Finite Group Databasebeta

← C67×#26155 #30705406

Subgroups — C67×#26155 #30705406

Order 17152.

854 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C67C211yesmaximal, characteristic, complemented
2C2×#428×C67C211yesmaximal, characteristic, complemented
3C67×#2417C211yesmaximal, characteristic
4C67×#2354C211yesmaximal, characteristic
5C67×#2096C211yesmaximal, characteristic, complemented
6C67×#2084C211yesmaximal, characteristic, complemented
7C67×#2077C211yesmaximal, characteristic, complemented
8C67×#2035C211yesmaximal, characteristic, complemented
9C67×#1928C211yesmaximal, characteristic, complemented
10C67×#1921C211yesmaximal, characteristic, complemented
11C67×#1894C211yesmaximal, characteristic, complemented
12C67×#1873C211yesmaximal, characteristic, complemented
13C67×#1870C211yesmaximal, characteristic
14C67×#1854C211yesmaximal, characteristic, complemented
15C67×#1853C211yesmaximal, characteristic, complemented
16C22×M16×C67C2211yescharacteristic
17C2×C22⋊Q8×C67C2211yescharacteristic
18C2×C22⋊Q8×C67C2211yescharacteristic
19C2×C4×D4×C67C2211yescharacteristic
20C2×#117×C67C2211yescharacteristic
21C2×#117×C67C2211yescharacteristic
22C22×C4⋊C4×C67C2211yescharacteristic
23#485×C67—24no—
24#428×C67—24no—
25C2×#107×C67C2211yescharacteristic
26C2×#107×C67C2211yescharacteristic
27C2×#106×C67C2211yescharacteristic
28C2×#106×C67C2211yescharacteristic
29C2×#106×C67C2211yescharacteristic
30C2×#106×C67C2211yescharacteristic
31C2×#103×C67C2211yescharacteristic
32C2×#103×C67C2211yescharacteristic
33C2×#103×C67C2211yescharacteristic
34C2×#103×C67C2211yescharacteristic
35C2×C22⋊C8×C67C2211yescharacteristic
36C2×C22⋊C8×C67C2211yescharacteristic
37C2×C22⋊C8×C67C2211yescharacteristic
38#398×C67—21no—
39#396×C67—21no—
40#391×C67C2211yescharacteristic
41#390×C67—21no—
42#389×C67C2211yescharacteristic
43#388×C67—21no—
44#388×C67—21no—
45#386×C67—21no—
46#384×C67C2211yescharacteristic
47#380×C67—21no—
48#380×C67C2211yescharacteristic
49#380×C67C2211yescharacteristic
50#380×C67C2211yescharacteristic
51C4×C4⋊C4×C67—21no—
52C4×C4⋊C4×C67C2211yescharacteristic
53#340×C67C2211yescharacteristic
54#340×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#336×C67C2211yescharacteristic
60#336×C67C2211yescharacteristic
61C22×Q8×C67C2311yescharacteristic
62C22×D4×C67D411yescharacteristic
63C23×C4×C67—21no—
64C23×C4×C67C2311yescharacteristic
65C23×C4×C67C2311yescharacteristic
66C2×M16×C67—22no—
67C2×M16×C67—22no—
68C2×M16×C67—22no—
69C22×C8×C67C2311yescharacteristic
70C22×C8×C67C2311yescharacteristic
71C22×C8×C67C2311yescharacteristic
72C22×C8×C67C2311yescharacteristic
73C22⋊Q8×C67—22no—
74C22⋊Q8×C67—22no—
75C22⋊Q8×C67—22no—
76C22⋊Q8×C67—41no—
77C4×D4×C67—22no—
78C4×D4×C67—22no—
79#117×C67—22no—
80#117×C67—22no—
81#117×C67—41no—
82#117×C67—41no—
83C2×C4⋊C4×C67—22no—
84C2×C4⋊C4×C67—21no—
85C2×C4⋊C4×C67—21no—
86C2×C4⋊C4×C67—21no—
87C2×C4⋊C4×C67—21no—
88C2×C4⋊C4×C67—21no—
89C2×C4⋊C4×C67—21no—
90C2×C4⋊C4×C67—41no—
91C2×C4⋊C4×C67D411yescharacteristic
92C2×C4⋊C4×C67C2311yescharacteristic
93C2×C4⋊C4×C67C2311yescharacteristic
94C2×C4⋊C4×C67C2311yescharacteristic
95C2×C4⋊C4×C67C2311yescharacteristic
96C2×C4⋊C4×C67C2311yescharacteristic
97C2×C4⋊C4×C67C2311yescharacteristic
98C2×C4⋊C4×C67C2311yescharacteristic
99C2×C22⋊C4×C67—21no—
100C2×C22⋊C4×C67—21no—
101C2×C22⋊C4×C67—21no—
102C2×C22⋊C4×C67—21no—
103C2×C22⋊C4×C67—21no—
104C2×C22⋊C4×C67—21no—
105C2×C22⋊C4×C67—21no—
106C2×C22⋊C4×C67D411yescharacteristic
107C2×C22⋊C4×C67D411yescharacteristic
108C2×C42×C67—21no—
109C2×C42×C67—21no—
110C2×C42×C67—21no—
111C2×C42×C67C2311yescharacteristic
112#107×C67—22no—
113#107×C67D414yescomplemented
114#106×C67—22no—
115#106×C67—22no—
116#106×C67—22no—
117#106×C67—41no—
118#103×C67—22no—
119#103×C67—22no—
120#103×C67—22no—
121#103×C67—41no—
122C22⋊C8×C67—22no—
123C22⋊C8×C67—22no—
124C22⋊C8×C67—22no—
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—
132C24×C67C2×D411yescharacteristic
133C24×C67C2×D411yescharacteristic
134C2×Q8×C67—21no—
135C2×Q8×C67—21no—
136C2×Q8×C67—21no—
137C2×Q8×C67—21no—
138C2×Q8×C67—21no—
139C2×Q8×C67—21no—
140C2×D4×C67—22no—
141C2×D4×C67—22no—
142C2×D4×C67—41no—
143C22×C4×C67—21no—
144C22×C4×C67—21no—
145C22×C4×C67—21no—
146C22×C4×C67—21no—
147C22×C4×C67—21no—
148C22×C4×C67—21no—
149C22×C4×C67—21no—
150C22×C4×C67—21no—
151C22×C4×C67—21no—
152C22×C4×C67—21no—
153C22×C4×C67—21no—
154C22×C4×C67—21no—
155C22×C4×C67—21no—
156C22×C4×C67—21no—
157C22×C4×C67—21no—
158C22×C4×C67—21no—
159C22×C4×C67—21no—
160C22×C4×C67—21no—
161C22×C4×C67—42no—
162C22×C4×C67—42no—
163C22×C4×C67—81no—
164C22×C4×C67C2×D411yescharacteristic
165C22×C4×C67C2×D411yescharacteristic
166C22×C4×C67C2×D411yescharacteristic
167C22×C4×C67C2×D411yescharacteristic
168C22×C4×C67#4112yes—
169C22×C4×C67#4112yes—
170C22×C4×C67C2411yescharacteristic
171M16×C67—28no—
172C2×C8×C67—21no—
173C2×C8×C67—21no—
174C2×C8×C67—21no—
175C2×C8×C67—21no—
176C2×C8×C67—21no—
177C2×C8×C67—21no—
178C2×C8×C67—21no—
179C2×C8×C67—21no—
180C2×C8×C67—21no—
181C2×C8×C67—21no—
182C2×C8×C67C2×D412yes—
183C2×C8×C67#4112yes—
184C4⋊C4×C67—22no—
185C4⋊C4×C67—21no—
186C4⋊C4×C67—21no—
187C4⋊C4×C67—21no—
188C4⋊C4×C67—21no—
189C4⋊C4×C67—21no—
190C4⋊C4×C67—21no—
191C4⋊C4×C67—21no—
192C4⋊C4×C67—21no—
193C4⋊C4×C67—21no—
194C4⋊C4×C67—21no—
195C4⋊C4×C67—21no—
196C4⋊C4×C67—21no—
197C4⋊C4×C67—42no—
198C4⋊C4×C67—42no—
199C4⋊C4×C67—42no—
200C4⋊C4×C67—42no—
201C4⋊C4×C67—81no—
202C4⋊C4×C67—81no—
203C4⋊C4×C67C2×D412yes—
204C4⋊C4×C67C2×D412yes—
205C22⋊C4×C67—22no—
206C22⋊C4×C67—22no—
207C22⋊C4×C67—42no—
208C22⋊C4×C67—42no—
209C22⋊C4×C67—42no—
210C22⋊C4×C67—42no—
211C22⋊C4×C67—81no—
212C22⋊C4×C67—81no—
213C22⋊C4×C67—81no—
214C42×C67—21no—
215C42×C67—21no—
216C42×C67—42no—
217C42×C67—42no—
218C42×C67—42no—
219C23×C67—21no—
220C23×C67—21no—
221C23×C67—21no—
222C23×C67—21no—
223C23×C67—21no—
224C23×C67—21no—
225C23×C67—21no—
226C23×C67—21no—
227C23×C67—21no—
228C23×C67—21no—
229C23×C67—21no—
230C23×C67—21no—
231C23×C67—21no—
232C23×C67#12312yes—
233C23×C67C22×D411yescharacteristic
234Q8×C67—41no—
235Q8×C67—41no—
236Q8×C67—41no—
237Q8×C67—41no—
238D4×C67—44no—
239C2×C4×C67—21no—
240C2×C4×C67—21no—
241C2×C4×C67—21no—
242C2×C4×C67—21no—
243C2×C4×C67—22no—
244C2×C4×C67—22no—
245C2×C4×C67—22no—
246C2×C4×C67—22no—
247C2×C4×C67—21no—
248C2×C4×C67—21no—
249C2×C4×C67—22no—
250C2×C4×C67—21no—
251C2×C4×C67—22no—
252C2×C4×C67—21no—
253C2×C4×C67—21no—
254C2×C4×C67—21no—
255C2×C4×C67—41no—
256C2×C4×C67—41no—
257C2×C4×C67—41no—
258C2×C4×C67—41no—
259C2×C4×C67—41no—
260C2×C4×C67—41no—
261C2×C4×C67—41no—
262C2×C4×C67—41no—
263C2×C4×C67—41no—
264C2×C4×C67—41no—
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—84no—
282C2×C4×C67#12312yes—
283C2×C4×C67#13712yes—
284C2×C4×C67C22×D411yescharacteristic
285C2×C4×C67C2×#4111yescharacteristic
286C2×C4×C67C2×#4111yescharacteristic
287C2×C4×C67C2×#4111yescharacteristic
288C2×C4×C67H(5,𝔽2)11yescharacteristic
289C2×C4×C672−1+411yescharacteristic
290C8×C67—22no—
291C8×C67—22no—
292C8×C67—41no—
293C8×C67—41no—
294C22×C67—22no—
295C22×C67—22no—
296C22×C67—22no—
297C22×C67—41no—
298C22×C67—41no—
299C22×C67—41no—
300C22×C67—41no—
301C22×C67—41no—
302C22×C67—41no—
303C22×C67—41no—
304C22×C67—41no—
305C22×C67—41no—
306C22×C67—41no—
307C22×C67—41no—
308C22×C67C2×#12311yescharacteristic
309C22×C67D4211yescharacteristic
310C22×C67#54711yescharacteristic
311C22×C67C2×#13711yescharacteristic
312C22×C67#57511yescharacteristic
313C22×C67#57711yescharacteristic
314C22×C67#57711yescharacteristic
315C4×C67—22no—
316C4×C67—22no—
317C4×C67—41no—
318C4×C67—41no—
319C4×C67—42no—
320C4×C67—42no—
321C4×C67—81no—
322C4×C67—81no—
323C4×C67—81no—
324C4×C67—81no—
325C4×C67—81no—
326C4×C67—81no—
327C4×C67#52511yescharacteristic
328C4×C67#53911yescharacteristic
329C4×C67#54811yescharacteristic
330C4×C67#55311yescharacteristic
331#26155C6711yesmaximal, characteristic, direct product factor, Sylow
332C2×C67—42no—
333C2×C67—81no—
334C2×C67#244311yescharacteristic
335C2×C67#309511yescharacteristic
336C2×C67#309911yescharacteristic
337C2×C67#326711yescharacteristic
338C2×C67#327811yescharacteristic
339C2×C67#334811yescharacteristic
340C2×C67#335611yescharacteristic
341C2×#485C2×C6711yescharacteristic, complemented
342C2×#428C2×C6711yescharacteristic, complemented
343#2417C2×C6711yescharacteristic
344#2354C2×C6711yescharacteristic
345#2096C2×C6711yescharacteristic, complemented
346#2084C2×C6711yescharacteristic, complemented
347#2077C2×C6711yescharacteristic, complemented
348#2035C2×C6711yescharacteristic, complemented
349#1928C2×C6711yescharacteristic, complemented
350#1921C2×C6711yescharacteristic, complemented
351#1894C2×C6711yescharacteristic, complemented
352#1873C2×C6711yescharacteristic, complemented
353#1870C2×C6711yescharacteristic
354#1854C2×C6711yescharacteristic, complemented
355#1853C2×C6711yescharacteristic, complemented
356C67#2615511yescharacteristic, direct product factor, Sylow
357C22×M16C22×C6711yescharacteristic
358C2×C22⋊Q8C22×C6711yescharacteristic
359C2×C22⋊Q8C22×C6711yescharacteristic
360C2×C4×D4C22×C6711yescharacteristic
361C2×#117C22×C6711yescharacteristic
362C2×#117C22×C6711yescharacteristic
363C22×C4⋊C4C22×C6711yescharacteristic
364#485—24no—
365#428—24no—
366C2×#107C22×C6711yescharacteristic
367C2×#107C22×C6711yescharacteristic
368C2×#106C22×C6711yescharacteristic
369C2×#106C22×C6711yescharacteristic
370C2×#106C22×C6711yescharacteristic
371C2×#106C22×C6711yescharacteristic
372C2×#103C22×C6711yescharacteristic
373C2×#103C22×C6711yescharacteristic
374C2×#103C22×C6711yescharacteristic
375C2×#103C22×C6711yescharacteristic
376C2×C22⋊C8C22×C6711yescharacteristic
377C2×C22⋊C8C22×C6711yescharacteristic
378C2×C22⋊C8C22×C6711yescharacteristic
379#398—21no—
380#396—21no—
381#391C22×C6711yescharacteristic
382#390—21no—
383#389C22×C6711yescharacteristic
384#388—21no—
385#388—21no—
386#386—21no—
387#384C22×C6711yescharacteristic
388#380—21no—
389#380C22×C6711yescharacteristic
390#380C22×C6711yescharacteristic
391#380C22×C6711yescharacteristic
392C4×C4⋊C4—21no—
393C4×C4⋊C4C22×C6711yescharacteristic
394#340C22×C6711yescharacteristic
395#340C22×C6711yescharacteristic
396#340C22×C6711yescharacteristic
397#340C22×C6711yescharacteristic
398#340C22×C6711yescharacteristic
399#340C22×C6711yescharacteristic
400#336C22×C6711yescharacteristic
401#336C22×C6711yescharacteristic
402C22×Q8C23×C6711yescharacteristic
403C22×D4D4×C6711yescharacteristic
404C23×C4—21no—
405C23×C4C23×C6711yescharacteristic
406C23×C4C23×C6711yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C22×C8C23×C6711yescharacteristic
411C22×C8C23×C6711yescharacteristic
412C22×C8C23×C6711yescharacteristic
413C22×C8C23×C6711yescharacteristic
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—41no—
418C4×D4—22no—
419C4×D4—22no—
420#117—22no—
421#117—22no—
422#117—41no—
423#117—41no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4D4×C6711yescharacteristic
433C2×C4⋊C4C23×C6711yescharacteristic
434C2×C4⋊C4C23×C6711yescharacteristic
435C2×C4⋊C4C23×C6711yescharacteristic
436C2×C4⋊C4C23×C6711yescharacteristic
437C2×C4⋊C4C23×C6711yescharacteristic
438C2×C4⋊C4C23×C6711yescharacteristic
439C2×C4⋊C4C23×C6711yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C6711yescharacteristic
448C2×C22⋊C4D4×C6711yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C6711yescharacteristic
453#107—22no—
454#107D4×C6714yescomplemented
455#106—22no—
456#106—22no—
457#106—22no—
458#106—41no—
459#103—22no—
460#103—22no—
461#103—22no—
462#103—41no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473C24C2×D4×C6711yescharacteristic
474C24C2×D4×C6711yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—41no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4C2×D4×C6711yescharacteristic
506C22×C4C2×D4×C6711yescharacteristic
507C22×C4C2×D4×C6711yescharacteristic
508C22×C4C2×D4×C6711yescharacteristic
509C22×C4#41×C6712yes—
510C22×C4#41×C6712yes—
511C22×C4C24×C6711yescharacteristic
512M16—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8C2×D4×C6712yes—
524C2×C8#41×C6712yes—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4C2×D4×C6712yes—
545C4⋊C4C2×D4×C6712yes—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C42—42no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#123×C6712yes—
574C23C22×D4×C6711yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—44no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
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—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4#123×C6712yes—
624C2×C4#137×C6712yes—
625C2×C4C22×D4×C6711yescharacteristic
626C2×C4C2×#41×C6711yescharacteristic
627C2×C4C2×#41×C6711yescharacteristic
628C2×C4C2×#41×C6711yescharacteristic
629C2×C4H(5,𝔽2)×C6711yescharacteristic
630C2×C42−1+4×C6711yescharacteristic
631C8—22no—
632C8—22no—
633C8—41no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#123×C6711yescharacteristic
650C22D42×C6711yescharacteristic
651C22#547×C6711yescharacteristic
652C22C2×#137×C6711yescharacteristic
653C22#575×C6711yescharacteristic
654C22#577×C6711yescharacteristic
655C22#577×C6711yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4#525×C6711yescharacteristic
669C4#539×C6711yescharacteristic
670C4#548×C6711yescharacteristic
671C4#553×C6711yescharacteristic
672C2—42no—
673C2—81no—
674C2C67×#244311yescharacteristic
675C2C67×#309511yescharacteristic
676C2C67×#309911yescharacteristic
677C2C67×#326711yescharacteristic
678C2C67×#327811yescharacteristic
679C2C67×#334811yescharacteristic
680C2C67×#335611yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC22×D4×C67D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C67C2semidirect
2. C2×#428×C67C2semidirect
5. C67×#2096C2semidirect
6. C67×#2084C2semidirect
7. C67×#2077C2semidirect
8. C67×#2035C2semidirect
9. C67×#1928C2semidirect
10. C67×#1921C2semidirect
11. C67×#1894C2semidirect
12. C67×#1873C2semidirect
14. C67×#1854C2semidirect
15. C67×#1853C2semidirect
113. #107×C67D4semidirect
331. #26155C67direct (N × H)
341. C2×#485C2×C67semidirect
342. C2×#428C2×C67semidirect
345. #2096C2×C67semidirect
346. #2084C2×C67semidirect
347. #2077C2×C67semidirect
348. #2035C2×C67semidirect
349. #1928C2×C67semidirect
350. #1921C2×C67semidirect
351. #1894C2×C67semidirect
352. #1873C2×C67semidirect
354. #1854C2×C67semidirect
355. #1853C2×C67semidirect
356. C67#26155direct (N × H)
454. #107D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C672
C2×#428×C672
C67×#24172
C67×#23542
C67×#20962
C67×#20842
C67×#20772
C67×#20352
C67×#19282
C67×#19212
C67×#18942
C67×#18732
C67×#18702
C67×#18542
C67×#18532
#2615567