Finite Group Databasebeta

← C67×#14098 #30693349

Subgroups — C67×#14098 #30693349

Order 17152.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C67C211yesmaximal, characteristic
2C2×#391×C67C211yesmaximal, characteristic, complemented
3C2×#388×C67C211yesmaximal, characteristic, complemented
4C2×#386×C67C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
6C67×#1446C211yesmaximal, characteristic, complemented
7C67×#1440C211yesmaximal, characteristic, complemented
8C67×#1439C211yesmaximal, characteristic, complemented
9C67×#1438C211yesmaximal, characteristic
10C67×#1437C211yesmaximal, characteristic, complemented
11C67×#1437C211yesmaximal, characteristic, complemented
12C67×#1437C211yesmaximal, characteristic, complemented
13C67×#1434C211yesmaximal, characteristic, complemented
14C67×C22⋊#95C211yesmaximal, characteristic, complemented
15C4×#95×C67C211yesmaximal, characteristic, complemented
16C23×Q8×C67C2211yescharacteristic
17C23×D4×C67C2211yescharacteristic
18C24×C4×C67C2211yescharacteristic
19C2×#124×C67—24no—
20C2×#124×C67—24no—
21C2×#124×C67C418yescomplemented
22C22×C4⋊C4×C67C2211yescharacteristic
23C22×C22⋊C4×C67C2211yescharacteristic
24C22×C22⋊C4×C67C2211yescharacteristic
25C22×C22⋊C4×C67C2211yescharacteristic
26C22×C22⋊C4×C67C2211yescharacteristic
27C22×C22⋊C4×C67C2211yescharacteristic
28C22×C22⋊C4×C67C2211yescharacteristic
29C22×C22⋊C4×C67C2211yescharacteristic
30C22×C22⋊C4×C67C2211yescharacteristic
31C22×C22⋊C4×C67C2211yescharacteristic
32C22×C22⋊C4×C67C2211yescharacteristic
33C22×C22⋊C4×C67C2211yescharacteristic
34C22×C42×C67C2211yescharacteristic
35C22×C42×C67C2211yescharacteristic
36C22×C42×C67C2211yescharacteristic
37C22×C42×C67C2211yescharacteristic
38#391×C67—24no—
39#388×C67—24no—
40#386×C67—24no—
41C4×C22⋊C4×C67—24no—
42C2×#95×C67C2211yescharacteristic
43C2×#95×C67C2211yescharacteristic
44C2×#95×C67C2211yescharacteristic
45C2×#95×C67C2211yescharacteristic
46C2×#95×C67C2211yescharacteristic
47C2×#95×C67C2211yescharacteristic
48C2×#95×C67C2211yescharacteristic
49C2×#95×C67C2211yescharacteristic
50C2×#95×C67C2211yescharacteristic
51C2×#95×C67C2211yescharacteristic
52C2×#95×C67C2211yescharacteristic
53C2×#95×C67C2211yescharacteristic
54C2×#95×C67C2211yescharacteristic
55C2×#95×C67C2211yescharacteristic
56C2×#95×C67C2211yescharacteristic
57C2×#95×C67C2211yescharacteristic
58C25×C67C2311yescharacteristic
59C25×C67C2311yescharacteristic
60C22×Q8×C67—22no—
61C22×Q8×C67—22no—
62C22×Q8×C67—22no—
63C22×Q8×C67—22no—
64C22×Q8×C67—41no—
65C22×Q8×C67—41no—
66C22×Q8×C67C2×C414yescomplemented
67C22×D4×C67—22no—
68C22×D4×C67—22no—
69C22×D4×C67—22no—
70C22×D4×C67—22no—
71C22×D4×C67—41no—
72C22×D4×C67—41no—
73C22×D4×C67C2×C414yes—
74C23×C4×C67—22no—
75C23×C4×C67—22no—
76C23×C4×C67—22no—
77C23×C4×C67—22no—
78C23×C4×C67—22no—
79C23×C4×C67—41no—
80C23×C4×C67—41no—
81C23×C4×C67C2311yescharacteristic
82C23×C4×C67C2311yescharacteristic
83C23×C4×C67C2311yescharacteristic
84C23×C4×C67C2311yescharacteristic
85C23×C4×C67C2311yescharacteristic
86C23×C4×C67C2311yescharacteristic
87C23×C4×C67C2311yescharacteristic
88C23×C4×C67C2311yescharacteristic
89C23×C4×C67C2311yescharacteristic
90C23×C4×C67C2311yescharacteristic
91C23×C4×C67C2311yescharacteristic
92C23×C4×C67C2311yescharacteristic
93C23×C4×C67C2311yescharacteristic
94#124×C67—232no—
95C2×C4⋊C4×C67—22no—
96C2×C4⋊C4×C67—22no—
97C2×C4⋊C4×C67—41no—
98C2×C22⋊C4×C67—22no—
99C2×C22⋊C4×C67—22no—
100C2×C22⋊C4×C67—22no—
101C2×C22⋊C4×C67—22no—
102C2×C22⋊C4×C67—22no—
103C2×C22⋊C4×C67—22no—
104C2×C22⋊C4×C67—22no—
105C2×C22⋊C4×C67—22no—
106C2×C22⋊C4×C67—22no—
107C2×C22⋊C4×C67—22no—
108C2×C22⋊C4×C67—22no—
109C2×C22⋊C4×C67—22no—
110C2×C22⋊C4×C67—22no—
111C2×C22⋊C4×C67—22no—
112C2×C22⋊C4×C67—22no—
113C2×C22⋊C4×C67—22no—
114C2×C22⋊C4×C67—22no—
115C2×C22⋊C4×C67—22no—
116C2×C22⋊C4×C67—22no—
117C2×C22⋊C4×C67—22no—
118C2×C22⋊C4×C67—22no—
119C2×C22⋊C4×C67—41no—
120C2×C22⋊C4×C67—41no—
121C2×C22⋊C4×C67—41no—
122C2×C22⋊C4×C67—41no—
123C2×C22⋊C4×C67—41no—
124C2×C22⋊C4×C67—41no—
125C2×C22⋊C4×C67C2×C414yes—
126C2×C22⋊C4×C67C2×C414yes—
127C2×C22⋊C4×C67C2×C414yescomplemented
128C2×C22⋊C4×C67C2×C414yescomplemented
129C2×C22⋊C4×C67D414yes—
130C2×C22⋊C4×C67D414yes—
131C2×C42×C67—22no—
132C2×C42×C67—22no—
133C2×C42×C67—22no—
134C2×C42×C67—22no—
135C2×C42×C67—22no—
136C2×C42×C67—22no—
137C2×C42×C67—22no—
138C2×C42×C67—22no—
139C2×C42×C67—41no—
140C2×C42×C67—41no—
141C2×C42×C67—41no—
142C2×C42×C67C2×C414yescomplemented
143#95×C67—22no—
144#95×C67—22no—
145#95×C67—22no—
146#95×C67—22no—
147#95×C67—22no—
148#95×C67—22no—
149#95×C67—22no—
150#95×C67—22no—
151#95×C67—22no—
152#95×C67—22no—
153#95×C67—22no—
154#95×C67—22no—
155#95×C67—22no—
156#95×C67—41no—
157#95×C67—41no—
158#95×C67D414yes—
159C24×C67—21no—
160C24×C67—21no—
161C24×C67—21no—
162C24×C67—21no—
163C24×C67—21no—
164C24×C67—21no—
165C24×C67—21no—
166C24×C67—21no—
167C24×C67—21no—
168C24×C67—21no—
169C24×C67—21no—
170C24×C67—21no—
171C24×C67—21no—
172C24×C67—21no—
173C24×C67—21no—
174C24×C67—21no—
175C24×C67—21no—
176C24×C67—21no—
177C24×C67—21no—
178C24×C67—21no—
179C24×C67—21no—
180C24×C67—21no—
181C24×C67—21no—
182C24×C67—21no—
183C24×C67—21no—
184C24×C67—21no—
185C24×C67C22×C412yes—
186C24×C67C22×C412yes—
187C24×C67C2×D412yes—
188C24×C67C2×D412yes—
189C24×C67C2411yescharacteristic
190C2×Q8×C67—28no—
191C2×Q8×C67—28no—
192C2×Q8×C67—44no—
193C2×Q8×C67—44no—
194C2×Q8×C67—44no—
195C2×Q8×C67—44no—
196C2×Q8×C67—44no—
197C2×D4×C67—28no—
198C2×D4×C67—28no—
199C2×D4×C67—44no—
200C2×D4×C67—44no—
201C2×D4×C67—44no—
202C2×D4×C67—44no—
203C2×D4×C67—44no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
208C22×C4×C67—21no—
209C22×C4×C67—21no—
210C22×C4×C67—21no—
211C22×C4×C67—21no—
212C22×C4×C67—21no—
213C22×C4×C67—21no—
214C22×C4×C67—21no—
215C22×C4×C67—21no—
216C22×C4×C67—21no—
217C22×C4×C67—21no—
218C22×C4×C67—21no—
219C22×C4×C67—21no—
220C22×C4×C67—28no—
221C22×C4×C67—21no—
222C22×C4×C67—21no—
223C22×C4×C67—21no—
224C22×C4×C67—21no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—21no—
228C22×C4×C67—21no—
229C22×C4×C67—21no—
230C22×C4×C67—21no—
231C22×C4×C67—21no—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—21no—
238C22×C4×C67—21no—
239C22×C4×C67—21no—
240C22×C4×C67—21no—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67—21no—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67—21no—
253C22×C4×C67—21no—
254C22×C4×C67—21no—
255C22×C4×C67—21no—
256C22×C4×C67—21no—
257C22×C4×C67—21no—
258C22×C4×C67—21no—
259C22×C4×C67—21no—
260C22×C4×C67—21no—
261C22×C4×C67—21no—
262C22×C4×C67—21no—
263C22×C4×C67—21no—
264C22×C4×C67—21no—
265C22×C4×C67—21no—
266C22×C4×C67—21no—
267C22×C4×C67—21no—
268C22×C4×C67—21no—
269C22×C4×C67—21no—
270C22×C4×C67—21no—
271C22×C4×C67—21no—
272C22×C4×C67—21no—
273C22×C4×C67—21no—
274C22×C4×C67—21no—
275C22×C4×C67—21no—
276C22×C4×C67—21no—
277C22×C4×C67—44no—
278C22×C4×C67—44no—
279C22×C4×C67—44no—
280C22×C4×C67—44no—
281C22×C4×C67—44no—
282C22×C4×C67—44no—
283C22×C4×C67C22×C412yes—
284C22×C4×C67C22×C412yes—
285C22×C4×C67C22×C412yes—
286C22×C4×C67C22×C412yes—
287C22×C4×C67C22×C412yes—
288C22×C4×C67C2×D412yes—
289C22×C4×C67C2×D412yes—
290C22×C4×C67C2×D412yes—
291C22×C4×C67C2×D412yes—
292C22×C4×C67C2×D412yes—
293C22×C4×C67C2×D412yes—
294C22×C4×C67C2×D412yes—
295C22×C4×C67#4112yes—
296C22×C4×C67#4112yes—
297C22×C4×C67#4112yes—
298C22×C4×C67#4112yes—
299C22×C4×C67#4112yes—
300C22×C4×C67#4112yes—
301C22×C4×C67#4112yes—
302C4⋊C4×C67—44no—
303C22⋊C4×C67—28no—
304C22⋊C4×C67—28no—
305C22⋊C4×C67—28no—
306C22⋊C4×C67—28no—
307C22⋊C4×C67—44no—
308C22⋊C4×C67—44no—
309C22⋊C4×C67—44no—
310C22⋊C4×C67—44no—
311C22⋊C4×C67—44no—
312C22⋊C4×C67—44no—
313C22⋊C4×C67C22⋊C4116yescomplemented
314C42×C67—28no—
315C42×C67—44no—
316C42×C67—44no—
317C42×C67—44no—
318C23×C67—22no—
319C23×C67—22no—
320C23×C67—22no—
321C23×C67—22no—
322C23×C67—22no—
323C23×C67—22no—
324C23×C67—22no—
325C23×C67—22no—
326C23×C67—22no—
327C23×C67—22no—
328C23×C67—22no—
329C23×C67—22no—
330C23×C67—22no—
331C23×C67—22no—
332C23×C67—22no—
333C23×C67—22no—
334C23×C67—22no—
335C23×C67—22no—
336C23×C67—22no—
337C23×C67—22no—
338C23×C67—22no—
339C23×C67—22no—
340C23×C67—22no—
341C23×C67—22no—
342C23×C67—22no—
343C23×C67—41no—
344C23×C67—41no—
345C23×C67—41no—
346C23×C67—41no—
347C23×C67—41no—
348C23×C67—41no—
349C23×C67—41no—
350C23×C67—41no—
351C23×C67—41no—
352C23×C67—41no—
353C23×C67—41no—
354C23×C67—41no—
355C23×C67—41no—
356C23×C67—41no—
357C23×C67—41no—
358C23×C67—41no—
359C23×C67—41no—
360C23×C67—41no—
361C23×C67—41no—
362C23×C67—41no—
363C23×C67—41no—
364C23×C67—41no—
365C23×C67—41no—
366C23×C67—41no—
367C23×C67—41no—
368C23×C67—41no—
369C23×C67—41no—
370C23×C67—41no—
371C23×C67—41no—
372C23×C67—41no—
373C23×C67—41no—
374C23×C67—41no—
375C23×C67—41no—
376C23×C67—41no—
377C23×C67—41no—
378C23×C67—41no—
379C23×C67—41no—
380C23×C67—41no—
381C23×C67—41no—
382C23×C67—41no—
383C23×C67—41no—
384C23×C67—41no—
385C23×C67—41no—
386C23×C67—41no—
387C23×C67C2×C22⋊C414yes—
388C23×C67C23×C411yescharacteristic
389C23×C67C22×D411yescharacteristic
390C23×C67C22×D411yescharacteristic
391C23×C67C22×D411yescharacteristic
392C23×C67C2×#4111yescharacteristic
393C23×C67C2×#4111yescharacteristic
394C23×C67C2×#4111yescharacteristic
395C23×C67C2×#4111yescharacteristic
396C23×C67C2×#4111yescharacteristic
397C23×C67C2×#4111yescharacteristic
398C23×C67C2×#4111yescharacteristic
399C23×C67H(5,𝔽2)11yescharacteristic
400C23×C67H(5,𝔽2)11yescharacteristic
401C23×C67H(5,𝔽2)11yescharacteristic
402C23×C672−1+411yescharacteristic
403Q8×C67—416no—
404D4×C67—416no—
405C2×C4×C67—22no—
406C2×C4×C67—22no—
407C2×C4×C67—22no—
408C2×C4×C67—22no—
409C2×C4×C67—22no—
410C2×C4×C67—22no—
411C2×C4×C67—22no—
412C2×C4×C67—22no—
413C2×C4×C67—22no—
414C2×C4×C67—22no—
415C2×C4×C67—22no—
416C2×C4×C67—22no—
417C2×C4×C67—22no—
418C2×C4×C67—22no—
419C2×C4×C67—22no—
420C2×C4×C67—22no—
421C2×C4×C67—22no—
422C2×C4×C67—22no—
423C2×C4×C67—22no—
424C2×C4×C67—22no—
425C2×C4×C67—22no—
426C2×C4×C67—22no—
427C2×C4×C67—22no—
428C2×C4×C67—22no—
429C2×C4×C67—22no—
430C2×C4×C67—22no—
431C2×C4×C67—22no—
432C2×C4×C67—22no—
433C2×C4×C67—22no—
434C2×C4×C67—22no—
435C2×C4×C67—22no—
436C2×C4×C67—22no—
437C2×C4×C67—22no—
438C2×C4×C67—22no—
439C2×C4×C67—22no—
440C2×C4×C67—22no—
441C2×C4×C67—22no—
442C2×C4×C67—22no—
443C2×C4×C67—22no—
444C2×C4×C67—22no—
445C2×C4×C67—22no—
446C2×C4×C67—22no—
447C2×C4×C67—22no—
448C2×C4×C67—22no—
449C2×C4×C67—22no—
450C2×C4×C67—416no—
451C2×C4×C67—41no—
452C2×C4×C67—41no—
453C2×C4×C67—41no—
454C2×C4×C67—41no—
455C2×C4×C67—41no—
456C2×C4×C67—41no—
457C2×C4×C67—41no—
458C2×C4×C67—41no—
459C2×C4×C67—41no—
460C2×C4×C67—41no—
461C2×C4×C67—41no—
462C2×C4×C67—41no—
463C2×C4×C67—41no—
464C2×C4×C67—41no—
465C2×C4×C67—41no—
466C2×C4×C67—41no—
467C2×C4×C67—41no—
468C2×C4×C67—41no—
469C2×C4×C67—41no—
470C2×C4×C67—41no—
471C2×C4×C67—41no—
472C2×C4×C67—41no—
473C2×C4×C67—41no—
474C2×C4×C67—41no—
475C2×C4×C67—41no—
476C2×C4×C67—41no—
477C2×C4×C67—41no—
478C2×C4×C67—41no—
479C2×C4×C67—41no—
480C2×C4×C67—41no—
481C2×C4×C67—41no—
482C2×C4×C67—41no—
483C2×C4×C67—41no—
484C2×C4×C67—41no—
485C2×C4×C67—41no—
486C2×C4×C67—41no—
487C2×C4×C67—41no—
488C2×C4×C67—41no—
489C2×C4×C67—41no—
490C2×C4×C67—41no—
491C2×C4×C67—41no—
492C2×C4×C67—41no—
493C2×C4×C67C2×C22⋊C414yes—
494C2×C4×C67C2×C22⋊C414yes—
495C2×C4×C67C4×D414yes—
496C2×C4×C67#12414yescomplemented
497C22×C67—24no—
498C22×C67—24no—
499C22×C67—24no—
500C22×C67—42no—
501C22×C67—42no—
502C22×C67—42no—
503C22×C67—42no—
504C22×C67—42no—
505C22×C67—42no—
506C22×C67—42no—
507C22×C67—42no—
508C22×C67—42no—
509C22×C67—42no—
510C22×C67—42no—
511C22×C67—42no—
512C22×C67—42no—
513C22×C67—42no—
514C22×C67—42no—
515C22×C67—42no—
516C22×C67—42no—
517C22×C67—42no—
518C22×C67—42no—
519C22×C67—81no—
520C22×C67—81no—
521C22×C67—81no—
522C22×C67—81no—
523C22×C67—81no—
524C22×C67—81no—
525C22×C67—81no—
526C22×C67—81no—
527C22×C67C22×C22⋊C411yescharacteristic
528C22×C67C2×C4×D411yescharacteristic
529C22×C67C4×#4111yescharacteristic
530C22×C67C4×#4111yescharacteristic
531C22×C67C4×#4111yescharacteristic
532C22×C67#51811yescharacteristic
533C22×C67#52011yescharacteristic
534C22×C67#52511yescharacteristic
535C22×C67#52511yescharacteristic
536C22×C67C2×#12411yescharacteristic
537C22×C67#52911yescharacteristic
538C22×C67#52911yescharacteristic
539C22×C67#53211yescharacteristic
540C22×C67#53211yescharacteristic
541C22×C67#53211yescharacteristic
542C22×C67#53811yescharacteristic
543C22×C67#53811yescharacteristic
544C22×C67#54211yescharacteristic
545C22×C67#54211yescharacteristic
546C22×C67D4211yescharacteristic
547C22×C67D4211yescharacteristic
548C22×C67#54611yescharacteristic
549C22×C67#54611yescharacteristic
550C22×C67#54611yescharacteristic
551C22×C67#54611yescharacteristic
552C22×C67#54611yescharacteristic
553C22×C67#54711yescharacteristic
554C22×C67#54711yescharacteristic
555C22×C67#54811yescharacteristic
556C22×C67#55111yescharacteristic
557C22×C67#55111yescharacteristic
558C22×C67#55511yescharacteristic
559C22×C67#55511yescharacteristic
560C22×C67#55611yescharacteristic
561C22×C67#55911yescharacteristic
562C4×C67—24no—
563C4×C67—24no—
564C4×C67—24no—
565C4×C67—24no—
566C4×C67—42no—
567C4×C67—42no—
568C4×C67—42no—
569C4×C67—42no—
570C4×C67—42no—
571C4×C67—42no—
572C4×C67—42no—
573C4×C67—81no—
574C4×C67—81no—
575#14098C6711yesmaximal, characteristic, direct product factor, Sylow
576C2×C67—44no—
577C2×C67—82no—
578C2×C67#229711yescharacteristic
579C2×C67C4×#12411yescharacteristic
580C2×C67#233711yescharacteristic
581C2×C67D4×C22⋊C411yescharacteristic
582C2×C67#233911yescharacteristic
583C2×C67#236711yescharacteristic
584C2×C67#237211yescharacteristic
585C2×C67#245911yescharacteristic
586C2×C67#246111yescharacteristic
587C2×C67#247211yescharacteristic
588C2×C67#247411yescharacteristic
589C2×C67#249111yescharacteristic
590C2×C67#252111yescharacteristic
591C2×C67#255511yescharacteristic
592C2×C67#255711yescharacteristic
593C22×#124C2×C6711yescharacteristic
594C2×#391C2×C6711yescharacteristic, complemented
595C2×#388C2×C6711yescharacteristic, complemented
596C2×#386C2×C6711yescharacteristic
597C2×C4×C22⋊C4C2×C6711yescharacteristic, complemented
598#1446C2×C6711yescharacteristic, complemented
599#1440C2×C6711yescharacteristic, complemented
600#1439C2×C6711yescharacteristic, complemented
601#1438C2×C6711yescharacteristic
602#1437C2×C6711yescharacteristic, complemented
603#1437C2×C6711yescharacteristic, complemented
604#1437C2×C6711yescharacteristic, complemented
605#1434C2×C6711yescharacteristic, complemented
606C22⋊#95C2×C6711yescharacteristic, complemented
607C4×#95C2×C6711yescharacteristic, complemented
608C67#1409811yescharacteristic, direct product factor, Sylow
609C23×Q8C22×C6711yescharacteristic
610C23×D4C22×C6711yescharacteristic
611C24×C4C22×C6711yescharacteristic
612C2×#124—24no—
613C2×#124—24no—
614C2×#124C4×C6718yescomplemented
615C22×C4⋊C4C22×C6711yescharacteristic
616C22×C22⋊C4C22×C6711yescharacteristic
617C22×C22⋊C4C22×C6711yescharacteristic
618C22×C22⋊C4C22×C6711yescharacteristic
619C22×C22⋊C4C22×C6711yescharacteristic
620C22×C22⋊C4C22×C6711yescharacteristic
621C22×C22⋊C4C22×C6711yescharacteristic
622C22×C22⋊C4C22×C6711yescharacteristic
623C22×C22⋊C4C22×C6711yescharacteristic
624C22×C22⋊C4C22×C6711yescharacteristic
625C22×C22⋊C4C22×C6711yescharacteristic
626C22×C22⋊C4C22×C6711yescharacteristic
627C22×C42C22×C6711yescharacteristic
628C22×C42C22×C6711yescharacteristic
629C22×C42C22×C6711yescharacteristic
630C22×C42C22×C6711yescharacteristic
631#391—24no—
632#388—24no—
633#386—24no—
634C4×C22⋊C4—24no—
635C2×#95C22×C6711yescharacteristic
636C2×#95C22×C6711yescharacteristic
637C2×#95C22×C6711yescharacteristic
638C2×#95C22×C6711yescharacteristic
639C2×#95C22×C6711yescharacteristic
640C2×#95C22×C6711yescharacteristic
641C2×#95C22×C6711yescharacteristic
642C2×#95C22×C6711yescharacteristic
643C2×#95C22×C6711yescharacteristic
644C2×#95C22×C6711yescharacteristic
645C2×#95C22×C6711yescharacteristic
646C2×#95C22×C6711yescharacteristic
647C2×#95C22×C6711yescharacteristic
648C2×#95C22×C6711yescharacteristic
649C2×#95C22×C6711yescharacteristic
650C2×#95C22×C6711yescharacteristic
651C25C23×C6711yescharacteristic
652C25C23×C6711yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C2×C4×C6714yescomplemented
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C2×C4×C6714yes—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4C23×C6711yescharacteristic
675C23×C4C23×C6711yescharacteristic
676C23×C4C23×C6711yescharacteristic
677C23×C4C23×C6711yescharacteristic
678C23×C4C23×C6711yescharacteristic
679C23×C4C23×C6711yescharacteristic
680C23×C4C23×C6711yescharacteristic
681C23×C4C23×C6711yescharacteristic
682C23×C4C23×C6711yescharacteristic
683C23×C4C23×C6711yescharacteristic
684C23×C4C23×C6711yescharacteristic
685C23×C4C23×C6711yescharacteristic
686C23×C4C23×C6711yescharacteristic
687#124—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4C2×C4×C6714yes—
719C2×C22⋊C4C2×C4×C6714yes—
720C2×C22⋊C4C2×C4×C6714yescomplemented
721C2×C22⋊C4C2×C4×C6714yescomplemented
722C2×C22⋊C4D4×C6714yes—
723C2×C22⋊C4D4×C6714yes—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—41no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42C2×C4×C6714yescomplemented
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—22no—
749#95—41no—
750#95—41no—
751#95D4×C6714yes—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×C4×C6712yes—
779C24C22×C4×C6712yes—
780C24C2×D4×C6712yes—
781C24C2×D4×C6712yes—
782C24C24×C6711yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—28no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4C22×C4×C6712yes—
877C22×C4C22×C4×C6712yes—
878C22×C4C22×C4×C6712yes—
879C22×C4C22×C4×C6712yes—
880C22×C4C22×C4×C6712yes—
881C22×C4C2×D4×C6712yes—
882C22×C4C2×D4×C6712yes—
883C22×C4C2×D4×C6712yes—
884C22×C4C2×D4×C6712yes—
885C22×C4C2×D4×C6712yes—
886C22×C4C2×D4×C6712yes—
887C22×C4C2×D4×C6712yes—
888C22×C4#41×C6712yes—
889C22×C4#41×C6712yes—
890C22×C4#41×C6712yes—
891C22×C4#41×C6712yes—
892C22×C4#41×C6712yes—
893C22×C4#41×C6712yes—
894C22×C4#41×C6712yes—
895C4⋊C4—44no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4C22⋊C4×C67116yescomplemented
907C42—28no—
908C42—44no—
909C42—44no—
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊C4×C6714yes—
981C23C23×C4×C6711yescharacteristic
982C23C22×D4×C6711yescharacteristic
983C23C22×D4×C6711yescharacteristic
984C23C22×D4×C6711yescharacteristic
985C23C2×#41×C6711yescharacteristic
986C23C2×#41×C6711yescharacteristic
987C23C2×#41×C6711yescharacteristic
988C23C2×#41×C6711yescharacteristic
989C23C2×#41×C6711yescharacteristic
990C23C2×#41×C6711yescharacteristic
991C23C2×#41×C6711yescharacteristic
992C23H(5,𝔽2)×C6711yescharacteristic
993C23H(5,𝔽2)×C6711yescharacteristic
994C23H(5,𝔽2)×C6711yescharacteristic
995C232−1+4×C6711yescharacteristic
996Q8—416no—
997D4—416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—416no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4C2×C22⋊C4×C6714yes—
1087C2×C4C2×C22⋊C4×C6714yes—
1088C2×C4C4×D4×C6714yes—
1089C2×C4#124×C6714yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C22⋊C4×C6711yescharacteristic
1121C22C2×C4×D4×C6711yescharacteristic
1122C22C4×#41×C6711yescharacteristic
1123C22C4×#41×C6711yescharacteristic
1124C22C4×#41×C6711yescharacteristic
1125C22#518×C6711yescharacteristic
1126C22#520×C6711yescharacteristic
1127C22#525×C6711yescharacteristic
1128C22#525×C6711yescharacteristic
1129C22C2×#124×C6711yescharacteristic
1130C22#529×C6711yescharacteristic
1131C22#529×C6711yescharacteristic
1132C22#532×C6711yescharacteristic
1133C22#532×C6711yescharacteristic
1134C22#532×C6711yescharacteristic
1135C22#538×C6711yescharacteristic
1136C22#538×C6711yescharacteristic
1137C22#542×C6711yescharacteristic
1138C22#542×C6711yescharacteristic
1139C22D42×C6711yescharacteristic
1140C22D42×C6711yescharacteristic
1141C22#546×C6711yescharacteristic
1142C22#546×C6711yescharacteristic
1143C22#546×C6711yescharacteristic
1144C22#546×C6711yescharacteristic
1145C22#546×C6711yescharacteristic
1146C22#547×C6711yescharacteristic
1147C22#547×C6711yescharacteristic
1148C22#548×C6711yescharacteristic
1149C22#551×C6711yescharacteristic
1150C22#551×C6711yescharacteristic
1151C22#555×C6711yescharacteristic
1152C22#555×C6711yescharacteristic
1153C22#556×C6711yescharacteristic
1154C22#559×C6711yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—82no—
1170C2C67×#229711yescharacteristic
1171C2C4×#124×C6711yescharacteristic
1172C2C67×#233711yescharacteristic
1173C2D4×C22⋊C4×C6711yescharacteristic
1174C2C67×#233911yescharacteristic
1175C2C67×#236711yescharacteristic
1176C2C67×#237211yescharacteristic
1177C2C67×#245911yescharacteristic
1178C2C67×#246111yescharacteristic
1179C2C67×#247211yescharacteristic
1180C2C67×#247411yescharacteristic
1181C2C67×#249111yescharacteristic
1182C2C67×#252111yescharacteristic
1183C2C67×#255511yescharacteristic
1184C2C67×#255711yescharacteristic
subgroupG/H
center, socleC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC23×D4×C67C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#391×C67C2semidirect
3. C2×#388×C67C2semidirect
5. C2×C4×C22⋊C4×C67C2semidirect
6. C67×#1446C2semidirect
7. C67×#1440C2semidirect
8. C67×#1439C2semidirect
10. C67×#1437C2semidirect
11. C67×#1437C2semidirect
12. C67×#1437C2semidirect
13. C67×#1434C2semidirect
14. C67×C22⋊#95C2semidirect
15. C4×#95×C67C2semidirect
21. C2×#124×C67C4semidirect
66. C22×Q8×C67C2×C4semidirect
127. C2×C22⋊C4×C67C2×C4semidirect
128. C2×C22⋊C4×C67C2×C4semidirect
142. C2×C42×C67C2×C4semidirect
313. C22⋊C4×C67C22⋊C4semidirect
496. C2×C4×C67#124semidirect
575. #14098C67direct (N × H)
594. C2×#391C2×C67semidirect
595. C2×#388C2×C67semidirect
597. C2×C4×C22⋊C4C2×C67semidirect
598. #1446C2×C67semidirect
599. #1440C2×C67semidirect
600. #1439C2×C67semidirect
602. #1437C2×C67semidirect
603. #1437C2×C67semidirect
604. #1437C2×C67semidirect
605. #1434C2×C67semidirect
606. C22⋊#95C2×C67semidirect
607. C4×#95C2×C67semidirect
608. C67#14098direct (N × H)
614. C2×#124C4×C67semidirect
659. C22×Q8C2×C4×C67semidirect
720. C2×C22⋊C4C2×C4×C67semidirect
721. C2×C22⋊C4C2×C4×C67semidirect
735. C2×C42C2×C4×C67semidirect
906. C22⋊C4C22⋊C4×C67semidirect
1089. C2×C4#124×C67semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C672
C2×#391×C672
C2×#388×C672
C2×#386×C672
C2×C4×C22⋊C4×C672
C67×#14462
C67×#14402
C67×#14392
C67×#14382
C67×#14372
C67×#14342
C67×C22⋊#952
C4×#95×C672
#1409867