Finite Group Databasebeta

← C2×#14545307 #17978998

Subgroups — C2×#14545307 #17978998

Order 4352.

3830 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×#595C211yesmaximal, characteristic
2C22×#10587677C211yesmaximal, characteristic, complemented
3#14545307C2116yesmaximal, direct product factor
4C2×#11763760C211yesmaximal, characteristic, complemented
5C2×#11763759C211yesmaximal, characteristic, complemented
6C2×#11763759C211yesmaximal, characteristic, complemented
7C2×#11763758C211yesmaximal, characteristic, complemented
8C2×#11763758C211yesmaximal, characteristic, complemented
9C2×#11763757C211yesmaximal, characteristic
10C2×#11763756C211yesmaximal, characteristic, complemented
11C2×#11763756C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×#595C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×#595C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×#595C211yesmaximal, characteristic, complemented
15C22×(C2×#595)⋊C4C211yesmaximal, characteristic, complemented
16C2×#123×D17C211yesmaximal, characteristic
17C24×#595C2211yescharacteristic
18C24×#595C2211yescharacteristic
19C24×#595C2211yescharacteristic
20C2×D4×#595—28no—
21C2×D4×#595C2218yes—
22C2×#10587677—28no—
23C2×#10587677C2218yescomplemented
24C22×C4⋊#595C2211yescharacteristic
25C22×C4⋊#595C2211yescharacteristic
26C22×C4⋊#595C2211yescharacteristic
27C22×C4⋊#595C2211yescharacteristic
28C22×C4⋊#595C2211yescharacteristic
29C22×C22⋊#595C2211yescharacteristic
30C22×C22⋊#595C2211yescharacteristic
31C22×C22⋊#595C2211yescharacteristic
32C22×C22⋊#595C2211yescharacteristic
33C22×C22⋊#595C2211yescharacteristic
34C22×C4×#595C2211yescharacteristic
35C22×C4×#595C2211yescharacteristic
36C22×C4×#595C2211yescharacteristic
37C22×C4×#595C2211yescharacteristic
38C22×C4×#595C2211yescharacteristic
39#11763760C2218yescomplemented
40#11763759C2218yescomplemented
41#11763759C2218yescomplemented
42#11763758C2218yescomplemented
43#11763758C2218yescomplemented
44#11763757C2218yes—
45#11763756C2218yescomplemented
46#11763756C2218yescomplemented
47C4⋊C4×#595C2218yescomplemented
48C22⋊C4×#595C2218yescomplemented
49C22⋊C4×#595C2218yescomplemented
50C2×(C2×#595)⋊C4C2211yescharacteristic
51C2×(C2×#595)⋊C4C2211yescharacteristic
52C2×(C2×#595)⋊C4C2211yescharacteristic
53C2×(C2×#595)⋊C4C2211yescharacteristic
54C2×(C2×#595)⋊C4C2211yescharacteristic
55C2×(C2×#595)⋊C4C2211yescharacteristic
56C2×(C2×#595)⋊C4C2211yescharacteristic
57C2×(C2×#595)⋊C4C2211yescharacteristic
58C2×(C2×#595)⋊C4C2211yescharacteristic
59C2×(C2×#595)⋊C4C2211yescharacteristic
60C2×(C2×#595)⋊C4C2218yescomplemented
61C22×D4×D17C2211yescharacteristic
62C23×C4×D17C2211yescharacteristic
63C2×#10587580C411yescharacteristic, complemented
64C2×#10587580C411yescharacteristic, complemented
65C2×#10587572C411yescharacteristic, complemented
66C2×#10587615C411yescharacteristic, complemented
67C2×#10587569C411yescharacteristic, complemented
68C2×#10587569C411yescharacteristic, complemented
69C2×#10587621C411yescharacteristic, complemented
70#123×D17C418yescomplemented
71#123×D17C2218yes—
72C2×C4⋊C4×D17C2211yescharacteristic
73C2×C4⋊C4×D17C2211yescharacteristic
74C2×C22⋊C4×D17C2211yescharacteristic
75C2×C22⋊C4×D17C2211yescharacteristic
76C2×C22⋊C4×D17C2211yescharacteristic
77C2×C17×#123C411yescharacteristic, complemented
78C24×D17C2311yescharacteristic
79C24×D17C2311yescharacteristic
80C23×#595—24no—
81C23×#595—24no—
82C23×#595—24no—
83C23×#595—24no—
84C23×#595—24no—
85C23×#595—24no—
86C23×#595—42no—
87C23×#595—42no—
88C23×#595—42no—
89C23×#595C2311yescharacteristic
90C23×#595C2311yescharacteristic
91C23×#595C2311yescharacteristic
92C23×#595C2311yescharacteristic
93C23×#595C2314yes—
94C23×#595C2314yes—
95C23×#595C2314yes—
96C23×#595C2311yescharacteristic
97C23×#595C2311yescharacteristic
98C23×#595C2311yescharacteristic
99C23×#595C2311yescharacteristic
100C22×D4×C17C2×C411yescharacteristic
101C23×C4×C17C2×C411yescharacteristic, complemented
102C22×C22⋊D17C2×C411yescharacteristic
103C22×C22⋊D17C2×C411yescharacteristic
104C23×Dic17C2×C411yescharacteristic, complemented
105C2×D4×D17—24no—
106C2×D4×D17—24no—
107C2×D4×D17C2×C414yes—
108C2×D4×D17C2314yes—
109C22×D68C2×C411yescharacteristic
110C22×C4×D17—24no—
111C22×C4×D17—24no—
112C22×C4×D17C2×C414yescomplemented
113C22×C4×D17C2×C411yescharacteristic, complemented
114C22×C4×D17C2×C411yescharacteristic, complemented
115C22×C4×D17C2311yescharacteristic
116C22×C4×D17C2311yescharacteristic
117C22×C4×D17C2311yescharacteristic
118C22×C4×D17C2311yescharacteristic
119C22×C4×D17C2311yescharacteristic
120C22×C4×D17C2314yes—
121C2×C22⋊#595—24no—
122C2×C22⋊#595—24no—
123C2×C22⋊#595—24no—
124C2×C22⋊#595—42no—
125C2×C22⋊#595D418yes—
126C2×C22⋊#595C2314yes—
127C2×C22⋊#595C2314yes—
128C2×C22⋊#595C2314yes—
129C2×C22⋊#595C2314yes—
130C2×C22⋊#595C2314yes—
131D4×#595—232no—
132#10587677—232no—
133C2×C4⋊#595—24no—
134C2×C4⋊#595—24no—
135C2×C4⋊#595—24no—
136C2×C4⋊#595—24no—
137C2×C4⋊#595—42no—
138C2×C4⋊#595C2314yes—
139C2×C4⋊#595C2314yes—
140C2×C4⋊#595C2314yes—
141C2×C4⋊#595C2314yes—
142C2×C4⋊#595C2314yes—
143C2×C4×#595—24no—
144C2×C4×#595—24no—
145C2×C4×#595—24no—
146C2×C4×#595—24no—
147C2×C4×#595—42no—
148C2×C4×#595C2314yes—
149C2×C4×#595C2314yes—
150C2×C4×#595C2314yes—
151C2×C4×#595C2314yes—
152C2×C4×#595C2314yes—
153C17×#123C2×C418yescomplemented
154C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
155C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
156C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
157C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
158C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
159C2×C22⋊Dic17C2×C411yescharacteristic, complemented
160C2×C22⋊Dic17C2×C411yescharacteristic, complemented
161C2×C22⋊Dic17C2×C411yescharacteristic, complemented
162#10587621C2×C418yescomplemented
163#10587615C2×C418yescomplemented
164C2×#63227C2×C411yescharacteristic, complemented
165C2×#63227C2×C411yescharacteristic, complemented
166C2×#63227C2×C411yescharacteristic, complemented
167C2×#63227C2×C411yescharacteristic, complemented
168C2×#63227C2×C411yescharacteristic, complemented
169C2×#63227C2×C411yescharacteristic, complemented
170C2×C4⋊Dic17C2×C411yescharacteristic, complemented
171C2×C4⋊Dic17C2×C411yescharacteristic, complemented
172C2×#63225C2×C411yescharacteristic, complemented
173C2×#63225C2×C411yescharacteristic, complemented
174C2×#63225C2×C411yescharacteristic, complemented
175C2×#63225C2×C411yescharacteristic, complemented
176#10587580C2×C418yescomplemented
177#10587580C2×C418yescomplemented
178C4⋊C4×D17C2×C414yescomplemented
179C4⋊C4×D17C2×C414yescomplemented
180C4⋊C4×D17C2314yes—
181C4⋊C4×D17C2314yes—
182#10587572C2×C418yescomplemented
183#10587569C2×C418yescomplemented
184#10587569C2×C418yescomplemented
185C22⋊C4×D17C2×C414yescomplemented
186C22⋊C4×D17C2×C414yescomplemented
187C22⋊C4×D17C2×C414yescomplemented
188C22⋊C4×D17C2314yes—
189C22⋊C4×D17C2314yes—
190C22⋊C4×D17C2314yes—
191(C2×#595)⋊C4C2314yes—
192(C2×#595)⋊C4C2314yes—
193(C2×#595)⋊C4C2314yes—
194(C2×#595)⋊C4C2314yes—
195(C2×#595)⋊C4C2314yes—
196(C2×#595)⋊C4C2314yes—
197(C2×#595)⋊C4C2314yes—
198(C2×#595)⋊C4C2314yes—
199(C2×#595)⋊C4C2314yes—
200(C2×#595)⋊C4C2314yes—
201C24×C17C22×C411yescharacteristic
202C24×C17C22×C411yescharacteristic
203C23×D17—22no—
204C23×D17—22no—
205C23×D17—22no—
206C23×D17—22no—
207C23×D17—22no—
208C23×D17—22no—
209C23×D17—22no—
210C23×D17—22no—
211C23×D17—22no—
212C23×D17—22no—
213C23×D17C22×C411yescharacteristic
214C23×D17C22×C412yes—
215C23×D17C22×C411yescharacteristic
216C23×D17C22×C412yes—
217C23×D17C2×D414yes—
218C23×D17#4114yes—
219C23×D17C2412yes—
220C23×D17C2412yes—
221C23×D17C2411yescharacteristic
222C22×#595—22no—
223C22×#595—22no—
224C22×#595—22no—
225C22×#595—22no—
226C22×#595—22no—
227C22×#595—22no—
228C22×#595—22no—
229C22×#595—22no—
230C22×#595—22no—
231C22×#595—22no—
232C22×#595—22no—
233C22×#595—28no—
234C22×#595—22no—
235C22×#595—22no—
236C22×#595—28no—
237C22×#595—22no—
238C22×#595—22no—
239C22×#595—22no—
240C22×#595—22no—
241C22×#595—22no—
242C22×#595—22no—
243C22×#595—22no—
244C22×#595—28no—
245C22×#595—28no—
246C22×#595—28no—
247C22×#595—28no—
248C22×#595—44no—
249C22×#595—44no—
250C22×#595—44no—
251C22×#595—416no—
252C22×#595—416no—
253C22×#595—416no—
254C22×#595C2×D414yes—
255C22×#595C2×D414yes—
256C22×#595#4114yes—
257C22×#595#4114yes—
258C22×#595C2412yes—
259C22×#595C2412yes—
260C22×#595C2412yes—
261C22×#595C2412yes—
262C22×#595C2412yes—
263C22×#595C2412yes—
264C22×#595C2412yes—
265C22×#595C2412yes—
266C2×D4×C17—24no—
267C2×D4×C17C22×C414yes—
268C22×C4×C17—24no—
269C22×C4×C17C22×C411yescharacteristic
270C22×C4×C17C22×C411yescharacteristic
271C22×C4×C17C22×C411yescharacteristic
272C22×C4×C17C22×C411yescharacteristic
273C22×C4×C17C22×C411yescharacteristic
274C22×C4×C17C22×C414yescomplemented
275C2×C22⋊D17—24no—
276C2×C22⋊D17—24no—
277C2×C22⋊D17C22×C414yes—
278C2×C22⋊D17C22×C414yes—
279C22×Dic17—24no—
280C22×Dic17C22×C411yescharacteristic
281C22×Dic17C22×C411yescharacteristic
282C22×Dic17C22×C411yescharacteristic
283C22×Dic17C22×C411yescharacteristic
284C22×Dic17C22×C411yescharacteristic
285C22×Dic17C22×C414yescomplemented
286D4×D17—216no—
287D4×D17—28no—
288D4×D17—28no—
289C2×D68—24no—
290C2×D68C22×C414yes—
291C2×C4×D17—216no—
292C2×C4×D17—24no—
293C2×C4×D17—24no—
294C2×C4×D17—22no—
295C2×C4×D17—22no—
296C2×C4×D17—22no—
297C2×C4×D17—28no—
298C2×C4×D17—22no—
299C2×C4×D17—22no—
300C2×C4×D17—22no—
301C2×C4×D17—22no—
302C2×C4×D17—28no—
303C2×C4×D17—22no—
304C2×C4×D17—22no—
305C2×C4×D17—22no—
306C2×C4×D17C22×C412yes—
307C2×C4×D17C22×C412yes—
308C2×C4×D17C22×C412yes—
309C2×C4×D17C22×C412yes—
310C2×C4×D17C22×C412yes—
311C2×C4×D17C22×C414yescomplemented
312C2×C4×D17C22×C414yescomplemented
313C2×C4×D17C2412yes—
314C2×C4×D17C2412yes—
315C2×C4×D17C2412yes—
316C2×C4×D17C2412yes—
317C2×C4×D17C2412yes—
318C22⋊#595—28no—
319C22⋊#595—28no—
320C22⋊#595—28no—
321C22⋊#595—44no—
322C22⋊#595C2×D4116yes—
323C4⋊#595—28no—
324C4⋊#595—28no—
325C4⋊#595—28no—
326C4⋊#595—28no—
327C4⋊#595—44no—
328C4×#595—28no—
329C4×#595—28no—
330C4×#595—28no—
331C4×#595—28no—
332C4×#595—44no—
333C4⋊C4×C17C22×C414yescomplemented
334C4⋊C4×C17C22×C414yescomplemented
335C22⋊C4×C17C22×C414yescomplemented
336C22⋊C4×C17C22×C414yescomplemented
337C22⋊C4×C17C22×C414yescomplemented
338C22⋊Dic17C22×C414yescomplemented
339C22⋊Dic17C22×C414yescomplemented
340C22⋊Dic17C22×C414yescomplemented
341#63227C22×C414yescomplemented
342#63227C22×C414yescomplemented
343#63227C22×C414yescomplemented
344#63227C22×C414yescomplemented
345#63227C22×C414yescomplemented
346#63227C22×C414yescomplemented
347C4⋊Dic17C22×C414yescomplemented
348C4⋊Dic17C22×C414yescomplemented
349#63225C22×C414yescomplemented
350#63225C22×C414yescomplemented
351#63225C22×C414yescomplemented
352#63225C22×C414yescomplemented
353C2×#2359—171nomaximal, Sylow
354C23×C17—22no—
355C23×C17—22no—
356C23×C17—22no—
357C23×C17—22no—
358C23×C17—22no—
359C23×C17C4×D414yes—
360C23×C17C23×C412yes—
361C23×C17C23×C412yes—
362C23×C17C23×C411yescharacteristic
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—24no—
366C22×D17—24no—
367C22×D17—28no—
368C22×D17—28no—
369C22×D17—28no—
370C22×D17—28no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—24no—
379C22×D17—24no—
380C22×D17—24no—
381C22×D17—22no—
382C22×D17—22no—
383C22×D17—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
387C22×D17—44no—
388C22×D17—44no—
389C22×D17—44no—
390C22×D17—44no—
391C22×D17C4×D414yes—
392C22×D17C4×D418yes—
393C22×D17C23×C412yes—
394C22×D17C23×C412yes—
395C22×D17C23×C411yescharacteristic
396C22×D17C22×D414yes—
397C22×D17C22×D412yes—
398C22×D17C2×#4114yes—
399C22×D17C2×#4112yes—
400C22×D17C2×#4112yes—
401C22×D17C2×#4112yes—
402C22×D17H(5,𝔽2)12yes—
403C22×D172−1+412yes—
404C22×D17C2511yescharacteristic
405C2×#595—28no—
406C2×#595—28no—
407C2×#595—28no—
408C2×#595—28no—
409C2×#595—22no—
410C2×#595—22no—
411C2×#595—22no—
412C2×#595—22no—
413C2×#595—22no—
414C2×#595—22no—
415C2×#595—22no—
416C2×#595—22no—
417C2×#595—22no—
418C2×#595—22no—
419C2×#595—22no—
420C2×#595—22no—
421C2×#595—22no—
422C2×#595—22no—
423C2×#595—22no—
424C2×#595—22no—
425C2×#595—22no—
426C2×#595—22no—
427C2×#595—22no—
428C2×#595—22no—
429C2×#595—416no—
430C2×#595—416no—
431C2×#595—416no—
432C2×#595—44no—
433C2×#595—44no—
434C2×#595—44no—
435C2×#595—44no—
436C2×#595C22×D414yes—
437C2×#595C22×D414yes—
438C2×#595C2×#4114yes—
439C2×#595C2×#4114yes—
440D4×C17—28no—
441C2×C4×C17—22no—
442C2×C4×C17—22no—
443C2×C4×C17—28no—
444C2×C4×C17—22no—
445C2×C4×C17—22no—
446C2×C4×C17—22no—
447C2×C4×C17C23×C412yes—
448C2×C4×C17C23×C412yes—
449C2×C4×C17C23×C412yes—
450C2×C4×C17C23×C412yes—
451C2×C4×C17C23×C412yes—
452C22⋊D17—28no—
453C22⋊D17—28no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—28no—
457C2×Dic17—22no—
458C2×Dic17—22no—
459C2×Dic17—22no—
460C2×Dic17C23×C412yes—
461C2×Dic17C23×C412yes—
462C2×Dic17C23×C412yes—
463C2×Dic17C23×C412yes—
464C2×Dic17C23×C412yes—
465D68—28no—
466C4×D17—24no—
467C4×D17—24no—
468C4×D17—28no—
469C4×D17—28no—
470C4×D17—24no—
471C4×D17—24no—
472C4×D17—24no—
473C4×D17—22no—
474C4×D17—22no—
475C4×D17—22no—
476C4×D17—22no—
477C4×D17—22no—
478C4×D17—22no—
479C4×D17—22no—
480C4×D17—22no—
481C4×D17—22no—
482C4×D17—22no—
483C22×#123—171no—
484C22×C4×D4—171no—
485C22×#117—171no—
486#2359—1716no—
487C2×#389—171no—
488C2×#388—171no—
489C2×#388—171no—
490C2×#387—171no—
491C2×#387—171no—
492C2×#386—171no—
493C2×#385—171no—
494C2×#385—171no—
495C2×C4×C4⋊C4—171no—
496C2×C4×C22⋊C4—171no—
497C2×C4×C22⋊C4—171no—
498C22×#95—171no—
499C22×C17—28no—
500C22×C17—22no—
501C22×C17—22no—
502C22×C17—22no—
503C22×C17—22no—
504C22×C17—22no—
505C22×C17—44no—
506C22×C17C2×C4×D414yes—
507C22×C17C2×C4×D412yes—
508C22×C17C4×#4112yes—
509C22×C17#52012yes—
510C22×C17C24×C411yescharacteristic
511C2×D17—28no—
512C2×D17—22no—
513C2×D17—22no—
514C2×D17—216no—
515C2×D17—24no—
516C2×D17—24no—
517C2×D17—24no—
518C2×D17—24no—
519C2×D17—22no—
520C2×D17—22no—
521C2×D17—22no—
522C2×D17—44no—
523C2×D17—48no—
524C2×D17—42no—
525C2×D17—42no—
526C2×D17—42no—
527C2×D17—42no—
528C2×D17C2×C4×D414yes—
529C2×D17C2×C4×D412yes—
530C2×D17C4×#4112yes—
531C2×D17#52012yes—
532C2×D17#54614yes—
533C2×D17#54714yes—
534C2×D17#55114yes—
535C2×D17#55214yes—
536C2×D17C23×D411yescharacteristic
537C2×D17C22×#4111yescharacteristic
538C2×D17C22×#4111yescharacteristic
539C2×D17C22×#4111yescharacteristic
540C2×D17C2×H(5,𝔽2)11yescharacteristic
541C2×D17C2×2−1+411yescharacteristic
542#595—24no—
543#595—24no—
544#595—24no—
545#595—24no—
546#595—42no—
547#595—42no—
548#595—42no—
549#595—42no—
550C4×C17—22no—
551C4×C17—22no—
552C4×C17—22no—
553C4×C17—22no—
554C4×C17—22no—
555Dic17—22no—
556Dic17—22no—
557Dic17—22no—
558Dic17—22no—
559Dic17—22no—
560C23×D4—171no—
561C24×C4—171no—
562C24×C4—171no—
563C24×C4—171no—
564C24×C4—171no—
565C2×#123—171no—
566C2×#123—171no—
567C2×#123—178no—
568C2×#123—178no—
569C2×#123—171no—
570C2×#123—171no—
571C2×#123—171no—
572C2×#123—171no—
573C2×#123—171no—
574C2×#123#59511yescharacteristic, complemented
575C2×C4×D4—178no—
576C2×C4×D4—348no—
577C2×#117—178no—
578C2×#117—348no—
579C22×C4⋊C4—171no—
580C22×C4⋊C4—171no—
581C22×C4⋊C4—171no—
582C22×C4⋊C4—171no—
583C22×C4⋊C4—171no—
584C22×C4⋊C4—171no—
585C22×C4⋊C4—171no—
586C22×C22⋊C4—171no—
587C22×C22⋊C4—171no—
588C22×C22⋊C4—171no—
589C22×C22⋊C4—171no—
590C22×C22⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C42—171no—
595C22×C42—171no—
596C22×C42—171no—
597C22×C42—171no—
598C22×C42—171no—
599#389—178no—
600#388—178no—
601#388—178no—
602#387—178no—
603#387—178no—
604#386—178no—
605#385—178no—
606#385—178no—
607C4×C4⋊C4—178no—
608C4×C22⋊C4—178no—
609C4×C22⋊C4—178no—
610C2×#95—171no—
611C2×#95—171no—
612C2×#95—171no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—178no—
621C2×C17—24no—
622C2×C17—42no—
623C2×C17#235914yescomplemented
624C2×C17C22×C4×D411yescharacteristic
625C2×C17C2×C4×#4111yescharacteristic
626C2×C17C2×#52011yescharacteristic
627D17—24no—
628D17—42no—
629D17#235914yescomplemented
630D17C2×#54611yescharacteristic
631D17C2×#54711yescharacteristic
632D17C2×#55111yescharacteristic
633D17C2×#55211yescharacteristic
634C25—171no—
635C25—171no—
636C22×D4—171no—
637C22×D4—171no—
638C22×D4—174no—
639C22×D4—174no—
640C22×D4—171no—
641C22×D4—344no—
642C22×D4—344no—
643C22×D4C2×#59511yescharacteristic
644C23×C4—171no—
645C23×C4—171no—
646C23×C4—171no—
647C23×C4—171no—
648C23×C4—171no—
649C23×C4—171no—
650C23×C4—171no—
651C23×C4—171no—
652C23×C4—171no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—174no—
657C23×C4—174no—
658C23×C4—171no—
659C23×C4—171no—
660C23×C4—171no—
661C23×C4—171no—
662C23×C4—174no—
663C23×C4—174no—
664C23×C4—174no—
665C23×C4—344no—
666C23×C4—344no—
667C23×C4—344no—
668C23×C4—344no—
669C23×C4—344no—
670C23×C4—344no—
671C23×C4—344no—
672C23×C4—344no—
673C23×C4—682no—
674C23×C4—682no—
675C23×C4—682no—
676C23×C4C2×#59511yescharacteristic, complemented
677#123—178no—
678#123—178no—
679#123—178no—
680#123—178no—
681#123—178no—
682#123—178no—
683#123—178no—
684#123C2×#59518yescomplemented
685C4×D4—3432no—
686#117—3432no—
687C2×C4⋊C4—171no—
688C2×C4⋊C4—171no—
689C2×C4⋊C4—171no—
690C2×C4⋊C4—171no—
691C2×C4⋊C4—171no—
692C2×C4⋊C4—171no—
693C2×C4⋊C4—174no—
694C2×C4⋊C4—174no—
695C2×C4⋊C4—174no—
696C2×C4⋊C4—174no—
697C2×C4⋊C4—174no—
698C2×C4⋊C4—174no—
699C2×C4⋊C4—174no—
700C2×C4⋊C4—174no—
701C2×C4⋊C4—174no—
702C2×C4⋊C4—344no—
703C2×C4⋊C4—344no—
704C2×C4⋊C4—344no—
705C2×C4⋊C4—344no—
706C2×C4⋊C4—682no—
707C2×C4⋊C4C2×#59511yescharacteristic, complemented
708C2×C4⋊C4C2×#59511yescharacteristic, complemented
709C2×C22⋊C4—174no—
710C2×C22⋊C4—178no—
711C2×C22⋊C4—171no—
712C2×C22⋊C4—171no—
713C2×C22⋊C4—171no—
714C2×C22⋊C4—171no—
715C2×C22⋊C4—171no—
716C2×C22⋊C4—171no—
717C2×C22⋊C4—171no—
718C2×C22⋊C4—171no—
719C2×C22⋊C4—171no—
720C2×C22⋊C4—174no—
721C2×C22⋊C4—174no—
722C2×C22⋊C4—174no—
723C2×C22⋊C4—174no—
724C2×C22⋊C4—174no—
725C2×C22⋊C4—174no—
726C2×C22⋊C4—174no—
727C2×C22⋊C4—174no—
728C2×C22⋊C4—174no—
729C2×C22⋊C4—174no—
730C2×C22⋊C4—344no—
731C2×C22⋊C4—344no—
732C2×C22⋊C4—344no—
733C2×C22⋊C4—682no—
734C2×C22⋊C4C2×#59511yescharacteristic, complemented
735C2×C22⋊C4C2×#59511yescharacteristic, complemented
736C2×C22⋊C4C2×#59511yescharacteristic, complemented
737C2×C42—174no—
738C2×C42—174no—
739C2×C42—174no—
740C2×C42—174no—
741C2×C42—174no—
742C2×C42—344no—
743C2×C42—344no—
744C2×C42—344no—
745C2×C42—344no—
746C2×C42—682no—
747#95—174no—
748#95—174no—
749#95—174no—
750#95—174no—
751#95—174no—
752#95—174no—
753#95—174no—
754#95—174no—
755#95—174no—
756#95—174no—
757C17C2×#235911yescharacteristic, complemented, Sylow
758C24—171no—
759C24—174no—
760C24—174no—
761C24—172no—
762C24—172no—
763C24—171no—
764C24—172no—
765C24—172no—
766C24—171no—
767C24—342no—
768C24—342no—
769C24—342no—
770C24—342no—
771C24—342no—
772C24—342no—
773C24—342no—
774C24—342no—
775C24—342no—
776C24—342no—
777C24C22×#59511yescharacteristic
778C24C22×#59511yescharacteristic
779C2×D4—24no—
780C2×D4—174no—
781C2×D4—174no—
782C2×D4—174no—
783C2×D4—344no—
784C2×D4—348no—
785C2×D4—348no—
786C2×D4—3416no—
787C2×D4—344no—
788C2×D4—344no—
789C2×D4C22×#59514yes—
790C22×C4—24no—
791C22×C4—174no—
792C22×C4—174no—
793C22×C4—174no—
794C22×C4—174no—
795C22×C4—172no—
796C22×C4—172no—
797C22×C4—172no—
798C22×C4—172no—
799C22×C4—174no—
800C22×C4—171no—
801C22×C4—171no—
802C22×C4—171no—
803C22×C4—171no—
804C22×C4—171no—
805C22×C4—172no—
806C22×C4—172no—
807C22×C4—172no—
808C22×C4—172no—
809C22×C4—172no—
810C22×C4—174no—
811C22×C4—174no—
812C22×C4—172no—
813C22×C4—172no—
814C22×C4—172no—
815C22×C4—172no—
816C22×C4—172no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—172no—
820C22×C4—172no—
821C22×C4—342no—
822C22×C4—342no—
823C22×C4—342no—
824C22×C4—342no—
825C22×C4—342no—
826C22×C4—342no—
827C22×C4—348no—
828C22×C4—342no—
829C22×C4—342no—
830C22×C4—342no—
831C22×C4—344no—
832C22×C4—344no—
833C22×C4—348no—
834C22×C4—3416no—
835C22×C4—342no—
836C22×C4—348no—
837C22×C4—348no—
838C22×C4—348no—
839C22×C4—348no—
840C22×C4—342no—
841C22×C4—342no—
842C22×C4—342no—
843C22×C4—342no—
844C22×C4—342no—
845C22×C4—342no—
846C22×C4—342no—
847C22×C4—342no—
848C22×C4—344no—
849C22×C4—342no—
850C22×C4—342no—
851C22×C4—342no—
852C22×C4—342no—
853C22×C4—342no—
854C22×C4—342no—
855C22×C4—342no—
856C22×C4—342no—
857C22×C4—348no—
858C22×C4—342no—
859C22×C4—348no—
860C22×C4—342no—
861C22×C4—342no—
862C22×C4—342no—
863C22×C4—684no—
864C22×C4—684no—
865C22×C4—684no—
866C22×C4—6816no—
867C22×C4—6816no—
868C22×C4—6816no—
869C22×C4C22×#59511yescharacteristic
870C22×C4C22×#59511yescharacteristic
871C22×C4C22×#59511yescharacteristic
872C22×C4C22×#59511yescharacteristic
873C22×C4C22×#59511yescharacteristic
874C22×C4C22×#59514yescomplemented
875C4⋊C4—174no—
876C4⋊C4—174no—
877C4⋊C4—174no—
878C4⋊C4—174no—
879C4⋊C4—174no—
880C4⋊C4—174no—
881C4⋊C4—348no—
882C4⋊C4—348no—
883C4⋊C4—348no—
884C4⋊C4—348no—
885C4⋊C4—684no—
886C4⋊C4C22×#59514yescomplemented
887C4⋊C4C22×#59514yescomplemented
888C22⋊C4—1716no—
889C22⋊C4—174no—
890C22⋊C4—174no—
891C22⋊C4—174no—
892C22⋊C4—174no—
893C22⋊C4—174no—
894C22⋊C4—174no—
895C22⋊C4—174no—
896C22⋊C4—174no—
897C22⋊C4—174no—
898C22⋊C4—348no—
899C22⋊C4—348no—
900C22⋊C4—348no—
901C22⋊C4—684no—
902C22⋊C4C22×#59514yescomplemented
903C22⋊C4C22×#59514yescomplemented
904C22⋊C4C22×#59514yescomplemented
905C42—348no—
906C42—348no—
907C42—348no—
908C42—348no—
909C42—684no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—172no—
916C23—172no—
917C23—172no—
918C23—172no—
919C23—172no—
920C23—172no—
921C23—171no—
922C23—171no—
923C23—174no—
924C23—174no—
925C23—178no—
926C23—174no—
927C23—172no—
928C23—172no—
929C23—342no—
930C23—342no—
931C23—342no—
932C23—348no—
933C23—348no—
934C23—344no—
935C23—342no—
936C23—344no—
937C23—348no—
938C23—348no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—342no—
944C23—344no—
945C23—344no—
946C23—342no—
947C23—344no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—684no—
954C23—684no—
955C23—684no—
956C23—684no—
957C23D4×#59514yes—
958C23C23×#59512yes—
959C23C23×#59512yes—
960C23C23×#59511yescharacteristic
961D4—28no—
962D4—348no—
963D4—348no—
964D4—348no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—174no—
972C2×C4—174no—
973C2×C4—174no—
974C2×C4—174no—
975C2×C4—172no—
976C2×C4—172no—
977C2×C4—172no—
978C2×C4—172no—
979C2×C4—172no—
980C2×C4—342no—
981C2×C4—342no—
982C2×C4—342no—
983C2×C4—342no—
984C2×C4—342no—
985C2×C4—342no—
986C2×C4—342no—
987C2×C4—342no—
988C2×C4—344no—
989C2×C4—344no—
990C2×C4—348no—
991C2×C4—348no—
992C2×C4—342no—
993C2×C4—344no—
994C2×C4—344no—
995C2×C4—342no—
996C2×C4—344no—
997C2×C4—342no—
998C2×C4—342no—
999C2×C4—342no—
1000C2×C4—342no—
1001C2×C4—342no—
1002C2×C4—342no—
1003C2×C4—342no—
1004C2×C4—348no—
1005C2×C4—348no—
1006C2×C4—348no—
1007C2×C4—342no—
1008C2×C4—348no—
1009C2×C4—348no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—342no—
1018C2×C4—342no—
1019C2×C4—342no—
1020C2×C4—342no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
1026C2×C4—342no—
1027C2×C4—6816no—
1028C2×C4—6816no—
1029C2×C4—6816no—
1030C2×C4—684no—
1031C2×C4—684no—
1032C2×C4—684no—
1033C2×C4—684no—
1034C2×C4C23×#59512yes—
1035C2×C4C23×#59512yes—
1036C2×C4C23×#59512yes—
1037C2×C4C23×#59512yes—
1038C2×C4C23×#59512yes—
1039C22—22no—
1040C22—22no—
1041C22—28no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—44no—
1046C22—171no—
1047C22—171no—
1048C22—172no—
1049C22—171no—
1050C22—171no—
1051C22—172no—
1052C22—171no—
1053C22—171no—
1054C22—172no—
1055C22—174no—
1056C22—174no—
1057C22—174no—
1058C22—174no—
1059C22—174no—
1060C22—344no—
1061C22—344no—
1062C22—344no—
1063C22—3416no—
1064C22—344no—
1065C22—342no—
1066C22—342no—
1067C22—348no—
1068C22—342no—
1069C22—342no—
1070C22—342no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—688no—
1075C22—682no—
1076C22—684no—
1077C22C2×D4×#59514yes—
1078C22C2×D4×#59512yes—
1079C22#41×#59512yes—
1080C22#1176387812yes—
1081C22C24×#59511yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—344no—
1088C4—344no—
1089C4—344no—
1090C4—344no—
1091C4—342no—
1092C4—342no—
1093C4—342no—
1094C4—342no—
1095C4—342no—
1096C4—682no—
1097C4—682no—
1098C4—682no—
1099C4—682no—
1100C2—24no—
1101C2—42no—
1102C2—171no—
1103C2—171no—
1104C2—171no—
1105C2—174no—
1106C2—171no—
1107C2—344no—
1108C2—682no—
1109C2#1454530714yesdirect product factor
1110C2C22×D4×#59511yescharacteristic
1111C2C2×#41×#59511yescharacteristic
1112C2C2×#1176387811yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#123C4
socleC23×C17C23×C4
prime radicalC22×D4×D17C22
cosocleC22×D17C25
hypercenterC2×#123#595
hypocenterC17C2×#2359
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C22×#10587677C2semidirect
3. #14545307C2direct (N × H)
4. C2×#11763760C2semidirect
5. C2×#11763759C2semidirect
6. C2×#11763759C2semidirect
7. C2×#11763758C2semidirect
8. C2×#11763758C2semidirect
10. C2×#11763756C2semidirect
11. C2×#11763756C2semidirect
12. C2×C4⋊C4×#595C2semidirect
13. C2×C22⋊C4×#595C2semidirect
14. C2×C22⋊C4×#595C2semidirect
15. C22×(C2×#595)⋊C4C2semidirect
23. C2×#10587677C22semidirect
39. #11763760C22semidirect
40. #11763759C22semidirect
41. #11763759C22semidirect
42. #11763758C22semidirect
43. #11763758C22semidirect
45. #11763756C22semidirect
46. #11763756C22semidirect
47. C4⋊C4×#595C22semidirect
48. C22⋊C4×#595C22semidirect
49. C22⋊C4×#595C22semidirect
60. C2×(C2×#595)⋊C4C22semidirect
63. C2×#10587580C4semidirect
64. C2×#10587580C4semidirect
65. C2×#10587572C4semidirect
66. C2×#10587615C4semidirect
67. C2×#10587569C4semidirect
68. C2×#10587569C4semidirect
69. C2×#10587621C4semidirect
70. #123×D17C4semidirect
77. C2×C17×#123C4semidirect
101. C23×C4×C17C2×C4semidirect
104. C23×Dic17C2×C4semidirect
112. C22×C4×D17C2×C4semidirect
113. C22×C4×D17C2×C4semidirect
114. C22×C4×D17C2×C4semidirect
153. C17×#123C2×C4semidirect
154. C2×C4⋊C4×C17C2×C4semidirect
155. C2×C4⋊C4×C17C2×C4semidirect
156. C2×C22⋊C4×C17C2×C4semidirect
157. C2×C22⋊C4×C17C2×C4semidirect
158. C2×C22⋊C4×C17C2×C4semidirect
159. C2×C22⋊Dic17C2×C4semidirect
160. C2×C22⋊Dic17C2×C4semidirect
161. C2×C22⋊Dic17C2×C4semidirect
162. #10587621C2×C4semidirect
163. #10587615C2×C4semidirect
164. C2×#63227C2×C4semidirect
165. C2×#63227C2×C4semidirect
166. C2×#63227C2×C4semidirect
167. C2×#63227C2×C4semidirect
168. C2×#63227C2×C4semidirect
169. C2×#63227C2×C4semidirect
170. C2×C4⋊Dic17C2×C4semidirect
171. C2×C4⋊Dic17C2×C4semidirect
172. C2×#63225C2×C4semidirect
173. C2×#63225C2×C4semidirect
174. C2×#63225C2×C4semidirect
175. C2×#63225C2×C4semidirect
176. #10587580C2×C4semidirect
177. #10587580C2×C4semidirect
178. C4⋊C4×D17C2×C4semidirect
179. C4⋊C4×D17C2×C4semidirect
182. #10587572C2×C4semidirect
183. #10587569C2×C4semidirect
184. #10587569C2×C4semidirect
185. C22⋊C4×D17C2×C4semidirect
186. C22⋊C4×D17C2×C4semidirect
187. C22⋊C4×D17C2×C4semidirect
274. C22×C4×C17C22×C4semidirect
285. C22×Dic17C22×C4semidirect
311. C2×C4×D17C22×C4semidirect
312. C2×C4×D17C22×C4semidirect
333. C4⋊C4×C17C22×C4semidirect
334. C4⋊C4×C17C22×C4semidirect
335. C22⋊C4×C17C22×C4semidirect
336. C22⋊C4×C17C22×C4semidirect
337. C22⋊C4×C17C22×C4semidirect
338. C22⋊Dic17C22×C4semidirect
339. C22⋊Dic17C22×C4semidirect
340. C22⋊Dic17C22×C4semidirect
341. #63227C22×C4semidirect
342. #63227C22×C4semidirect
343. #63227C22×C4semidirect
344. #63227C22×C4semidirect
345. #63227C22×C4semidirect
346. #63227C22×C4semidirect
347. C4⋊Dic17C22×C4semidirect
348. C4⋊Dic17C22×C4semidirect
349. #63225C22×C4semidirect
350. #63225C22×C4semidirect
351. #63225C22×C4semidirect
352. #63225C22×C4semidirect
574. C2×#123#595semidirect
623. C2×C17#2359semidirect
629. D17#2359semidirect
676. C23×C4C2×#595semidirect
684. #123C2×#595semidirect
707. C2×C4⋊C4C2×#595semidirect
708. C2×C4⋊C4C2×#595semidirect
734. C2×C22⋊C4C2×#595semidirect
735. C2×C22⋊C4C2×#595semidirect
736. C2×C22⋊C4C2×#595semidirect
757. C17C2×#2359semidirect
874. C22×C4C22×#595semidirect
886. C4⋊C4C22×#595semidirect
887. C4⋊C4C22×#595semidirect
902. C22⋊C4C22×#595semidirect
903. C22⋊C4C22×#595semidirect
904. C22⋊C4C22×#595semidirect
1109. C2#14545307direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×#5952
C22×#105876772
#145453072
C2×#117637602
C2×#117637592
C2×#117637582
C2×#117637572
C2×#117637562
C2×C4⋊C4×#5952
C2×C22⋊C4×#5952
C22×(C2×#595)⋊C42
C2×#123×D172
C2×#235917