋊Q8C22×C6713yes—
339C2×C22⋊Q8C22×C6713yes—
340#519—28no—
341C2×C4×Q8—28no—
342C2×C4×Q8C22×C6713yes—
343C2×C4×Q8C22×C6713yes—
344C2×C4×Q8C22×C6711yescharacteristic
345C2×C4×Q8C22×C6711yescharacteristic
346C2×C4×Q8C22×C6711yescharacteristic
347C2×C4×Q8C22×C6713yes—
348C2×C4×Q8C22×C6713yes—
349C2×C4×Q8C22×C6711yescharacteristic
350C2×C4×Q8C22×C6711yescharacteristic
351C2×C4×D4C22×C6713yes—
352C2×#117C22×C6713yes—
353C2×#117C22×C6713yes—
354C22×C4⋊C4C22×C6713yes—
355C22×C42C22×C6713yes—
356#391C22×C6713yes—
357#391C22×C6713yes—
358#391C22×C6713yes—
359#391C22×C6713yes—
360#389C22×C6713yes—
361#389C22×C6716yes—
362#389C22×C6713yes—
363#388C22×C6713yes—
364#388C22×C6716yes—
365#388C22×C6713yes—
366#387C22×C6716yes—
367#387C22×C6713yes—
368#387C22×C6716yes—
369#387C22×C6716yes—
370#387C22×C6713yes—
371#386C22×C6713yes—
372#386C22×C6711yescharacteristic
373#385C22×C6713yes—
374#385C22×C6713yes—
375#382C22×C6713yes—
376#380C22×C6713yes—
377#380C22×C6713yes—
378C4×C4⋊C4C22×C6713yes—
379C4×C4⋊C4C22×C6713yes—
380C4×C4⋊C4C22×C6713yes—
381C4×C4⋊C4C22×C6713yes—
382C4×C4⋊C4C22×C6716yes—
383C4×C22⋊C4C22×C6713yes—
384C4×C22⋊C4C22×C6713yes—
385C4×C22⋊C4C22×C6716yes—
386#376C22×C6713yes—
387C22×Q8—24no—
388C22×Q8—24no—
389C22×Q8—24no—
390C22×Q8—24no—
391C22×Q8C2×C4×C6718yes—
392C22×Q8C2×C4×C6718yescomplemented
393C22×Q8C23×C6713yes—
394C22×Q8C23×C6713yes—
395C22×Q8C23×C6711yescharacteristic
396C22×D4C23×C6711yescharacteristic
397C23×C4C23×C6711yescharacteristic
398C23×C4C23×C6713yes—
399C23×C4C23×C6713yes—
400C23×C4C23×C6713yes—
401C4⋊Q8C2×C4×C67124yescomplemented
402C22⋊Q8C2×C4×C67124yes—
403C22⋊Q8C2×C4×C67124yescomplemented
404C4×Q8—24no—
405C4×Q8—24no—
406C4×Q8—24no—
407C4×Q8—212no—
408C4×Q8—212no—
409C4×Q8—212no—
410C4×Q8—212no—
411C4×Q8C2×C4×C6718yescomplemented
412C4×Q8D4×C6718yescomplemented
413C4×D4C2×C4×C67124yes—
414#117—212no—
415#117—212no—
416C2×C4⋊C4—212no—
417C2×C4⋊C4C23×C6713yes—
418C2×C4⋊C4C23×C6716yes—
419C2×C4⋊C4C23×C6713yes—
420C2×C4⋊C4C23×C6713yes—
421C2×C4⋊C4C23×C6713yes—
422C2×C4⋊C4C23×C6713yes—
423C2×C4⋊C4C23×C6713yes—
424C2×C4⋊C4C23×C6713yes—
425C2×C4⋊C4C23×C6713yes—
426C2×C4⋊C4C23×C6713yes—
427C2×C4⋊C4C23×C6716yes—
428C2×C4⋊C4C23×C6713yes—
429C2×C22⋊C4C23×C6713yes—
430C2×C22⋊C4C23×C6711yescharacteristic
431C2×C22⋊C4C23×C6713yes—
432C2×C22⋊C4C23×C6711yescharacteristic
433C2×C22⋊C4C23×C6711yescharacteristic
434C2×C22⋊C4C23×C6713yes—
435C2×C22⋊C4C23×C6713yes—
436C2×C22⋊C4C23×C6713yes—
437C2×C42—212no—
438C2×C42C23×C6716yes—
439C2×C42C23×C6713yes—
440C2×C42C23×C6713yes—
441C2×C42C23×C6713yes—
442C2×C42C23×C6713yes—
443C2×C42C23×C6713yes—
444C2×C42C23×C6716yes—
445C2×C42C23×C6713yes—
446C2×C42C23×C6713yes—
447#95C23×C6711yescharacteristic
448#95C23×C6713yes—
449#95C23×C6713yes—
450#95C23×C6713yes—
451#95C23×C6713yes—
452#95C23×C6716yes—
453#95C23×C6716yes—
454#95C23×C6713yes—
455#95C23×C6713yes—
456#95C23×C6713yes—
457#95C23×C6711yescharacteristic
458#95C23×C6716yes—
459#95C23×C6713yes—
460C24C24×C6711yescharacteristic
461C24C24×C6711yescharacteristic
462C2×Q8—232no—
463C2×Q8—232no—
464C2×Q8—26no—
465C2×Q8—26no—
466C2×Q8—26no—
467C2×Q8—26no—
468C2×Q8C22×C4×C67112yes—
469C2×Q8C22×C4×C67112yes—
470C2×Q8C22×C4×C6714yes—
471C2×Q8C2×D4×C6714yes—
472C2×Q8#41×C6714yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4C22×C4×C6714yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—26no—
479C22×C4—26no—
480C22×C4—26no—
481C22×C4—26no—
482C22×C4—22no—
483C22×C4—26no—
484C22×C4—26no—
485C22×C4—43no—
486C22×C4C22×C4×C67112yes—
487C22×C4C22×C4×C67112yes—
488C22×C4C24×C6711yescharacteristic
489C22×C4C24×C6713yes—
490C22×C4C24×C6713yes—
491C22×C4C24×C6713yes—
492C22×C4C24×C6711yescharacteristic
493C22×C4C24×C6711yescharacteristic
494C22×C4C24×C6713yes—
495C22×C4C24×C6713yes—
496C22×C4C24×C6713yes—
497C22×C4C24×C6711yescharacteristic
498C22×C4C24×C6713yes—
499C22×C4C24×C6711yescharacteristic
500C22×C4C24×C6713yes—
501C4⋊C4—212no—
502C4⋊C4—26no—
503C4⋊C4—26no—
504C4⋊C4—26no—
505C4⋊C4—26no—
506C4⋊C4—26no—
507C4⋊C4—26no—
508C4⋊C4—43no—
509C4⋊C4C22×C4×C67112yes—
510C4⋊C4C22×C4×C67112yes—
511C4⋊C4C22×C4×C67124yes—
512C4⋊C4C2×D4×C67112yes—
513C22⋊C4—26no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—26no—
517C22⋊C4—22no—
518C22⋊C4—43no—
519C22⋊C4C22×C4×C67112yes—
520C22⋊C4C22×C4×C67112yes—
521C42—26no—
522C42—26no—
523C42—26no—
524C42—212no—
525C42—26no—
526C42—26no—
527C42—46no—
528C42C22×C4×C67112yes—
529C42C2×D4×C67112yes—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23C23×C4×C6712yes—
541C23C23×C4×C6712yes—
542C232−1+4×C6712yes—
543C232−1+4×C6712yes—
544C23C25×C6711yescharacteristic
545Q8—224no—
546Q8—224no—
547Q8C4×D4×C67116yes—
548D4—28no—
549C2×C4—28no—
550C2×C4—21no—
551C2×C4—23no—
552C2×C4—23no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—23no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—23no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—23no—
563C2×C4—23no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—23no—
567C2×C4—21no—
568C2×C4—23no—
569C2×C4—21no—
570C2×C4—23no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—23no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—21no—
581C2×C4—412no—
582C2×C4C23×C4×C6712yes—
583C2×C4C23×C4×C6716yes—
584C2×C4C23×C4×C6716yes—
585C2×C4C23×C4×C6716yes—
586C2×C4C23×C4×C6716yes—
587C2×C4C22×D4×C6712yes—
588C2×C4C22×D4×C6716yes—
589C2×C4C22×D4×C6716yes—
590C2×C4C2×#41×C6716yes—
591C2×C42−1+4×C6712yes—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#519×C6714yescomplemented
606C22C24×C4×C6711yescharacteristic
607C22C23×D4×C6711yescharacteristic
608C22C22×#41×C6711yescharacteristic
609C22C2×2−1+4×C6711yescharacteristic
610C22C2×2−1+4×C6711yescharacteristic
611C22C2×2−1+4×C6711yescharacteristic
612C22#585×C6711yescharacteristic
613C4—26no—
614C4—26no—
615C4—22no—
616C4—26no—
617C4—22no—
618C4—22no—
619C4—26no—
620C4—41no—
621C4—43no—
622C4—43no—
623C4—41no—
624C4—43no—
625C4C2×C4×D4×C67112yes—
626C2—24no—
627C2—42no—
628C2C22×C4×D4×C6711yescharacteristic
629C2C2×#519×C6711yescharacteristic
630C2C4×2−1+4×C6711yescharacteristic
631C2C67×#348611yescharacteristic
632C2C67×#348911yescharacteristic
633C2C67×#351611yescharacteristic
634C2C67×#352311yescharacteristic
subgroupG/H
center, socleC23×C67C25
commutatorC22C24×C4×C67
Frattini, cosocleC23C25×C67
prime radicalC22×D4×C67C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#519×C67C2semidirect
3. C22×C4×Q8×C67C2semidirect
4. C67×#2365C2semidirect
5. C67×#2362C2semidirect
6. C67×#2360C2semidirect
8. C67×#2351C2semidirect
9. Q8×C22⋊C4×C67C2semidirect
10. Q8×C22⋊C4×C67C2semidirect
11. C67×#2327C2semidirect
12. C67×#2323C2semidirect
13. C4×C22⋊Q8×C67C2semidirect
15. C67×#2276C2semidirect
18. D4×Q8×C67C4semidirect
74. C22×Q8×C67C2×C4semidirect
83. C4⋊Q8×C67C2×C4semidirect
85. C22⋊Q8×C67C2×C4semidirect
93. C4×Q8×C67C2×C4semidirect
94. C4×Q8×C67D4semidirect
287. C22×C67#519semidirect
308. #34291C67direct (N × H)
319. C2×#519C2×C67semidirect
320. C22×C4×Q8C2×C67semidirect
321. #2365C2×C67semidirect
322. #2362C2×C67semidirect
323. #2360C2×C67semidirect
325. #2351C2×C67semidirect
326. Q8×C22⋊C4C2×C67semidirect
327. Q8×C22⋊C4C2×C67semidirect
328. #2327C2×C67semidirect
329. #2323C2×C67semidirect
330. C4×C22⋊Q8C2×C67semidirect
332. #2276C2×C67semidirect
333. C67#34291direct (N × H)
336. D4×Q8C4×C67semidirect
392. C22×Q8C2×C4×C67semidirect
401. C4⋊Q8C2×C4×C67semidirect
403. C22⋊Q8C2×C4×C67semidirect
411. C4×Q8C2×C4×C67semidirect
412. C4×Q8D4×C67semidirect
605. C22#519×C67semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C672
C2×#519×C672
C22×C4×Q8×C672
C67×#23652
C67×#23622
C67×#23602
C67×#23522
C67×#23512
Q8×C22⋊C4×C672
C67×#23272
C67×#23232
C4×C22⋊Q8×C672
C67×#22902
C67×#22762
#3429167