Finite Group Databasebeta

← #30779557

Subgroups — #30779557

Order 17152.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863294C211yesmaximal, characteristic
2C2×#16863294C211yesmaximal, characteristic
3C2×#16863294C211yesmaximal, characteristic
4C2×C4×C4⋊Dic67C211yesmaximal, characteristic
5#22558472C212yesmaximal
6#22558460C212yesmaximal
7#22558441C212yesmaximal
8#22558439C211yesmaximal, characteristic
9#22558439C211yesmaximal, characteristic
10Dic67⋊#95C212yesmaximal
11C2×C4×C4⋊C4×C67C211yesmaximal, characteristic
12C22×C4⋊Dic67C2211yescharacteristic
13C22×C4⋊Dic67C2211yescharacteristic
14C22×C4⋊Dic67C2211yescharacteristic
15C22×C4⋊Dic67C2211yescharacteristic
16C22×Dic67⋊C4C2212yes—
17C22×Dic67⋊C4C2212yes—
18C22×Dic67⋊C4C2212yes—
19C22×C4×Dic67C2212yes—
20#16863294—24no—
21#16863294—24no—
22#16863294C418yescomplemented
23C4×C4⋊Dic67—24no—
24C2×C67⋊#95C2212yes—
25C2×C67⋊#95C2212yes—
26C2×C67⋊#95C2212yes—
27C2×C67⋊#95C2212yes—
28C2×C67⋊#95C2212yes—
29C2×C67⋊#95C2212yes—
30C2×C67⋊#95C2212yes—
31C2×C67⋊#95C2212yes—
32C22×C4⋊C4×C67C2211yescharacteristic
33C22×C4⋊C4×C67C2211yescharacteristic
34C22×C42×C67C2211yescharacteristic
35C22×C42×C67C2211yescharacteristic
36C22×C42×C67C2211yescharacteristic
37C4×C4⋊C4×C67—24no—
38C2×#95×C67C2211yescharacteristic
39C2×#95×C67C2211yescharacteristic
40C23×Dic67C2312yes—
41C23×Dic67C2312yes—
42C23×Dic67C2312yes—
43C23×Dic67C2312yes—
44C2×C4⋊Dic67—22no—
45C2×C4⋊Dic67—22no—
46C2×C4⋊Dic67—22no—
47C2×C4⋊Dic67—22no—
48C2×C4⋊Dic67—22no—
49C2×C4⋊Dic67—22no—
50C2×C4⋊Dic67—22no—
51C2×C4⋊Dic67C2×C414yes—
52C2×C4⋊Dic67C2×C414yes—
53C2×C4⋊Dic67D414yes—
54C2×C4⋊Dic67Q814yes—
55C2×C4⋊Dic67Q814yes—
56C2×Dic67⋊C4—24no—
57C2×Dic67⋊C4—24no—
58C2×Dic67⋊C4—24no—
59C2×Dic67⋊C4—42no—
60C2×Dic67⋊C4—42no—
61C2×Dic67⋊C4—42no—
62C2×Dic67⋊C4—42no—
63C2×Dic67⋊C4—42no—
64C2×Dic67⋊C4C2×C418yes—
65C2×C4×Dic67—24no—
66C2×C4×Dic67—24no—
67C2×C4×Dic67—42no—
68C67⋊#95—24no—
69C67⋊#95—24no—
70C67⋊#95—24no—
71C67⋊#95—24no—
72C67⋊#95—42no—
73C67⋊#95—42no—
74C67⋊#95—42no—
75C67⋊#95C2×C418yes—
76C23×C4×C67C2311yescharacteristic
77C23×C4×C67C2311yescharacteristic
78C23×C4×C67C2311yescharacteristic
79C23×C4×C67C2311yescharacteristic
80C23×C4×C67C2311yescharacteristic
81C23×C4×C67C2311yescharacteristic
82C23×C4×C67C2311yescharacteristic
83C2×C4⋊C4×C67—22no—
84C2×C4⋊C4×C67—22no—
85C2×C4⋊C4×C67—22no—
86C2×C4⋊C4×C67—22no—
87C2×C4⋊C4×C67—22no—
88C2×C4⋊C4×C67Q814yes—
89C2×C42×C67—22no—
90C2×C42×C67—22no—
91C2×C42×C67—22no—
92C2×C42×C67—22no—
93C2×C42×C67—22no—
94C2×C42×C67—22no—
95C2×C42×C67—22no—
96C2×C42×C67C2×C414yes—
97C2×C42×C67D414yes—
98#95×C67—22no—
99#95×C67—22no—
100C22×Dic67—22no—
101C22×Dic67—22no—
102C22×Dic67—22no—
103C22×Dic67—22no—
104C22×Dic67—22no—
105C22×Dic67—22no—
106C22×Dic67—22no—
107C22×Dic67—22no—
108C22×Dic67—22no—
109C22×Dic67—22no—
110C22×Dic67—22no—
111C22×Dic67—22no—
112C22×Dic67—22no—
113C22×Dic67—22no—
114C22×Dic67—22no—
115C22×Dic67—22no—
116C22×Dic67—22no—
117C22×Dic67—22no—
118C22×Dic67—22no—
119C22×Dic67—22no—
120C22×Dic67—22no—
121C22×Dic67—22no—
122C22×Dic67—22no—
123C22×Dic67C22×C414yes—
124C22×Dic67C22×C414yes—
125C22×Dic67C2×D414yes—
126C22×Dic67C2×Q814yes—
127C22×Dic67C2×Q814yes—
128C4⋊Dic67—28no—
129C4⋊Dic67—28no—
130C4⋊Dic67—44no—
131C4⋊Dic67C4⋊C4116yescomplemented
132Dic67⋊C4—48no—
133Dic67⋊C4—48no—
134Dic67⋊C4—48no—
135C4×Dic67—48no—
136C24×C67C2411yescharacteristic
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—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—21no—
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×C67C22×C412yes—
170C22×C4×C67C22×C412yes—
171C22×C4×C67C22×C412yes—
172C22×C4×C67C2×D412yes—
173C22×C4×C67C2×D412yes—
174C22×C4×C67C2×D412yes—
175C22×C4×C67C2×D412yes—
176C22×C4×C67C2×Q812yes—
177C22×C4×C67C2×Q812yes—
178C22×C4×C67C2×Q812yes—
179C22×C4×C67C2×Q812yes—
180C22×C4×C67C2×Q812yes—
181C22×C4×C67#4112yes—
182C22×C4×C67#4112yes—
183C22×C4×C67#4112yes—
184C22×C4×C67#4112yes—
185C22×C4×C67#4112yes—
186C4⋊C4×C67—28no—
187C4⋊C4×C67—28no—
188C42×C67—28no—
189C42×C67—28no—
190C42×C67—44no—
191C23×C67C23×C411yescharacteristic
192C23×C67C22×D411yescharacteristic
193C23×C67C22×D411yescharacteristic
194C23×C67C22×Q811yescharacteristic
195C23×C67C22×Q811yescharacteristic
196C23×C67C22×Q811yescharacteristic
197C23×C67C2×#4111yescharacteristic
198C23×C67C2×#4111yescharacteristic
199C23×C67C2×#4111yescharacteristic
200C23×C67C2×#4111yescharacteristic
201C23×C67C2×#4111yescharacteristic
202C23×C67H(5,𝔽2)11yescharacteristic
203C23×C67H(5,𝔽2)11yescharacteristic
204C23×C67H(5,𝔽2)11yescharacteristic
205C23×C672−1+411yescharacteristic
206C2×C4×C67—22no—
207C2×C4×C67—22no—
208C2×C4×C67—22no—
209C2×C4×C67—22no—
210C2×C4×C67—22no—
211C2×C4×C67—22no—
212C2×C4×C67—22no—
213C2×C4×C67—22no—
214C2×C4×C67—22no—
215C2×C4×C67—22no—
216C2×C4×C67—22no—
217C2×C4×C67—22no—
218C2×C4×C67—22no—
219C2×C4×C67—22no—
220C2×C4×C67—22no—
221C2×C4×C67—22no—
222C2×C4×C67—22no—
223C2×C4×C67—22no—
224C2×C4×C67—22no—
225C2×C4×C67—22no—
226C2×C4×C67—22no—
227C2×C4×C67—22no—
228C2×C4×C67—22no—
229C2×C4×C67—22no—
230C2×C4×C67—41no—
231C2×C4×C67—41no—
232C2×C4×C67—41no—
233C2×C4×C67—41no—
234C2×C4×C67—41no—
235C2×C4×C67—41no—
236C2×C4×C67—41no—
237C2×C4×C67—41no—
238C2×C4×C67—41no—
239C2×C4×C67—41no—
240C2×C4×C67—41no—
241C2×C4×C67—41no—
242C2×C4×C67—41no—
243C2×C4×C67—41no—
244C2×C4×C67—41no—
245C2×C4×C67—41no—
246C2×C4×C67C2×C4⋊C414yes—
247C2×C4×C67C4×D414yes—
248C2×C4×C67C4×Q814yes—
249C2×C4×C67C4×Q814yes—
250C2×C4×C67#12114yes—
251C2×C4×C67C22⋊Q814yes—
252C2×C4×C67C22⋊Q814yes—
253C2×C4×C67#12514yes—
254C2×C4×C67C4⋊Q814yes—
255C2×Dic67—24no—
256C2×Dic67—24no—
257C2×Dic67—24no—
258C2×Dic67—24no—
259C2×Dic67—24no—
260C2×Dic67—24no—
261C2×Dic67—24no—
262C2×Dic67—24no—
263C2×Dic67—24no—
264C2×Dic67—24no—
265C2×Dic67—24no—
266C2×Dic67—24no—
267C2×Dic67—42no—
268C2×Dic67—42no—
269C2×Dic67—42no—
270C2×Dic67—42no—
271C2×Dic67—42no—
272C2×Dic67—42no—
273C2×Dic67—42no—
274C2×Dic67—42no—
275C2×Dic67—42no—
276C2×Dic67—42no—
277C2×Dic67—42no—
278C2×Dic67—42no—
279C2×Dic67—42no—
280C2×Dic67—42no—
281C2×Dic67—42no—
282C2×Dic67C2×C4⋊C418yes—
283C22×C67C22×C4⋊C411yescharacteristic
284C22×C67C2×C4×D411yescharacteristic
285C22×C67C2×C4×Q811yescharacteristic
286C22×C67C2×C4×Q811yescharacteristic
287C22×C67C4×#4111yescharacteristic
288C22×C67#51811yescharacteristic
289C22×C67#52011yescharacteristic
290C22×C67C2×#12111yescharacteristic
291C22×C67C2×C22⋊Q811yescharacteristic
292C22×C67C2×C22⋊Q811yescharacteristic
293C22×C67#52511yescharacteristic
294C22×C67C2×#12511yescharacteristic
295C22×C67#52911yescharacteristic
296C22×C67C2×C4⋊Q811yescharacteristic
297C22×C67#53311yescharacteristic
298C22×C67#53511yescharacteristic
299C22×C67#53711yescharacteristic
300C22×C67#54011yescharacteristic
301C22×C67#54211yescharacteristic
302C22×C67#54611yescharacteristic
303C22×C67#54611yescharacteristic
304C22×C67D4×Q811yescharacteristic
305C22×C67#55011yescharacteristic
306C22×C67#55211yescharacteristic
307C22×C67#55311yescharacteristic
308C22×C67#55411yescharacteristic
309C22×C67#55411yescharacteristic
310C22×C67#55411yescharacteristic
311C22×C67#55411yescharacteristic
312C22×C67#55411yescharacteristic
313C22×C67#55511yescharacteristic
314C22×C67#55711yescharacteristic
315C22×C67#55711yescharacteristic
316C22×C67Q8211yescharacteristic
317C22×C67Q8211yescharacteristic
318C4×C67—24no—
319C4×C67—24no—
320C4×C67—42no—
321C4×C67—42no—
322C4×C67—42no—
323C4×C67—42no—
324C4×C67#38918yes—
325Dic67—28no—
326Dic67—44no—
327Dic67—44no—
328Dic67—82no—
329#14045—671nomaximal, Sylow
330C2×C67C2×#38911yescharacteristic
331C2×C67C4×C22⋊Q811yescharacteristic
332C2×C67#232411yescharacteristic
333C2×C67#234911yescharacteristic
334C2×C67Q8×C4⋊C411yescharacteristic
335C2×C67#236911yescharacteristic
336C2×C67#237011yescharacteristic
337C2×C67#241411yescharacteristic
338C2×C67#241711yescharacteristic
339C2×C67#245111yescharacteristic
340C2×C67#245411yescharacteristic
341C2×C67#250711yescharacteristic
342C2×C67#250811yescharacteristic
343C2×C67#256711yescharacteristic
344C2×C67#258411yescharacteristic
345C2×#389—671no—
346C2×#389—671no—
347C2×#389—671no—
348C2×C4×C4⋊C4—671no—
349C2×C4×C4⋊C4D6711yescharacteristic
350#1444—672no—
351#1441—672no—
352#1436—672no—
353C4⋊#95—671no—
354C4⋊#95—671no—
355C4⋊#95—672no—
356C67#1404511yescharacteristic, complemented, Sylow
357C22×C4⋊C4—672no—
358C22×C4⋊C4—672no—
359C22×C4⋊C4—672no—
360C22×C4⋊C4—671no—
361C22×C4⋊C4—671no—
362C22×C4⋊C4—671no—
363C22×C4⋊C4—671no—
364C22×C4⋊C4C2×D6711yescharacteristic
365C22×C4⋊C4C2×D6711yescharacteristic
366C22×C42—672no—
367C22×C42C2×D6711yescharacteristic
368C22×C42C2×D6711yescharacteristic
369C22×C42C2×D6711yescharacteristic
370#389—678no—
371#389—1344no—
372#389—1344no—
373C4×C4⋊C4—24no—
374C4×C4⋊C4—1344no—
375C2×#95—672no—
376C2×#95—672no—
377C2×#95—672no—
378C2×#95—672no—
379C2×#95—672no—
380C2×#95—672no—
381C2×#95—672no—
382C2×#95—672no—
383C2×#95C2×D6711yescharacteristic
384C2×#95C2×D6711yescharacteristic
385C23×C4—672no—
386C23×C4—672no—
387C23×C4—672no—
388C23×C4—672no—
389C23×C4C22×D6711yescharacteristic
390C23×C4C22×D6711yescharacteristic
391C23×C4C22×D6711yescharacteristic
392C23×C4C22×D6711yescharacteristic
393C23×C4C22×D6711yescharacteristic
394C23×C4C22×D6711yescharacteristic
395C23×C4C22×D6711yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—2682no—
402C2×C4⋊C4—2682no—
403C2×C4⋊C4—2682no—
404C2×C4⋊C4—2682no—
405C2×C4⋊C4—2682no—
406C2×C4⋊C4—678no—
407C2×C4⋊C4—674no—
408C2×C4⋊C4—674no—
409C2×C4⋊C4—674no—
410C2×C4⋊C4—674no—
411C2×C4⋊C4—674no—
412C2×C4⋊C4—1344no—
413C2×C4⋊C4—1342no—
414C2×C4⋊C4—1344no—
415C2×C4⋊C4—1342no—
416C2×C4⋊C4—1342no—
417C2×C4⋊C4—1344no—
418C2×C4⋊C4—1342no—
419C2×C4⋊C4—1342no—
420C2×C4⋊C4—1342no—
421C2×C4⋊C4—1342no—
422C2×C4⋊C4Dic13414yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—2682no—
431C2×C42—1344no—
432C2×C42—1344no—
433C2×C42C4×D6714yes—
434C2×C42C22⋊D6714yes—
435#95—22no—
436#95—22no—
437#95—2682no—
438#95—2682no—
439#95—2682no—
440#95—678no—
441#95—1344no—
442#95—1344no—
443#95—1344no—
444#95—1344no—
445C24C23×D6711yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
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—674no—
479C22×C4—674no—
480C22×C4—674no—
481C22×C4—674no—
482C22×C4—674no—
483C22×C4—1342no—
484C22×C4—1342no—
485C22×C4—1342no—
486C22×C4—1342no—
487C22×C4—1342no—
488C22×C4—1342no—
489C22×C4—1342no—
490C22×C4—1342no—
491C22×C4—1342no—
492C22×C4—1342no—
493C22×C4—1342no—
494C22×C4—1342no—
495C22×C4—1342no—
496C22×C4—1342no—
497C22×C4—1342no—
498C22×C4—1342no—
499C22×C4—1342no—
500C22×C4—1342no—
501C22×C4—1342no—
502C22×C4—1342no—
503C22×C4—1342no—
504C22×C4—1342no—
505C22×C4—1342no—
506C22×C4C2×C4×D6712yes—
507C22×C4C2×C4×D6712yes—
508C22×C4C2×C4×D6712yes—
509C22×C4D4×D6712yes—
510C22×C4C2×C22⋊D6712yes—
511C22×C4C2×C22⋊D6712yes—
512C22×C4C2×C22⋊D6712yes—
513C22×C4Q8×D6712yes—
514C22×C4Q8×D6712yes—
515C22×C4C2×Dic13412yes—
516C22×C4C2×Dic13412yes—
517C22×C4C2×Dic13412yes—
518C22×C4#1176162712yes—
519C22×C4#1176162812yes—
520C22×C4#1176162812yes—
521C22×C4#1176162812yes—
522C22×C4#1176162812yes—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—2688no—
526C4⋊C4—2688no—
527C4⋊C4—2688no—
528C4⋊C4—2684no—
529C4⋊C4—6716no—
530C4⋊C4—1348no—
531C4⋊C4—1348no—
532C42—28no—
533C42—28no—
534C42—44no—
535C42—2688no—
536C23C22×C4×D6711yescharacteristic
537C23C2×D4×D6711yescharacteristic
538C23C22×C22⋊D6711yescharacteristic
539C23C2×Q8×D6711yescharacteristic
540C23C2×Q8×D6711yescharacteristic
541C23C22×Dic13411yescharacteristic
542C23C2×#1176162711yescharacteristic
543C23C2×#1176162811yescharacteristic
544C23C2×#1176162811yescharacteristic
545C23C2×#1176162811yescharacteristic
546C23C2×#1176162811yescharacteristic
547C23#1452408911yescharacteristic
548C23#1452408911yescharacteristic
549C23#1452408911yescharacteristic
550C23#1452409011yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—2682no—
592C2×C4—2682no—
593C2×C4—2682no—
594C2×C4—2682no—
595C2×C4—2682no—
596C2×C4—2682no—
597C2×C4—2682no—
598C2×C4—2682no—
599C2×C4—2682no—
600C2×C4—2682no—
601C2×C4—2682no—
602C2×C4—2682no—
603C2×C4—2682no—
604C2×C4—2682no—
605C2×C4—2682no—
606C2×C4—678no—
607C2×C4—1344no—
608C2×C4—1344no—
609C2×C4—1344no—
610C2×C4—1344no—
611C2×C4—1344no—
612C2×C4—1344no—
613C2×C4—1344no—
614C2×C4—1344no—
615C2×C4—1344no—
616C2×C4—1344no—
617C2×C4—1344no—
618C2×C4—1344no—
619C2×C4C4⋊C4×D6714yes—
620C2×C4C4×C22⋊D6714yes—
621C2×C4#1452400814yes—
622C2×C4C4×Dic13414yes—
623C2×C4#1452401514yes—
624C2×C4#1452402114yes—
625C2×C4#1452402214yes—
626C2×C4#1452403314yes—
627C2×C4#1452404114yes—
628C22C2×C4⋊C4×D6711yescharacteristic
629C22C2×C4×C22⋊D6711yescharacteristic
630C22C2×#1452400811yescharacteristic
631C22C2×C4×Dic13411yescharacteristic
632C22C4×#1176162811yescharacteristic
633C22#1686387011yescharacteristic
634C22#1686387611yescharacteristic
635C22C2×#1452401511yescharacteristic
636C22C2×#1452402111yescharacteristic
637C22C2×#1452402211yescharacteristic
638C22#1686390711yescharacteristic
639C22C2×#1452403311yescharacteristic
640C22#1686393011yescharacteristic
641C22C2×#1452404111yescharacteristic
642C22#1686395311yescharacteristic
643C22#1686396011yescharacteristic
644C22#1686397411yescharacteristic
645C22#1686400111yescharacteristic
646C22#1686401711yescharacteristic
647C22#1686404211yescharacteristic
648C22#1686404211yescharacteristic
649C22D4×Dic13411yescharacteristic
650C22#1686406711yescharacteristic
651C22#1686408611yescharacteristic
652C22#1686409211yescharacteristic
653C22#1686410311yescharacteristic
654C22#1686410611yescharacteristic
655C22#1686410611yescharacteristic
656C22#1686410611yescharacteristic
657C22#1686410611yescharacteristic
658C22#1686411111yescharacteristic
659C22#1686412411yescharacteristic
660C22#1686412411yescharacteristic
661C22Q8×Dic13411yescharacteristic
662C22Q8×Dic13411yescharacteristic
663C4—24no—
664C4—24no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4—2684no—
670C4—2684no—
671C4—5362no—
672C4—1348no—
673C4#1686329118yes—
674C2C2×#1686329111yescharacteristic
675C2C4×#1452402211yescharacteristic
676C2#2256290211yescharacteristic
677C2#2256312011yescharacteristic
678C2C4⋊C4×Dic13411yescharacteristic
679C2#2256329811yescharacteristic
680C2#2256330311yescharacteristic
681C2#2256362711yescharacteristic
682C2#2256366011yescharacteristic
683C2#2256404811yescharacteristic
684C2#2256408111yescharacteristic
685C2#2256473611yescharacteristic
686C2#2256474711yescharacteristic
687C2#2256541411yescharacteristic
688C2#2256559711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D67
commutatorC23×C67C23×C4
FittingC2×C4×C4⋊C4×C67C2
socle, prime radical, cosocleC24×C67C24
hypercenterC2×C4×C4⋊C4D67
hypocenterC67#14045
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #16863294C4semidirect
131. C4⋊Dic67C4⋊C4semidirect
356. C67#14045semidirect

Maximal subgroups

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

subgroupindex
C2×#168632942
C2×C4×C4⋊Dic672
#225584722
#225584602
#225584412
#225584392
Dic67⋊#952
C2×C4×C4⋊C4×C672
#1404567