Finite Group Databasebeta

← C67×#34295 #30713546

Subgroups — C67×#34295 #30713546

Order 17152.

3200 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C67C211yesmaximal, characteristic
2C2×#520×C67C211yesmaximal, characteristic, complemented
3C2×C4×#41×C67C211yesmaximal, characteristic, complemented
4C67×#2366C213yesmaximal, complemented
5C67×#2363C213yesmaximal, complemented
6C67×#2361C213yesmaximal, complemented
7C67×#2352C213yesmaximal, complemented
8C67×#2351C211yesmaximal, characteristic, complemented
9C67×#2341C211yesmaximal, characteristic, complemented
10C67×#2341C211yesmaximal, characteristic, complemented
11C67×#2328C213yesmaximal, complemented
12C67×#2324C213yesmaximal, complemented
13C4×#121×C67C213yesmaximal, complemented
14C67×#2290C213yesmaximal, complemented
15C67×#2276C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C22×#41×C67C2211yescharacteristic
18#550×C67C4116yescomplemented
19C2×#127×C67C2213yes—
20C2×#121×C67C2213yes—
21C2×#121×C67C2213yes—
22#520×C67—28no—
23C4×#41×C67—28no—
24C2×C4×Q8×C67C2211yescharacteristic
25C2×C4×Q8×C67C2211yescharacteristic
26C2×C4×Q8×C67C2211yescharacteristic
27C2×C4×Q8×C67C2211yescharacteristic
28C2×C4×Q8×C67C2211yescharacteristic
29C2×C4×D4×C67C2213yes—
30C2×C4×D4×C67C2213yes—
31C2×C4×D4×C67C2213yes—
32C2×C4×D4×C67C2213yes—
33C2×C4×D4×C67C2216yes—
34C2×C4×D4×C67C2213yes—
35C2×#117×C67C2213yes—
36C2×#117×C67C2213yes—
37C22×C4⋊C4×C67C2213yes—
38C22×C42×C67C2213yes—
39#390×C67C2213yes—
40#390×C67C2213yes—
41#390×C67C2216yes—
42#390×C67C2213yes—
43#390×C67C2213yes—
44#389×C67C2213yes—
45#389×C67C2213yes—
46#388×C67C2213yes—
47#388×C67C2213yes—
48#388×C67C2216yes—
49#387×C67C2211yescharacteristic
50#387×C67C2213yes—
51#386×C67C2213yes—
52#386×C67C2213yes—
53#386×C67C2216yes—
54#386×C67C2216yes—
55#386×C67C2216yes—
56#385×C67C2213yes—
57#385×C67C2213yes—
58#382×C67C2213yes—
59#380×C67C2213yes—
60#380×C67C2213yes—
61C4×C4⋊C4×C67C2213yes—
62C4×C4⋊C4×C67C2213yes—
63C4×C4⋊C4×C67C2213yes—
64C4×C4⋊C4×C67C2213yes—
65C4×C22⋊C4×C67C2213yes—
66C4×C22⋊C4×C67C2213yes—
67C4×C22⋊C4×C67C2216yes—
68#376×C67C2213yes—
69C2×#41×C67—24no—
70C2×#41×C67—24no—
71C2×#41×C67—24no—
72C2×#41×C67—24no—
73C2×#41×C67C2×C418yescomplemented
74C2×#41×C67C2×C418yescomplemented
75C22×Q8×C67C2311yescharacteristic
76C22×D4×C67C2313yes—
77C22×D4×C67C2313yes—
78C22×D4×C67C2316yes—
79C22×D4×C67C2313yes—
80C23×C4×C67C2313yes—
81C23×C4×C67C2313yes—
82C23×C4×C67C2313yes—
83C23×C4×C67C2313yes—
84C23×C4×C67C2316yes—
85#127×C67C2×C4124yescomplemented
86#121×C67C2×C4124yescomplemented
87#121×C67C2×C4124yescomplemented
88C4×Q8×C67—24no—
89C4×Q8×C67—24no—
90C4×Q8×C67—24no—
91C4×Q8×C67C2×C418yescomplemented
92C4×Q8×C67D418yescomplemented
93C4×D4×C67—212no—
94C4×D4×C67—212no—
95C4×D4×C67—212no—
96C4×D4×C67—212no—
97C4×D4×C67—412no—
98C4×D4×C67C2×C4124yescomplemented
99#117×C67—212no—
100#117×C67—212no—
101C2×C4⋊C4×C67—212no—
102C2×C4⋊C4×C67C2313yes—
103C2×C4⋊C4×C67C2313yes—
104C2×C4⋊C4×C67C2311yescharacteristic
105C2×C4⋊C4×C67C2313yes—
106C2×C4⋊C4×C67C2313yes—
107C2×C4⋊C4×C67C2313yes—
108C2×C4⋊C4×C67C2313yes—
109C2×C4⋊C4×C67C2311yescharacteristic
110C2×C4⋊C4×C67C2313yes—
111C2×C4⋊C4×C67C2313yes—
112C2×C22⋊C4×C67C2313yes—
113C2×C22⋊C4×C67C2316yes—
114C2×C22⋊C4×C67C2313yes—
115C2×C22⋊C4×C67C2313yes—
116C2×C22⋊C4×C67C2316yes—
117C2×C22⋊C4×C67C2316yes—
118C2×C22⋊C4×C67C2313yes—
119C2×C22⋊C4×C67C2313yes—
120C2×C22⋊C4×C67C2313yes—
121C2×C22⋊C4×C67C2313yes—
122C2×C22⋊C4×C67C2313yes—
123C2×C42×C67—212no—
124C2×C42×C67C2311yescharacteristic
125C2×C42×C67C2313yes—
126C2×C42×C67C2313yes—
127C2×C42×C67C2313yes—
128C2×C42×C67C2313yes—
129C2×C42×C67C2316yes—
130C2×C42×C67C2313yes—
131C2×C42×C67C2313yes—
132#95×C67C2311yescharacteristic
133#95×C67C2313yes—
134#95×C67C2313yes—
135#95×C67C2313yes—
136#95×C67C2313yes—
137#95×C67C2311yescharacteristic
138#95×C67C2311yescharacteristic
139#95×C67C2313yes—
140#95×C67C2316yes—
141#95×C67C2311yescharacteristic
142#95×C67C2313yes—
143C24×C67C2413yes—
144C24×C67C2413yes—
145#41×C67—232no—
146#41×C67—232no—
147C2×Q8×C67C22×C414yes—
148C2×Q8×C67C2×D414yes—
149C2×Q8×C67#4114yes—
150C2×D4×C67—26no—
151C2×D4×C67—26no—
152C2×D4×C67—26no—
153C2×D4×C67—26no—
154C2×D4×C67—46no—
155C2×D4×C67—46no—
156C2×D4×C67—43no—
157C2×D4×C67—43no—
158C2×D4×C67C22×C4112yes—
159C2×D4×C67C22×C4112yes—
160C2×D4×C67C22×C4112yes—
161C2×D4×C67C22×C4124yes—
162C22×C4×C67—26no—
163C22×C4×C67—26no—
164C22×C4×C67—26no—
165C22×C4×C67—26no—
166C22×C4×C67—26no—
167C22×C4×C67—26no—
168C22×C4×C67—26no—
169C22×C4×C67—212no—
170C22×C4×C67—43no—
171C22×C4×C67—43no—
172C22×C4×C67—43no—
173C22×C4×C67—46no—
174C22×C4×C67—46no—
175C22×C4×C67C22×C4112yes—
176C22×C4×C67C22×C4112yes—
177C22×C4×C67C2411yescharacteristic
178C22×C4×C67C2413yes—
179C22×C4×C67C2411yescharacteristic
180C22×C4×C67C2413yes—
181C22×C4×C67C2413yes—
182C22×C4×C67C2411yescharacteristic
183C22×C4×C67C2413yes—
184C22×C4×C67C2411yescharacteristic
185C22×C4×C67C2411yescharacteristic
186C22×C4×C67C2413yes—
187C22×C4×C67C2411yescharacteristic
188C22×C4×C67C2411yescharacteristic
189C22×C4×C67C2413yes—
190C4⋊C4×C67—26no—
191C4⋊C4×C67—26no—
192C4⋊C4×C67—22no—
193C4⋊C4×C67—26no—
194C4⋊C4×C67—26no—
195C4⋊C4×C67—26no—
196C4⋊C4×C67—43no—
197C4⋊C4×C67C22×C414yes—
198C4⋊C4×C67C22×C4112yes—
199C4⋊C4×C67C2×D4112yes—
200C22⋊C4×C67—26no—
201C22⋊C4×C67—212no—
202C22⋊C4×C67—26no—
203C22⋊C4×C67—26no—
204C22⋊C4×C67—43no—
205C22⋊C4×C67—46no—
206C22⋊C4×C67—43no—
207C22⋊C4×C67—43no—
208C22⋊C4×C67—46no—
209C22⋊C4×C67C22×C4112yes—
210C22⋊C4×C67C22×C4112yes—
211C42×C67—22no—
212C42×C67—26no—
213C42×C67—26no—
214C42×C67—26no—
215C42×C67—26no—
216C42×C67—46no—
217C42×C67C22×C4112yes—
218C42×C67C2×D4112yes—
219C23×C67—23no—
220C23×C67—23no—
221C23×C67—23no—
222C23×C67—23no—
223C23×C67—23no—
224C23×C67—23no—
225C23×C67—23no—
226C23×C67—23no—
227C23×C67—23no—
228C23×C67—23no—
229C23×C67—23no—
230C23×C67—23no—
231C23×C67C23×C416yes—
232C23×C67C23×C416yes—
233C23×C67C2511yescharacteristic
234Q8×C67C4×D4116yescomplemented
235D4×C67—224no—
236D4×C67—224no—
237D4×C67—412no—
238D4×C67—424no—
239C2×C4×C67—21no—
240C2×C4×C67—21no—
241C2×C4×C67—21no—
242C2×C4×C67—21no—
243C2×C4×C67—21no—
244C2×C4×C67—23no—
245C2×C4×C67—23no—
246C2×C4×C67—23no—
247C2×C4×C67—21no—
248C2×C4×C67—21no—
249C2×C4×C67—21no—
250C2×C4×C67—23no—
251C2×C4×C67—21no—
252C2×C4×C67—21no—
253C2×C4×C67—224no—
254C2×C4×C67—224no—
255C2×C4×C67—21no—
256C2×C4×C67—23no—
257C2×C4×C67—23no—
258C2×C4×C67—21no—
259C2×C4×C67—23no—
260C2×C4×C67—23no—
261C2×C4×C67—23no—
262C2×C4×C67—21no—
263C2×C4×C67—23no—
264C2×C4×C67—21no—
265C2×C4×C67—21no—
266C2×C4×C67—23no—
267C2×C4×C67—23no—
268C2×C4×C67—23no—
269C2×C4×C67—21no—
270C2×C4×C67—412no—
271C2×C4×C67—412no—
272C2×C4×C67—812no—
273C2×C4×C67C23×C412yes—
274C2×C4×C67C23×C416yes—
275C2×C4×C67C23×C412yes—
276C2×C4×C67C23×C412yes—
277C2×C4×C67C23×C416yes—
278C2×C4×C67C22×D412yes—
279C2×C4×C67C22×D416yes—
280C2×C4×C67C22×D416yes—
281C2×C4×C67C2×#4116yes—
282C2×C4×C67H(5,𝔽2)12yes—
283C22×C67—26no—
284C22×C67—26no—
285C22×C67—26no—
286C22×C67—26no—
287C22×C67—26no—
288C22×C67—26no—
289C22×C67—43no—
290C22×C67—43no—
291C22×C67—43no—
292C22×C67—43no—
293C22×C67—43no—
294C22×C67—43no—
295C22×C67—43no—
296C22×C67—43no—
297C22×C67C24×C411yescharacteristic
298C22×C67C23×D411yescharacteristic
299C22×C67C22×#4111yescharacteristic
300C22×C67C2×H(5,𝔽2)11yescharacteristic
301C22×C67#58511yescharacteristic
302C22×C67#58511yescharacteristic
303C22×C67#58511yescharacteristic
304C4×C67—22no—
305C4×C67—22no—
306C4×C67—22no—
307C4×C67—26no—
308C4×C67—22no—
309C4×C67—22no—
310C4×C67—26no—
311C4×C67—41no—
312C4×C67—43no—
313C4×C67—43no—
314C4×C67—43no—
315C4×C67—41no—
316C4×C67C2×C4×D4112yes—
317#34295C6711yesmaximal, characteristic, direct product factor, Sylow
318C2×C67—46no—
319C2×C67—46no—
320C2×C67C22×C4×D411yescharacteristic
321C2×C67#342811yescharacteristic
322C2×C67C4×H(5,𝔽2)11yescharacteristic
323C2×C67#348711yescharacteristic
324C2×C67#348811yescharacteristic
325C2×C67#351711yescharacteristic
326C2×C67#352411yescharacteristic
327C2×#550C2×C6711yescharacteristic
328C2×#520C2×C6711yescharacteristic, complemented
329C2×C4×#41C2×C6711yescharacteristic, complemented
330#2366C2×C6713yescomplemented
331#2363C2×C6713yescomplemented
332#2361C2×C6713yescomplemented
333#2352C2×C6713yescomplemented
334#2351C2×C6711yescharacteristic, complemented
335#2341C2×C6711yescharacteristic, complemented
336#2341C2×C6711yescharacteristic, complemented
337#2328C2×C6713yescomplemented
338#2324C2×C6713yescomplemented
339C4×#121C2×C6713yescomplemented
340#2290C2×C6713yescomplemented
341#2276C2×C6711yescharacteristic, complemented
342C67#3429511yescharacteristic, direct product factor, Sylow
343C22×#41C22×C6711yescharacteristic
344C22×#41C22×C6711yescharacteristic
345#550C4×C67116yescomplemented
346C2×#127C22×C6713yes—
347C2×#121C22×C6713yes—
348C2×#121C22×C6713yes—
349#520—28no—
350C4×#41—28no—
351C2×C4×Q8C22×C6711yescharacteristic
352C2×C4×Q8C22×C6711yescharacteristic
353C2×C4×Q8C22×C6711yescharacteristic
354C2×C4×Q8C22×C6711yescharacteristic
355C2×C4×Q8C22×C6711yescharacteristic
356C2×C4×D4C22×C6713yes—
357C2×C4×D4C22×C6713yes—
358C2×C4×D4C22×C6713yes—
359C2×C4×D4C22×C6713yes—
360C2×C4×D4C22×C6716yes—
361C2×C4×D4C22×C6713yes—
362C2×#117C22×C6713yes—
363C2×#117C22×C6713yes—
364C22×C4⋊C4C22×C6713yes—
365C22×C42C22×C6713yes—
366#390C22×C6713yes—
367#390C22×C6716yes—
368#390C22×C6713yes—
369#390C22×C6713yes—
370#390C22×C6713yes—
371#389C22×C6713yes—
372#389C22×C6713yes—
373#388C22×C6716yes—
374#388C22×C6713yes—
375#388C22×C6713yes—
376#387C22×C6713yes—
377#387C22×C6711yescharacteristic
378#386C22×C6716yes—
379#386C22×C6713yes—
380#386C22×C6716yes—
381#386C22×C6716yes—
382#386C22×C6713yes—
383#385C22×C6713yes—
384#385C22×C6713yes—
385#382C22×C6713yes—
386#380C22×C6713yes—
387#380C22×C6713yes—
388C4×C4⋊C4C22×C6713yes—
389C4×C4⋊C4C22×C6713yes—
390C4×C4⋊C4C22×C6713yes—
391C4×C4⋊C4C22×C6713yes—
392C4×C22⋊C4C22×C6713yes—
393C4×C22⋊C4C22×C6713yes—
394C4×C22⋊C4C22×C6716yes—
395#376C22×C6713yes—
396C2×#41—24no—
397C2×#41—24no—
398C2×#41—24no—
399C2×#41—24no—
400C2×#41C2×C4×C6718yescomplemented
401C2×#41C2×C4×C6718yescomplemented
402C22×Q8C23×C6711yescharacteristic
403C22×D4C23×C6713yes—
404C22×D4C23×C6713yes—
405C22×D4C23×C6716yes—
406C22×D4C23×C6713yes—
407C23×C4C23×C6713yes—
408C23×C4C23×C6713yes—
409C23×C4C23×C6713yes—
410C23×C4C23×C6716yes—
411C23×C4C23×C6713yes—
412#127C2×C4×C67124yescomplemented
413#121C2×C4×C67124yescomplemented
414#121C2×C4×C67124yescomplemented
415C4×Q8—24no—
416C4×Q8—24no—
417C4×Q8—24no—
418C4×Q8C2×C4×C6718yescomplemented
419C4×Q8D4×C6718yescomplemented
420C4×D4—212no—
421C4×D4—212no—
422C4×D4—212no—
423C4×D4—212no—
424C4×D4—412no—
425C4×D4C2×C4×C67124yescomplemented
426#117—212no—
427#117—212no—
428C2×C4⋊C4—212no—
429C2×C4⋊C4C23×C6713yes—
430C2×C4⋊C4C23×C6713yes—
431C2×C4⋊C4C23×C6711yescharacteristic
432C2×C4⋊C4C23×C6713yes—
433C2×C4⋊C4C23×C6713yes—
434C2×C4⋊C4C23×C6713yes—
435C2×C4⋊C4C23×C6713yes—
436C2×C4⋊C4C23×C6711yescharacteristic
437C2×C4⋊C4C23×C6713yes—
438C2×C4⋊C4C23×C6713yes—
439C2×C22⋊C4C23×C6713yes—
440C2×C22⋊C4C23×C6716yes—
441C2×C22⋊C4C23×C6713yes—
442C2×C22⋊C4C23×C6713yes—
443C2×C22⋊C4C23×C6716yes—
444C2×C22⋊C4C23×C6716yes—
445C2×C22⋊C4C23×C6713yes—
446C2×C22⋊C4C23×C6713yes—
447C2×C22⋊C4C23×C6713yes—
448C2×C22⋊C4C23×C6713yes—
449C2×C22⋊C4C23×C6713yes—
450C2×C42—212no—
451C2×C42C23×C6713yes—
452C2×C42C23×C6713yes—
453C2×C42C23×C6713yes—
454C2×C42C23×C6713yes—
455C2×C42C23×C6711yescharacteristic
456C2×C42C23×C6716yes—
457C2×C42C23×C6713yes—
458C2×C42C23×C6713yes—
459#95C23×C6711yescharacteristic
460#95C23×C6713yes—
461#95C23×C6713yes—
462#95C23×C6713yes—
463#95C23×C6713yes—
464#95C23×C6711yescharacteristic
465#95C23×C6711yescharacteristic
466#95C23×C6713yes—
467#95C23×C6716yes—
468#95C23×C6711yescharacteristic
469#95C23×C6713yes—
470C24C24×C6713yes—
471C24C24×C6713yes—
472#41—232no—
473#41—232no—
474C2×Q8C22×C4×C6714yes—
475C2×Q8C2×D4×C6714yes—
476C2×Q8#41×C6714yes—
477C2×D4—26no—
478C2×D4—26no—
479C2×D4—26no—
480C2×D4—26no—
481C2×D4—46no—
482C2×D4—46no—
483C2×D4—43no—
484C2×D4—43no—
485C2×D4C22×C4×C67112yes—
486C2×D4C22×C4×C67112yes—
487C2×D4C22×C4×C67112yes—
488C2×D4C22×C4×C67124yes—
489C22×C4—26no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—26no—
494C22×C4—26no—
495C22×C4—26no—
496C22×C4—212no—
497C22×C4—43no—
498C22×C4—43no—
499C22×C4—43no—
500C22×C4—46no—
501C22×C4—46no—
502C22×C4C22×C4×C67112yes—
503C22×C4C22×C4×C67112yes—
504C22×C4C24×C6711yescharacteristic
505C22×C4C24×C6713yes—
506C22×C4C24×C6713yes—
507C22×C4C24×C6713yes—
508C22×C4C24×C6711yescharacteristic
509C22×C4C24×C6711yescharacteristic
510C22×C4C24×C6711yescharacteristic
511C22×C4C24×C6713yes—
512C22×C4C24×C6711yescharacteristic
513C22×C4C24×C6711yescharacteristic
514C22×C4C24×C6713yes—
515C22×C4C24×C6711yescharacteristic
516C22×C4C24×C6713yes—
517C4⋊C4—26no—
518C4⋊C4—26no—
519C4⋊C4—22no—
520C4⋊C4—26no—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—43no—
524C4⋊C4C22×C4×C6714yes—
525C4⋊C4C22×C4×C67112yes—
526C4⋊C4C2×D4×C67112yes—
527C22⋊C4—26no—
528C22⋊C4—212no—
529C22⋊C4—26no—
530C22⋊C4—26no—
531C22⋊C4—46no—
532C22⋊C4—43no—
533C22⋊C4—46no—
534C22⋊C4—43no—
535C22⋊C4—43no—
536C22⋊C4C22×C4×C67112yes—
537C22⋊C4C22×C4×C67112yes—
538C42—22no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—26no—
543C42—46no—
544C42C22×C4×C67112yes—
545C42C2×D4×C67112yes—
546C23—23no—
547C23—23no—
548C23—23no—
549C23—23no—
550C23—23no—
551C23—23no—
552C23—23no—
553C23—23no—
554C23—23no—
555C23—23no—
556C23—23no—
557C23—23no—
558C23C23×C4×C6716yes—
559C23C23×C4×C6716yes—
560C23C25×C6711yescharacteristic
561Q8C4×D4×C67116yescomplemented
562D4—224no—
563D4—224no—
564D4—412no—
565D4—424no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—23no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—21no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—21no—
586C2×C4—23no—
587C2×C4—23no—
588C2×C4—23no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—23no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—23no—
596C2×C4—21no—
597C2×C4—412no—
598C2×C4—412no—
599C2×C4—812no—
600C2×C4C23×C4×C6712yes—
601C2×C4C23×C4×C6716yes—
602C2×C4C23×C4×C6712yes—
603C2×C4C23×C4×C6712yes—
604C2×C4C23×C4×C6716yes—
605C2×C4C22×D4×C6712yes—
606C2×C4C22×D4×C6716yes—
607C2×C4C22×D4×C6716yes—
608C2×C4C2×#41×C6716yes—
609C2×C4H(5,𝔽2)×C6712yes—
610C22—26no—
611C22—26no—
612C22—26no—
613C22—26no—
614C22—26no—
615C22—26no—
616C22—43no—
617C22—43no—
618C22—43no—
619C22—43no—
620C22—43no—
621C22—43no—
622C22—43no—
623C22—43no—
624C22C24×C4×C6711yescharacteristic
625C22C23×D4×C6711yescharacteristic
626C22C22×#41×C6711yescharacteristic
627C22C2×H(5,𝔽2)×C6711yescharacteristic
628C22#585×C6711yescharacteristic
629C22#585×C6711yescharacteristic
630C22#585×C6711yescharacteristic
631C4—22no—
632C4—22no—
633C4—22no—
634C4—26no—
635C4—22no—
636C4—22no—
637C4—26no—
638C4—41no—
639C4—43no—
640C4—41no—
641C4—43no—
642C4—43no—
643C4C2×C4×D4×C67112yes—
644C2—46no—
645C2—46no—
646C2C22×C4×D4×C6711yescharacteristic
647C2C67×#342811yescharacteristic
648C2C4×H(5,𝔽2)×C6711yescharacteristic
649C2C67×#348711yescharacteristic
650C2C67×#348811yescharacteristic
651C2C67×#351711yescharacteristic
652C2C67×#352411yescharacteristic
subgroupG/H
center, socleC23×C67C25
commutatorC22C24×C4×C67
Frattini, cosocleC23C25×C67
prime radicalC2×#550×C67C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#520×C67C2semidirect
3. C2×C4×#41×C67C2semidirect
4. C67×#2366C2semidirect
5. C67×#2363C2semidirect
6. C67×#2361C2semidirect
7. C67×#2352C2semidirect
8. C67×#2351C2semidirect
9. C67×#2341C2semidirect
10. C67×#2341C2semidirect
11. C67×#2328C2semidirect
12. C67×#2324C2semidirect
13. C4×#121×C67C2semidirect
14. C67×#2290C2semidirect
15. C67×#2276C2semidirect
18. #550×C67C4semidirect
73. C2×#41×C67C2×C4semidirect
74. C2×#41×C67C2×C4semidirect
85. #127×C67C2×C4semidirect
86. #121×C67C2×C4semidirect
87. #121×C67C2×C4semidirect
91. C4×Q8×C67C2×C4semidirect
92. C4×Q8×C67D4semidirect
98. C4×D4×C67C2×C4semidirect
234. Q8×C67C4×D4semidirect
317. #34295C67direct (N × H)
328. C2×#520C2×C67semidirect
329. C2×C4×#41C2×C67semidirect
330. #2366C2×C67semidirect
331. #2363C2×C67semidirect
332. #2361C2×C67semidirect
333. #2352C2×C67semidirect
334. #2351C2×C67semidirect
335. #2341C2×C67semidirect
336. #2341C2×C67semidirect
337. #2328C2×C67semidirect
338. #2324C2×C67semidirect
339. C4×#121C2×C67semidirect
340. #2290C2×C67semidirect
341. #2276C2×C67semidirect
342. C67#34295direct (N × H)
345. #550C4×C67semidirect
400. C2×#41C2×C4×C67semidirect
401. C2×#41C2×C4×C67semidirect
412. #127C2×C4×C67semidirect
413. #121C2×C4×C67semidirect
414. #121C2×C4×C67semidirect
418. C4×Q8C2×C4×C67semidirect
419. C4×Q8D4×C67semidirect
425. C4×D4C2×C4×C67semidirect
561. Q8C4×D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C672
C2×#520×C672
C2×C4×#41×C672
C67×#23662
C67×#23632
C67×#23612
C67×#23522
C67×#23512
C67×#23412
C67×#23282
C67×#23242
C4×#121×C672
C67×#22902
C67×#22762
#3429567