Finite Group Databasebeta

← #30823110

Subgroups — #30823110

Order 17152.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863360C211yesmaximal, characteristic, complemented
2#22562592C211yesmaximal, characteristic, complemented
3#22558752C214yesmaximal, complemented
4#22558742C212yesmaximal, complemented
5#22558738C212yesmaximal, complemented
6#22558700C214yesmaximal, complemented
7C2×#525×C67C211yesmaximal, characteristic
8C22×#11761612—21no—
9C2×#14524002—21no—
10#16863360—21no—
11#16863360—21no—
12#16863360C2212yes—
13#16863360C2212yescomplemented
14C2×C22⋊(C67⋊C8)—21no—
15C2×C22⋊(C67⋊C8)C2212yescomplemented
16#16863259C2212yes—
17#16863256—21no—
18#16863256C2212yescomplemented
19#16863252—21no—
20C4×C22⋊Dic67—21no—
21C4×C22⋊Dic67C2212yescomplemented
22#16863133C2218yescomplemented
23#16863130C2218yescomplemented
24C22×#41×C67C411yescharacteristic, complemented
25C24×C4×C67C2211yescharacteristic
26#525×C67—21no—
27#525×C67—21no—
28#525×C67—21no—
29#525×C67—21no—
30#525×C67C412yescomplemented
31#525×C67C412yescomplemented
32#525×C67C2212yes—
33#525×C67C2212yes—
34C2×#123×C67—21no—
35C2×C22⋊Q8×C67C411yescharacteristic, complemented
36C2×C22⋊Q8×C67C2211yescharacteristic
37C2×#121×C67C411yescharacteristic, complemented
38C2×#121×C67C2211yescharacteristic
39C2×#120×C67—21no—
40C2×C4×D4×C67—21no—
41C2×C4×D4×C67—21no—
42C2×#117×C67C411yescharacteristic, complemented
43C2×#11761612—22no—
44C2×#11761612—22no—
45C2×#11761612—44no—
46C22×C67⋊C8—22no—
47#14524002—44no—
48C2×C4⋊Dic67—22no—
49C2×C22⋊Dic67—22no—
50C2×C22⋊Dic67—22no—
51C2×C22⋊Dic67—22no—
52C2×C4×Dic67—22no—
53C22⋊(C67⋊C8)—22no—
54C22⋊(C67⋊C8)—22no—
55C22⋊(C67⋊C8)—22no—
56C22⋊(C67⋊C8)C2314yes—
57C67⋊#95—22no—
58C67⋊#95C2314yes—
59C25×C67D411yescharacteristic
60C2×#41×C67—21no—
61C2×#41×C67—21no—
62C2×#41×C67—44no—
63C2×#41×C67C2×C412yes—
64C2×#41×C67C2×C412yes—
65C22×Q8×C67C2×C411yescharacteristic
66C22×D4×C67—21no—
67C22×D4×C67—21no—
68C22×D4×C67—21no—
69C22×D4×C67C2×C411yescharacteristic
70C23×C4×C67—21no—
71C23×C4×C67—44no—
72C23×C4×C67C2×C411yescharacteristic
73C23×C4×C67C2×C411yescharacteristic
74C23×C4×C67C2×C411yescharacteristic
75C23×C4×C67C2×C411yescharacteristic
76C23×C4×C67D411yescharacteristic
77C23×C4×C67D411yescharacteristic
78C23×C4×C67D411yescharacteristic
79C23×C4×C67D411yescharacteristic
80C23×C4×C67D411yescharacteristic
81C23×C4×C67D411yescharacteristic
82C23×C4×C67D411yescharacteristic
83C23×C4×C67C2311yescharacteristic
84C23×C4×C67C2311yescharacteristic
85C23×C4×C67C2311yescharacteristic
86#123×C67—22no—
87#123×C67—22no—
88#123×C67—22no—
89#123×C67—22no—
90C22⋊Q8×C67—21no—
91C22⋊Q8×C67—21no—
92C22⋊Q8×C67—21no—
93C22⋊Q8×C67—21no—
94C22⋊Q8×C67C2×C412yes—
95C22⋊Q8×C67C2×C412yes—
96C22⋊Q8×C67C2×C412yes—
97C22⋊Q8×C67C2312yes—
98#121×C67—21no—
99#121×C67—21no—
100#121×C67—21no—
101#121×C67—21no—
102#121×C67C2×C412yes—
103#121×C67C2×C412yes—
104#121×C67C2×C412yes—
105#121×C67C2312yes—
106#120×C67—22no—
107#120×C67—22no—
108#120×C67—22no—
109#120×C67—22no—
110C4×D4×C67—22no—
111C4×D4×C67—22no—
112C4×D4×C67—22no—
113C4×D4×C67—22no—
114C4×D4×C67—22no—
115C4×D4×C67—22no—
116C4×D4×C67—22no—
117C4×D4×C67—22no—
118#117×C67—21no—
119#117×C67—21no—
120#117×C67C2×C412yes—
121#117×C67C2×C412yes—
122C2×C4⋊C4×C67—21no—
123C2×C4⋊C4×C67—21no—
124C2×C4⋊C4×C67C2×C411yescharacteristic
125C2×C4⋊C4×C67C2×C411yescharacteristic
126C2×C22⋊C4×C67—21no—
127C2×C22⋊C4×C67—21no—
128C2×C22⋊C4×C67—21no—
129C2×C22⋊C4×C67—21no—
130C2×C22⋊C4×C67—21no—
131C2×C42×C67—21no—
132C22×Dic67—24no—
133#11761612—44no—
134#11761612—44no—
135C2×C67⋊C8—24no—
136C2×C67⋊C8—44no—
137C4⋊Dic67—44no—
138C22⋊Dic67—44no—
139C22⋊Dic67—44no—
140C22⋊Dic67—44no—
141C4×Dic67—44no—
142C24×C67—21no—
143C24×C67—42no—
144C24×C67—42no—
145C24×C67—42no—
146C24×C67C22⋊C411yescharacteristic
147C24×C67C22⋊C411yescharacteristic
148C24×C67C22⋊C411yescharacteristic
149C24×C67C22⋊C411yescharacteristic
150C24×C67C2×D411yescharacteristic
151C24×C67C2×D411yescharacteristic
152C24×C67C2×D411yescharacteristic
153#41×C67—44no—
154#41×C67—44no—
155#41×C67—44no—
156#41×C67—44no—
157C2×Q8×C67—21no—
158C2×Q8×C67—42no—
159C2×Q8×C67C22×C412yes—
160C2×D4×C67—22no—
161C2×D4×C67—22no—
162C2×D4×C67—22no—
163C2×D4×C67—22no—
164C2×D4×C67—22no—
165C2×D4×C67—22no—
166C2×D4×C67—21no—
167C2×D4×C67—42no—
168C2×D4×C67—44no—
169C2×D4×C67—44no—
170C2×D4×C67—44no—
171C2×D4×C67C22×C412yes—
172C22×C4×C67—24no—
173C22×C4×C67—24no—
174C22×C4×C67—24no—
175C22×C4×C67—21no—
176C22×C4×C67—21no—
177C22×C4×C67—21no—
178C22×C4×C67—22no—
179C22×C4×C67—22no—
180C22×C4×C67—42no—
181C22×C4×C67—42no—
182C22×C4×C67—42no—
183C22×C4×C67—42no—
184C22×C4×C67—42no—
185C22×C4×C67—42no—
186C22×C4×C67—42no—
187C22×C4×C67—42no—
188C22×C4×C67—42no—
189C22×C4×C67—42no—
190C22×C4×C67—42no—
191C22×C4×C67—44no—
192C22×C4×C67C22⋊C411yescharacteristic
193C22×C4×C67C22⋊C411yescharacteristic
194C22×C4×C67C22⋊C411yescharacteristic
195C22×C4×C67C22⋊C411yescharacteristic
196C22×C4×C67C22⋊C411yescharacteristic
197C22×C4×C67C22⋊C411yescharacteristic
198C22×C4×C67C22⋊C411yescharacteristic
199C22×C4×C67C22⋊C411yescharacteristic
200C22×C4×C67C22⋊C411yescharacteristic
201C22×C4×C67C22⋊C411yescharacteristic
202C22×C4×C67C22⋊C411yescharacteristic
203C22×C4×C67C22⋊C411yescharacteristic
204C22×C4×C67C22×C411yescharacteristic
205C22×C4×C67C22×C411yescharacteristic
206C22×C4×C67C22×C411yescharacteristic
207C22×C4×C67C22×C411yescharacteristic
208C22×C4×C67C22×C411yescharacteristic
209C22×C4×C67C22×C411yescharacteristic
210C22×C4×C67C2×D411yescharacteristic
211C22×C4×C67C2×D411yescharacteristic
212C22×C4×C67C2×D411yescharacteristic
213C22×C4×C67C2×D411yescharacteristic
214C22×C4×C67C2×D411yescharacteristic
215C22×C4×C67C2×D411yescharacteristic
216C22×C4×C67C2×D411yescharacteristic
217C22×C4×C67C2×D411yescharacteristic
218C22×C4×C67C2×D411yescharacteristic
219C22×C4×C67C2411yescharacteristic
220C4⋊C4×C67—22no—
221C4⋊C4×C67—22no—
222C4⋊C4×C67—22no—
223C4⋊C4×C67—21no—
224C4⋊C4×C67—21no—
225C4⋊C4×C67—22no—
226C4⋊C4×C67C22×C412yes—
227C4⋊C4×C67C22×C412yes—
228C22⋊C4×C67—22no—
229C22⋊C4×C67—22no—
230C22⋊C4×C67—22no—
231C22⋊C4×C67—22no—
232C22⋊C4×C67—22no—
233C22⋊C4×C67—22no—
234C22⋊C4×C67—22no—
235C22⋊C4×C67—22no—
236C22⋊C4×C67—22no—
237C22⋊C4×C67—22no—
238C42×C67—22no—
239C42×C67—22no—
240C23×C67—22no—
241C23×C67—22no—
242C23×C67—22no—
243C23×C67—22no—
244C23×C67—22no—
245C23×C67—22no—
246C23×C67—22no—
247C23×C67—22no—
248C23×C67—22no—
249C23×C67—22no—
250C23×C67—41no—
251C23×C67—41no—
252C23×C67—41no—
253C23×C67—41no—
254C23×C67—41no—
255C23×C67—41no—
256C23×C67—41no—
257C23×C67—41no—
258C23×C67—41no—
259C23×C67—41no—
260C23×C67—41no—
261C23×C67—41no—
262C23×C67—42no—
263C23×C67—42no—
264C23×C67—416no—
265C23×C67—42no—
266C23×C67C2×C22⋊C411yescharacteristic
267C23×C67C2×C22⋊C411yescharacteristic
268C23×C67C2×C22⋊C411yescharacteristic
269C23×C67C2×C22⋊C411yescharacteristic
270C23×C67C2×C22⋊C411yescharacteristic
271C23×C67C2×C22⋊C411yescharacteristic
272C23×C67C22×D411yescharacteristic
273Q8×C67—42no—
274Q8×C67—42no—
275D4×C67—42no—
276D4×C67—42no—
277D4×C67—44no—
278D4×C67—44no—
279D4×C67—44no—
280D4×C67—44no—
281D4×C67—44no—
282D4×C67—44no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—41no—
302C2×C4×C67—41no—
303C2×C4×C67—41no—
304C2×C4×C67—41no—
305C2×C4×C67—41no—
306C2×C4×C67—41no—
307C2×C4×C67—41no—
308C2×C4×C67—41no—
309C2×C4×C67—41no—
310C2×C4×C67—41no—
311C2×C4×C67—41no—
312C2×C4×C67—41no—
313C2×C4×C67—42no—
314C2×C4×C67—42no—
315C2×C4×C67—42no—
316C2×C4×C67—44no—
317C2×C4×C67—44no—
318C2×C4×C67#9914yes—
319C2×C4×C67C2×C22⋊C411yescharacteristic
320C2×C4×C67C2×C22⋊C411yescharacteristic
321C2×C4×C67C2×C22⋊C411yescharacteristic
322C2×C4×C67C2×C22⋊C411yescharacteristic
323C2×C4×C67C2×C22⋊C411yescharacteristic
324C2×C4×C67C2×C22⋊C411yescharacteristic
325C2×C4×C67C23×C411yescharacteristic
326C2×C4×C67C22×D411yescharacteristic
327C2×Dic67—44no—
328C2×Dic67—44no—
329C2×Dic67—44no—
330C67⋊C8—44no—
331C22×C67—21no—
332C22×C67—21no—
333C22×C67—21no—
334C22×C67—21no—
335C22×C67—21no—
336C22×C67—21no—
337C22×C67—21no—
338C22×C67—21no—
339C22×C67—21no—
340C22×C67—21no—
341C22×C67—21no—
342C22×C67—21no—
343C22×C67—21no—
344C22×C67—21no—
345C22×C67—21no—
346C22×C67—21no—
347C22×C67—21no—
348C22×C67—21no—
349C22×C67—44no—
350C22×C67—44no—
351C22×C67—44no—
352C22×C67—44no—
353C22×C67—44no—
354C22×C67—44no—
355C22×C67—44no—
356C22×C67—42no—
357C22×C67—42no—
358C22×C67—42no—
359C22×C67—84no—
360C22×C67C2×#9912yes—
361C22×C67#42112yes—
362C22×C67C22×C22⋊C411yescharacteristic
363C22×C67#57512yes—
364C4×C67—21no—
365C4×C67—21no—
366C4×C67—21no—
367C4×C67—21no—
368C4×C67—21no—
369C4×C67—21no—
370C4×C67—42no—
371C4×C67—42no—
372C4×C67—42no—
373C4×C67C2×#9912yes—
374C4×C67C2×#9912yes—
375Dic67—84no—
376#17559—671nomaximal, Sylow
377C2×C67—22no—
378C2×C67—22no—
379C2×C67—22no—
380C2×C67—41no—
381C2×C67—41no—
382C2×C67—41no—
383C2×C67—41no—
384C2×C67—82no—
385C2×C67C22×#9911yescharacteristic
386C2×C67#289611yescharacteristic
387C2×C67C2×#42111yescharacteristic
388C2×#525D6711yescharacteristic
389C2×#407—671no—
390#2280—671no—
391#1513—674no—
392#1511—672no—
393#1510—672no—
394#1501—674no—
395C67#1755911yescharacteristic, complemented, Sylow
396C22×#41Dic6711yescharacteristic, complemented
397C24×C4C2×D6711yescharacteristic
398C22×M16—1341no—
399#525—21no—
400#525—21no—
401#525—21no—
402#525—21no—
403#525Dic6712yescomplemented
404#525Dic6712yescomplemented
405#525C2×D6712yes—
406#525C2×D6712yes—
407C2×#123—21no—
408C2×C22⋊Q8Dic6711yescharacteristic, complemented
409C2×C22⋊Q8C2×D6711yescharacteristic
410C2×#121Dic6711yescharacteristic, complemented
411C2×#121C2×D6711yescharacteristic
412C2×#120—21no—
413C2×C4×D4—21no—
414C2×C4×D4—21no—
415C2×#117—1341no—
416C2×#117Dic6711yescharacteristic, complemented
417#407—672no—
418#407—672no—
419#407—1341no—
420#407—1341no—
421C2×C22⋊C8—672no—
422C2×C22⋊C8—1341no—
423#381—672no—
424#380—672no—
425#380—1341no—
426#379—1341no—
427C4×C22⋊C4—672no—
428C4×C22⋊C4—1341no—
429#328—678no—
430#327—678no—
431C25C22⋊D6711yescharacteristic
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—44no—
435C2×#41C2×Dic6712yes—
436C2×#41C2×Dic6712yes—
437C22×Q8C2×Dic6711yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C2×Dic6711yescharacteristic
442C23×C4—21no—
443C23×C4—44no—
444C23×C4C2×Dic6711yescharacteristic
445C23×C4C2×Dic6711yescharacteristic
446C23×C4C2×Dic6711yescharacteristic
447C23×C4C2×Dic6711yescharacteristic
448C23×C4C22⋊D6711yescharacteristic
449C23×C4C22⋊D6711yescharacteristic
450C23×C4C22⋊D6711yescharacteristic
451C23×C4C22⋊D6711yescharacteristic
452C23×C4C22⋊D6711yescharacteristic
453C23×C4C22⋊D6711yescharacteristic
454C23×C4C22⋊D6711yescharacteristic
455C23×C4C22×D6711yescharacteristic
456C23×C4C22×D6711yescharacteristic
457C23×C4C22×D6711yescharacteristic
458C2×M16—2684no—
459C2×M16—1342no—
460C2×M16—1342no—
461C22×C8—1342no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—22no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8C2×Dic6712yes—
471C22⋊Q8C2×Dic6712yes—
472C22⋊Q8C2×Dic6712yes—
473C22⋊Q8C22×D6712yes—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121C2×Dic6712yes—
479#121C2×Dic6712yes—
480#121C2×Dic6712yes—
481#121C22×D6712yes—
482#120—22no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494#117—21no—
495#117—21no—
496#117—2684no—
497#117C2×Dic6712yes—
498#117C2×Dic6712yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—1342no—
502C2×C4⋊C4C2×Dic6711yescharacteristic
503C2×C4⋊C4C2×Dic6711yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1342no—
510C2×C22⋊C4—1342no—
511C2×C22⋊C4—1342no—
512C2×C42—21no—
513C2×C42—1342no—
514C22⋊C8—674no—
515C22⋊C8—1342no—
516C22⋊C8—1342no—
517C22⋊C8—1342no—
518#95—674no—
519#95—1342no—
520C24—21no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24C22⋊Dic6711yescharacteristic
525C24C22⋊Dic6711yescharacteristic
526C24C22⋊Dic6711yescharacteristic
527C24C22⋊Dic6711yescharacteristic
528C24C2×C22⋊D6711yescharacteristic
529C24C2×C22⋊D6711yescharacteristic
530C24C2×C22⋊D6711yescharacteristic
531#41—44no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—42no—
537C2×Q8C22×Dic6712yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4C22×Dic6712yes—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—44no—
570C22×C4—1344no—
571C22×C4C22⋊Dic6711yescharacteristic
572C22×C4C22⋊Dic6711yescharacteristic
573C22×C4C22⋊Dic6711yescharacteristic
574C22×C4C22⋊Dic6711yescharacteristic
575C22×C4C22⋊Dic6711yescharacteristic
576C22×C4C22⋊Dic6711yescharacteristic
577C22×C4C22⋊Dic6711yescharacteristic
578C22×C4C22⋊Dic6711yescharacteristic
579C22×C4C22⋊Dic6711yescharacteristic
580C22×C4C22⋊Dic6711yescharacteristic
581C22×C4C22⋊Dic6711yescharacteristic
582C22×C4C22⋊Dic6711yescharacteristic
583C22×C4C22×Dic6711yescharacteristic
584C22×C4C22×Dic6711yescharacteristic
585C22×C4C22×Dic6711yescharacteristic
586C22×C4C22×Dic6711yescharacteristic
587C22×C4C22×Dic6711yescharacteristic
588C22×C4C22×Dic6711yescharacteristic
589C22×C4C2×C22⋊D6711yescharacteristic
590C22×C4C2×C22⋊D6711yescharacteristic
591C22×C4C2×C22⋊D6711yescharacteristic
592C22×C4C2×C22⋊D6711yescharacteristic
593C22×C4C2×C22⋊D6711yescharacteristic
594C22×C4C2×C22⋊D6711yescharacteristic
595C22×C4C2×C22⋊D6711yescharacteristic
596C22×C4C2×C22⋊D6711yescharacteristic
597C22×C4C2×C22⋊D6711yescharacteristic
598C22×C4C23×D6711yescharacteristic
599M16—2684no—
600M16—2684no—
601C2×C8—2684no—
602C2×C8—1344no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4—2684no—
610C4⋊C4C22×Dic6712yes—
611C4⋊C4C22×Dic6712yes—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—2684no—
623C22⋊C4—2684no—
624C22⋊C4—2684no—
625C42—22no—
626C42—22no—
627C42—2684no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—416no—
653C23—42no—
654C23C2×C22⋊Dic6711yescharacteristic
655C23C2×C22⋊Dic6711yescharacteristic
656C23C2×C22⋊Dic6711yescharacteristic
657C23C2×C22⋊Dic6711yescharacteristic
658C23C2×C22⋊Dic6711yescharacteristic
659C23C2×C22⋊Dic6711yescharacteristic
660C23C22×C22⋊D6711yescharacteristic
661Q8—42no—
662Q8—42no—
663D4—42no—
664D4—42no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—2684no—
707C2×C4—2684no—
708C2×C4—2684no—
709C2×C4#1452395814yes—
710C2×C4C2×C22⋊Dic6711yescharacteristic
711C2×C4C2×C22⋊Dic6711yescharacteristic
712C2×C4C2×C22⋊Dic6711yescharacteristic
713C2×C4C2×C22⋊Dic6711yescharacteristic
714C2×C4C2×C22⋊Dic6711yescharacteristic
715C2×C4C2×C22⋊Dic6711yescharacteristic
716C2×C4C23×Dic6711yescharacteristic
717C2×C4C22×C22⋊D6711yescharacteristic
718C8—2684no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22C2×#1452395812yes—
749C22#1686341312yes—
750C22C22×C22⋊Dic6711yescharacteristic
751C22#1686419412yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—5364no—
762C4C2×#1452395812yes—
763C4C2×#1452395812yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×#1452395811yescharacteristic
773C2#2256872811yescharacteristic
774C2C2×#1686341311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
Fitting, prime radicalC2×#525×C67C2
socleC22×C67C22×C22⋊C4
cosocleC22×C4×C67C24
hypercenterC2×#525D67
hypocenterC67#17559
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16863360C2semidirect
2. #22562592C2semidirect
3. #22558752C2semidirect
4. #22558742C2semidirect
5. #22558738C2semidirect
6. #22558700C2semidirect
13. #16863360C22semidirect
15. C2×C22⋊(C67⋊C8)C22semidirect
18. #16863256C22semidirect
21. C4×C22⋊Dic67C22semidirect
22. #16863133C22semidirect
23. #16863130C22semidirect
24. C22×#41×C67C4semidirect
30. #525×C67C4semidirect
31. #525×C67C4semidirect
35. C2×C22⋊Q8×C67C4semidirect
37. C2×#121×C67C4semidirect
42. C2×#117×C67C4semidirect
395. C67#17559semidirect
396. C22×#41Dic67semidirect
403. #525Dic67semidirect
404. #525Dic67semidirect
408. C2×C22⋊Q8Dic67semidirect
410. C2×#121Dic67semidirect
416. C2×#117Dic67semidirect

Maximal subgroups

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

subgroupindex
C2×#168633602
#225625922
#225587522
#225587422
#225587382
#225587002
C2×#525×C672
#1755967