Finite Group Databasebeta

← C67×#23580 #30702831

Subgroups — C67×#23580 #30702831

Order 17152.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C67C211yesmaximal, characteristic, complemented
2C2×#442×C67C211yesmaximal, characteristic, complemented
3C2×C4×D8×C67C211yesmaximal, characteristic, complemented
4C67×#2324C211yesmaximal, characteristic, complemented
5C67×#2059C211yesmaximal, characteristic, complemented
6C67×#2041C211yesmaximal, characteristic, complemented
7C67×#2034C211yesmaximal, characteristic, complemented
8C67×#2033C211yesmaximal, characteristic, complemented
9C67×#2025C211yesmaximal, characteristic, complemented
10C67×#2011C211yesmaximal, characteristic, complemented
11C67×#1999C211yesmaximal, characteristic, complemented
12C67×#1999C211yesmaximal, characteristic, complemented
13C67×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C67C211yesmaximal, characteristic, complemented
15C67×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C67C2211yescharacteristic
17C22×D8×C67C2211yescharacteristic
18#540×C67—24no—
19#540×C67—24no—
20C2×#127×C67C2211yescharacteristic
21C2×#125×C67C2211yescharacteristic
22C2×#123×C67—21no—
23C2×#123×C67—21no—
24C2×#121×C67—21no—
25C2×#121×C67—21no—
26C2×#121×C67C2211yescharacteristic
27C2×#121×C67C2211yescharacteristic
28C2×#121×C67C2211yescharacteristic
29C2×C4×D4×C67C2211yescharacteristic
30C2×C4×D4×C67C2211yescharacteristic
31C2×C4×D4×C67C2211yescharacteristic
32C2×#117×C67C2211yescharacteristic
33#442×C67—24no—
34C4×D8×C67—24no—
35C2×#107×C67C2211yescharacteristic
36C2×#106×C67C2211yescharacteristic
37C2×#102×C67C2211yescharacteristic
38C2×#102×C67C2211yescharacteristic
39C2×#102×C67C2211yescharacteristic
40C2×#102×C67C2211yescharacteristic
41C2×#102×C67C2211yescharacteristic
42C2×#102×C67C2211yescharacteristic
43C2×#102×C67C2211yescharacteristic
44C2×#102×C67C2211yescharacteristic
45C2×C22⋊C8×C67C2211yescharacteristic
46C2×C22⋊C8×C67C2211yescharacteristic
47C2×#97×C67C2211yescharacteristic
48C2×C4×C8×C67C2211yescharacteristic
49#390×C67—21no—
50#390×C67C2211yescharacteristic
51#389×C67C2211yescharacteristic
52#388×C67—21no—
53#386×C67—21no—
54#385×C67—21no—
55#380×C67C2211yescharacteristic
56C4×C4⋊C4×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61#336×C67C2211yescharacteristic
62#336×C67C2211yescharacteristic
63C22×D4×C67—21no—
64C22×D4×C67—21no—
65C22×D4×C67—21no—
66C22×D4×C67—21no—
67C22×D4×C67—21no—
68C22×D4×C67C2311yescharacteristic
69C22×D4×C67C2311yescharacteristic
70C22×D4×C67C2311yescharacteristic
71C23×C4×C67—21no—
72C23×C4×C67—21no—
73C23×C4×C67—21no—
74C23×C4×C67C2311yescharacteristic
75C2×D8×C67—22no—
76C2×D8×C67—22no—
77C2×D8×C67—22no—
78C2×D8×C67—22no—
79C2×D8×C67—22no—
80C2×D8×C67—22no—
81C22×C8×C67C2311yescharacteristic
82C22×C8×C67C2311yescharacteristic
83C22×C8×C67C2311yescharacteristic
84C22×C8×C67C2311yescharacteristic
85#127×C67—22no—
86#127×C67—22no—
87#125×C67—22no—
88#125×C67—22no—
89#123×C67—28no—
90#123×C67—28no—
91#121×C67—28no—
92#121×C67—28no—
93#121×C67—22no—
94#121×C67—22no—
95#121×C67—22no—
96#121×C67—22no—
97#121×C67—22no—
98#121×C67—22no—
99C4×D4×C67—22no—
100C4×D4×C67—22no—
101C4×D4×C67—22no—
102C4×D4×C67—22no—
103C4×D4×C67D414yescomplemented
104C4×D4×C67D414yescomplemented
105#117×C67—22no—
106#117×C67—22no—
107C2×C4⋊C4×C67—21no—
108C2×C4⋊C4×C67—21no—
109C2×C4⋊C4×C67—21no—
110C2×C4⋊C4×C67D411yescharacteristic
111C2×C4⋊C4×C67D411yescharacteristic
112C2×C4⋊C4×C67C2311yescharacteristic
113C2×C4⋊C4×C67C2311yescharacteristic
114C2×C4⋊C4×C67C2311yescharacteristic
115C2×C4⋊C4×C67C2311yescharacteristic
116C2×C4⋊C4×C67C2311yescharacteristic
117C2×C22⋊C4×C67—21no—
118C2×C22⋊C4×C67—21no—
119C2×C22⋊C4×C67—21no—
120C2×C22⋊C4×C67—21no—
121C2×C22⋊C4×C67—21no—
122C2×C22⋊C4×C67—21no—
123C2×C22⋊C4×C67—21no—
124C2×C22⋊C4×C67—21no—
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67D411yescharacteristic
127C2×C22⋊C4×C67D411yescharacteristic
128C2×C42×C67—21no—
129C2×C42×C67C2311yescharacteristic
130C2×C42×C67C2311yescharacteristic
131#107×C67—22no—
132#106×C67—22no—
133#102×C67—22no—
134#102×C67—22no—
135#102×C67—22no—
136#102×C67—22no—
137#102×C67—22no—
138#102×C67—22no—
139#102×C67—22no—
140#102×C67—22no—
141C22⋊C8×C67—22no—
142C22⋊C8×C67—22no—
143#97×C67—22no—
144C4×C8×C67—22no—
145#95×C67—21no—
146#95×C67—21no—
147#95×C67—21no—
148C24×C67—21no—
149C24×C67—21no—
150C24×C67—21no—
151C24×C67C2×D411yescharacteristic
152C2×D4×C67—24no—
153C2×D4×C67—24no—
154C2×D4×C67—24no—
155C2×D4×C67—24no—
156C2×D4×C67—24no—
157C2×D4×C67—21no—
158C2×D4×C67—21no—
159C2×D4×C67—21no—
160C2×D4×C67—21no—
161C2×D4×C67—21no—
162C2×D4×C67—21no—
163C2×D4×C67—21no—
164C2×D4×C67—21no—
165C2×D4×C67—21no—
166C2×D4×C67—21no—
167C2×D4×C67—21no—
168C2×D4×C67—21no—
169C2×D4×C67—21no—
170C2×D4×C67—21no—
171C2×D4×C67—21no—
172C2×D4×C67—81no—
173C2×D4×C67—81no—
174C2×D4×C67—81no—
175C2×D4×C67—81no—
176C2×D4×C67—81no—
177C2×D4×C67—81no—
178C2×D4×C67—81no—
179C2×D4×C67—81no—
180C2×D4×C67—81no—
181C2×D4×C67—81no—
182C2×D4×C67C2×D412yes—
183C2×D4×C67C2×D412yes—
184C2×D4×C67#4112yes—
185C22×C4×C67—21no—
186C22×C4×C67—21no—
187C22×C4×C67—21no—
188C22×C4×C67—21no—
189C22×C4×C67—21no—
190C22×C4×C67—21no—
191C22×C4×C67—21no—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—24no—
195C22×C4×C67—24no—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—42no—
199C22×C4×C67—81no—
200C22×C4×C67—81no—
201C22×C4×C67—81no—
202C22×C4×C67—81no—
203C22×C4×C67—81no—
204C22×C4×C67—81no—
205C22×C4×C67C2×D411yescharacteristic
206C22×C4×C67C2×D411yescharacteristic
207C22×C4×C67C2×D411yescharacteristic
208C22×C4×C67C2×D411yescharacteristic
209C22×C4×C67C2×D411yescharacteristic
210C22×C4×C67C2411yescharacteristic
211D8×C67—28no—
212D8×C67—28no—
213C2×C8×C67—21no—
214C2×C8×C67—21no—
215C2×C8×C67—21no—
216C2×C8×C67—21no—
217C2×C8×C67—21no—
218C2×C8×C67—21no—
219C2×C8×C67—21no—
220C2×C8×C67—21no—
221C2×C8×C67—21no—
222C2×C8×C67—21no—
223C2×C8×C67#4112yes—
224C2×C8×C67#4112yes—
225C4⋊C4×C67—24no—
226C4⋊C4×C67—24no—
227C4⋊C4×C67—22no—
228C4⋊C4×C67—22no—
229C4⋊C4×C67—21no—
230C4⋊C4×C67—21no—
231C4⋊C4×C67—21no—
232C4⋊C4×C67—21no—
233C4⋊C4×C67—21no—
234C4⋊C4×C67—21no—
235C4⋊C4×C67—21no—
236C4⋊C4×C67—81no—
237C4⋊C4×C67C2×D412yes—
238C4⋊C4×C67C2×D412yes—
239C4⋊C4×C67#4112yes—
240C22⋊C4×C67—24no—
241C22⋊C4×C67—24no—
242C22⋊C4×C67—24no—
243C22⋊C4×C67—24no—
244C22⋊C4×C67—24no—
245C22⋊C4×C67—22no—
246C22⋊C4×C67—22no—
247C22⋊C4×C67—42no—
248C22⋊C4×C67—81no—
249C22⋊C4×C67—81no—
250C22⋊C4×C67—81no—
251C42×C67—21no—
252C42×C67—21no—
253C42×C67—81no—
254C42×C67C2×D412yes—
255C42×C67C2×D412yes—
256C23×C67—21no—
257C23×C67—22no—
258C23×C67—22no—
259C23×C67—22no—
260C23×C67—21no—
261C23×C67—21no—
262C23×C67—21no—
263C23×C67—21no—
264C23×C67—21no—
265C23×C67—21no—
266C23×C67—41no—
267C23×C67—41no—
268C23×C67—41no—
269C23×C67—41no—
270C23×C67—41no—
271C23×C67—41no—
272C23×C67—41no—
273C23×C67—41no—
274C23×C67—41no—
275C23×C67—41no—
276C23×C67—41no—
277C23×C67—41no—
278C23×C67—41no—
279C23×C67—41no—
280C23×C67—41no—
281C23×C67—41no—
282C23×C67—41no—
283C23×C67—41no—
284C23×C67C22×D411yescharacteristic
285D4×C67—22no—
286D4×C67—22no—
287D4×C67—22no—
288D4×C67—22no—
289D4×C67—22no—
290D4×C67—22no—
291D4×C67—41no—
292D4×C67—41no—
293D4×C67—41no—
294D4×C67—41no—
295D4×C67—41no—
296D4×C67—41no—
297D4×C67—84no—
298D4×C67—84no—
299D4×C67—84no—
300D4×C67—84no—
301D4×C67—84no—
302C2×C4×C67—21no—
303C2×C4×C67—21no—
304C2×C4×C67—21no—
305C2×C4×C67—21no—
306C2×C4×C67—21no—
307C2×C4×C67—21no—
308C2×C4×C67—21no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—21no—
312C2×C4×C67—22no—
313C2×C4×C67—21no—
314C2×C4×C67—21no—
315C2×C4×C67—21no—
316C2×C4×C67—21no—
317C2×C4×C67—21no—
318C2×C4×C67—41no—
319C2×C4×C67—41no—
320C2×C4×C67—41no—
321C2×C4×C67—41no—
322C2×C4×C67—41no—
323C2×C4×C67—41no—
324C2×C4×C67—41no—
325C2×C4×C67—41no—
326C2×C4×C67—41no—
327C2×C4×C67—41no—
328C2×C4×C67—41no—
329C2×C4×C67—41no—
330C2×C4×C67—41no—
331C2×C4×C67—41no—
332C2×C4×C67—41no—
333C2×C4×C67—41no—
334C2×C4×C67—84no—
335C2×C4×C67—84no—
336C2×C4×C67—84no—
337C2×C4×C67#12012yes—
338C2×C4×C67#12012yes—
339C2×C4×C67C22×D411yescharacteristic
340C2×C4×C67C22×D411yescharacteristic
341C2×C4×C67C2×#4111yescharacteristic
342C2×C4×C67C2×#4111yescharacteristic
343C2×C4×C67C2×#4111yescharacteristic
344C2×C4×C67C2×#4111yescharacteristic
345C8×C67—22no—
346C8×C67—22no—
347C8×C67—41no—
348C8×C67—41no—
349C22×C67—41no—
350C22×C67—42no—
351C22×C67—41no—
352C22×C67—42no—
353C22×C67—41no—
354C22×C67—42no—
355C22×C67—42no—
356C22×C67—42no—
357C22×C67—41no—
358C22×C67—41no—
359C22×C67—42no—
360C22×C67—41no—
361C22×C67—42no—
362C22×C67—42no—
363C22×C67—41no—
364C22×C67—42no—
365C22×C67—81no—
366C22×C67—81no—
367C22×C67—81no—
368C22×C67—81no—
369C22×C67—81no—
370C22×C67—81no—
371C22×C67—81no—
372C22×C67—81no—
373C22×C67—81no—
374C22×C67—81no—
375C22×C67—81no—
376C22×C67—81no—
377C22×C67C2×#12011yescharacteristic
378C22×C67#52511yescharacteristic
379C22×C67#53211yescharacteristic
380C22×C67#57611yescharacteristic
381C22×C67#57611yescharacteristic
382C22×C67#57611yescharacteristic
383C22×C67#57711yescharacteristic
384C4×C67—22no—
385C4×C67—22no—
386C4×C67—42no—
387C4×C67—41no—
388C4×C67—41no—
389C4×C67—42no—
390C4×C67—41no—
391C4×C67—42no—
392C4×C67—81no—
393C4×C67—81no—
394C4×C67#52511yescharacteristic
395C4×C67#52511yescharacteristic
396C4×C67#53211yescharacteristic
397C4×C67#53211yescharacteristic
398#23580C6711yesmaximal, characteristic, direct product factor, Sylow
399C2×C67—81no—
400C2×C67—82no—
401C2×C67—82no—
402C2×C67—82no—
403C2×C67#238811yescharacteristic
404C2×C67#300811yescharacteristic
405C2×C67#301211yescharacteristic
406C2×C67#311911yescharacteristic
407C2×C67#312211yescharacteristic
408C2×C67#317611yescharacteristic
409C2×C67#317911yescharacteristic
410C2×#540C2×C6711yescharacteristic, complemented
411C2×#442C2×C6711yescharacteristic, complemented
412C2×C4×D8C2×C6711yescharacteristic, complemented
413#2324C2×C6711yescharacteristic, complemented
414#2059C2×C6711yescharacteristic, complemented
415#2041C2×C6711yescharacteristic, complemented
416#2034C2×C6711yescharacteristic, complemented
417#2033C2×C6711yescharacteristic, complemented
418#2025C2×C6711yescharacteristic, complemented
419#2011C2×C6711yescharacteristic, complemented
420#1999C2×C6711yescharacteristic, complemented
421#1999C2×C6711yescharacteristic, complemented
422#1762C2×C6711yescharacteristic, complemented
423C4×#102C2×C6711yescharacteristic, complemented
424#1750C2×C6711yescharacteristic, complemented
425C67#2358011yescharacteristic, direct product factor, Sylow
426C22×D8C22×C6711yescharacteristic
427C22×D8C22×C6711yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C6711yescharacteristic
431C2×#125C22×C6711yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C6711yescharacteristic
437C2×#121C22×C6711yescharacteristic
438C2×#121C22×C6711yescharacteristic
439C2×C4×D4C22×C6711yescharacteristic
440C2×C4×D4C22×C6711yescharacteristic
441C2×C4×D4C22×C6711yescharacteristic
442C2×#117C22×C6711yescharacteristic
443#442—24no—
444C4×D8—24no—
445C2×#107C22×C6711yescharacteristic
446C2×#106C22×C6711yescharacteristic
447C2×#102C22×C6711yescharacteristic
448C2×#102C22×C6711yescharacteristic
449C2×#102C22×C6711yescharacteristic
450C2×#102C22×C6711yescharacteristic
451C2×#102C22×C6711yescharacteristic
452C2×#102C22×C6711yescharacteristic
453C2×#102C22×C6711yescharacteristic
454C2×#102C22×C6711yescharacteristic
455C2×C22⋊C8C22×C6711yescharacteristic
456C2×C22⋊C8C22×C6711yescharacteristic
457C2×#97C22×C6711yescharacteristic
458C2×C4×C8C22×C6711yescharacteristic
459#390—21no—
460#390C22×C6711yescharacteristic
461#389C22×C6711yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C6711yescharacteristic
466C4×C4⋊C4C22×C6711yescharacteristic
467#340C22×C6711yescharacteristic
468#340C22×C6711yescharacteristic
469#340C22×C6711yescharacteristic
470#340C22×C6711yescharacteristic
471#336C22×C6711yescharacteristic
472#336C22×C6711yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C6711yescharacteristic
479C22×D4C23×C6711yescharacteristic
480C22×D4C23×C6711yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C6711yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C6711yescharacteristic
492C22×C8C23×C6711yescharacteristic
493C22×C8C23×C6711yescharacteristic
494C22×C8C23×C6711yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C6714yescomplemented
514C4×D4D4×C6714yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C6711yescharacteristic
521C2×C4⋊C4D4×C6711yescharacteristic
522C2×C4⋊C4C23×C6711yescharacteristic
523C2×C4⋊C4C23×C6711yescharacteristic
524C2×C4⋊C4C23×C6711yescharacteristic
525C2×C4⋊C4C23×C6711yescharacteristic
526C2×C4⋊C4C23×C6711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C6711yescharacteristic
537C2×C22⋊C4D4×C6711yescharacteristic
538C2×C42—21no—
539C2×C42C23×C6711yescharacteristic
540C2×C42C23×C6711yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C6711yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C6712yes—
593C2×D4C2×D4×C6712yes—
594C2×D4#41×C6712yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C6711yescharacteristic
616C22×C4C2×D4×C6711yescharacteristic
617C22×C4C2×D4×C6711yescharacteristic
618C22×C4C2×D4×C6711yescharacteristic
619C22×C4C2×D4×C6711yescharacteristic
620C22×C4C24×C6711yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C6712yes—
634C2×C8#41×C6712yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C6712yes—
648C4⋊C4C2×D4×C6712yes—
649C4⋊C4#41×C6712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C6712yes—
665C42C2×D4×C6712yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C6711yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C6712yes—
748C2×C4#120×C6712yes—
749C2×C4C22×D4×C6711yescharacteristic
750C2×C4C22×D4×C6711yescharacteristic
751C2×C4C2×#41×C6711yescharacteristic
752C2×C4C2×#41×C6711yescharacteristic
753C2×C4C2×#41×C6711yescharacteristic
754C2×C4C2×#41×C6711yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C6711yescharacteristic
788C22#525×C6711yescharacteristic
789C22#532×C6711yescharacteristic
790C22#576×C6711yescharacteristic
791C22#576×C6711yescharacteristic
792C22#576×C6711yescharacteristic
793C22#577×C6711yescharacteristic
794C4—22no—
795C4—22no—
796C4—41no—
797C4—42no—
798C4—42no—
799C4—41no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4#525×C6711yescharacteristic
805C4#525×C6711yescharacteristic
806C4#532×C6711yescharacteristic
807C4#532×C6711yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C67×#238811yescharacteristic
813C2C67×#300811yescharacteristic
814C2C67×#301211yescharacteristic
815C2C67×#311911yescharacteristic
816C2C67×#312211yescharacteristic
817C2C67×#317611yescharacteristic
818C2C67×#317911yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×#117×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C67C2semidirect
2. C2×#442×C67C2semidirect
3. C2×C4×D8×C67C2semidirect
4. C67×#2324C2semidirect
5. C67×#2059C2semidirect
6. C67×#2041C2semidirect
7. C67×#2034C2semidirect
8. C67×#2033C2semidirect
9. C67×#2025C2semidirect
10. C67×#2011C2semidirect
11. C67×#1999C2semidirect
12. C67×#1999C2semidirect
13. C67×#1762C2semidirect
14. C4×#102×C67C2semidirect
15. C67×#1750C2semidirect
103. C4×D4×C67D4semidirect
104. C4×D4×C67D4semidirect
398. #23580C67direct (N × H)
410. C2×#540C2×C67semidirect
411. C2×#442C2×C67semidirect
412. C2×C4×D8C2×C67semidirect
413. #2324C2×C67semidirect
414. #2059C2×C67semidirect
415. #2041C2×C67semidirect
416. #2034C2×C67semidirect
417. #2033C2×C67semidirect
418. #2025C2×C67semidirect
419. #2011C2×C67semidirect
420. #1999C2×C67semidirect
421. #1999C2×C67semidirect
422. #1762C2×C67semidirect
423. C4×#102C2×C67semidirect
424. #1750C2×C67semidirect
425. C67#23580direct (N × H)
513. C4×D4D4×C67semidirect
514. C4×D4D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C672
C2×#442×C672
C2×C4×D8×C672
C67×#23242
C67×#20592
C67×#20412
C67×#20342
C67×#20332
C67×#20252
C67×#20112
C67×#19992
C67×#17622
C4×#102×C672
C67×#17502
#2358067