Finite Group Databasebeta

← C67×#22017 #30701268

Subgroups — C67×#22017 #30701268

Order 17152.

744 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#2290C211yesmaximal, characteristic
2C67×#1955C211yesmaximal, characteristic
3C67×#1954C211yesmaximal, characteristic
4C67×#1940C211yesmaximal, characteristic, complemented
5C67×#1939C211yesmaximal, characteristic, complemented
6C67×#1924C211yesmaximal, characteristic, complemented
7C67×#1924C211yesmaximal, characteristic, complemented
8C67×#1923C211yesmaximal, characteristic, complemented
9C67×#1923C211yesmaximal, characteristic, complemented
10C67×#1818C211yesmaximal, characteristic, complemented
11C67×#1817C211yesmaximal, characteristic, complemented
12C67×#1798C211yesmaximal, characteristic, complemented
13C67×#1797C211yesmaximal, characteristic, complemented
14C67×#1768C211yesmaximal, characteristic, complemented
15C67×#1746C211yesmaximal, characteristic, complemented
16C2×C4×D4×C67C2211yescharacteristic
17C2×#117×C67C2211yescharacteristic
18C22×C42×C67C2211yescharacteristic
19C2×C4⋊C8×C67C2211yescharacteristic
20C2×C4⋊C8×C67C2211yescharacteristic
21C2×C4⋊C8×C67C2211yescharacteristic
22C2×C4⋊C8×C67C2211yescharacteristic
23C2×C4⋊C8×C67C2211yescharacteristic
24C2×C4⋊C8×C67C2211yescharacteristic
25C2×C22⋊C8×C67C2211yescharacteristic
26C2×C22⋊C8×C67C2211yescharacteristic
27C2×C22⋊C8×C67C2211yescharacteristic
28C2×C22⋊C8×C67C2211yescharacteristic
29C2×C22⋊C8×C67C2211yescharacteristic
30C2×C22⋊C8×C67C2211yescharacteristic
31C2×C22⋊C8×C67C2211yescharacteristic
32C2×C22⋊C8×C67C2211yescharacteristic
33C2×#97×C67C2211yescharacteristic
34C2×#97×C67C2211yescharacteristic
35C2×C4×C8×C67C2211yescharacteristic
36C2×C4×C8×C67C2211yescharacteristic
37#388×C67C411yescharacteristic
38#388×C67C411yescharacteristic
39#387×C67C411yescharacteristic
40#387×C67C411yescharacteristic
41#386×C67C411yescharacteristic
42#386×C67C411yescharacteristic
43#385×C67C411yescharacteristic
44#385×C67C411yescharacteristic
45C4×C4⋊C4×C67C2211yescharacteristic
46C4×C22⋊C4×C67C2211yescharacteristic
47C4×C22⋊C4×C67C2211yescharacteristic
48#376×C67C2211yescharacteristic
49#336×C67C2211yescharacteristic
50#336×C67C2211yescharacteristic
51#336×C67C2211yescharacteristic
52#336×C67C2211yescharacteristic
53#336×C67C2211yescharacteristic
54#336×C67C2211yescharacteristic
55#336×C67C2211yescharacteristic
56#336×C67C2211yescharacteristic
57#336×C67C2211yescharacteristic
58#336×C67C2211yescharacteristic
59C22×D4×C67C2×C411yescharacteristic
60C23×C4×C67C2×C411yescharacteristic
61C23×C4×C67C2×C411yescharacteristic
62C23×C4×C67C2311yescharacteristic
63C23×C4×C67C2311yescharacteristic
64C22×C8×C67C2311yescharacteristic
65C22×C8×C67C2311yescharacteristic
66C22×C8×C67C2311yescharacteristic
67C22×C8×C67C2311yescharacteristic
68C22×C8×C67C2311yescharacteristic
69C22×C8×C67C2311yescharacteristic
70C22×C8×C67C2311yescharacteristic
71C22×C8×C67C2311yescharacteristic
72C4×D4×C67—22no—
73C4×D4×C67—22no—
74#117×C67—41no—
75#117×C67—41no—
76C2×C4⋊C4×C67C2×C411yescharacteristic
77C2×C4⋊C4×C67C2×C411yescharacteristic
78C2×C4⋊C4×C67C2×C411yescharacteristic
79C2×C4⋊C4×C67C2×C411yescharacteristic
80C2×C4⋊C4×C67C2×C411yescharacteristic
81C2×C22⋊C4×C67C2×C411yescharacteristic
82C2×C22⋊C4×C67C2×C411yescharacteristic
83C2×C22⋊C4×C67C2×C411yescharacteristic
84C2×C22⋊C4×C67C2×C411yescharacteristic
85C2×C22⋊C4×C67C2×C411yescharacteristic
86C2×C22⋊C4×C67C2×C411yescharacteristic
87C2×C22⋊C4×C67C2×C411yescharacteristic
88C2×C22⋊C4×C67C2×C411yescharacteristic
89C2×C42×C67—41no—
90C2×C42×C67—41no—
91C2×C42×C67C2×C411yescharacteristic
92C2×C42×C67C2×C411yescharacteristic
93C2×C42×C67C2311yescharacteristic
94C2×C42×C67C2311yescharacteristic
95C2×C42×C67C2311yescharacteristic
96C2×C42×C67C2311yescharacteristic
97C2×C42×C67C2311yescharacteristic
98C4⋊C8×C67—22no—
99C4⋊C8×C67—22no—
100C4⋊C8×C67—41no—
101C4⋊C8×C67—41no—
102C4⋊C8×C67—41no—
103C4⋊C8×C67—41no—
104C22⋊C8×C67—41no—
105C22⋊C8×C67—41no—
106C22⋊C8×C67—41no—
107C22⋊C8×C67—41no—
108C22⋊C8×C67—41no—
109C22⋊C8×C67—41no—
110C22⋊C8×C67—41no—
111C22⋊C8×C67—41no—
112#97×C67—22no—
113#97×C67—41no—
114C4×C8×C67—22no—
115C4×C8×C67—41no—
116#95×C67C2×C411yescharacteristic
117#95×C67C2×C411yescharacteristic
118#95×C67C2×C411yescharacteristic
119#95×C67C2×C411yescharacteristic
120#95×C67C2×C411yescharacteristic
121#95×C67C2×C411yescharacteristic
122#95×C67C2×C411yescharacteristic
123#95×C67C2×C411yescharacteristic
124#95×C67C2×C411yescharacteristic
125#95×C67C2×C411yescharacteristic
126C24×C67C22×C411yescharacteristic
127C24×C67C22×C411yescharacteristic
128C2×D4×C67—22no—
129C2×D4×C67—22no—
130C2×D4×C67—41no—
131C22×C4×C67—22no—
132C22×C4×C67—22no—
133C22×C4×C67—21no—
134C22×C4×C67—21no—
135C22×C4×C67—21no—
136C22×C4×C67—21no—
137C22×C4×C67—21no—
138C22×C4×C67—21no—
139C22×C4×C67—21no—
140C22×C4×C67—21no—
141C22×C4×C67—21no—
142C22×C4×C67—21no—
143C22×C4×C67—21no—
144C22×C4×C67—21no—
145C22×C4×C67—41no—
146C22×C4×C67—41no—
147C22×C4×C67—41no—
148C22×C4×C67—41no—
149C22×C4×C67C22×C411yescharacteristic
150C22×C4×C67C22×C411yescharacteristic
151C22×C4×C67C22×C411yescharacteristic
152C22×C4×C67C22×C411yescharacteristic
153C22×C4×C67C22×C411yescharacteristic
154C22×C4×C67C22×C411yescharacteristic
155C22×C4×C67C22×C411yescharacteristic
156C22×C4×C67C22×C411yescharacteristic
157C22×C4×C67C22×C411yescharacteristic
158C22×C4×C67C22×C411yescharacteristic
159C22×C4×C67C22×C411yescharacteristic
160C22×C4×C67C22×C411yescharacteristic
161C22×C4×C67C2411yescharacteristic
162C2×C8×C67—21no—
163C2×C8×C67—21no—
164C2×C8×C67—21no—
165C2×C8×C67—21no—
166C2×C8×C67—21no—
167C2×C8×C67—21no—
168C2×C8×C67—21no—
169C2×C8×C67—21no—
170C2×C8×C67—21no—
171C2×C8×C67—21no—
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×C67—21no—
183C2×C8×C67—21no—
184C2×C8×C67—21no—
185C2×C8×C67—21no—
186C4⋊C4×C67—22no—
187C4⋊C4×C67—22no—
188C4⋊C4×C67—41no—
189C4⋊C4×C67—41no—
190C4⋊C4×C67—41no—
191C22⋊C4×C67—22no—
192C22⋊C4×C67—22no—
193C22⋊C4×C67—22no—
194C22⋊C4×C67—22no—
195C22⋊C4×C67—41no—
196C22⋊C4×C67—41no—
197C22⋊C4×C67—41no—
198C22⋊C4×C67—41no—
199C42×C67—21no—
200C42×C67—21no—
201C42×C67—21no—
202C42×C67—21no—
203C42×C67—21no—
204C42×C67—21no—
205C42×C67—21no—
206C42×C67—21no—
207C42×C67—41no—
208C42×C67—41no—
209C42×C67#4112yes—
210C42×C67#4112yes—
211C23×C67—21no—
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×C67—21no—
223C23×C67—21no—
224C23×C67#13112yes—
225C23×C67C23×C411yescharacteristic
226D4×C67—44no—
227C2×C4×C67—21no—
228C2×C4×C67—21no—
229C2×C4×C67—21no—
230C2×C4×C67—21no—
231C2×C4×C67—21no—
232C2×C4×C67—21no—
233C2×C4×C67—21no—
234C2×C4×C67—21no—
235C2×C4×C67—21no—
236C2×C4×C67—21no—
237C2×C4×C67—21no—
238C2×C4×C67—21no—
239C2×C4×C67—21no—
240C2×C4×C67—21no—
241C2×C4×C67—21no—
242C2×C4×C67—21no—
243C2×C4×C67—21no—
244C2×C4×C67—21no—
245C2×C4×C67—21no—
246C2×C4×C67—21no—
247C2×C4×C67—21no—
248C2×C4×C67—21no—
249C2×C4×C67—21no—
250C2×C4×C67—21no—
251C2×C4×C67—21no—
252C2×C4×C67—21no—
253C2×C4×C67—21no—
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—44no—
261C2×C4×C67—44no—
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#11712yes—
271C2×C4×C67#11712yes—
272C2×C4×C67#13112yes—
273C2×C4×C67C2×#4111yescharacteristic
274C2×C4×C67C2×#4111yescharacteristic
275C2×C4×C67H(5,𝔽2)11yescharacteristic
276C2×C4×C67H(5,𝔽2)11yescharacteristic
277C2×C4×C67H(5,𝔽2)11yescharacteristic
278C2×C4×C672−1+411yescharacteristic
279C8×C67—41no—
280C8×C67—41no—
281C8×C67—41no—
282C8×C67—41no—
283C8×C67—41no—
284C8×C67—41no—
285C8×C67—41no—
286C8×C67—41no—
287C22×C67—22no—
288C22×C67—22no—
289C22×C67—22no—
290C22×C67—41no—
291C22×C67—41no—
292C22×C67—41no—
293C22×C67—41no—
294C22×C67—41no—
295C22×C67—41no—
296C22×C67—41no—
297C22×C67—41no—
298C22×C67—41no—
299C22×C67—41no—
300C22×C67—41no—
301C22×C67C2×#11711yescharacteristic
302C22×C67#51811yescharacteristic
303C22×C67#52011yescharacteristic
304C22×C67C2×#13111yescharacteristic
305C22×C67C2×#13111yescharacteristic
306C22×C67#56811yescharacteristic
307C22×C67#56811yescharacteristic
308C4×C67—22no—
309C4×C67—22no—
310C4×C67—22no—
311C4×C67—41no—
312C4×C67—41no—
313C4×C67—41no—
314C4×C67—41no—
315C4×C67—41no—
316C4×C67—41no—
317C4×C67—41no—
318C4×C67—41no—
319C4×C67—41no—
320C4×C67#54011yescharacteristic
321C4×C67#54011yescharacteristic
322C4×C67#54211yescharacteristic
323C4×C67#54211yescharacteristic
324#22017C6711yesmaximal, characteristic, direct product factor, Sylow
325C2×C67—42no—
326C2×C67—81no—
327C2×C67#231911yescharacteristic
328C2×C67#292411yescharacteristic
329C2×C67#292511yescharacteristic
330C2×C67#297711yescharacteristic
331C2×C67#297811yescharacteristic
332C2×C67#299211yescharacteristic
333C2×C67#299311yescharacteristic
334#2290C2×C6711yescharacteristic
335#1955C2×C6711yescharacteristic
336#1954C2×C6711yescharacteristic
337#1940C2×C6711yescharacteristic, complemented
338#1939C2×C6711yescharacteristic, complemented
339#1924C2×C6711yescharacteristic, complemented
340#1924C2×C6711yescharacteristic, complemented
341#1923C2×C6711yescharacteristic, complemented
342#1923C2×C6711yescharacteristic, complemented
343#1818C2×C6711yescharacteristic, complemented
344#1817C2×C6711yescharacteristic, complemented
345#1798C2×C6711yescharacteristic, complemented
346#1797C2×C6711yescharacteristic, complemented
347#1768C2×C6711yescharacteristic, complemented
348#1746C2×C6711yescharacteristic, complemented
349C67#2201711yescharacteristic, direct product factor, Sylow
350C2×C4×D4C22×C6711yescharacteristic
351C2×#117C22×C6711yescharacteristic
352C22×C42C22×C6711yescharacteristic
353C2×C4⋊C8C22×C6711yescharacteristic
354C2×C4⋊C8C22×C6711yescharacteristic
355C2×C4⋊C8C22×C6711yescharacteristic
356C2×C4⋊C8C22×C6711yescharacteristic
357C2×C4⋊C8C22×C6711yescharacteristic
358C2×C4⋊C8C22×C6711yescharacteristic
359C2×C22⋊C8C22×C6711yescharacteristic
360C2×C22⋊C8C22×C6711yescharacteristic
361C2×C22⋊C8C22×C6711yescharacteristic
362C2×C22⋊C8C22×C6711yescharacteristic
363C2×C22⋊C8C22×C6711yescharacteristic
364C2×C22⋊C8C22×C6711yescharacteristic
365C2×C22⋊C8C22×C6711yescharacteristic
366C2×C22⋊C8C22×C6711yescharacteristic
367C2×#97C22×C6711yescharacteristic
368C2×#97C22×C6711yescharacteristic
369C2×C4×C8C22×C6711yescharacteristic
370C2×C4×C8C22×C6711yescharacteristic
371#388C4×C6711yescharacteristic
372#388C4×C6711yescharacteristic
373#387C4×C6711yescharacteristic
374#387C4×C6711yescharacteristic
375#386C4×C6711yescharacteristic
376#386C4×C6711yescharacteristic
377#385C4×C6711yescharacteristic
378#385C4×C6711yescharacteristic
379C4×C4⋊C4C22×C6711yescharacteristic
380C4×C22⋊C4C22×C6711yescharacteristic
381C4×C22⋊C4C22×C6711yescharacteristic
382#376C22×C6711yescharacteristic
383#336C22×C6711yescharacteristic
384#336C22×C6711yescharacteristic
385#336C22×C6711yescharacteristic
386#336C22×C6711yescharacteristic
387#336C22×C6711yescharacteristic
388#336C22×C6711yescharacteristic
389#336C22×C6711yescharacteristic
390#336C22×C6711yescharacteristic
391#336C22×C6711yescharacteristic
392#336C22×C6711yescharacteristic
393C22×D4C2×C4×C6711yescharacteristic
394C23×C4C2×C4×C6711yescharacteristic
395C23×C4C2×C4×C6711yescharacteristic
396C23×C4C23×C6711yescharacteristic
397C23×C4C23×C6711yescharacteristic
398C22×C8C23×C6711yescharacteristic
399C22×C8C23×C6711yescharacteristic
400C22×C8C23×C6711yescharacteristic
401C22×C8C23×C6711yescharacteristic
402C22×C8C23×C6711yescharacteristic
403C22×C8C23×C6711yescharacteristic
404C22×C8C23×C6711yescharacteristic
405C22×C8C23×C6711yescharacteristic
406C4×D4—22no—
407C4×D4—22no—
408#117—41no—
409#117—41no—
410C2×C4⋊C4C2×C4×C6711yescharacteristic
411C2×C4⋊C4C2×C4×C6711yescharacteristic
412C2×C4⋊C4C2×C4×C6711yescharacteristic
413C2×C4⋊C4C2×C4×C6711yescharacteristic
414C2×C4⋊C4C2×C4×C6711yescharacteristic
415C2×C22⋊C4C2×C4×C6711yescharacteristic
416C2×C22⋊C4C2×C4×C6711yescharacteristic
417C2×C22⋊C4C2×C4×C6711yescharacteristic
418C2×C22⋊C4C2×C4×C6711yescharacteristic
419C2×C22⋊C4C2×C4×C6711yescharacteristic
420C2×C22⋊C4C2×C4×C6711yescharacteristic
421C2×C22⋊C4C2×C4×C6711yescharacteristic
422C2×C22⋊C4C2×C4×C6711yescharacteristic
423C2×C42—41no—
424C2×C42—41no—
425C2×C42C2×C4×C6711yescharacteristic
426C2×C42C2×C4×C6711yescharacteristic
427C2×C42C23×C6711yescharacteristic
428C2×C42C23×C6711yescharacteristic
429C2×C42C23×C6711yescharacteristic
430C2×C42C23×C6711yescharacteristic
431C2×C42C23×C6711yescharacteristic
432C4⋊C8—22no—
433C4⋊C8—22no—
434C4⋊C8—41no—
435C4⋊C8—41no—
436C4⋊C8—41no—
437C4⋊C8—41no—
438C22⋊C8—41no—
439C22⋊C8—41no—
440C22⋊C8—41no—
441C22⋊C8—41no—
442C22⋊C8—41no—
443C22⋊C8—41no—
444C22⋊C8—41no—
445C22⋊C8—41no—
446#97—22no—
447#97—41no—
448C4×C8—22no—
449C4×C8—41no—
450#95C2×C4×C6711yescharacteristic
451#95C2×C4×C6711yescharacteristic
452#95C2×C4×C6711yescharacteristic
453#95C2×C4×C6711yescharacteristic
454#95C2×C4×C6711yescharacteristic
455#95C2×C4×C6711yescharacteristic
456#95C2×C4×C6711yescharacteristic
457#95C2×C4×C6711yescharacteristic
458#95C2×C4×C6711yescharacteristic
459#95C2×C4×C6711yescharacteristic
460C24C22×C4×C6711yescharacteristic
461C24C22×C4×C6711yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—41no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4C22×C4×C6711yescharacteristic
484C22×C4C22×C4×C6711yescharacteristic
485C22×C4C22×C4×C6711yescharacteristic
486C22×C4C22×C4×C6711yescharacteristic
487C22×C4C22×C4×C6711yescharacteristic
488C22×C4C22×C4×C6711yescharacteristic
489C22×C4C22×C4×C6711yescharacteristic
490C22×C4C22×C4×C6711yescharacteristic
491C22×C4C22×C4×C6711yescharacteristic
492C22×C4C22×C4×C6711yescharacteristic
493C22×C4C22×C4×C6711yescharacteristic
494C22×C4C22×C4×C6711yescharacteristic
495C22×C4C24×C6711yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—41no—
542C42—41no—
543C42#41×C6712yes—
544C42#41×C6712yes—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23#131×C6712yes—
559C23C23×C4×C6711yescharacteristic
560D4—44no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—44no—
595C2×C4—44no—
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#117×C6712yes—
605C2×C4#117×C6712yes—
606C2×C4#131×C6712yes—
607C2×C4C2×#41×C6711yescharacteristic
608C2×C4C2×#41×C6711yescharacteristic
609C2×C4H(5,𝔽2)×C6711yescharacteristic
610C2×C4H(5,𝔽2)×C6711yescharacteristic
611C2×C4H(5,𝔽2)×C6711yescharacteristic
612C2×C42−1+4×C6711yescharacteristic
613C8—41no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#117×C6711yescharacteristic
636C22#518×C6711yescharacteristic
637C22#520×C6711yescharacteristic
638C22C2×#131×C6711yescharacteristic
639C22C2×#131×C6711yescharacteristic
640C22#568×C6711yescharacteristic
641C22#568×C6711yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4#540×C6711yescharacteristic
655C4#540×C6711yescharacteristic
656C4#542×C6711yescharacteristic
657C4#542×C6711yescharacteristic
658C2—42no—
659C2—81no—
660C2C67×#231911yescharacteristic
661C2C67×#292411yescharacteristic
662C2C67×#292511yescharacteristic
663C2C67×#297711yescharacteristic
664C2C67×#297811yescharacteristic
665C2C67×#299211yescharacteristic
666C2C67×#299311yescharacteristic
subgroupG/H
centerC22×C4×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC22×C4C24×C67
socleC23×C67C23×C4
prime radicalC22×D4×C67C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
4. C67×#1940C2semidirect
5. C67×#1939C2semidirect
6. C67×#1924C2semidirect
7. C67×#1924C2semidirect
8. C67×#1923C2semidirect
9. C67×#1923C2semidirect
10. C67×#1818C2semidirect
11. C67×#1817C2semidirect
12. C67×#1798C2semidirect
13. C67×#1797C2semidirect
14. C67×#1768C2semidirect
15. C67×#1746C2semidirect
324. #22017C67direct (N × H)
337. #1940C2×C67semidirect
338. #1939C2×C67semidirect
339. #1924C2×C67semidirect
340. #1924C2×C67semidirect
341. #1923C2×C67semidirect
342. #1923C2×C67semidirect
343. #1818C2×C67semidirect
344. #1817C2×C67semidirect
345. #1798C2×C67semidirect
346. #1797C2×C67semidirect
347. #1768C2×C67semidirect
348. #1746C2×C67semidirect
349. C67#22017direct (N × H)

Maximal subgroups

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

subgroupindex
C67×#22902
C67×#19552
C67×#19542
C67×#19402
C67×#19392
C67×#19242
C67×#19232
C67×#18182
C67×#18172
C67×#17982
C67×#17972
C67×#17682
C67×#17462
#2201767