Finite Group Databasebeta

← #31726588

Subgroups — #31726588

Order 17152.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863907C211yesmaximal, characteristic
2#22571039C214yesmaximal, complemented
3#22571030C212yesmaximal, complemented
4#22571011C212yesmaximal, complemented
5#22570990C214yesmaximal, complemented
6#22570981C212yesmaximal, complemented
7#22570962C212yesmaximal, complemented
8#22570153C212yesmaximal, complemented
9#22570132C212yesmaximal, complemented
10#22569835C214yesmaximal, complemented
11#22569467C212yesmaximal, complemented
12#22569443C212yesmaximal, complemented
13C2×#16863360C211yesmaximal, characteristic, complemented
14C22×C22⋊Q8×C67C211yesmaximal, characteristic, complemented
15C22×#11761628C2211yescharacteristic
16C2×#14524074C2214yescomplemented
17C22×#11761612C2212yescomplemented
18#16863907—21no—
19#16863907—21no—
20#16863907—21no—
21#16863907—21no—
22#16863907C2212yes—
23#16863907C2212yes—
24#16863907C2212yes—
25#16863907C2212yes—
26C2×#14524026—21no—
27C2×#14524022C2211yescharacteristic
28C2×#14524022C2211yescharacteristic
29C2×#14524017C2211yescharacteristic
30C2×#14524017C2211yescharacteristic
31C2×#14524012—21no—
32C2×C4×C22⋊D67—21no—
33C2×C4×C22⋊D67—21no—
34C2×#14524002C2211yescharacteristic
35#16863734C2218yescomplemented
36#16863731C2214yescomplemented
37#16863729C2214yescomplemented
38#16863726C2214yescomplemented
39#16863724C2214yescomplemented
40#16863714C2214yescomplemented
41#16863709C2214yescomplemented
42#16863652C2218yescomplemented
43#16863644C2218yescomplemented
44#16863635C2218yescomplemented
45#16863627C2218yescomplemented
46#16863556C2218yescomplemented
47#16863552C2214yescomplemented
48#16863552C2214yescomplemented
49#16863551C2214yescomplemented
50#16863546C2214yescomplemented
51#16863535C2214yescomplemented
52#16863535C2214yescomplemented
53#16863436C2214yescomplemented
54#16863405C2214yescomplemented
55#16863395C2214yescomplemented
56#16863360C2212yes—
57#16863360C2212yes—
58#16863360C2212yescomplemented
59#16863360C2212yescomplemented
60C2×C22⋊(C67⋊C8)C2212yes—
61C2×C22⋊(C67⋊C8)C2212yescomplemented
62C23×Q8×C67C2211yescharacteristic, complemented
63C24×C4×C67C2211yescharacteristic
64C2×C22⋊Q8×C67—21no—
65C2×C22⋊Q8×C67—21no—
66C2×C22⋊Q8×C67—21no—
67C2×C22⋊Q8×C67—21no—
68C2×C22⋊Q8×C67—21no—
69C2×C22⋊Q8×C67—21no—
70C2×C22⋊Q8×C67C2212yes—
71C2×C22⋊Q8×C67C2212yes—
72C2×C22⋊Q8×C67C2212yes—
73C2×C22⋊Q8×C67C2212yescomplemented
74C2×C22⋊Q8×C67C2212yescomplemented
75C2×C22⋊Q8×C67C2212yescomplemented
76C22×C4⋊C4×C67—21no—
77C22×C4⋊C4×C67C2211yescharacteristic, complemented
78C22×C22⋊C4×C67—21no—
79C2×#11761628—21no—
80C2×#11761628—21no—
81C2×#11761628—44no—
82C2×#11761628C2312yes—
83C2×#11761628C2312yes—
84C22×Dic134C2311yescharacteristic
85C22×D268C2311yescharacteristic
86C22×C22⋊D67—21no—
87C22×C22⋊D67—21no—
88C22×C22⋊D67—21no—
89C22×C4×D67—21no—
90#14524074—48no—
91C2×#11761618C2318yescomplemented
92C2×#11761615C2318yescomplemented
93C2×#11761612—44no—
94C2×#11761612C2314yes—
95C2×#11761612C2314yes—
96C22×C67⋊C8C2314yes—
97#14524026—22no—
98#14524026—22no—
99#14524026—22no—
100#14524026—22no—
101#14524022—21no—
102#14524022—21no—
103#14524022—21no—
104#14524022—21no—
105#14524022C2312yes—
106#14524022C2312yes—
107#14524022C2312yes—
108#14524022C2312yes—
109#14524017—21no—
110#14524017—21no—
111#14524017—21no—
112#14524017—21no—
113#14524017C2312yes—
114#14524017C2312yes—
115#14524017C2312yes—
116#14524017C2312yes—
117#14524012—22no—
118#14524012—22no—
119#14524012—22no—
120#14524012—22no—
121C4×C22⋊D67—22no—
122C4×C22⋊D67—22no—
123C4×C22⋊D67—22no—
124C4×C22⋊D67—22no—
125C4×C22⋊D67—22no—
126C4×C22⋊D67—22no—
127C4×C22⋊D67—22no—
128C4×C22⋊D67—22no—
129#14524002—21no—
130#14524002—21no—
131#14524002C2312yes—
132#14524002C2312yes—
133C2×C4⋊Dic67C2311yescharacteristic
134C2×C4⋊Dic67C2311yescharacteristic
135C2×Dic67⋊C4—21no—
136C2×Dic67⋊C4—21no—
137C2×C22⋊Dic67—21no—
138C2×C22⋊Dic67—21no—
139C2×C22⋊Dic67—21no—
140C2×(C2×D67)⋊C4—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×C4×Dic67—21no—
143#14523976C2318yescomplemented
144#14523974C2318yescomplemented
145#14523967C2318yescomplemented
146#14523967C2318yescomplemented
147#14523966C2318yescomplemented
148#14523963C2318yescomplemented
149C22⋊(C67⋊C8)C2314yes—
150C22⋊(C67⋊C8)C2314yes—
151C22⋊(C67⋊C8)C2314yes—
152C22⋊(C67⋊C8)C2314yes—
153C25×C67D411yescharacteristic
154C22×Q8×C67—21no—
155C22×Q8×C67—21no—
156C22×Q8×C67—21no—
157C22×Q8×C67—44no—
158C22×Q8×C67C2312yes—
159C22×Q8×C67C2312yes—
160C22×Q8×C67C2312yes—
161C23×C4×C67—21no—
162C23×C4×C67—21no—
163C23×C4×C67—44no—
164C23×C4×C67D411yescharacteristic
165C23×C4×C67D411yescharacteristic
166C23×C4×C67D411yescharacteristic
167C23×C4×C67D411yescharacteristic
168C23×C4×C67D411yescharacteristic
169C23×C4×C67D411yescharacteristic
170C23×C4×C67D411yescharacteristic
171C23×C4×C67C2311yescharacteristic
172C23×C4×C67C2311yescharacteristic
173C23×C4×C67C2311yescharacteristic
174C23×C4×C67C2311yescharacteristic
175C23×C4×C67C2311yescharacteristic
176C23×C4×C67C2311yescharacteristic
177C23×C4×C67C2311yescharacteristic
178C22⋊Q8×C67—22no—
179C22⋊Q8×C67—22no—
180C22⋊Q8×C67—22no—
181C22⋊Q8×C67—22no—
182C22⋊Q8×C67—22no—
183C22⋊Q8×C67—22no—
184C22⋊Q8×C67—22no—
185C22⋊Q8×C67—22no—
186C22⋊Q8×C67—22no—
187C22⋊Q8×C67—22no—
188C22⋊Q8×C67—22no—
189C22⋊Q8×C67—22no—
190C22⋊Q8×C67C2314yes—
191C22⋊Q8×C67C2314yes—
192C22⋊Q8×C67C2314yes—
193C22⋊Q8×C67C2314yes—
194C2×C4⋊C4×C67—22no—
195C2×C4⋊C4×C67—22no—
196C2×C4⋊C4×C67—22no—
197C2×C4⋊C4×C67—22no—
198C2×C4⋊C4×C67—22no—
199C2×C4⋊C4×C67—22no—
200C2×C4⋊C4×C67—21no—
201C2×C4⋊C4×C67—21no—
202C2×C4⋊C4×C67—21no—
203C2×C4⋊C4×C67C2312yes—
204C2×C4⋊C4×C67C2312yes—
205C2×C4⋊C4×C67C2312yes—
206C2×C22⋊C4×C67—22no—
207C2×C22⋊C4×C67—22no—
208C2×C22⋊C4×C67—22no—
209C2×C22⋊C4×C67—22no—
210C2×C22⋊C4×C67—22no—
211C2×C22⋊C4×C67—22no—
212C23×D67—21no—
213#11761628—28no—
214#11761628—44no—
215#11761628—44no—
216#11761628—44no—
217C2×Dic134—21no—
218C2×Dic134—42no—
219C2×Dic134C2412yes—
220C2×D268—21no—
221C2×D268—42no—
222C2×D268C2412yes—
223C2×C22⋊D67—22no—
224C2×C22⋊D67—22no—
225C2×C22⋊D67—22no—
226C2×C22⋊D67—22no—
227C2×C22⋊D67—22no—
228C2×C22⋊D67—22no—
229C2×C22⋊D67—44no—
230C2×C22⋊D67—44no—
231C2×C22⋊D67—44no—
232C22×Dic67—21no—
233C22×Dic67—21no—
234C22×Dic67—21no—
235C2×C4×D67—22no—
236C2×C4×D67—22no—
237C2×C4×D67—44no—
238#11761618—48no—
239#11761615—48no—
240#11761612—28no—
241#11761612—44no—
242C2×C67⋊C8—44no—
243C2×C67⋊C8C2418yes—
244C4⋊Dic67—21no—
245C4⋊Dic67—21no—
246C4⋊Dic67C2412yes—
247C4⋊Dic67C2412yes—
248Dic67⋊C4—22no—
249Dic67⋊C4—22no—
250Dic67⋊C4—22no—
251Dic67⋊C4—22no—
252C22⋊Dic67—22no—
253C22⋊Dic67—22no—
254C22⋊Dic67—22no—
255C22⋊Dic67—22no—
256C22⋊Dic67—22no—
257C22⋊Dic67—22no—
258(C2×D67)⋊C4—22no—
259(C2×D67)⋊C4—22no—
260(C2×D67)⋊C4—22no—
261(C2×D67)⋊C4—22no—
262C4×Dic67—22no—
263C4×Dic67—22no—
264C24×C67—24no—
265C24×C67—42no—
266C24×C67—42no—
267C24×C67C2×D411yescharacteristic
268C24×C67C2×D411yescharacteristic
269C24×C67C2×D411yescharacteristic
270C24×C67C2×D411yescharacteristic
271C24×C67C2×D411yescharacteristic
272C24×C67C2×D411yescharacteristic
273C24×C67C2×D411yescharacteristic
274C2×Q8×C67—22no—
275C2×Q8×C67—22no—
276C2×Q8×C67—22no—
277C2×Q8×C67—28no—
278C2×Q8×C67—44no—
279C2×Q8×C67—44no—
280C2×Q8×C67—44no—
281C2×Q8×C67—44no—
282C2×Q8×C67—44no—
283C2×Q8×C67C2414yes—
284C22×C4×C67—24no—
285C22×C4×C67—24no—
286C22×C4×C67—24no—
287C22×C4×C67—22no—
288C22×C4×C67—22no—
289C22×C4×C67—22no—
290C22×C4×C67—22no—
291C22×C4×C67—22no—
292C22×C4×C67—22no—
293C22×C4×C67—42no—
294C22×C4×C67—42no—
295C22×C4×C67—42no—
296C22×C4×C67—42no—
297C22×C4×C67—42no—
298C22×C4×C67—42no—
299C22×C4×C67—42no—
300C22×C4×C67—42no—
301C22×C4×C67—42no—
302C22×C4×C67—42no—
303C22×C4×C67—42no—
304C22×C4×C67—44no—
305C22×C4×C67—44no—
306C22×C4×C67C2×D411yescharacteristic
307C22×C4×C67C2×D411yescharacteristic
308C22×C4×C67C2×D411yescharacteristic
309C22×C4×C67C2×D411yescharacteristic
310C22×C4×C67C2×D411yescharacteristic
311C22×C4×C67C2×D411yescharacteristic
312C22×C4×C67C2×D411yescharacteristic
313C22×C4×C67C2×D411yescharacteristic
314C22×C4×C67C2×D411yescharacteristic
315C22×C4×C67C2×D411yescharacteristic
316C22×C4×C67C2×D411yescharacteristic
317C22×C4×C67C2×D411yescharacteristic
318C22×C4×C67C2×D411yescharacteristic
319C22×C4×C67C2×D411yescharacteristic
320C22×C4×C67C2×D411yescharacteristic
321C22×C4×C67C2×D411yescharacteristic
322C22×C4×C67C2×D411yescharacteristic
323C22×C4×C67C2×D411yescharacteristic
324C22×C4×C67C2×D411yescharacteristic
325C22×C4×C67C2×D411yescharacteristic
326C22×C4×C67C2×D411yescharacteristic
327C22×C4×C67C2411yescharacteristic
328C22×C4×C67C2411yescharacteristic
329C22×C4×C67C2411yescharacteristic
330C22×C4×C67C2411yescharacteristic
331C22×C4×C67C2411yescharacteristic
332C22×C4×C67C2411yescharacteristic
333C22×C4×C67C2411yescharacteristic
334C4⋊C4×C67—24no—
335C4⋊C4×C67—24no—
336C4⋊C4×C67—24no—
337C4⋊C4×C67—24no—
338C4⋊C4×C67—22no—
339C4⋊C4×C67—22no—
340C4⋊C4×C67—22no—
341C4⋊C4×C67C2414yes—
342C22⋊C4×C67—24no—
343C22⋊C4×C67—24no—
344C22⋊C4×C67—24no—
345C22⋊C4×C67—24no—
346C23×C67—22no—
347C23×C67—22no—
348C23×C67—22no—
349C23×C67—22no—
350C23×C67—22no—
351C23×C67—22no—
352C23×C67—22no—
353C23×C67—22no—
354C23×C67—22no—
355C23×C67—22no—
356C23×C67—22no—
357C23×C67—22no—
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—416no—
367C23×C67#13714yescomplemented
368C23×C67C22×D411yescharacteristic
369C23×C67C22×D411yescharacteristic
370C23×C67C22×D411yescharacteristic
371C23×C67C22×D411yescharacteristic
372C23×C67C22×D411yescharacteristic
373C23×C67C22×D411yescharacteristic
374C23×C67C22×D411yescharacteristic
375C22×D67—22no—
376C22×D67—42no—
377C22×D67—42no—
378C22×D67—42no—
379Q8×C67—28no—
380Q8×C67—44no—
381Q8×C67—44no—
382Q8×C67—44no—
383C2×C4×C67—22no—
384C2×C4×C67—22no—
385C2×C4×C67—22no—
386C2×C4×C67—22no—
387C2×C4×C67—22no—
388C2×C4×C67—22no—
389C2×C4×C67—22no—
390C2×C4×C67—22no—
391C2×C4×C67—22no—
392C2×C4×C67—22no—
393C2×C4×C67—22no—
394C2×C4×C67—22no—
395C2×C4×C67—22no—
396C2×C4×C67—22no—
397C2×C4×C67—22no—
398C2×C4×C67—24no—
399C2×C4×C67—24no—
400C2×C4×C67—41no—
401C2×C4×C67—41no—
402C2×C4×C67—41no—
403C2×C4×C67—41no—
404C2×C4×C67—41no—
405C2×C4×C67—41no—
406C2×C4×C67—41no—
407C2×C4×C67—41no—
408C2×C4×C67—41no—
409C2×C4×C67—41no—
410C2×C4×C67—41no—
411C2×C4×C67—41no—
412C2×C4×C67—44no—
413C2×C4×C67—44no—
414C2×C4×C67—44no—
415C2×C4×C67—44no—
416C2×C4×C67—44no—
417C2×C4×C67—44no—
418C2×C4×C67C22×D411yescharacteristic
419C2×C4×C67C22×D411yescharacteristic
420C2×C4×C67C22×D411yescharacteristic
421C2×C4×C67C22×D411yescharacteristic
422C2×C4×C67C22×D411yescharacteristic
423C2×C4×C67C22×D411yescharacteristic
424C2×C4×C67C22×D411yescharacteristic
425C2×C4×C67H(5,𝔽2)14yes—
426C2×C4×C67C2511yescharacteristic
427C22⋊D67—44no—
428C22⋊D67—44no—
429C22⋊D67—44no—
430C22⋊D67—44no—
431C22⋊D67—44no—
432C22⋊D67—44no—
433C2×Dic67—22no—
434C2×Dic67—22no—
435C2×Dic67—22no—
436C2×Dic67—42no—
437C2×Dic67—42no—
438C2×Dic67—42no—
439D268—24no—
440D268—42no—
441C4×D67—44no—
442C4×D67—44no—
443Dic134—24no—
444Dic134—42no—
445C67⋊C8—28no—
446C22×C67—28no—
447C22×C67—21no—
448C22×C67—21no—
449C22×C67—21no—
450C22×C67—21no—
451C22×C67—21no—
452C22×C67—21no—
453C22×C67—21no—
454C22×C67—21no—
455C22×C67—21no—
456C22×C67—21no—
457C22×C67—21no—
458C22×C67—21no—
459C22×C67—21no—
460C22×C67—21no—
461C22×C67—21no—
462C22×C67—21no—
463C22×C67—44no—
464C22×C67—44no—
465C22×C67—44no—
466C22×C67—44no—
467C22×C67—44no—
468C22×C67—44no—
469C22×C67#53412yes—
470C22×C67C2×#13712yes—
471C22×C67C2×#13712yes—
472C22×C67C2×#13712yes—
473C22×C67#57512yes—
474C22×C67C23×D411yescharacteristic
475C2×D67—42no—
476C2×D67—42no—
477C2×D67—42no—
478C2×D67—84no—
479C4×C67—21no—
480C4×C67—21no—
481C4×C67—21no—
482C4×C67—21no—
483C4×C67—21no—
484C4×C67—21no—
485C4×C67—44no—
486C4×C67—44no—
487C4×C67#53412yes—
488C4×C67C2×H(5,𝔽2)12yes—
489Dic67—42no—
490Dic67—42no—
491Dic67—42no—
492#60751—671nomaximal, Sylow
493C2×C67—22no—
494C2×C67—22no—
495C2×C67—22no—
496C2×C67—22no—
497C2×C67—22no—
498C2×C67—41no—
499C2×C67—41no—
500C2×C67C2×#53411yescharacteristic
501C2×C67C22×#13711yescharacteristic
502C2×C67C2×#57511yescharacteristic
503D67—82no—
504C2×#525—671no—
505C22×C22⋊Q8D6711yescharacteristic, complemented
506#3196—674no—
507#3195—672no—
508#3193—672no—
509#3190—674no—
510#3189—672no—
511#3187—672no—
512#3095—672no—
513#3092—672no—
514#3056—674no—
515#3007—672no—
516#3004—672no—
517C2×#407—671no—
518C67#6075111yescharacteristic, complemented, Sylow
519C22×#41—671no—
520C23×Q8C2×D6711yescharacteristic, complemented
521C24×C4C2×D6711yescharacteristic
522C2×#137—674no—
523C22×M16—672no—
524#525—672no—
525#525—672no—
526#525—672no—
527#525—672no—
528#525—1341no—
529#525—1341no—
530#525—1341no—
531#525—1341no—
532C2×#123—1341no—
533C2×C22⋊Q8—21no—
534C2×C22⋊Q8—21no—
535C2×C22⋊Q8—21no—
536C2×C22⋊Q8—21no—
537C2×C22⋊Q8—21no—
538C2×C22⋊Q8—21no—
539C2×C22⋊Q8—671no—
540C2×C22⋊Q8—671no—
541C2×C22⋊Q8C2×D6712yes—
542C2×C22⋊Q8C2×D6712yes—
543C2×C22⋊Q8C2×D6712yes—
544C2×C22⋊Q8C2×D6712yescomplemented
545C2×C22⋊Q8C2×D6712yescomplemented
546C2×C22⋊Q8C2×D6712yescomplemented
547C2×#121—671no—
548C2×#121—671no—
549C2×#120—1341no—
550C2×C4×D4—1341no—
551C2×C4×D4—1341no—
552C2×#117—671no—
553C22×C4⋊C4—21no—
554C22×C4⋊C4C2×D6711yescharacteristic, complemented
555C22×C22⋊C4—21no—
556#485—678no—
557#484—674no—
558#484—674no—
559#483—674no—
560#483—674no—
561#481—674no—
562#480—674no—
563#470—678no—
564#468—678no—
565#467—678no—
566#465—678no—
567#452—678no—
568#451—674no—
569#451—674no—
570#451—674no—
571#450—674no—
572#448—674no—
573#448—674no—
574#428—674no—
575#419—674no—
576#417—674no—
577#407—672no—
578#407—672no—
579#407—672no—
580#407—672no—
581C2×C22⋊C8—672no—
582C2×C22⋊C8—672no—
583C25C22⋊D6711yescharacteristic
584C2×#41—2684no—
585C2×#41—672no—
586C2×#41—672no—
587C2×#41—1341no—
588C2×#41—1341no—
589C22×Q8—21no—
590C22×Q8—21no—
591C22×Q8—21no—
592C22×Q8—44no—
593C22×Q8—671no—
594C22×Q8C22×D6712yes—
595C22×Q8C22×D6712yes—
596C22×Q8C22×D6712yes—
597C22×D4—671no—
598C22×D4—1341no—
599C22×D4—1341no—
600C22×D4—1341no—
601C23×C4—21no—
602C23×C4—21no—
603C23×C4—44no—
604C23×C4—1341no—
605C23×C4C22⋊D6711yescharacteristic
606C23×C4C22⋊D6711yescharacteristic
607C23×C4C22⋊D6711yescharacteristic
608C23×C4C22⋊D6711yescharacteristic
609C23×C4C22⋊D6711yescharacteristic
610C23×C4C22⋊D6711yescharacteristic
611C23×C4C22⋊D6711yescharacteristic
612C23×C4C22×D6711yescharacteristic
613C23×C4C22×D6711yescharacteristic
614C23×C4C22×D6711yescharacteristic
615C23×C4C22×D6711yescharacteristic
616C23×C4C22×D6711yescharacteristic
617C23×C4C22×D6711yescharacteristic
618C23×C4C22×D6711yescharacteristic
619#137—2688no—
620C2×Q16—678no—
621C2×SD16—678no—
622C2×M16—2684no—
623C2×M16—674no—
624C2×M16—674no—
625C22×C8—674no—
626#123—1342no—
627#123—1342no—
628#123—1342no—
629#123—1342no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
633C22⋊Q8—22no—
634C22⋊Q8—22no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—672no—
643C22⋊Q8—672no—
644C22⋊Q8—672no—
645C22⋊Q8—672no—
646C22⋊Q8—1341no—
647C22⋊Q8—1341no—
648C22⋊Q8—1341no—
649C22⋊Q8—1341no—
650C22⋊Q8C22×D6714yes—
651C22⋊Q8C22×D6714yes—
652C22⋊Q8C22×D6714yes—
653C22⋊Q8C22×D6714yes—
654#121—672no—
655#121—672no—
656#121—672no—
657#121—672no—
658#121—1341no—
659#121—1341no—
660#121—1341no—
661#121—1341no—
662#120—1342no—
663#120—1342no—
664#120—1342no—
665#120—1342no—
666C4×D4—1342no—
667C4×D4—1342no—
668C4×D4—1342no—
669C4×D4—1342no—
670C4×D4—1342no—
671C4×D4—1342no—
672C4×D4—1342no—
673C4×D4—1342no—
674#117—672no—
675#117—672no—
676#117—1341no—
677#117—1341no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—671no—
688C2×C4⋊C4—671no—
689C2×C4⋊C4—1341no—
690C2×C4⋊C4—1341no—
691C2×C4⋊C4C22×D6712yes—
692C2×C4⋊C4C22×D6712yes—
693C2×C4⋊C4C22×D6712yes—
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—1341no—
701C2×C22⋊C4—1341no—
702C2×C22⋊C4—1341no—
703C2×C22⋊C4—1341no—
704C2×C22⋊C4—1341no—
705C2×C42—1341no—
706#107—678no—
707#106—678no—
708#103—678no—
709#103—678no—
710#103—678no—
711#102—678no—
712C22⋊C8—674no—
713C22⋊C8—674no—
714C22⋊C8—674no—
715C22⋊C8—674no—
716C24—24no—
717C24—42no—
718C24—42no—
719C24—1341no—
720C24C2×C22⋊D6711yescharacteristic
721C24C2×C22⋊D6711yescharacteristic
722C24C2×C22⋊D6711yescharacteristic
723C24C2×C22⋊D6711yescharacteristic
724C24C2×C22⋊D6711yescharacteristic
725C24C2×C22⋊D6711yescharacteristic
726C24C2×C22⋊D6711yescharacteristic
727#41—2684no—
728#41—2684no—
729#41—2684no—
730#41—1348no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—28no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—2682no—
741C2×Q8—672no—
742C2×Q8—1341no—
743C2×Q8C23×D6714yes—
744C2×D4—2682no—
745C2×D4—2684no—
746C2×D4—2684no—
747C2×D4—2684no—
748C2×D4—672no—
749C2×D4—1342no—
750C2×D4—1342no—
751C2×D4—1342no—
752C2×D4—1342no—
753C2×D4—1342no—
754C2×D4—1342no—
755C2×D4—1341no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—2684no—
779C22×C4—1341no—
780C22×C4—1341no—
781C22×C4—1341no—
782C22×C4—1342no—
783C22×C4—1342no—
784C22×C4C2×C22⋊D6711yescharacteristic
785C22×C4C2×C22⋊D6711yescharacteristic
786C22×C4C2×C22⋊D6711yescharacteristic
787C22×C4C2×C22⋊D6711yescharacteristic
788C22×C4C2×C22⋊D6711yescharacteristic
789C22×C4C2×C22⋊D6711yescharacteristic
790C22×C4C2×C22⋊D6711yescharacteristic
791C22×C4C2×C22⋊D6711yescharacteristic
792C22×C4C2×C22⋊D6711yescharacteristic
793C22×C4C2×C22⋊D6711yescharacteristic
794C22×C4C2×C22⋊D6711yescharacteristic
795C22×C4C2×C22⋊D6711yescharacteristic
796C22×C4C2×C22⋊D6711yescharacteristic
797C22×C4C2×C22⋊D6711yescharacteristic
798C22×C4C2×C22⋊D6711yescharacteristic
799C22×C4C2×C22⋊D6711yescharacteristic
800C22×C4C2×C22⋊D6711yescharacteristic
801C22×C4C2×C22⋊D6711yescharacteristic
802C22×C4C2×C22⋊D6711yescharacteristic
803C22×C4C2×C22⋊D6711yescharacteristic
804C22×C4C2×C22⋊D6711yescharacteristic
805C22×C4C23×D6711yescharacteristic
806C22×C4C23×D6711yescharacteristic
807C22×C4C23×D6711yescharacteristic
808C22×C4C23×D6711yescharacteristic
809C22×C4C23×D6711yescharacteristic
810C22×C4C23×D6711yescharacteristic
811C22×C4C23×D6711yescharacteristic
812Q16—2688no—
813SD16—2688no—
814M16—2684no—
815M16—1348no—
816C2×C8—2684no—
817C2×C8—678no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—672no—
826C4⋊C4—672no—
827C4⋊C4—1341no—
828C4⋊C4—1341no—
829C4⋊C4—1342no—
830C4⋊C4—1342no—
831C4⋊C4—1342no—
832C4⋊C4—1342no—
833C4⋊C4C23×D6714yes—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—1342no—
839C22⋊C4—1342no—
840C22⋊C4—1342no—
841C22⋊C4—1342no—
842C22⋊C4—1342no—
843C22⋊C4—1342no—
844C22⋊C4—1342no—
845C22⋊C4—1342no—
846C22⋊C4—1342no—
847C22⋊C4—1342no—
848C42—1342no—
849C42—1342no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—416no—
871C23—2682no—
872C23—2682no—
873C23—2682no—
874C23—1342no—
875C23#1452407414yescomplemented
876C23C22×C22⋊D6711yescharacteristic
877C23C22×C22⋊D6711yescharacteristic
878C23C22×C22⋊D6711yescharacteristic
879C23C22×C22⋊D6711yescharacteristic
880C23C22×C22⋊D6711yescharacteristic
881C23C22×C22⋊D6711yescharacteristic
882C23C22×C22⋊D6711yescharacteristic
883Q8—28no—
884Q8—44no—
885Q8—44no—
886Q8—44no—
887Q8—2682no—
888Q8—1344no—
889D4—2682no—
890D4—2684no—
891D4—2684no—
892D4—2684no—
893D4—2684no—
894D4—2684no—
895D4—2684no—
896D4—1344no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—2684no—
933C2×C4—2682no—
934C2×C4—2682no—
935C2×C4—2682no—
936C2×C4—2684no—
937C2×C4—1342no—
938C2×C4—1342no—
939C2×C4—1342no—
940C2×C4C22×C22⋊D6711yescharacteristic
941C2×C4C22×C22⋊D6711yescharacteristic
942C2×C4C22×C22⋊D6711yescharacteristic
943C2×C4C22×C22⋊D6711yescharacteristic
944C2×C4C22×C22⋊D6711yescharacteristic
945C2×C4C22×C22⋊D6711yescharacteristic
946C2×C4C22×C22⋊D6711yescharacteristic
947C2×C4#1452408814yes—
948C2×C4C24×D6711yescharacteristic
949C8—1348no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—2682no—
974C22—2682no—
975C22—2682no—
976C22—5364no—
977C22#1686395512yes—
978C22C2×#1452407412yes—
979C22C2×#1452407412yes—
980C22C2×#1452407412yes—
981C22#1686419412yes—
982C22C23×C22⋊D6711yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—44no—
990C4—44no—
991C4—2682no—
992C4—2682no—
993C4—2682no—
994C4#1686395512yes—
995C4C2×#1452408812yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—5362no—
1004C2C2×#1686395511yescharacteristic
1005C2C22×#1452407411yescharacteristic
1006C2C2×#1686419411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC22×C22⋊Q8×C67C2
socleC22×C67C23×D4
prime radicalC2×#16863907C2
hypercenterC22×C22⋊Q8D67
hypocenterC67#60751
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #22571039C2semidirect
3. #22571030C2semidirect
4. #22571011C2semidirect
5. #22570990C2semidirect
6. #22570981C2semidirect
7. #22570962C2semidirect
8. #22570153C2semidirect
9. #22570132C2semidirect
10. #22569835C2semidirect
11. #22569467C2semidirect
12. #22569443C2semidirect
13. C2×#16863360C2semidirect
14. C22×C22⋊Q8×C67C2semidirect
16. C2×#14524074C22semidirect
17. C22×#11761612C22semidirect
35. #16863734C22semidirect
36. #16863731C22semidirect
37. #16863729C22semidirect
38. #16863726C22semidirect
39. #16863724C22semidirect
40. #16863714C22semidirect
41. #16863709C22semidirect
42. #16863652C22semidirect
43. #16863644C22semidirect
44. #16863635C22semidirect
45. #16863627C22semidirect
46. #16863556C22semidirect
47. #16863552C22semidirect
48. #16863552C22semidirect
49. #16863551C22semidirect
50. #16863546C22semidirect
51. #16863535C22semidirect
52. #16863535C22semidirect
53. #16863436C22semidirect
54. #16863405C22semidirect
55. #16863395C22semidirect
58. #16863360C22semidirect
59. #16863360C22semidirect
61. C2×C22⋊(C67⋊C8)C22semidirect
62. C23×Q8×C67C22semidirect
73. C2×C22⋊Q8×C67C22semidirect
74. C2×C22⋊Q8×C67C22semidirect
75. C2×C22⋊Q8×C67C22semidirect
77. C22×C4⋊C4×C67C22semidirect
91. C2×#11761618C23semidirect
92. C2×#11761615C23semidirect
143. #14523976C23semidirect
144. #14523974C23semidirect
145. #14523967C23semidirect
146. #14523967C23semidirect
147. #14523966C23semidirect
148. #14523963C23semidirect
367. C23×C67#137semidirect
505. C22×C22⋊Q8D67semidirect
518. C67#60751semidirect
520. C23×Q8C2×D67semidirect
544. C2×C22⋊Q8C2×D67semidirect
545. C2×C22⋊Q8C2×D67semidirect
546. C2×C22⋊Q8C2×D67semidirect
554. C22×C4⋊C4C2×D67semidirect
875. C23#14524074semidirect

Maximal subgroups

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

subgroupindex
C2×#168639072
#225710392
#225710302
#225710112
#225709902
#225709812
#225709622
#225701532
#225701322
#225698352
#225694672
#225694432
C2×#168633602
C22×C22⋊Q8×C672
#6075167