Finite Group Databasebeta

← C67×#25957 #30705208

Subgroups — C67×#25957 #30705208

Order 17152.

946 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#479×C67C211yesmaximal, characteristic, complemented
2C22×#103×C67C211yesmaximal, characteristic
3C67×#2442C211yesmaximal, characteristic
4Q8×C22⋊C4×C67C211yesmaximal, characteristic
5C67×#2097C211yesmaximal, characteristic, complemented
6C67×#2068C211yesmaximal, characteristic, complemented
7C67×#2066C211yesmaximal, characteristic, complemented
8C67×#2026C211yesmaximal, characteristic, complemented
9C67×#1865C211yesmaximal, characteristic, complemented
10C67×#1863C211yesmaximal, characteristic, complemented
11C67×#1852C211yesmaximal, characteristic
12C67×#1850C211yesmaximal, characteristic
13C67×#1807C211yesmaximal, characteristic
14C67×#1805C211yesmaximal, characteristic, complemented
15C67×#1787C211yesmaximal, characteristic
16C23×Q8×C67C2211yescharacteristic
17C23×C8×C67C2211yescharacteristic
18C2×#125×C67C2211yescharacteristic
19C2×C4×Q8×C67C2211yescharacteristic
20C2×C4×Q8×C67C2211yescharacteristic
21C22×C4⋊C4×C67C2211yescharacteristic
22#479×C67—24no—
23C2×#107×C67C2211yescharacteristic
24C2×#107×C67C2211yescharacteristic
25C2×#106×C67C2211yescharacteristic
26C2×#106×C67C2211yescharacteristic
27C2×C4⋊C8×C67C2211yescharacteristic
28C2×C4⋊C8×C67C2211yescharacteristic
29C2×#103×C67—24no—
30C2×#103×C67C2211yescharacteristic
31C2×#103×C67C2211yescharacteristic
32C2×#103×C67C2211yescharacteristic
33C2×#103×C67C2211yescharacteristic
34C2×#103×C67C2211yescharacteristic
35C2×#103×C67C2211yescharacteristic
36C2×#103×C67C2211yescharacteristic
37C2×#103×C67C2211yescharacteristic
38C2×C22⋊C8×C67C2211yescharacteristic
39#400×C67—21no—
40#398×C67—21no—
41#391×C67—21no—
42#391×C67—21no—
43#391×C67C2211yescharacteristic
44#391×C67C2211yescharacteristic
45#389×C67C2211yescharacteristic
46#389×C67C2211yescharacteristic
47#385×C67—21no—
48#382×C67C2211yescharacteristic
49#380×C67—21no—
50#380×C67—21no—
51#380×C67C2211yescharacteristic
52#380×C67C2211yescharacteristic
53C4×C22⋊C4×C67—21no—
54C4×C22⋊C4×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#336×C67C2211yescharacteristic
60#336×C67C2211yescharacteristic
61C22×Q8×C67—21no—
62C22×Q8×C67—22no—
63C22×Q8×C67—22no—
64C22×Q8×C67—22no—
65C22×Q8×C67—41no—
66C22×Q8×C67—41no—
67C22×Q8×C67Q814yes—
68C22×Q8×C67C2311yescharacteristic
69C22×Q8×C67C2311yescharacteristic
70C23×C4×C67—21no—
71C23×C4×C67—21no—
72C23×C4×C67C2311yescharacteristic
73C22×C8×C67—22no—
74C22×C8×C67—22no—
75C22×C8×C67—41no—
76C22×C8×C67C2311yescharacteristic
77C22×C8×C67C2311yescharacteristic
78C22×C8×C67C2311yescharacteristic
79C22×C8×C67C2311yescharacteristic
80#125×C67—22no—
81#125×C67—41no—
82C4×Q8×C67—22no—
83C4×Q8×C67—22no—
84C4×Q8×C67—41no—
85C4×Q8×C67—41no—
86C2×C4⋊C4×C67—22no—
87C2×C4⋊C4×C67—21no—
88C2×C4⋊C4×C67—21no—
89C2×C4⋊C4×C67—21no—
90C2×C4⋊C4×C67—21no—
91C2×C4⋊C4×C67—21no—
92C2×C4⋊C4×C67—21no—
93C2×C4⋊C4×C67—21no—
94C2×C4⋊C4×C67—41no—
95C2×C4⋊C4×C67C2311yescharacteristic
96C2×C4⋊C4×C67C2311yescharacteristic
97C2×C4⋊C4×C67C2311yescharacteristic
98C2×C4⋊C4×C67C2311yescharacteristic
99C2×C4⋊C4×C67C2311yescharacteristic
100C2×C4⋊C4×C67C2311yescharacteristic
101C2×C22⋊C4×C67—21no—
102C2×C22⋊C4×C67—21no—
103C2×C22⋊C4×C67D411yescharacteristic
104C2×C22⋊C4×C67D411yescharacteristic
105C2×C42×C67—21no—
106C2×C42×C67—21no—
107C2×C42×C67C2311yescharacteristic
108C2×C42×C67C2311yescharacteristic
109#107×C67—22no—
110#107×C67—41no—
111#106×C67—22no—
112#106×C67—41no—
113C4⋊C8×C67—22no—
114C4⋊C8×C67—41no—
115#103×C67—22no—
116#103×C67—22no—
117#103×C67—22no—
118#103×C67—22no—
119#103×C67—22no—
120#103×C67—41no—
121#103×C67—41no—
122#103×C67D414yes—
123C22⋊C8×C67—22no—
124#95×C67—21no—
125#95×C67—21no—
126#95×C67—21no—
127#95×C67—21no—
128#95×C67—21no—
129#95×C67—21no—
130#95×C67—21no—
131#95×C67—21no—
132#95×C67—21no—
133#95×C67—21no—
134#95×C67D411yescharacteristic
135#95×C67D411yescharacteristic
136C24×C67C2×D411yescharacteristic
137C2×Q8×C67—24no—
138C2×Q8×C67—21no—
139C2×Q8×C67—21no—
140C2×Q8×C67—21no—
141C2×Q8×C67—21no—
142C2×Q8×C67—28no—
143C2×Q8×C67—21no—
144C2×Q8×C67—21no—
145C2×Q8×C67—21no—
146C2×Q8×C67—21no—
147C2×Q8×C67—42no—
148C2×Q8×C67—42no—
149C2×Q8×C67—44no—
150C2×Q8×C67—44no—
151C2×Q8×C67—44no—
152C2×Q8×C67C2×D412yes—
153C2×Q8×C67C2×Q812yes—
154C2×Q8×C67C2×Q812yes—
155C2×Q8×C67#4112yes—
156C22×C4×C67—21no—
157C22×C4×C67—21no—
158C22×C4×C67—21no—
159C22×C4×C67—21no—
160C22×C4×C67—21no—
161C22×C4×C67—24no—
162C22×C4×C67—21no—
163C22×C4×C67—21no—
164C22×C4×C67—21no—
165C22×C4×C67—21no—
166C22×C4×C67—21no—
167C22×C4×C67—21no—
168C22×C4×C67—21no—
169C22×C4×C67—42no—
170C22×C4×C67—42no—
171C22×C4×C67—42no—
172C22×C4×C67—42no—
173C22×C4×C67—81no—
174C22×C4×C67C2×D411yescharacteristic
175C22×C4×C67C2×D411yescharacteristic
176C22×C4×C67C2×D411yescharacteristic
177C22×C4×C67C2×D411yescharacteristic
178C22×C4×C67C2×D411yescharacteristic
179C22×C4×C67C2×Q812yes—
180C22×C4×C67#4112yes—
181C22×C4×C67C2411yescharacteristic
182C2×C8×C67—21no—
183C2×C8×C67—21no—
184C2×C8×C67—21no—
185C2×C8×C67—21no—
186C2×C8×C67—21no—
187C2×C8×C67—21no—
188C2×C8×C67—21no—
189C2×C8×C67—21no—
190C2×C8×C67—21no—
191C2×C8×C67—21no—
192C2×C8×C67—21no—
193C2×C8×C67—44no—
194C2×C8×C67C2×D412yes—
195C4⋊C4×C67—21no—
196C4⋊C4×C67—21no—
197C4⋊C4×C67—21no—
198C4⋊C4×C67—21no—
199C4⋊C4×C67—21no—
200C4⋊C4×C67—21no—
201C4⋊C4×C67—21no—
202C4⋊C4×C67—21no—
203C4⋊C4×C67—21no—
204C4⋊C4×C67—21no—
205C4⋊C4×C67—21no—
206C4⋊C4×C67—42no—
207C4⋊C4×C67—42no—
208C4⋊C4×C67—42no—
209C4⋊C4×C67—42no—
210C4⋊C4×C67—42no—
211C4⋊C4×C67—81no—
212C4⋊C4×C67—81no—
213C4⋊C4×C67C2×D412yes—
214C22⋊C4×C67—22no—
215C22⋊C4×C67—22no—
216C22⋊C4×C67—42no—
217C22⋊C4×C67—42no—
218C42×C67—21no—
219C42×C67—21no—
220C42×C67—21no—
221C42×C67—21no—
222C42×C67—42no—
223C42×C67—42no—
224C23×C67—21no—
225C23×C67—21no—
226C23×C67—21no—
227C23×C67—21no—
228C23×C67C22⋊Q812yes—
229C23×C67#13512yes—
230C23×C67#13712yes—
231C23×C67C22×D411yescharacteristic
232Q8×C67—22no—
233Q8×C67—22no—
234Q8×C67—22no—
235Q8×C67—22no—
236Q8×C67—22no—
237Q8×C67—48no—
238Q8×C67—41no—
239Q8×C67—41no—
240Q8×C67C22⋊Q814yes—
241C2×C4×C67—22no—
242C2×C4×C67—22no—
243C2×C4×C67—21no—
244C2×C4×C67—22no—
245C2×C4×C67—21no—
246C2×C4×C67—22no—
247C2×C4×C67—22no—
248C2×C4×C67—22no—
249C2×C4×C67—22no—
250C2×C4×C67—22no—
251C2×C4×C67—21no—
252C2×C4×C67—21no—
253C2×C4×C67—22no—
254C2×C4×C67—21no—
255C2×C4×C67—21no—
256C2×C4×C67—21no—
257C2×C4×C67—21no—
258C2×C4×C67—21no—
259C2×C4×C67—21no—
260C2×C4×C67—21no—
261C2×C4×C67—21no—
262C2×C4×C67—21no—
263C2×C4×C67—21no—
264C2×C4×C67—48no—
265C2×C4×C67—41no—
266C2×C4×C67—41no—
267C2×C4×C67—41no—
268C2×C4×C67—41no—
269C2×C4×C67—41no—
270C2×C4×C67—41no—
271C2×C4×C67—41no—
272C2×C4×C67—41no—
273C2×C4×C67—41no—
274C2×C4×C67—41no—
275C2×C4×C67—41no—
276C2×C4×C67—41no—
277C2×C4×C67—41no—
278C2×C4×C67—41no—
279C2×C4×C67—41no—
280C2×C4×C67—41no—
281C2×C4×C67—41no—
282C2×C4×C67—41no—
283C2×C4×C67—41no—
284C2×C4×C67—84no—
285C2×C4×C67C22⋊Q812yes—
286C2×C4×C67C22×D411yescharacteristic
287C2×C4×C67C22×Q811yescharacteristic
288C2×C4×C67C2×#4111yescharacteristic
289C2×C4×C67C2×#4111yescharacteristic
290C2×C4×C67H(5,𝔽2)11yescharacteristic
291C2×C4×C67H(5,𝔽2)11yescharacteristic
292C8×C67—22no—
293C8×C67—41no—
294C8×C67—41no—
295C8×C67—41no—
296C22×C67—22no—
297C22×C67—22no—
298C22×C67—22no—
299C22×C67—22no—
300C22×C67—22no—
301C22×C67—22no—
302C22×C67#47914yescomplemented
303C22×C67C2×C22⋊Q811yescharacteristic
304C22×C67D4211yescharacteristic
305C22×C67#54611yescharacteristic
306C22×C67C2×#13511yescharacteristic
307C22×C67C2×#13711yescharacteristic
308C22×C67#57711yescharacteristic
309C22×C67#57811yescharacteristic
310C4×C67—22no—
311C4×C67—24no—
312C4×C67—42no—
313C4×C67—41no—
314C4×C67—41no—
315C4×C67—42no—
316C4×C67—41no—
317C4×C67—41no—
318C4×C67—81no—
319C4×C67—81no—
320C4×C67—81no—
321C4×C67—81no—
322C4×C67—81no—
323C4×C67C2×C22⋊Q811yescharacteristic
324C4×C67#54311yescharacteristic
325C4×C67#54611yescharacteristic
326C4×C67#55111yescharacteristic
327#25957C6711yesmaximal, characteristic, direct product factor, Sylow
328C2×C67—24no—
329C2×C67#243711yescharacteristic
330C2×C67C2×#47911yescharacteristic
331C2×C67#308211yescharacteristic
332C2×C67#327011yescharacteristic
333C2×C67#328211yescharacteristic
334C2×C67#330011yescharacteristic
335C2×C67#332011yescharacteristic
336C2×#479C2×C6711yescharacteristic, complemented
337C22×#103C2×C6711yescharacteristic
338#2442C2×C6711yescharacteristic
339Q8×C22⋊C4C2×C6711yescharacteristic
340#2097C2×C6711yescharacteristic, complemented
341#2068C2×C6711yescharacteristic, complemented
342#2066C2×C6711yescharacteristic, complemented
343#2026C2×C6711yescharacteristic, complemented
344#1865C2×C6711yescharacteristic, complemented
345#1863C2×C6711yescharacteristic, complemented
346#1852C2×C6711yescharacteristic
347#1850C2×C6711yescharacteristic
348#1807C2×C6711yescharacteristic
349#1805C2×C6711yescharacteristic, complemented
350#1787C2×C6711yescharacteristic
351C67#2595711yescharacteristic, direct product factor, Sylow
352C23×Q8C22×C6711yescharacteristic
353C23×C8C22×C6711yescharacteristic
354C2×#125C22×C6711yescharacteristic
355C2×C4×Q8C22×C6711yescharacteristic
356C2×C4×Q8C22×C6711yescharacteristic
357C22×C4⋊C4C22×C6711yescharacteristic
358#479—24no—
359C2×#107C22×C6711yescharacteristic
360C2×#107C22×C6711yescharacteristic
361C2×#106C22×C6711yescharacteristic
362C2×#106C22×C6711yescharacteristic
363C2×C4⋊C8C22×C6711yescharacteristic
364C2×C4⋊C8C22×C6711yescharacteristic
365C2×#103—24no—
366C2×#103C22×C6711yescharacteristic
367C2×#103C22×C6711yescharacteristic
368C2×#103C22×C6711yescharacteristic
369C2×#103C22×C6711yescharacteristic
370C2×#103C22×C6711yescharacteristic
371C2×#103C22×C6711yescharacteristic
372C2×#103C22×C6711yescharacteristic
373C2×#103C22×C6711yescharacteristic
374C2×C22⋊C8C22×C6711yescharacteristic
375#400—21no—
376#398—21no—
377#391—21no—
378#391—21no—
379#391C22×C6711yescharacteristic
380#391C22×C6711yescharacteristic
381#389C22×C6711yescharacteristic
382#389C22×C6711yescharacteristic
383#385—21no—
384#382C22×C6711yescharacteristic
385#380—21no—
386#380—21no—
387#380C22×C6711yescharacteristic
388#380C22×C6711yescharacteristic
389C4×C22⋊C4—21no—
390C4×C22⋊C4C22×C6711yescharacteristic
391#340C22×C6711yescharacteristic
392#340C22×C6711yescharacteristic
393#340C22×C6711yescharacteristic
394#340C22×C6711yescharacteristic
395#336C22×C6711yescharacteristic
396#336C22×C6711yescharacteristic
397C22×Q8—21no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—41no—
402C22×Q8—41no—
403C22×Q8Q8×C6714yes—
404C22×Q8C23×C6711yescharacteristic
405C22×Q8C23×C6711yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4C23×C6711yescharacteristic
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—41no—
412C22×C8C23×C6711yescharacteristic
413C22×C8C23×C6711yescharacteristic
414C22×C8C23×C6711yescharacteristic
415C22×C8C23×C6711yescharacteristic
416#125—22no—
417#125—41no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—41no—
421C4×Q8—41no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4C23×C6711yescharacteristic
432C2×C4⋊C4C23×C6711yescharacteristic
433C2×C4⋊C4C23×C6711yescharacteristic
434C2×C4⋊C4C23×C6711yescharacteristic
435C2×C4⋊C4C23×C6711yescharacteristic
436C2×C4⋊C4C23×C6711yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4D4×C6711yescharacteristic
440C2×C22⋊C4D4×C6711yescharacteristic
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C6711yescharacteristic
444C2×C42C23×C6711yescharacteristic
445#107—22no—
446#107—41no—
447#106—22no—
448#106—41no—
449C4⋊C8—22no—
450C4⋊C8—41no—
451#103—22no—
452#103—22no—
453#103—22no—
454#103—22no—
455#103—22no—
456#103—41no—
457#103—41no—
458#103D4×C6714yes—
459C22⋊C8—22no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95D4×C6711yescharacteristic
471#95D4×C6711yescharacteristic
472C24C2×D4×C6711yescharacteristic
473C2×Q8—24no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—28no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8C2×D4×C6712yes—
489C2×Q8C2×Q8×C6712yes—
490C2×Q8C2×Q8×C6712yes—
491C2×Q8#41×C6712yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—81no—
510C22×C4C2×D4×C6711yescharacteristic
511C22×C4C2×D4×C6711yescharacteristic
512C22×C4C2×D4×C6711yescharacteristic
513C22×C4C2×D4×C6711yescharacteristic
514C22×C4C2×D4×C6711yescharacteristic
515C22×C4C2×Q8×C6712yes—
516C22×C4#41×C6712yes—
517C22×C4C24×C6711yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—44no—
530C2×C8C2×D4×C6712yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—81no—
548C4⋊C4—81no—
549C4⋊C4C2×D4×C6712yes—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42—42no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23C22⋊Q8×C6712yes—
565C23#135×C6712yes—
566C23#137×C6712yes—
567C23C22×D4×C6711yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8C22⋊Q8×C6714yes—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—48no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—84no—
621C2×C4C22⋊Q8×C6712yes—
622C2×C4C22×D4×C6711yescharacteristic
623C2×C4C22×Q8×C6711yescharacteristic
624C2×C4C2×#41×C6711yescharacteristic
625C2×C4C2×#41×C6711yescharacteristic
626C2×C4H(5,𝔽2)×C6711yescharacteristic
627C2×C4H(5,𝔽2)×C6711yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22#479×C6714yescomplemented
639C22C2×C22⋊Q8×C6711yescharacteristic
640C22D42×C6711yescharacteristic
641C22#546×C6711yescharacteristic
642C22C2×#135×C6711yescharacteristic
643C22C2×#137×C6711yescharacteristic
644C22#577×C6711yescharacteristic
645C22#578×C6711yescharacteristic
646C4—22no—
647C4—24no—
648C4—41no—
649C4—41no—
650C4—42no—
651C4—41no—
652C4—41no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4C2×C22⋊Q8×C6711yescharacteristic
660C4#543×C6711yescharacteristic
661C4#546×C6711yescharacteristic
662C4#551×C6711yescharacteristic
663C2—24no—
664C2C67×#243711yescharacteristic
665C2C2×#479×C6711yescharacteristic
666C2C67×#308211yescharacteristic
667C2C67×#327011yescharacteristic
668C2C67×#328211yescharacteristic
669C2C67×#330011yescharacteristic
670C2C67×#332011yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC24×C67C2×D4
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×#479×C67C2semidirect
5. C67×#2097C2semidirect
6. C67×#2068C2semidirect
7. C67×#2066C2semidirect
8. C67×#2026C2semidirect
9. C67×#1865C2semidirect
10. C67×#1863C2semidirect
14. C67×#1805C2semidirect
302. C22×C67#479semidirect
327. #25957C67direct (N × H)
336. C2×#479C2×C67semidirect
340. #2097C2×C67semidirect
341. #2068C2×C67semidirect
342. #2066C2×C67semidirect
343. #2026C2×C67semidirect
344. #1865C2×C67semidirect
345. #1863C2×C67semidirect
349. #1805C2×C67semidirect
351. C67#25957direct (N × H)
638. C22#479×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#479×C672
C22×#103×C672
C67×#24422
Q8×C22⋊C4×C672
C67×#20972
C67×#20682
C67×#20662
C67×#20262
C67×#18652
C67×#18632
C67×#18522
C67×#18502
C67×#18072
C67×#18052
C67×#17872
#2595767