Finite Group Databasebeta

← #30779559

Subgroups — #30779559

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×#16863295C211yesmaximal, characteristic
2C2×#16863295C211yesmaximal, characteristic
3C2×C4⋊C4×Dic67C211yesmaximal, characteristic
4C2×C4×C4⋊Dic67C211yesmaximal, characteristic
5#22558474C212yesmaximal
6#22558462C212yesmaximal
7#22558443C212yesmaximal
8#22558439C211yesmaximal, characteristic
9#22558438C212yesmaximal
10#22558438C211yesmaximal, characteristic
11C2×#389×C67C211yesmaximal, characteristic
12C22×C4⋊Dic67C2211yescharacteristic
13C22×C4⋊Dic67C2211yescharacteristic
14C22×C4⋊Dic67C2212yes—
15C22×C4⋊Dic67C2211yescharacteristic
16C22×C4⋊Dic67C2211yescharacteristic
17C22×C4⋊Dic67C2212yes—
18C22×C4×Dic67C2211yescharacteristic
19C22×C4×Dic67C2212yes—
20C22×C4×Dic67C2211yescharacteristic
21#16863295—24no—
22#16863295—24no—
23C4⋊C4×Dic67—24no—
24C4×C4⋊Dic67—24no—
25C2×C67⋊#95C2212yes—
26C2×C67⋊#95C2212yes—
27C2×C67⋊#95C2212yes—
28C2×C67⋊#95C2212yes—
29C2×C67⋊#95C2211yescharacteristic
30C2×C67⋊#95C2211yescharacteristic
31C2×C67⋊#95C2212yes—
32C2×C67⋊#95C2212yes—
33C2×C67⋊#95C2212yes—
34C22×C4⋊C4×C67C2211yescharacteristic
35C22×C4⋊C4×C67C2212yes—
36C22×C4⋊C4×C67C2211yescharacteristic
37C22×C42×C67C2211yescharacteristic
38#389×C67C418yescomplemented
39C2×#95×C67C2212yes—
40C23×Dic67C2312yes—
41C23×Dic67C2311yescharacteristic
42C23×Dic67C2311yescharacteristic
43C23×Dic67C2312yes—
44C23×Dic67C2311yescharacteristic
45C23×Dic67C2311yescharacteristic
46C2×C4⋊Dic67—22no—
47C2×C4⋊Dic67—22no—
48C2×C4⋊Dic67—22no—
49C2×C4⋊Dic67—22no—
50C2×C4⋊Dic67—24no—
51C2×C4⋊Dic67—24no—
52C2×C4⋊Dic67—22no—
53C2×C4⋊Dic67—22no—
54C2×C4⋊Dic67—24no—
55C2×C4⋊Dic67—22no—
56C2×C4⋊Dic67—22no—
57C2×C4⋊Dic67—22no—
58C2×C4⋊Dic67—22no—
59C2×C4⋊Dic67—42no—
60C2×C4⋊Dic67—42no—
61C2×C4⋊Dic67—42no—
62C2×C4⋊Dic67Q814yes—
63C2×C4⋊Dic67Q814yes—
64C2×C4×Dic67—24no—
65C2×C4×Dic67—22no—
66C2×C4×Dic67—22no—
67C2×C4×Dic67—24no—
68C2×C4×Dic67—22no—
69C2×C4×Dic67—22no—
70C2×C4×Dic67—22no—
71C2×C4×Dic67—42no—
72C2×C4×Dic67D414yes—
73C67⋊#95—22no—
74C67⋊#95—22no—
75C67⋊#95—24no—
76C67⋊#95—24no—
77C67⋊#95—24no—
78C67⋊#95—24no—
79C67⋊#95—42no—
80C67⋊#95—42no—
81C67⋊#95—42no—
82C23×C4×C67C2311yescharacteristic
83C23×C4×C67C2312yes—
84C23×C4×C67C2312yes—
85C23×C4×C67C2311yescharacteristic
86C23×C4×C67C2311yescharacteristic
87C2×C4⋊C4×C67—22no—
88C2×C4⋊C4×C67—22no—
89C2×C4⋊C4×C67—42no—
90C2×C4⋊C4×C67—42no—
91C2×C4⋊C4×C67C2×C414yes—
92C2×C4⋊C4×C67C2×C418yes—
93C2×C4⋊C4×C67C2×C414yes—
94C2×C4⋊C4×C67D414yes—
95C2×C4⋊C4×C67Q814yes—
96C2×C42×C67—22no—
97C2×C42×C67—22no—
98C2×C42×C67C2×C414yes—
99#95×C67C2×C418yes—
100C22×Dic67—21no—
101C22×Dic67—21no—
102C22×Dic67—21no—
103C22×Dic67—21no—
104C22×Dic67—21no—
105C22×Dic67—21no—
106C22×Dic67—21no—
107C22×Dic67—21no—
108C22×Dic67—22no—
109C22×Dic67—21no—
110C22×Dic67—22no—
111C22×Dic67—22no—
112C22×Dic67—21no—
113C22×Dic67—21no—
114C22×Dic67—21no—
115C22×Dic67—21no—
116C22×Dic67—21no—
117C22×Dic67—22no—
118C22×Dic67—21no—
119C22×Dic67—21no—
120C22×Dic67—21no—
121C22×Dic67—21no—
122C22×Dic67—22no—
123C22×Dic67—22no—
124C22×Dic67—21no—
125C22×Dic67—21no—
126C22×Dic67—21no—
127C22×Dic67—21no—
128C22×Dic67—22no—
129C22×Dic67—22no—
130C22×Dic67—22no—
131C22×Dic67—22no—
132C22×Dic67—22no—
133C22×Dic67—22no—
134C22×Dic67—22no—
135C22×Dic67C2×D412yes—
136C22×Dic67C2×D412yes—
137C22×Dic67C2×Q812yes—
138C22×Dic67C2×Q814yes—
139C22×Dic67C2×Q812yes—
140C22×Dic67#4112yes—
141C22×Dic67#4112yes—
142C4⋊Dic67—28no—
143C4⋊Dic67—28no—
144C4⋊Dic67—28no—
145C4⋊Dic67—48no—
146C4⋊Dic67—48no—
147C4⋊Dic67—44no—
148C4×Dic67—28no—
149C4×Dic67—48no—
150C4×Dic67—44no—
151C24×C67C2411yescharacteristic
152C22×C4×C67—21no—
153C22×C4×C67—21no—
154C22×C4×C67—22no—
155C22×C4×C67—21no—
156C22×C4×C67—21no—
157C22×C4×C67—22no—
158C22×C4×C67—22no—
159C22×C4×C67—22no—
160C22×C4×C67—21no—
161C22×C4×C67—22no—
162C22×C4×C67—21no—
163C22×C4×C67—22no—
164C22×C4×C67—21no—
165C22×C4×C67—21no—
166C22×C4×C67—22no—
167C22×C4×C67—22no—
168C22×C4×C67—21no—
169C22×C4×C67—22no—
170C22×C4×C67—21no—
171C22×C4×C67—22no—
172C22×C4×C67C22×C412yes—
173C22×C4×C67C22×C414yes—
174C22×C4×C67C22×C414yes—
175C22×C4×C67C22×C412yes—
176C22×C4×C67C22×C412yes—
177C22×C4×C67C2×D412yes—
178C22×C4×C67C2×D414yes—
179C22×C4×C67C2×D412yes—
180C22×C4×C67C2×Q812yes—
181C22×C4×C67C2×Q812yes—
182C22×C4×C67C2×Q814yes—
183C22×C4×C67C2×Q812yes—
184C22×C4×C67#4112yes—
185C22×C4×C67#4112yes—
186C22×C4×C67#4112yes—
187C4⋊C4×C67—28no—
188C4⋊C4×C67—48no—
189C4⋊C4×C67C4⋊C4116yescomplemented
190C42×C67—28no—
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—24no—
208C2×C4×C67—22no—
209C2×C4×C67—24no—
210C2×C4×C67—22no—
211C2×C4×C67—22no—
212C2×C4×C67—22no—
213C2×C4×C67—22no—
214C2×C4×C67—24no—
215C2×C4×C67—24no—
216C2×C4×C67—24no—
217C2×C4×C67—24no—
218C2×C4×C67—22no—
219C2×C4×C67—24no—
220C2×C4×C67—22no—
221C2×C4×C67—24no—
222C2×C4×C67—22no—
223C2×C4×C67—24no—
224C2×C4×C67—41no—
225C2×C4×C67—42no—
226C2×C4×C67—41no—
227C2×C4×C67—42no—
228C2×C4×C67—41no—
229C2×C4×C67—42no—
230C2×C4×C67—41no—
231C2×C4×C67—42no—
232C2×C4×C67C2×C4⋊C418yes—
233C2×C4×C67C2×C4⋊C414yes—
234C2×C4×C67C4×D414yes—
235C2×C4×C67C4×Q814yes—
236C2×C4×C67C4×Q814yes—
237C2×C4×C67#12114yes—
238C2×C4×C67C22⋊Q814yes—
239C2×C4×C67#12514yes—
240C2×C4×C67C4⋊Q814yes—
241C2×Dic67—22no—
242C2×Dic67—22no—
243C2×Dic67—22no—
244C2×Dic67—22no—
245C2×Dic67—22no—
246C2×Dic67—22no—
247C2×Dic67—22no—
248C2×Dic67—22no—
249C2×Dic67—24no—
250C2×Dic67—22no—
251C2×Dic67—22no—
252C2×Dic67—22no—
253C2×Dic67—22no—
254C2×Dic67—22no—
255C2×Dic67—22no—
256C2×Dic67—24no—
257C2×Dic67—22no—
258C2×Dic67—24no—
259C2×Dic67—41no—
260C2×Dic67—41no—
261C2×Dic67—42no—
262C2×Dic67—41no—
263C2×Dic67—41no—
264C2×Dic67—42no—
265C2×Dic67—42no—
266C2×Dic67—41no—
267C2×Dic67—41no—
268C2×Dic67—41no—
269C2×Dic67—41no—
270C2×Dic67—42no—
271C2×Dic67—41no—
272C2×Dic67—41no—
273C2×Dic67—41no—
274C2×Dic67—41no—
275C2×Dic67—42no—
276C2×Dic67—42no—
277C2×Dic67—42no—
278C2×Dic67—42no—
279C2×Dic67—42no—
280C2×Dic67—42no—
281C2×Dic67—42no—
282C2×Dic67C22⋊Q814yes—
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—28no—
319C4×C67—24no—
320C4×C67—42no—
321C4×C67—44no—
322C4×C67#38918yes—
323Dic67—24no—
324Dic67—42no—
325Dic67—42no—
326Dic67—42no—
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×#389D6711yescharacteristic
348C2×C4×C4⋊C4—671no—
349C2×C4×C4⋊C4—671no—
350#1444—672no—
351#1441—672no—
352#1436—672no—
353C4⋊#95—671no—
354C4⋊#95—672no—
355C4⋊#95—671no—
356C67#1404511yescharacteristic, complemented, Sylow
357C22×C4⋊C4—672no—
358C22×C4⋊C4—672no—
359C22×C4⋊C4—671no—
360C22×C4⋊C4—671no—
361C22×C4⋊C4—671no—
362C22×C4⋊C4—671no—
363C22×C4⋊C4C2×D6711yescharacteristic
364C22×C4⋊C4C2×D6712yes—
365C22×C4⋊C4C2×D6711yescharacteristic
366C22×C42—672no—
367C22×C42—671no—
368C22×C42—671no—
369C22×C42C2×D6711yescharacteristic
370#389—1344no—
371#389—1344no—
372#389Dic6718yescomplemented
373C4×C4⋊C4—1344no—
374C4×C4⋊C4—1344no—
375C2×#95—672no—
376C2×#95—672no—
377C2×#95—672no—
378C2×#95—671no—
379C2×#95—672no—
380C2×#95—672no—
381C2×#95—672no—
382C2×#95—671no—
383C2×#95—672no—
384C2×#95C2×D6712yes—
385C23×C4—671no—
386C23×C4—671no—
387C23×C4—671no—
388C23×C4—671no—
389C23×C4—672no—
390C23×C4—672no—
391C23×C4C22×D6712yes—
392C23×C4C22×D6711yescharacteristic
393C23×C4C22×D6712yes—
394C23×C4C22×D6711yescharacteristic
395C23×C4C22×D6711yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—2682no—
401C2×C4⋊C4—2682no—
402C2×C4⋊C4—2682no—
403C2×C4⋊C4—674no—
404C2×C4⋊C4—674no—
405C2×C4⋊C4—1344no—
406C2×C4⋊C4—1344no—
407C2×C4⋊C4—1342no—
408C2×C4⋊C4—1344no—
409C2×C4⋊C4—1342no—
410C2×C4⋊C4—1342no—
411C2×C4⋊C4—1342no—
412C2×C4⋊C4—1342no—
413C2×C4⋊C4—1342no—
414C2×C4⋊C4—1342no—
415C2×C4⋊C4—1342no—
416C2×C4⋊C4—1342no—
417C2×C4⋊C4—1342no—
418C2×C4⋊C4Dic13414yes—
419C2×C4⋊C4D26814yes—
420C2×C4⋊C4C2×Dic6714yes—
421C2×C4⋊C4C2×Dic6718yes—
422C2×C4⋊C4C2×Dic6714yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—2682no—
426C2×C42—674no—
427C2×C42—1344no—
428C2×C42—1342no—
429C2×C42—1344no—
430C2×C42—1342no—
431C2×C42—1342no—
432C2×C42—1342no—
433C2×C42—1342no—
434C2×C42C2×Dic6714yes—
435#95—2682no—
436#95—2682no—
437#95—2682no—
438#95—1342no—
439#95—1342no—
440#95—1344no—
441#95—1344no—
442#95—1344no—
443#95—1344no—
444#95C2×Dic6718yes—
445C24C23×D6711yescharacteristic
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—672no—
467C22×C4—672no—
468C22×C4—672no—
469C22×C4—672no—
470C22×C4—672no—
471C22×C4—674no—
472C22×C4—672no—
473C22×C4—1342no—
474C22×C4—1342no—
475C22×C4—1342no—
476C22×C4—1342no—
477C22×C4—1342no—
478C22×C4—1342no—
479C22×C4—1342no—
480C22×C4—1341no—
481C22×C4—1341no—
482C22×C4—1341no—
483C22×C4—1341no—
484C22×C4—1342no—
485C22×C4—1341no—
486C22×C4—1342no—
487C22×C4—1341no—
488C22×C4—1341no—
489C22×C4—1342no—
490C22×C4—1342no—
491C22×C4—1341no—
492C22×C4—1341no—
493C22×C4—1341no—
494C22×C4—1341no—
495C22×C4—1341no—
496C22×C4—1341no—
497C22×C4—1342no—
498C22×C4—1341no—
499C22×C4—1341no—
500C22×C4—1341no—
501C22×C4—1342no—
502C22×C4—1341no—
503C22×C4—1341no—
504C22×C4—1341no—
505C22×C4—1341no—
506C22×C4—1341no—
507C22×C4—1341no—
508C22×C4C22×Dic6714yes—
509C22×C4C22×Dic6712yes—
510C22×C4C22×Dic6714yes—
511C22×C4C22×Dic6712yes—
512C22×C4C22×Dic6712yes—
513C22×C4D4×D6712yes—
514C22×C4C2×D26814yes—
515C22×C4C2×D26812yes—
516C22×C4Q8×D6712yes—
517C22×C4Q8×D6712yes—
518C22×C4C2×Dic13414yes—
519C22×C4C2×Dic13412yes—
520C22×C4#1176162712yes—
521C22×C4#1176162912yes—
522C22×C4#1176162912yes—
523C4⋊C4—28no—
524C4⋊C4—48no—
525C4⋊C4—2688no—
526C4⋊C4—2688no—
527C4⋊C4—2684no—
528C4⋊C4—1348no—
529C4⋊C4—1348no—
530C4⋊C4—1348no—
531C4⋊C4C4⋊Dic67116yescomplemented
532C42—28no—
533C42—2688no—
534C42—2684no—
535C42—1348no—
536C23C23×Dic6711yescharacteristic
537C23C2×D4×D6711yescharacteristic
538C23C22×D26811yescharacteristic
539C23C2×Q8×D6711yescharacteristic
540C23C2×Q8×D6711yescharacteristic
541C23C22×Dic13411yescharacteristic
542C23#41×D6711yescharacteristic
543C23#41×D6711yescharacteristic
544C23C2×#1176162711yescharacteristic
545C23C2×#1176162911yescharacteristic
546C23C2×#1176162911yescharacteristic
547C23#1452408811yescharacteristic
548C23#1452408811yescharacteristic
549C23#1452408911yescharacteristic
550C23#1452409011yescharacteristic
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—2682no—
578C2×C4—2681no—
579C2×C4—2681no—
580C2×C4—2681no—
581C2×C4—2681no—
582C2×C4—2682no—
583C2×C4—2681no—
584C2×C4—2681no—
585C2×C4—2681no—
586C2×C4—2681no—
587C2×C4—2681no—
588C2×C4—2681no—
589C2×C4—2682no—
590C2×C4—2681no—
591C2×C4—2681no—
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—674no—
601C2×C4—1342no—
602C2×C4—1342no—
603C2×C4—1342no—
604C2×C4—1344no—
605C2×C4—1342no—
606C2×C4—1344no—
607C2×C4—1342no—
608C2×C4—1342no—
609C2×C4—1344no—
610C2×C4—1342no—
611C2×C4—1342no—
612C2×C4—1342no—
613C2×C4—1342no—
614C2×C4—1342no—
615C2×C4—1342no—
616C2×C4—1342no—
617C2×C4—1342no—
618C2×C4—1342no—
619C2×C4C2×C4⋊Dic6718yes—
620C2×C4C2×C4⋊Dic6714yes—
621C2×C4D4×Dic6714yes—
622C2×C4Q8×Dic6714yes—
623C2×C4Q8×Dic6714yes—
624C2×C4#1452401814yes—
625C2×C4#1452402314yes—
626C2×C4#1452403414yes—
627C2×C4#1452404214yes—
628C22C22×C4⋊Dic6711yescharacteristic
629C22C2×D4×Dic6711yescharacteristic
630C22C2×Q8×Dic6711yescharacteristic
631C22C2×Q8×Dic6711yescharacteristic
632C22#41×Dic6711yescharacteristic
633C22#1686387111yescharacteristic
634C22#1686387911yescharacteristic
635C22C2×#1452401811yescharacteristic
636C22C22⋊Q8×D6711yescharacteristic
637C22C2×#1452402311yescharacteristic
638C22#1686390911yescharacteristic
639C22C2×#1452403411yescharacteristic
640C22#1686393211yescharacteristic
641C22C2×#1452404211yescharacteristic
642C22#1686394811yescharacteristic
643C22#1686396211yescharacteristic
644C22#1686397511yescharacteristic
645C22#1686399911yescharacteristic
646C22#1686401311yescharacteristic
647C22#1686404111yescharacteristic
648C22#1686404111yescharacteristic
649C22Q8×D26811yescharacteristic
650C22#1686406811yescharacteristic
651C22#1686408411yescharacteristic
652C22#1686409911yescharacteristic
653C22#1686410211yescharacteristic
654C22#1686410511yescharacteristic
655C22#1686410511yescharacteristic
656C22#1686410711yescharacteristic
657C22#1686410711yescharacteristic
658C22#1686411211yescharacteristic
659C22#1686412311yescharacteristic
660C22#1686412511yescharacteristic
661C22#1686412611yescharacteristic
662C22Q8×Dic13411yescharacteristic
663C4—28no—
664C4—24no—
665C4—42no—
666C4—44no—
667C4—2682no—
668C4—2682no—
669C4—2682no—
670C4—2684no—
671C4—5362no—
672C4—1344no—
673C4#1686329518yes—
674C2C2×#1686329511yescharacteristic
675C2C22⋊Q8×Dic6711yescharacteristic
676C2#2256290411yescharacteristic
677C2#2256311911yescharacteristic
678C2Q8×C4⋊Dic6711yescharacteristic
679C2#2256329911yescharacteristic
680C2#2256330911yescharacteristic
681C2#2256362511yescharacteristic
682C2#2256365811yescharacteristic
683C2#2256404611yescharacteristic
684C2#2256407911yescharacteristic
685C2#2256473911yescharacteristic
686C2#2256475011yescharacteristic
687C2#2256541611yescharacteristic
688C2#2256559611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D67
commutatorC23×C67C23×C4
FittingC2×#389×C67C2
socle, prime radical, cosocleC24×C67C24
hypercenterC2×#389D67
hypocenterC67#14045
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
38. #389×C67C4semidirect
189. C4⋊C4×C67C4⋊C4semidirect
356. C67#14045semidirect
372. #389Dic67semidirect
531. C4⋊C4C4⋊Dic67semidirect

Maximal subgroups

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

subgroupindex
C2×#168632952
C2×C4⋊C4×Dic672
C2×C4×C4⋊Dic672
#225584742
#225584622
#225584432
#225584392
#225584382
C2×#389×C672
#1404567