Finite Group Databasebeta

← #30778243

Subgroups — #30778243

Order 17152.

1854 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic134C211yesmaximal, characteristic
2C2×#16863300C212yesmaximal
3C2×#16863265C211yesmaximal, characteristic
4C2×C4⋊C4×Dic67C211yesmaximal, characteristic
5#22558461C212yesmaximal
6#22558460C212yesmaximal
7#22558439C211yesmaximal, characteristic
8#22558438C211yesmaximal, characteristic
9#22558438C211yesmaximal, characteristic
10Dic67⋊#95C212yesmaximal
11C67×C4⋊#95C211yesmaximal, characteristic
12C23×Dic134C2211yescharacteristic
13C2×C4×Dic134—24no—
14C2×C4×Dic134—24no—
15C2×C4×Dic134C418yescomplemented
16C22×C4⋊Dic67C2211yescharacteristic
17C22×C4⋊Dic67C2211yescharacteristic
18C22×C4⋊Dic67C2211yescharacteristic
19C22×Dic67⋊C4C2212yes—
20C22×Dic67⋊C4C2211yescharacteristic
21C22×Dic67⋊C4C2211yescharacteristic
22C22×Dic67⋊C4C2212yes—
23C22×C4×Dic67C2212yes—
24C22×C4×Dic67C2211yescharacteristic
25C22×C4×Dic67C2211yescharacteristic
26#16863300—28no—
27#16863265—24no—
28C4⋊C4×Dic67—24no—
29C2×C67⋊#95C2212yes—
30C2×C67⋊#95C2212yes—
31C2×C67⋊#95C2212yes—
32C2×C67⋊#95C2212yes—
33C2×C67⋊#95C2212yes—
34C2×C67⋊#95C2212yes—
35C2×C67⋊#95C2212yes—
36C22×C4⋊C4×C67C2211yescharacteristic
37C22×C4⋊C4×C67C2211yescharacteristic
38C22×C42×C67C2211yescharacteristic
39C2×#95×C67C2212yes—
40C2×#95×C67C2212yes—
41C22×Dic134—22no—
42C22×Dic134—22no—
43C22×Dic134—22no—
44C22×Dic134—22no—
45C22×Dic134C2×C414yes—
46C22×Dic134D414yes—
47C22×Dic134Q814yes—
48C23×Dic67C2312yes—
49C23×Dic67C2311yescharacteristic
50C23×Dic67C2312yes—
51C23×Dic67C2311yescharacteristic
52C23×Dic67C2311yescharacteristic
53C23×Dic67C2311yescharacteristic
54C4×Dic134—232no—
55C2×C4⋊Dic67—22no—
56C2×C4⋊Dic67—22no—
57C2×C4⋊Dic67—22no—
58C2×C4⋊Dic67—22no—
59C2×C4⋊Dic67—22no—
60C2×C4⋊Dic67—22no—
61C2×C4⋊Dic67—22no—
62C2×C4⋊Dic67C2×C414yes—
63C2×C4⋊Dic67Q814yescomplemented
64C2×Dic67⋊C4—22no—
65C2×Dic67⋊C4—22no—
66C2×Dic67⋊C4—22no—
67C2×Dic67⋊C4—22no—
68C2×Dic67⋊C4—24no—
69C2×Dic67⋊C4—24no—
70C2×Dic67⋊C4—24no—
71C2×Dic67⋊C4—24no—
72C2×Dic67⋊C4—42no—
73C2×Dic67⋊C4—42no—
74C2×Dic67⋊C4C2×C414yes—
75C2×Dic67⋊C4C2×C414yes—
76C2×C4×Dic67—24no—
77C2×C4×Dic67—24no—
78C2×C4×Dic67—24no—
79C2×C4×Dic67—22no—
80C2×C4×Dic67—22no—
81C2×C4×Dic67C2×C414yes—
82C2×C4×Dic67C2×C414yes—
83C2×C4×Dic67D414yes—
84C2×C4×Dic67D414yes—
85C67⋊#95—24no—
86C67⋊#95—24no—
87C67⋊#95—24no—
88C67⋊#95—24no—
89C67⋊#95—42no—
90C67⋊#95—42no—
91C67⋊#95—42no—
92C23×C4×C67C2312yes—
93C23×C4×C67C2311yescharacteristic
94C23×C4×C67C2312yes—
95C23×C4×C67C2311yescharacteristic
96C23×C4×C67C2311yescharacteristic
97C2×C4⋊C4×C67—22no—
98C2×C4⋊C4×C67—22no—
99C2×C4⋊C4×C67—22no—
100C2×C4⋊C4×C67—22no—
101C2×C4⋊C4×C67—22no—
102C2×C4⋊C4×C67Q814yescomplemented
103C2×C42×C67—22no—
104C2×C42×C67—22no—
105C2×C42×C67C2×C414yes—
106#95×C67—24no—
107#95×C67—42no—
108C2×Dic134—28no—
109C2×Dic134—28no—
110C2×Dic134—28no—
111C2×Dic134—28no—
112C2×Dic134—28no—
113C2×Dic134—28no—
114C2×Dic134C4⋊C4116yescomplemented
115C22×Dic67—21no—
116C22×Dic67—21no—
117C22×Dic67—21no—
118C22×Dic67—21no—
119C22×Dic67—21no—
120C22×Dic67—21no—
121C22×Dic67—21no—
122C22×Dic67—21no—
123C22×Dic67—22no—
124C22×Dic67—22no—
125C22×Dic67—21no—
126C22×Dic67—21no—
127C22×Dic67—22no—
128C22×Dic67—22no—
129C22×Dic67—21no—
130C22×Dic67—21no—
131C22×Dic67—22no—
132C22×Dic67—21no—
133C22×Dic67—21no—
134C22×Dic67—22no—
135C22×Dic67—22no—
136C22×Dic67—22no—
137C22×Dic67—22no—
138C22×Dic67—22no—
139C22×Dic67—22no—
140C22×Dic67—22no—
141C22×Dic67—22no—
142C22×Dic67C22×C412yes—
143C22×Dic67C22×C412yes—
144C22×Dic67C22×C412yes—
145C22×Dic67C22×C412yes—
146C22×Dic67C2×D412yes—
147C22×Dic67C2×D412yes—
148C22×Dic67C2×D412yes—
149C22×Dic67C2×D412yes—
150C22×Dic67C2×D412yes—
151C22×Dic67C2×D412yes—
152C22×Dic67C2×Q814yes—
153C22×Dic67C2×Q812yes—
154C22×Dic67C2×Q812yes—
155C22×Dic67#4112yes—
156C22×Dic67#4112yes—
157C4⋊Dic67—28no—
158C4⋊Dic67—28no—
159C4⋊Dic67—44no—
160Dic67⋊C4—28no—
161Dic67⋊C4—28no—
162Dic67⋊C4—48no—
163Dic67⋊C4—48no—
164C4×Dic67—28no—
165C4×Dic67—48no—
166C4×Dic67C22⋊C4116yes—
167C24×C67C2411yescharacteristic
168C22×C4×C67—21no—
169C22×C4×C67—21no—
170C22×C4×C67—21no—
171C22×C4×C67—21no—
172C22×C4×C67—21no—
173C22×C4×C67—21no—
174C22×C4×C67—22no—
175C22×C4×C67—22no—
176C22×C4×C67—22no—
177C22×C4×C67—22no—
178C22×C4×C67—21no—
179C22×C4×C67—22no—
180C22×C4×C67—21no—
181C22×C4×C67—21no—
182C22×C4×C67—22no—
183C22×C4×C67—21no—
184C22×C4×C67—22no—
185C22×C4×C67—22no—
186C22×C4×C67—22no—
187C22×C4×C67—22no—
188C22×C4×C67—22no—
189C22×C4×C67—22no—
190C22×C4×C67—22no—
191C22×C4×C67C22×C412yes—
192C22×C4×C67C22×C412yes—
193C22×C4×C67C22×C412yes—
194C22×C4×C67C2×D412yes—
195C22×C4×C67C2×D412yes—
196C22×C4×C67C2×D412yes—
197C22×C4×C67C2×Q812yes—
198C22×C4×C67C2×Q812yes—
199C22×C4×C67C2×Q814yes—
200C22×C4×C67C2×Q812yes—
201C22×C4×C67#4112yes—
202C22×C4×C67#4112yes—
203C4⋊C4×C67—28no—
204C4⋊C4×C67—44no—
205C42×C67—28no—
206C23×C67C23×C411yescharacteristic
207C23×C67C22×D411yescharacteristic
208C23×C67C22×D411yescharacteristic
209C23×C67C22×D411yescharacteristic
210C23×C67C22×Q811yescharacteristic
211C23×C67C22×Q811yescharacteristic
212C23×C67C22×Q811yescharacteristic
213C23×C67C2×#4111yescharacteristic
214C23×C67C2×#4111yescharacteristic
215C23×C67C2×#4111yescharacteristic
216C23×C67C2×#4111yescharacteristic
217C23×C67H(5,𝔽2)11yescharacteristic
218C23×C67H(5,𝔽2)11yescharacteristic
219C23×C672−1+411yescharacteristic
220C23×C672−1+411yescharacteristic
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—24no—
231C2×C4×C67—24no—
232C2×C4×C67—24no—
233C2×C4×C67—42no—
234C2×C4×C67—41no—
235C2×C4×C67—41no—
236C2×C4×C67—41no—
237C2×C4×C67—42no—
238C2×C4×C67—41no—
239C2×C4×C67—42no—
240C2×C4×C67—42no—
241C2×C4×C67—42no—
242C2×C4×C67—42no—
243C2×C4×C67—42no—
244C2×C4×C67—42no—
245C2×C4×C67—42no—
246C2×C4×C67—42no—
247C2×C4×C67—42no—
248C2×C4×C67C2×C22⋊C414yes—
249C2×C4×C67C2×C4⋊C414yes—
250C2×C4×C67C4×Q814yes—
251C2×C4×C67C4×Q814yes—
252C2×C4×C67C22⋊Q814yes—
253C2×C4×C67C22⋊Q814yes—
254C2×C4×C67#12414yes—
255C2×C4×C67C4⋊Q814yes—
256C2×Dic67—22no—
257C2×Dic67—22no—
258C2×Dic67—22no—
259C2×Dic67—22no—
260C2×Dic67—22no—
261C2×Dic67—22no—
262C2×Dic67—22no—
263C2×Dic67—22no—
264C2×Dic67—22no—
265C2×Dic67—22no—
266C2×Dic67—22no—
267C2×Dic67—22no—
268C2×Dic67—22no—
269C2×Dic67—22no—
270C2×Dic67—22no—
271C2×Dic67—24no—
272C2×Dic67—24no—
273C2×Dic67—24no—
274C2×Dic67—42no—
275C2×Dic67—41no—
276C2×Dic67—41no—
277C2×Dic67—41no—
278C2×Dic67—41no—
279C2×Dic67—42no—
280C2×Dic67—42no—
281C2×Dic67—42no—
282C2×Dic67—42no—
283C2×Dic67—42no—
284C2×Dic67—42no—
285C2×Dic67—42no—
286C2×Dic67—42no—
287C2×Dic67—42no—
288C2×Dic67—42no—
289C2×Dic67C2×C22⋊C414yes—
290C2×Dic67C2×C22⋊C414yes—
291C2×Dic67C2×C4⋊C414yes—
292C2×Dic67C2×C4⋊C414yes—
293C2×Dic67#11714yes—
294C2×Dic67#12114yes—
295C2×Dic67#12114yes—
296C2×Dic67C22⋊Q814yes—
297C2×Dic67C22⋊Q814yes—
298Dic134—232no—
299C22×C67C22×C22⋊C411yescharacteristic
300C22×C67C22×C4⋊C411yescharacteristic
301C22×C67C2×#11711yescharacteristic
302C22×C67C2×C4×Q811yescharacteristic
303C22×C67C2×C4×Q811yescharacteristic
304C22×C67#52011yescharacteristic
305C22×C67#52011yescharacteristic
306C22×C67C2×#12111yescharacteristic
307C22×C67C2×#12111yescharacteristic
308C22×C67C2×C22⋊Q811yescharacteristic
309C22×C67C2×C22⋊Q811yescharacteristic
310C22×C67C2×C22⋊Q811yescharacteristic
311C22×C67C2×C22⋊Q811yescharacteristic
312C22×C67C2×#12411yescharacteristic
313C22×C67C2×C4⋊Q811yescharacteristic
314C22×C67#53511yescharacteristic
315C22×C67#53611yescharacteristic
316C22×C67#53711yescharacteristic
317C22×C67#53711yescharacteristic
318C22×C67D4×Q811yescharacteristic
319C22×C67D4×Q811yescharacteristic
320C22×C67#55011yescharacteristic
321C22×C67#55011yescharacteristic
322C22×C67#55411yescharacteristic
323C22×C67#55411yescharacteristic
324C22×C67#55611yescharacteristic
325C22×C67#55611yescharacteristic
326C22×C67#55711yescharacteristic
327C22×C67#55711yescharacteristic
328C22×C67#55711yescharacteristic
329C22×C67#55711yescharacteristic
330C22×C67Q8211yescharacteristic
331C22×C67Q8211yescharacteristic
332C22×C67#55911yescharacteristic
333C22×C67#55911yescharacteristic
334C4×C67—24no—
335C4×C67—42no—
336C4×C67—44no—
337C4×C67—82no—
338C4×C67#39118yescomplemented
339Dic67—24no—
340Dic67—24no—
341Dic67—42no—
342Dic67—44no—
343Dic67—82no—
344Dic67#38018yes—
345#13926—671nomaximal, Sylow
346C2×C67C2×#38011yescharacteristic
347C2×C67C2×#39111yescharacteristic
348C2×C67#231111yescharacteristic
349C2×C67Q8×C4⋊C411yescharacteristic
350C2×C67Q8×C4⋊C411yescharacteristic
351C2×C67#235511yescharacteristic
352C2×C67#235511yescharacteristic
353C2×C67#253811yescharacteristic
354C2×C67#253811yescharacteristic
355C2×C67#254611yescharacteristic
356C2×C67#254811yescharacteristic
357C2×C67#256711yescharacteristic
358C2×C67#256811yescharacteristic
359C2×C67#258211yescharacteristic
360C2×C67#258211yescharacteristic
361C22×C4×Q8—671no—
362C2×#391—672no—
363C2×#384—671no—
364C2×C4×C4⋊C4—671no—
365#1441—672no—
366#1441—672no—
367C4⋊#95—671no—
368C4⋊#95—672no—
369C4⋊#95—671no—
370C4⋊#95—671no—
371C4⋊#95D6711yescharacteristic
372C67#1392611yescharacteristic, complemented, Sylow
373C23×Q8—671no—
374C2×C4×Q8—678no—
375C2×C4×Q8—1344no—
376C2×C4×Q8—1344no—
377C22×C4⋊C4—672no—
378C22×C4⋊C4—671no—
379C22×C4⋊C4—671no—
380C22×C4⋊C4—671no—
381C22×C4⋊C4—671no—
382C22×C4⋊C4—672no—
383C22×C4⋊C4—671no—
384C22×C4⋊C4C2×D6711yescharacteristic
385C22×C4⋊C4C2×D6711yescharacteristic
386C22×C42—671no—
387C22×C42—671no—
388C22×C42—672no—
389C22×C42C2×D6711yescharacteristic
390#391—1348no—
391#384—1344no—
392C4×C4⋊C4—1344no—
393C2×#95—672no—
394C2×#95—672no—
395C2×#95—672no—
396C2×#95—672no—
397C2×#95—672no—
398C2×#95—672no—
399C2×#95—672no—
400C2×#95C2×D6712yes—
401C2×#95C2×D6712yes—
402C22×Q8—674no—
403C22×Q8—674no—
404C22×Q8—674no—
405C22×Q8—1342no—
406C22×Q8—1342no—
407C22×Q8—1342no—
408C22×Q8—1342no—
409C23×C4—671no—
410C23×C4—671no—
411C23×C4—671no—
412C23×C4—671no—
413C23×C4—672no—
414C23×C4—672no—
415C23×C4C22×D6712yes—
416C23×C4C22×D6711yescharacteristic
417C23×C4C22×D6712yes—
418C23×C4C22×D6711yescharacteristic
419C23×C4C22×D6711yescharacteristic
420C4×Q8—13432no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—2682no—
427C2×C4⋊C4—2682no—
428C2×C4⋊C4—674no—
429C2×C4⋊C4—674no—
430C2×C4⋊C4—674no—
431C2×C4⋊C4—674no—
432C2×C4⋊C4—1344no—
433C2×C4⋊C4—1344no—
434C2×C4⋊C4—1344no—
435C2×C4⋊C4—1344no—
436C2×C4⋊C4—1342no—
437C2×C4⋊C4—1342no—
438C2×C4⋊C4—1342no—
439C2×C4⋊C4—1342no—
440C2×C4⋊C4—1342no—
441C2×C4⋊C4—1342no—
442C2×C4⋊C4—1342no—
443C2×C4⋊C4—1342no—
444C2×C4⋊C4—1342no—
445C2×C4⋊C4—1342no—
446C2×C4⋊C4—1342no—
447C2×C4⋊C4Dic13414yescomplemented
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—674no—
451C2×C42—674no—
452C2×C42—674no—
453C2×C42—674no—
454C2×C42—1344no—
455C2×C42—1344no—
456C2×C42—1344no—
457C2×C42—1342no—
458C2×C42—1342no—
459C2×C42C4×D6714yes—
460#95—24no—
461#95—42no—
462#95—2682no—
463#95—2682no—
464#95—2682no—
465#95—1344no—
466#95—1344no—
467#95—1344no—
468#95—1344no—
469C24C23×D6711yescharacteristic
470C2×Q8—6716no—
471C2×Q8—1348no—
472C2×Q8—1348no—
473C2×Q8—1348no—
474C2×Q8—1348no—
475C2×Q8—1348no—
476C2×Q8—1348no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—672no—
501C22×C4—672no—
502C22×C4—672no—
503C22×C4—672no—
504C22×C4—672no—
505C22×C4—672no—
506C22×C4—672no—
507C22×C4—672no—
508C22×C4—672no—
509C22×C4—672no—
510C22×C4—672no—
511C22×C4—672no—
512C22×C4—672no—
513C22×C4—672no—
514C22×C4—674no—
515C22×C4—1342no—
516C22×C4—1342no—
517C22×C4—1342no—
518C22×C4—1342no—
519C22×C4—1342no—
520C22×C4—1342no—
521C22×C4—1342no—
522C22×C4—1342no—
523C22×C4—1342no—
524C22×C4—1341no—
525C22×C4—1341no—
526C22×C4—1342no—
527C22×C4—1342no—
528C22×C4—1341no—
529C22×C4—1342no—
530C22×C4—1341no—
531C22×C4—1341no—
532C22×C4—1342no—
533C22×C4—1341no—
534C22×C4—1341no—
535C22×C4—1341no—
536C22×C4—1341no—
537C22×C4—1341no—
538C22×C4—1341no—
539C22×C4—1341no—
540C22×C4—1341no—
541C22×C4—1341no—
542C22×C4C2×C4×D6712yes—
543C22×C4C2×C4×D6712yes—
544C22×C4C2×C4×D6712yes—
545C22×C4D4×D6712yes—
546C22×C4D4×D6712yes—
547C22×C4D4×D6712yes—
548C22×C4Q8×D6712yes—
549C22×C4Q8×D6712yes—
550C22×C4C2×Dic13414yes—
551C22×C4C2×Dic13412yes—
552C22×C4#1176162712yes—
553C22×C4#1176162812yes—
554C4⋊C4—28no—
555C4⋊C4—44no—
556C4⋊C4—2688no—
557C4⋊C4—2688no—
558C4⋊C4—2684no—
559C4⋊C4—1348no—
560C4⋊C4—1348no—
561C4⋊C4—1348no—
562C4⋊C4—1348no—
563C42—28no—
564C42—2688no—
565C42—6716no—
566C42—1348no—
567C23C22×C4×D6711yescharacteristic
568C23C2×D4×D6711yescharacteristic
569C23C2×D4×D6711yescharacteristic
570C23C2×D4×D6711yescharacteristic
571C23C2×Q8×D6711yescharacteristic
572C23C2×Q8×D6711yescharacteristic
573C23C22×Dic13411yescharacteristic
574C23#41×D6711yescharacteristic
575C23#41×D6711yescharacteristic
576C23C2×#1176162711yescharacteristic
577C23C2×#1176162811yescharacteristic
578C23#1452408811yescharacteristic
579C23#1452408911yescharacteristic
580C23#1452409011yescharacteristic
581C23#1452409111yescharacteristic
582Q8—13432no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—2682no—
611C2×C4—2682no—
612C2×C4—2682no—
613C2×C4—2681no—
614C2×C4—2681no—
615C2×C4—2681no—
616C2×C4—2682no—
617C2×C4—2681no—
618C2×C4—2682no—
619C2×C4—2682no—
620C2×C4—2682no—
621C2×C4—2682no—
622C2×C4—2682no—
623C2×C4—2682no—
624C2×C4—2682no—
625C2×C4—674no—
626C2×C4—674no—
627C2×C4—674no—
628C2×C4—674no—
629C2×C4—674no—
630C2×C4—674no—
631C2×C4—674no—
632C2×C4—674no—
633C2×C4—674no—
634C2×C4—1344no—
635C2×C4—1342no—
636C2×C4—1344no—
637C2×C4—1342no—
638C2×C4—1342no—
639C2×C4—1344no—
640C2×C4—1342no—
641C2×C4—1342no—
642C2×C4—1342no—
643C2×C4—1342no—
644C2×C4—1342no—
645C2×C4—1342no—
646C2×C4—1342no—
647C2×C4—1342no—
648C2×C4—1342no—
649C2×C4—1342no—
650C2×C4—1342no—
651C2×C4—1342no—
652C2×C4C22⋊C4×D6714yes—
653C2×C4C4⋊C4×D6714yes—
654C2×C4#1452400814yes—
655C2×C4C4×Dic13414yes—
656C2×C4#1452402014yes—
657C2×C4#1452402114yes—
658C2×C4#1452402914yes—
659C2×C4#1452404214yes—
660C22C2×C22⋊C4×D6711yescharacteristic
661C22C2×C4⋊C4×D6711yescharacteristic
662C22#117×D6711yescharacteristic
663C22C2×#1452400811yescharacteristic
664C22C2×C4×Dic13411yescharacteristic
665C22#1686387611yescharacteristic
666C22#1686387711yescharacteristic
667C22#121×D6711yescharacteristic
668C22#121×D6711yescharacteristic
669C22C22⋊Q8×D6711yescharacteristic
670C22C22⋊Q8×D6711yescharacteristic
671C22C2×#1452402011yescharacteristic
672C22C2×#1452402111yescharacteristic
673C22C2×#1452402911yescharacteristic
674C22C2×#1452404211yescharacteristic
675C22#1686396211yescharacteristic
676C22#1686396911yescharacteristic
677C22#1686397511yescharacteristic
678C22#1686397611yescharacteristic
679C22#1686406111yescharacteristic
680C22D4×Dic13411yescharacteristic
681C22#1686406611yescharacteristic
682C22#1686406711yescharacteristic
683C22#1686410211yescharacteristic
684C22#1686410511yescharacteristic
685C22#1686411511yescharacteristic
686C22#1686411811yescharacteristic
687C22#1686412111yescharacteristic
688C22#1686412211yescharacteristic
689C22#1686412311yescharacteristic
690C22#1686412411yescharacteristic
691C22#1686412611yescharacteristic
692C22Q8×Dic13411yescharacteristic
693C22#1686412811yescharacteristic
694C22#1686412911yescharacteristic
695C4—24no—
696C4—44no—
697C4—42no—
698C4—82no—
699C4—2684no—
700C4—2682no—
701C4—5362no—
702C4—678no—
703C4—1344no—
704C4—1344no—
705C4#1686330018yescomplemented
706C2#380×D6711yescharacteristic
707C2C2×#1686330011yescharacteristic
708C2#2256279811yescharacteristic
709C2#2256312111yescharacteristic
710C2C4⋊C4×Dic13411yescharacteristic
711C2#2256316111yescharacteristic
712C2#2256316711yescharacteristic
713C2#2256512911yescharacteristic
714C2#2256513011yescharacteristic
715C2#2256519611yescharacteristic
716C2#2256521011yescharacteristic
717C2#2256541611yescharacteristic
718C2#2256542311yescharacteristic
719C2#2256558011yescharacteristic
720C2#2256558111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D67
commutatorC23×C67C23×C4
FittingC67×C4⋊#95C2
socle, prime radical, cosocleC24×C67C24
hypercenterC4⋊#95D67
hypocenterC67#13926
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic134C4semidirect
63. C2×C4⋊Dic67Q8semidirect
102. C2×C4⋊C4×C67Q8semidirect
114. C2×Dic134C4⋊C4semidirect
338. C4×C67#391semidirect
372. C67#13926semidirect
447. C2×C4⋊C4Dic134semidirect
705. C4#16863300semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1342
C2×#168633002
C2×#168632652
C2×C4⋊C4×Dic672
#225584612
#225584602
#225584392
#225584382
Dic67⋊#952
C67×C4⋊#952
#1392667