Finite Group Databasebeta

← #17979065

Subgroups — #17979065

Order 4352.

4982 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763876C211yesmaximal, characteristic, complemented
2C23×C22⋊#595C211yesmaximal, characteristic, complemented
3#14545306C218yesmaximal, complemented
4#14545290C214yesmaximal, complemented
5D4×C22⋊#595C214yesmaximal, complemented
6#14545269C214yesmaximal, complemented
7#14545263C211yesmaximal, characteristic, complemented
8#14545256C211yesmaximal, characteristic, complemented
9#120×#595C214yesmaximal, complemented
10C2×#11763750C211yesmaximal, characteristic, complemented
11#14545220C211yesmaximal, characteristic, complemented
12C2×#120×D17C211yesmaximal, characteristic
13C24×#595C2212yescomplemented
14#11763876—28no—
15C2×D4×#595C2214yescomplemented
16C2×D4×#595C2214yescomplemented
17C2×D4×#595C2218yescomplemented
18C2×#10587677C2212yescomplemented
19C22×C22⋊#595—28no—
20C22×C22⋊#595C2211yescharacteristic
21C22×C22⋊#595C2211yescharacteristic
22C22×C22⋊#595C2211yescharacteristic
23C22×C22⋊#595C2214yes—
24C22×C22⋊#595C2211yescharacteristic
25C22×C22⋊#595C2212yescomplemented
26C22×C22⋊#595C2214yescomplemented
27C22×C22⋊#595C2212yescomplemented
28C22×C22⋊#595C2214yescomplemented
29#11763761C2218yescomplemented
30#11763759C2218yescomplemented
31#11763759C2218yescomplemented
32#11763757C2218yescomplemented
33#11763757C2214yescomplemented
34#11763757C2218yescomplemented
35#11763757C2214yescomplemented
36#11763756C2214yescomplemented
37#11763756C2218yescomplemented
38#11763756C2214yescomplemented
39#11763752C2212yescomplemented
40#11763751C2214yescomplemented
41#11763750C2214yes—
42#11763750C2212yescomplemented
43#11763750C2212yescomplemented
44#11763750C2212yescomplemented
45C22⋊C4×#595C2214yescomplemented
46C22⋊C4×#595C2214yescomplemented
47C22⋊C4×#595C2218yescomplemented
48C4×C22⋊#595C2214yescomplemented
49C25×D17C2211yescharacteristic
50C22×D4×D17C2211yescharacteristic
51C22×D4×D17C2212yes—
52C2×#10587568C412yescomplemented
53C2×#10587568C411yescharacteristic, complemented
54C2×#10587639C411yescharacteristic, complemented
55C2×#10587623C412yescomplemented
56C2×#10587623C411yescharacteristic, complemented
57#120×D17C414yescomplemented
58#120×D17C412yescomplemented
59#120×D17C412yescomplemented
60#120×D17C2212yes—
61#120×D17C2212yes—
62#120×D17C2214yes—
63C2×C22⋊C4×D17C2211yescharacteristic
64C2×C22⋊C4×D17C2212yes—
65C2×C17×#120C411yescharacteristic, complemented
66C25×C17C2×C411yescharacteristic, complemented
67C24×D17—24no—
68C24×D17—24no—
69C24×D17—48no—
70C24×D17C2×C411yescharacteristic, complemented
71C24×D17C2×C412yescomplemented
72C24×D17C2×C411yescharacteristic, complemented
73C24×D17C2×C411yescharacteristic, complemented
74C24×D17C2×C412yescomplemented
75C24×D17C2311yescharacteristic
76C24×D17C2312yes—
77C24×D17C2312yes—
78C24×D17C2311yescharacteristic
79C24×D17C2311yescharacteristic
80C24×D17C2311yescharacteristic
81C23×#595—28no—
82C23×#595—48no—
83C23×#595C2318yes—
84C23×#595C2312yes—
85C23×#595C2312yes—
86C23×#595C2312yes—
87C23×#595C2312yes—
88C23×#595C2314yescomplemented
89C22×D4×C17C2×C411yescharacteristic, complemented
90C22×D4×C17C2×C412yescomplemented
91C22×C22⋊D17C2×C411yescharacteristic, complemented
92C22×C22⋊D17C2×C411yescharacteristic, complemented
93C22×C22⋊D17C2×C412yescomplemented
94C22×C22⋊D17C2×C412yescomplemented
95C2×D4×D17—24no—
96C2×D4×D17—24no—
97C2×D4×D17—48no—
98C2×D4×D17C2×C412yescomplemented
99C2×D4×D17C2×C414yescomplemented
100C2×D4×D17C2×C412yescomplemented
101C2×D4×D17C2×C414yescomplemented
102C2×D4×D17C2312yes—
103C2×D4×D17C2314yes—
104C2×D4×D17C2312yes—
105C2×D4×D17C2314yes—
106C22×D68C2×C411yescharacteristic, complemented
107C22×D68C2×C412yescomplemented
108C22×C4×D17C2311yescharacteristic
109C22×C4×D17C2312yes—
110C2×C22⋊#595—24no—
111C2×C22⋊#595—24no—
112C2×C22⋊#595—24no—
113C2×C22⋊#595—28no—
114C2×C22⋊#595—216no—
115C2×C22⋊#595—28no—
116C2×C22⋊#595—216no—
117C2×C22⋊#595—48no—
118C2×C22⋊#595D418yescomplemented
119C2×C22⋊#595C2312yes—
120C2×C22⋊#595C2312yes—
121C2×C22⋊#595C2318yes—
122C2×C22⋊#595C2312yes—
123C2×C22⋊#595C2312yes—
124C2×C22⋊#595C2312yes—
125C2×C22⋊#595C2312yes—
126C2×C22⋊#595C2318yes—
127C2×C22⋊#595C2318yes—
128C2×C22⋊#595C2312yes—
129C2×C22⋊#595C2312yes—
130C2×C22⋊#595C2314yescomplemented
131C2×C22⋊#595C2318yescomplemented
132D4×#595—216no—
133D4×#595—216no—
134D4×#595—416no—
135#10587677—28no—
136C2×C4⋊#595C2314yescomplemented
137C2×C4⋊#595C2318yescomplemented
138C2×C4×#595C2314yescomplemented
139C2×C4×#595C2318yescomplemented
140C17×#120C2×C412yescomplemented
141C17×#120C2×C414yescomplemented
142C17×#120C2×C412yescomplemented
143C2×C22⋊C4×C17C2×C412yescomplemented
144C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
145#10587639C2×C412yescomplemented
146#10587639C2×C414yescomplemented
147#10587639C2×C412yescomplemented
148C2×C22⋊Dic17C2×C412yescomplemented
149C2×C22⋊Dic17C2×C411yescharacteristic, complemented
150#10587623C2×C412yescomplemented
151#10587623C2×C414yescomplemented
152#10587623C2×C414yescomplemented
153#10587623C2×C412yescomplemented
154#10587623C2×C414yescomplemented
155#10587623C2×C414yescomplemented
156#10587623C2×C414yescomplemented
157C2×#63227C2×C412yescomplemented
158C2×#63227C2×C412yescomplemented
159C2×#63227C2×C412yescomplemented
160#10587568C2×C412yescomplemented
161#10587568C2×C414yescomplemented
162#10587568C2×C414yescomplemented
163#10587568C2×C412yescomplemented
164#10587568C2×C414yescomplemented
165#10587568C2×C414yescomplemented
166#10587568C2×C414yescomplemented
167C22⋊C4×D17C2×C414yescomplemented
168C22⋊C4×D17C2×C412yescomplemented
169C22⋊C4×D17C2×C414yescomplemented
170C22⋊C4×D17C2×C412yescomplemented
171C22⋊C4×D17C2312yes—
172C22⋊C4×D17C2314yes—
173C22⋊C4×D17C2312yes—
174C22⋊C4×D17C2314yes—
175(C2×#595)⋊C4C2318yescomplemented
176(C2×#595)⋊C4C2318yescomplemented
177(C2×#595)⋊C4C2318yescomplemented
178C24×C17—24no—
179C24×C17—44no—
180C24×C17C22×C411yescharacteristic
181C24×C17C22×C412yes—
182C24×C17C22×C412yes—
183C24×C17C22×C411yescharacteristic
184C24×C17C22×C411yescharacteristic
185C24×C17C22×C411yescharacteristic, complemented
186C23×D17—22no—
187C23×D17—22no—
188C23×D17—28no—
189C23×D17—24no—
190C23×D17—24no—
191C23×D17—28no—
192C23×D17—28no—
193C23×D17—24no—
194C23×D17—24no—
195C23×D17—24no—
196C23×D17—22no—
197C23×D17—24no—
198C23×D17—24no—
199C23×D17—22no—
200C23×D17—28no—
201C23×D17—28no—
202C23×D17—22no—
203C23×D17—22no—
204C23×D17—44no—
205C23×D17—44no—
206C23×D17—44no—
207C23×D17—44no—
208C23×D17—44no—
209C23×D17—44no—
210C23×D17—44no—
211C23×D17—44no—
212C23×D17—44no—
213C23×D17—44no—
214C23×D17—44no—
215C23×D17—44no—
216C23×D17—432no—
217C23×D17—432no—
218C23×D17C22×C411yescharacteristic
219C23×D17C22×C412yes—
220C23×D17C22×C412yes—
221C23×D17C22×C412yes—
222C23×D17C22×C412yes—
223C23×D17C22×C412yes—
224C23×D17C22×C412yes—
225C23×D17C22×C412yes—
226C23×D17C22×C411yescharacteristic
227C23×D17C22×C412yes—
228C23×D17C22×C411yescharacteristic
229C23×D17C22×C411yescharacteristic
230C23×D17C22×C411yescharacteristic
231C23×D17C22×C411yescharacteristic, complemented
232C23×D17C22×C412yescomplemented
233C23×D17C2×D414yes—
234C23×D17#4114yes—
235C23×D17C2412yes—
236C23×D17C2412yes—
237C23×D17C2411yescharacteristic
238C23×D17C2411yescharacteristic
239C23×D17C2411yescharacteristic
240C23×D17C2412yes—
241C22×#595—24no—
242C22×#595—216no—
243C22×#595—24no—
244C22×#595—24no—
245C22×#595—216no—
246C22×#595—28no—
247C22×#595—44no—
248C22×#595—48no—
249C22×#595—44no—
250C22×#595—48no—
251C22×#595—44no—
252C22×#595—44no—
253C22×#595—432no—
254C22×#595C2×D418yescomplemented
255C22×#595C2414yes—
256C22×#595C2414yes—
257C22×#595C2414yes—
258C22×#595C2414yes—
259C2×D4×C17—24no—
260C2×D4×C17—44no—
261C2×D4×C17C22×C412yes—
262C2×D4×C17C22×C414yes—
263C2×D4×C17C22×C412yescomplemented
264C2×D4×C17C22×C414yescomplemented
265C22×C4×C17C22×C411yescharacteristic, complemented
266C22×C4×C17C22×C412yescomplemented
267C2×C22⋊D17—24no—
268C2×C22⋊D17—24no—
269C2×C22⋊D17—44no—
270C2×C22⋊D17—44no—
271C2×C22⋊D17C22×C412yes—
272C2×C22⋊D17C22×C414yes—
273C2×C22⋊D17C22×C412yes—
274C2×C22⋊D17C22×C414yes—
275C2×C22⋊D17C22×C412yescomplemented
276C2×C22⋊D17C22×C412yescomplemented
277C2×C22⋊D17C22×C414yescomplemented
278C2×C22⋊D17C22×C414yescomplemented
279C22×Dic17C22×C411yescharacteristic, complemented
280C22×Dic17C22×C412yescomplemented
281D4×D17—28no—
282D4×D17—28no—
283D4×D17—24no—
284D4×D17—24no—
285D4×D17—24no—
286D4×D17—24no—
287D4×D17—216no—
288D4×D17—48no—
289D4×D17—48no—
290D4×D17—48no—
291C2×D68—24no—
292C2×D68—44no—
293C2×D68C22×C412yes—
294C2×D68C22×C414yes—
295C2×D68C22×C412yescomplemented
296C2×D68C22×C414yescomplemented
297C2×C4×D17—22no—
298C2×C4×D17—22no—
299C2×C4×D17—44no—
300C2×C4×D17C22×C412yescomplemented
301C2×C4×D17C22×C414yescomplemented
302C2×C4×D17C2412yes—
303C2×C4×D17C2414yes—
304C22⋊#595—24no—
305C22⋊#595—24no—
306C22⋊#595—24no—
307C22⋊#595—24no—
308C22⋊#595—24no—
309C22⋊#595—24no—
310C22⋊#595—216no—
311C22⋊#595—28no—
312C22⋊#595—216no—
313C22⋊#595—48no—
314C22⋊#595—48no—
315C22⋊#595C2×D418yes—
316C22⋊#595C2×D418yescomplemented
317C4⋊#595—28no—
318C4⋊#595—48no—
319C4×#595—28no—
320C4×#595—48no—
321C22⋊C4×C17C22×C412yes—
322C22⋊C4×C17C22×C414yes—
323C22⋊C4×C17C22×C414yescomplemented
324C22⋊C4×C17C22×C412yescomplemented
325C22⋊Dic17C22×C412yes—
326C22⋊Dic17C22×C414yes—
327C22⋊Dic17C22×C414yescomplemented
328C22⋊Dic17C22×C412yescomplemented
329#63227C22×C414yes—
330#63227C22×C414yes—
331#63227C22×C414yes—
332#63227C22×C414yescomplemented
333#63227C22×C414yescomplemented
334#63227C22×C414yescomplemented
335#34198—171nomaximal, Sylow
336C23×C17—22no—
337C23×C17—24no—
338C23×C17—24no—
339C23×C17—24no—
340C23×C17—22no—
341C23×C17—24no—
342C23×C17—24no—
343C23×C17—22no—
344C23×C17—42no—
345C23×C17—42no—
346C23×C17—42no—
347C23×C17—42no—
348C23×C17—42no—
349C23×C17—416no—
350C23×C17C4×D414yescomplemented
351C23×C17C23×C412yes—
352C23×C17C23×C412yes—
353C23×C17C23×C411yescharacteristic
354C23×C17C23×C411yescharacteristic
355C23×C17C23×C411yescharacteristic
356C23×C17C23×C412yes—
357C22×D17—216no—
358C22×D17—216no—
359C22×D17—22no—
360C22×D17—24no—
361C22×D17—24no—
362C22×D17—24no—
363C22×D17—24no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—24no—
367C22×D17—24no—
368C22×D17—24no—
369C22×D17—24no—
370C22×D17—24no—
371C22×D17—24no—
372C22×D17—22no—
373C22×D17—24no—
374C22×D17—24no—
375C22×D17—22no—
376C22×D17—24no—
377C22×D17—24no—
378C22×D17—24no—
379C22×D17—24no—
380C22×D17—24no—
381C22×D17—24no—
382C22×D17—24no—
383C22×D17—24no—
384C22×D17—24no—
385C22×D17—22no—
386C22×D17—22no—
387C22×D17—22no—
388C22×D17—22no—
389C22×D17—24no—
390C22×D17—28no—
391C22×D17—24no—
392C22×D17—24no—
393C22×D17—48no—
394C22×D17—48no—
395C22×D17—42no—
396C22×D17—42no—
397C22×D17—42no—
398C22×D17—42no—
399C22×D17—42no—
400C22×D17—42no—
401C22×D17—42no—
402C22×D17—42no—
403C22×D17—42no—
404C22×D17—42no—
405C22×D17—42no—
406C22×D17—42no—
407C22×D17—416no—
408C22×D17—416no—
409C22×D17—416no—
410C22×D17—416no—
411C22×D17—42no—
412C22×D17—44no—
413C22×D17—416no—
414C22×D17—432no—
415C22×D17—432no—
416C22×D17—416no—
417C22×D17—48no—
418C22×D17—48no—
419C22×D17—416no—
420C22×D17—84no—
421C22×D17—84no—
422C22×D17C4×D414yescomplemented
423C22×D17C4×D414yescomplemented
424C22×D17C4×D414yescomplemented
425C22×D17C23×C412yes—
426C22×D17C23×C412yes—
427C22×D17C23×C411yescharacteristic
428C22×D17C23×C411yescharacteristic
429C22×D17C23×C411yescharacteristic
430C22×D17C23×C412yes—
431C22×D17C22×D412yes—
432C22×D17C22×D412yes—
433C22×D17C22×D412yes—
434C22×D17C2×#4112yes—
435C22×D17C2×#4112yes—
436C22×D17C2×#4112yes—
437C22×D17H(5,𝔽2)18yes—
438C22×D17C2511yescharacteristic
439C2×#595—28no—
440C2×#595—24no—
441C2×#595—24no—
442C2×#595—24no—
443C2×#595—28no—
444C2×#595—28no—
445C2×#595—28no—
446C2×#595—48no—
447C2×#595—432no—
448C2×#595—48no—
449C2×#595—88no—
450C2×#595—84no—
451C2×#595—84no—
452C2×#595C22×D418yes—
453D4×C17—24no—
454D4×C17—24no—
455D4×C17—28no—
456D4×C17—44no—
457C2×C4×C17—22no—
458C2×C4×C17—42no—
459C2×C4×C17C23×C412yes—
460C2×C4×C17C23×C414yes—
461C22⋊D17—24no—
462C22⋊D17—24no—
463C22⋊D17—28no—
464C22⋊D17—24no—
465C22⋊D17—24no—
466C22⋊D17—28no—
467C22⋊D17—44no—
468C22⋊D17—44no—
469C2×Dic17—22no—
470C2×Dic17—42no—
471C2×Dic17C23×C412yes—
472C2×Dic17C23×C414yes—
473D68—24no—
474D68—24no—
475D68—28no—
476D68—44no—
477C4×D17—24no—
478C4×D17—22no—
479C4×D17—22no—
480C4×D17—28no—
481C4×D17—44no—
482C22×#120—171no—
483C2×#518—171no—
484C23×C22⋊C4—171no—
485#2358—178no—
486#2342—174no—
487D4×C22⋊C4—174no—
488#2321—174no—
489#2315—171no—
490#2308—171no—
491C4×#120—174no—
492C2×#379—171no—
493#2273—171no—
494C22×C17—28no—
495C22×C17—22no—
496C22×C17—22no—
497C22×C17—22no—
498C22×C17—22no—
499C22×C17—22no—
500C22×C17—22no—
501C22×C17—22no—
502C22×C17—24no—
503C22×C17—22no—
504C22×C17—22no—
505C22×C17—44no—
506C22×C17—48no—
507C22×C17—48no—
508C22×C17—44no—
509C22×C17—82no—
510C22×C17C2×C4×D412yes—
511C22×C17C2×C4×D412yes—
512C22×C17C2×C4×D412yes—
513C22×C17#51814yescomplemented
514C22×C17C24×C411yescharacteristic
515C2×D17—216no—
516C2×D17—28no—
517C2×D17—22no—
518C2×D17—22no—
519C2×D17—22no—
520C2×D17—22no—
521C2×D17—22no—
522C2×D17—24no—
523C2×D17—28no—
524C2×D17—24no—
525C2×D17—24no—
526C2×D17—24no—
527C2×D17—24no—
528C2×D17—28no—
529C2×D17—24no—
530C2×D17—22no—
531C2×D17—22no—
532C2×D17—24no—
533C2×D17—22no—
534C2×D17—22no—
535C2×D17—44no—
536C2×D17—44no—
537C2×D17—44no—
538C2×D17—48no—
539C2×D17—48no—
540C2×D17—48no—
541C2×D17—48no—
542C2×D17—48no—
543C2×D17—48no—
544C2×D17—48no—
545C2×D17—44no—
546C2×D17—44no—
547C2×D17—44no—
548C2×D17—44no—
549C2×D17—44no—
550C2×D17—84no—
551C2×D17—82no—
552C2×D17C2×C4×D412yes—
553C2×D17C2×C4×D412yes—
554C2×D17C2×C4×D412yes—
555C2×D17#51814yescomplemented
556C2×D17C23×D411yescharacteristic
557C2×D17C22×#4111yescharacteristic
558C2×D17C2×H(5,𝔽2)14yes—
559#595—28no—
560#595—44no—
561#595—44no—
562#595—44no—
563C4×C17—22no—
564C4×C17—24no—
565Dic17—22no—
566Dic17—24no—
567C26—171no—
568C23×D4—171no—
569C23×D4—172no—
570C24×C4—172no—
571C2×#120—171no—
572C2×#120—172no—
573C2×#120—171no—
574C2×#120—172no—
575C2×#120—174no—
576C2×#120—172no—
577C2×#120—172no—
578C2×#120—174no—
579C2×#120—172no—
580C2×#120—171no—
581C2×#120—172no—
582C2×#120#59511yescharacteristic, complemented
583#518—348no—
584C2×C4×D4—174no—
585C2×C4×D4—174no—
586C2×C4×D4—178no—
587C2×#117—172no—
588C22×C22⋊C4—171no—
589C22×C22⋊C4—171no—
590C22×C22⋊C4—172no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—172no—
595C22×C22⋊C4—172no—
596C22×C22⋊C4—174no—
597C22×C22⋊C4—174no—
598C22×C22⋊C4—174no—
599C22×C22⋊C4—348no—
600#390—178no—
601#388—178no—
602#388—178no—
603#386—174no—
604#386—174no—
605#386—178no—
606#386—178no—
607#385—174no—
608#385—174no—
609#385—178no—
610#381—172no—
611#380—174no—
612#379—172no—
613#379—172no—
614#379—174no—
615#379—172no—
616C4×C22⋊C4—174no—
617C4×C22⋊C4—174no—
618C4×C22⋊C4—178no—
619C4×C22⋊C4—174no—
620C2×C17—22no—
621C2×C17—24no—
622C2×C17—22no—
623C2×C17—22no—
624C2×C17—42no—
625C2×C17—42no—
626C2×C17C22×C4×D411yescharacteristic
627C2×C17C2×#51812yes—
628D17—22no—
629D17—24no—
630D17—22no—
631D17—22no—
632D17—42no—
633D17—42no—
634D17#348412yes—
635D17#349012yes—
636C25—171no—
637C25—171no—
638C25—172no—
639C25—172no—
640C25—171no—
641C25—171no—
642C25—172no—
643C25—172no—
644C25—171no—
645C25—171no—
646C25—171no—
647C25—344no—
648C25—344no—
649C25—688no—
650C25C2×#59511yescharacteristic, complemented
651C22×D4—171no—
652C22×D4—171no—
653C22×D4—172no—
654C22×D4—172no—
655C22×D4—172no—
656C22×D4—174no—
657C22×D4—172no—
658C22×D4—172no—
659C22×D4—172no—
660C22×D4—174no—
661C22×D4—174no—
662C22×D4—174no—
663C22×D4—171no—
664C22×D4—172no—
665C22×D4—344no—
666C22×D4—344no—
667C22×D4—688no—
668C22×D4C2×#59511yescharacteristic, complemented
669C22×D4C2×#59512yescomplemented
670C23×C4—172no—
671C23×C4—171no—
672C23×C4—172no—
673C23×C4—178no—
674C23×C4—172no—
675C23×C4—172no—
676C23×C4—172no—
677C23×C4—174no—
678C23×C4—348no—
679C23×C4—688no—
680#120—172no—
681#120—174no—
682#120—172no—
683#120—172no—
684#120—174no—
685#120—174no—
686#120—172no—
687#120—174no—
688#120—174no—
689#120—174no—
690#120—172no—
691#120—174no—
692#120—174no—
693#120—172no—
694#120—174no—
695#120—174no—
696#120—174no—
697#120C2×#59512yescomplemented
698#120C2×#59514yescomplemented
699#120C2×#59512yescomplemented
700C4×D4—3416no—
701C4×D4—3416no—
702C4×D4—6816no—
703#117—348no—
704C2×C4⋊C4—174no—
705C2×C4⋊C4—178no—
706C2×C22⋊C4—172no—
707C2×C22⋊C4—172no—
708C2×C22⋊C4—178no—
709C2×C22⋊C4—172no—
710C2×C22⋊C4—171no—
711C2×C22⋊C4—172no—
712C2×C22⋊C4—172no—
713C2×C22⋊C4—172no—
714C2×C22⋊C4—172no—
715C2×C22⋊C4—174no—
716C2×C22⋊C4—174no—
717C2×C22⋊C4—172no—
718C2×C22⋊C4—172no—
719C2×C22⋊C4—174no—
720C2×C22⋊C4—174no—
721C2×C22⋊C4—172no—
722C2×C22⋊C4—172no—
723C2×C22⋊C4—172no—
724C2×C22⋊C4—178no—
725C2×C22⋊C4—172no—
726C2×C22⋊C4—172no—
727C2×C22⋊C4—174no—
728C2×C22⋊C4—178no—
729C2×C22⋊C4—172no—
730C2×C22⋊C4—172no—
731C2×C22⋊C4—178no—
732C2×C22⋊C4—178no—
733C2×C22⋊C4—3416no—
734C2×C22⋊C4—3416no—
735C2×C22⋊C4—348no—
736C2×C22⋊C4—348no—
737C2×C22⋊C4—344no—
738C2×C22⋊C4—344no—
739C2×C22⋊C4—344no—
740C2×C22⋊C4—688no—
741C2×C22⋊C4C2×#59512yescomplemented
742C2×C22⋊C4C2×#59511yescharacteristic, complemented
743C2×C42—174no—
744C2×C42—178no—
745#95—178no—
746#95—178no—
747#95—178no—
748C17#3419811yescharacteristic, complemented, Sylow
749C24—24no—
750C24—44no—
751C24—171no—
752C24—171no—
753C24—171no—
754C24—172no—
755C24—174no—
756C24—174no—
757C24—171no—
758C24—171no—
759C24—171no—
760C24—172no—
761C24—171no—
762C24—172no—
763C24—172no—
764C24—172no—
765C24—172no—
766C24—172no—
767C24—172no—
768C24—172no—
769C24—172no—
770C24—172no—
771C24—171no—
772C24—172no—
773C24—171no—
774C24—342no—
775C24—348no—
776C24—342no—
777C24—344no—
778C24—344no—
779C24—342no—
780C24—348no—
781C24—348no—
782C24—344no—
783C24—344no—
784C24—342no—
785C24—344no—
786C24—348no—
787C24—348no—
788C24—344no—
789C24—342no—
790C24—342no—
791C24—344no—
792C24—684no—
793C24—684no—
794C24—684no—
795C24—684no—
796C24—684no—
797C24—684no—
798C24—684no—
799C24—684no—
800C24—684no—
801C24—684no—
802C24—684no—
803C24—684no—
804C24—6832no—
805C24—6832no—
806C24C22×#59511yescharacteristic
807C24C22×#59512yes—
808C24C22×#59512yes—
809C24C22×#59511yescharacteristic
810C24C22×#59511yescharacteristic
811C24C22×#59511yescharacteristic, complemented
812C2×D4—24no—
813C2×D4—44no—
814C2×D4—172no—
815C2×D4—174no—
816C2×D4—172no—
817C2×D4—174no—
818C2×D4—172no—
819C2×D4—172no—
820C2×D4—174no—
821C2×D4—174no—
822C2×D4—172no—
823C2×D4—174no—
824C2×D4—172no—
825C2×D4—174no—
826C2×D4—344no—
827C2×D4—344no—
828C2×D4—344no—
829C2×D4—3416no—
830C2×D4—344no—
831C2×D4—348no—
832C2×D4—344no—
833C2×D4—348no—
834C2×D4—344no—
835C2×D4—344no—
836C2×D4—684no—
837C2×D4—688no—
838C2×D4—688no—
839C2×D4—688no—
840C2×D4—684no—
841C2×D4—684no—
842C2×D4C22×#59512yes—
843C2×D4C22×#59514yes—
844C2×D4C22×#59512yescomplemented
845C2×D4C22×#59514yescomplemented
846C22×C4—174no—
847C22×C4—171no—
848C22×C4—178no—
849C22×C4—172no—
850C22×C4—172no—
851C22×C4—172no—
852C22×C4—174no—
853C22×C4—174no—
854C22×C4—174no—
855C22×C4—174no—
856C22×C4—174no—
857C22×C4—342no—
858C22×C4—342no—
859C22×C4—3416no—
860C22×C4—348no—
861C22×C4—344no—
862C22×C4—3416no—
863C22×C4—344no—
864C22×C4—344no—
865C22×C4—684no—
866C22×C4—684no—
867C22×C4—688no—
868C22×C4—684no—
869C22×C4—684no—
870C22×C4—684no—
871C22×C4—688no—
872C22×C4—6832no—
873C22×C4C22×#59511yescharacteristic, complemented
874C22×C4C22×#59512yescomplemented
875C4⋊C4—348no—
876C4⋊C4—688no—
877C22⋊C4—178no—
878C22⋊C4—178no—
879C22⋊C4—172no—
880C22⋊C4—174no—
881C22⋊C4—174no—
882C22⋊C4—172no—
883C22⋊C4—174no—
884C22⋊C4—174no—
885C22⋊C4—174no—
886C22⋊C4—174no—
887C22⋊C4—174no—
888C22⋊C4—174no—
889C22⋊C4—3416no—
890C22⋊C4—348no—
891C22⋊C4—344no—
892C22⋊C4—344no—
893C22⋊C4—344no—
894C22⋊C4—344no—
895C22⋊C4—344no—
896C22⋊C4—344no—
897C22⋊C4—3416no—
898C22⋊C4—688no—
899C22⋊C4—688no—
900C22⋊C4C22×#59512yes—
901C22⋊C4C22×#59514yes—
902C22⋊C4C22×#59514yescomplemented
903C22⋊C4C22×#59512yescomplemented
904C42—348no—
905C42—688no—
906C23—22no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—22no—
911C23—24no—
912C23—24no—
913C23—22no—
914C23—42no—
915C23—42no—
916C23—42no—
917C23—42no—
918C23—42no—
919C23—416no—
920C23—171no—
921C23—172no—
922C23—172no—
923C23—172no—
924C23—172no—
925C23—172no—
926C23—172no—
927C23—178no—
928C23—171no—
929C23—171no—
930C23—172no—
931C23—171no—
932C23—174no—
933C23—174no—
934C23—174no—
935C23—172no—
936C23—172no—
937C23—342no—
938C23—344no—
939C23—344no—
940C23—344no—
941C23—344no—
942C23—342no—
943C23—344no—
944C23—344no—
945C23—344no—
946C23—342no—
947C23—342no—
948C23—344no—
949C23—348no—
950C23—342no—
951C23—344no—
952C23—344no—
953C23—344no—
954C23—344no—
955C23—344no—
956C23—342no—
957C23—344no—
958C23—344no—
959C23—344no—
960C23—344no—
961C23—344no—
962C23—344no—
963C23—3416no—
964C23—3416no—
965C23—342no—
966C23—344no—
967C23—344no—
968C23—344no—
969C23—342no—
970C23—344no—
971C23—344no—
972C23—342no—
973C23—682no—
974C23—682no—
975C23—682no—
976C23—682no—
977C23—682no—
978C23—682no—
979C23—682no—
980C23—682no—
981C23—682no—
982C23—682no—
983C23—682no—
984C23—682no—
985C23—682no—
986C23—684no—
987C23—6816no—
988C23—688no—
989C23—688no—
990C23—6816no—
991C23—6816no—
992C23—6816no—
993C23—6816no—
994C23—6816no—
995C23—6832no—
996C23—6832no—
997C23—688no—
998C23—688no—
999C23—6816no—
1000C23—1364no—
1001C23—1364no—
1002C23D4×#59514yescomplemented
1003C23C23×#59512yes—
1004C23C23×#59512yes—
1005C23C23×#59511yescharacteristic
1006C23C23×#59511yescharacteristic
1007C23C23×#59511yescharacteristic
1008C23C23×#59512yes—
1009D4—24no—
1010D4—24no—
1011D4—28no—
1012D4—44no—
1013D4—344no—
1014D4—344no—
1015D4—348no—
1016D4—344no—
1017D4—344no—
1018D4—348no—
1019D4—344no—
1020D4—344no—
1021D4—348no—
1022D4—684no—
1023D4—684no—
1024D4—684no—
1025C2×C4—22no—
1026C2×C4—42no—
1027C2×C4—178no—
1028C2×C4—172no—
1029C2×C4—174no—
1030C2×C4—342no—
1031C2×C4—348no—
1032C2×C4—342no—
1033C2×C4—344no—
1034C2×C4—348no—
1035C2×C4—342no—
1036C2×C4—344no—
1037C2×C4—348no—
1038C2×C4—344no—
1039C2×C4—344no—
1040C2×C4—348no—
1041C2×C4—348no—
1042C2×C4—684no—
1043C2×C4—682no—
1044C2×C4—688no—
1045C2×C4—6832no—
1046C2×C4—688no—
1047C2×C4—1368no—
1048C2×C4—1364no—
1049C2×C4—1364no—
1050C2×C4C23×#59512yes—
1051C2×C4C23×#59514yes—
1052C22—28no—
1053C22—22no—
1054C22—22no—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—24no—
1061C22—22no—
1062C22—22no—
1063C22—44no—
1064C22—48no—
1065C22—48no—
1066C22—44no—
1067C22—82no—
1068C22—171no—
1069C22—171no—
1070C22—174no—
1071C22—172no—
1072C22—172no—
1073C22—172no—
1074C22—174no—
1075C22—344no—
1076C22—348no—
1077C22—344no—
1078C22—344no—
1079C22—344no—
1080C22—348no—
1081C22—344no—
1082C22—344no—
1083C22—348no—
1084C22—3416no—
1085C22—342no—
1086C22—342no—
1087C22—342no—
1088C22—342no—
1089C22—342no—
1090C22—342no—
1091C22—342no—
1092C22—344no—
1093C22—342no—
1094C22—342no—
1095C22—684no—
1096C22—684no—
1097C22—684no—
1098C22—688no—
1099C22—688no—
1100C22—688no—
1101C22—688no—
1102C22—684no—
1103C22—684no—
1104C22—684no—
1105C22—684no—
1106C22—684no—
1107C22—688no—
1108C22—688no—
1109C22—688no—
1110C22—1362no—
1111C22—1364no—
1112C22C2×D4×#59512yes—
1113C22C2×D4×#59512yes—
1114C22C2×D4×#59512yes—
1115C22#1176387614yescomplemented
1116C22C24×#59511yescharacteristic
1117C4—22no—
1118C4—24no—
1119C4—348no—
1120C4—342no—
1121C4—344no—
1122C4—684no—
1123C4—684no—
1124C4—684no—
1125C2—22no—
1126C2—24no—
1127C2—22no—
1128C2—22no—
1129C2—42no—
1130C2—42no—
1131C2—172no—
1132C2—172no—
1133C2—342no—
1134C2—344no—
1135C2—342no—
1136C2—342no—
1137C2—682no—
1138C2—682no—
1139C2C22×D4×#59511yescharacteristic
1140C2C2×#1176387612yes—
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC2×C17×#120C4
prime radicalC2×#120×D17C2
cosocleC22×D17C25
hypercenterC2×#120#595
hypocenterC17#34198
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#11763876C2semidirect
2. C23×C22⋊#595C2semidirect
3. #14545306C2semidirect
4. #14545290C2semidirect
5. D4×C22⋊#595C2semidirect
6. #14545269C2semidirect
7. #14545263C2semidirect
8. #14545256C2semidirect
9. #120×#595C2semidirect
10. C2×#11763750C2semidirect
11. #14545220C2semidirect
13. C24×#595C22semidirect
15. C2×D4×#595C22semidirect
16. C2×D4×#595C22semidirect
17. C2×D4×#595C22semidirect
18. C2×#10587677C22semidirect
25. C22×C22⋊#595C22semidirect
26. C22×C22⋊#595C22semidirect
27. C22×C22⋊#595C22semidirect
28. C22×C22⋊#595C22semidirect
29. #11763761C22semidirect
30. #11763759C22semidirect
31. #11763759C22semidirect
32. #11763757C22semidirect
33. #11763757C22semidirect
34. #11763757C22semidirect
35. #11763757C22semidirect
36. #11763756C22semidirect
37. #11763756C22semidirect
38. #11763756C22semidirect
39. #11763752C22semidirect
40. #11763751C22semidirect
42. #11763750C22semidirect
43. #11763750C22semidirect
44. #11763750C22semidirect
45. C22⋊C4×#595C22semidirect
46. C22⋊C4×#595C22semidirect
47. C22⋊C4×#595C22semidirect
48. C4×C22⋊#595C22semidirect
52. C2×#10587568C4semidirect
53. C2×#10587568C4semidirect
54. C2×#10587639C4semidirect
55. C2×#10587623C4semidirect
56. C2×#10587623C4semidirect
57. #120×D17C4semidirect
58. #120×D17C4semidirect
59. #120×D17C4semidirect
65. C2×C17×#120C4semidirect
66. C25×C17C2×C4semidirect
70. C24×D17C2×C4semidirect
71. C24×D17C2×C4semidirect
72. C24×D17C2×C4semidirect
73. C24×D17C2×C4semidirect
74. C24×D17C2×C4semidirect
88. C23×#595C23semidirect
89. C22×D4×C17C2×C4semidirect
90. C22×D4×C17C2×C4semidirect
91. C22×C22⋊D17C2×C4semidirect
92. C22×C22⋊D17C2×C4semidirect
93. C22×C22⋊D17C2×C4semidirect
94. C22×C22⋊D17C2×C4semidirect
98. C2×D4×D17C2×C4semidirect
99. C2×D4×D17C2×C4semidirect
100. C2×D4×D17C2×C4semidirect
101. C2×D4×D17C2×C4semidirect
106. C22×D68C2×C4semidirect
107. C22×D68C2×C4semidirect
118. C2×C22⋊#595D4semidirect
130. C2×C22⋊#595C23semidirect
131. C2×C22⋊#595C23semidirect
136. C2×C4⋊#595C23semidirect
137. C2×C4⋊#595C23semidirect
138. C2×C4×#595C23semidirect
139. C2×C4×#595C23semidirect
140. C17×#120C2×C4semidirect
141. C17×#120C2×C4semidirect
142. C17×#120C2×C4semidirect
143. C2×C22⋊C4×C17C2×C4semidirect
144. C2×C22⋊C4×C17C2×C4semidirect
145. #10587639C2×C4semidirect
146. #10587639C2×C4semidirect
147. #10587639C2×C4semidirect
148. C2×C22⋊Dic17C2×C4semidirect
149. C2×C22⋊Dic17C2×C4semidirect
150. #10587623C2×C4semidirect
151. #10587623C2×C4semidirect
152. #10587623C2×C4semidirect
153. #10587623C2×C4semidirect
154. #10587623C2×C4semidirect
155. #10587623C2×C4semidirect
156. #10587623C2×C4semidirect
157. C2×#63227C2×C4semidirect
158. C2×#63227C2×C4semidirect
159. C2×#63227C2×C4semidirect
160. #10587568C2×C4semidirect
161. #10587568C2×C4semidirect
162. #10587568C2×C4semidirect
163. #10587568C2×C4semidirect
164. #10587568C2×C4semidirect
165. #10587568C2×C4semidirect
166. #10587568C2×C4semidirect
167. C22⋊C4×D17C2×C4semidirect
168. C22⋊C4×D17C2×C4semidirect
169. C22⋊C4×D17C2×C4semidirect
170. C22⋊C4×D17C2×C4semidirect
175. (C2×#595)⋊C4C23semidirect
176. (C2×#595)⋊C4C23semidirect
177. (C2×#595)⋊C4C23semidirect
185. C24×C17C22×C4semidirect
231. C23×D17C22×C4semidirect
232. C23×D17C22×C4semidirect
254. C22×#595C2×D4semidirect
263. C2×D4×C17C22×C4semidirect
264. C2×D4×C17C22×C4semidirect
265. C22×C4×C17C22×C4semidirect
266. C22×C4×C17C22×C4semidirect
275. C2×C22⋊D17C22×C4semidirect
276. C2×C22⋊D17C22×C4semidirect
277. C2×C22⋊D17C22×C4semidirect
278. C2×C22⋊D17C22×C4semidirect
279. C22×Dic17C22×C4semidirect
280. C22×Dic17C22×C4semidirect
295. C2×D68C22×C4semidirect
296. C2×D68C22×C4semidirect
300. C2×C4×D17C22×C4semidirect
301. C2×C4×D17C22×C4semidirect
316. C22⋊#595C2×D4semidirect
323. C22⋊C4×C17C22×C4semidirect
324. C22⋊C4×C17C22×C4semidirect
327. C22⋊Dic17C22×C4semidirect
328. C22⋊Dic17C22×C4semidirect
332. #63227C22×C4semidirect
333. #63227C22×C4semidirect
334. #63227C22×C4semidirect
350. C23×C17C4×D4semidirect
422. C22×D17C4×D4semidirect
423. C22×D17C4×D4semidirect
424. C22×D17C4×D4semidirect
513. C22×C17#518semidirect
555. C2×D17#518semidirect
582. C2×#120#595semidirect
650. C25C2×#595semidirect
668. C22×D4C2×#595semidirect
669. C22×D4C2×#595semidirect
697. #120C2×#595semidirect
698. #120C2×#595semidirect
699. #120C2×#595semidirect
741. C2×C22⋊C4C2×#595semidirect
742. C2×C22⋊C4C2×#595semidirect
748. C17#34198semidirect
811. C24C22×#595semidirect
844. C2×D4C22×#595semidirect
845. C2×D4C22×#595semidirect
873. C22×C4C22×#595semidirect
874. C22×C4C22×#595semidirect
902. C22⋊C4C22×#595semidirect
903. C22⋊C4C22×#595semidirect
1002. C23D4×#595semidirect
1115. C22#11763876semidirect

Maximal subgroups

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

subgroupindex
C2×#117638762
C23×C22⋊#5952
#145453062
#145452902
D4×C22⋊#5952
#145452692
#145452632
#145452562
#120×#5952
C2×#117637502
#145452202
C2×#120×D172
#3419817