Finite Group Databasebeta

← C2×#21433032 #29453057

Subgroups — C2×#21433032 #29453057

Order 15104.

1894 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837956C211yesmaximal, characteristic
2#21433032C2116yesmaximal, direct product factor
3C2×#16837533C211yesmaximal, characteristic, complemented
4C2×#16837532C211yesmaximal, characteristic, complemented
5C2×#16837531C211yesmaximal, characteristic, complemented
6C2×#16837531C211yesmaximal, characteristic, complemented
7C2×#16837530C211yesmaximal, characteristic, complemented
8C2×#16837530C211yesmaximal, characteristic, complemented
9C2×#16837529C211yesmaximal, characteristic, complemented
10C2×#16837427C211yesmaximal, characteristic
11C2×#16837427C211yesmaximal, characteristic
12C2×#16837424C211yesmaximal, characteristic
13C2×#16837359C211yesmaximal, characteristic
14C2×#16837356C211yesmaximal, characteristic
15C2×#97×D59C211yesmaximal, characteristic
16C2×C59×#446C211yesmaximal, characteristic, complemented
17C22×#11745659C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16837956C418yes—
22#16837956C2218yes—
23C2×#14273726C411yescharacteristic
24C2×#14273725C411yescharacteristic
25C2×#14273717C411yescharacteristic
26C2×#14273717C411yescharacteristic
27C2×#14273707C411yescharacteristic
28C2×#14273705C411yescharacteristic
29C2×#14273705C411yescharacteristic
30C2×#14273703C411yescharacteristic
31C2×C4×Dic118C2211yescharacteristic
32C2×C4×Dic118C2211yescharacteristic
33C2×C4×Dic118C2211yescharacteristic
34C2×#14273684C2211yescharacteristic
35C2×#14273684C2211yescharacteristic
36C2×C42×D59C2211yescharacteristic
37#16837533C2218yescomplemented
38#16837532C2218yescomplemented
39#16837531C2218yescomplemented
40#16837531C2218yescomplemented
41#16837530C2218yescomplemented
42#16837530C2218yescomplemented
43#16837529C2218yescomplemented
44#16837427C2218yes—
45#16837427C2218yes—
46#16837424C2218yes—
47C2×C4⋊(C59⋊C8)C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49C2×C4⋊(C59⋊C8)C2211yescharacteristic
50C2×Dic59⋊C8C2211yescharacteristic
51C2×Dic59⋊C8C2211yescharacteristic
52C2×Dic59⋊C8C2211yescharacteristic
53C2×Dic59⋊C8C2211yescharacteristic
54C2×Dic59⋊C8C2211yescharacteristic
55C2×Dic59⋊C8C2211yescharacteristic
56#16837359C2218yes—
57#16837356C2218yes—
58C2×#14273638C2211yescharacteristic
59C2×#14273638C2211yescharacteristic
60C2×#14273637C2211yescharacteristic
61C2×#14273637C2211yescharacteristic
62C2×#14273637C2211yescharacteristic
63C2×#14273637C2211yescharacteristic
64#97×D59C2218yes—
65C2×C4×C59⋊C8C2211yescharacteristic
66C2×C8×Dic59C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C4×Q8×C59C2211yescharacteristic
69C59×#446C2218yescomplemented
70C2×C4⋊C8×C59C2211yescharacteristic
71C2×C4⋊C8×C59C2211yescharacteristic
72C2×C4⋊C8×C59C2211yescharacteristic
73C2×#97×C59C2211yescharacteristic
74C2×#97×C59C2211yescharacteristic
75C2×C4×C8×C59C2211yescharacteristic
76C22×Dic118C2×C411yescharacteristic
77C22×Dic118C2×C411yescharacteristic
78C22×Dic118C2×C411yescharacteristic
79C22×C4×D59C2×C411yescharacteristic
80C22×C4×D59C2×C411yescharacteristic
81C22×C4×D59C2311yescharacteristic
82C2×#11745659—24no—
83C2×#11745659—24no—
84C2×#11745659C2314yes—
85C2×#11745659C2314yes—
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C2×C8×D59—24no—
91C2×C8×D59Q818yescomplemented
92C2×C8×D59C2314yes—
93C2×C8×D59C2314yes—
94#14273726C2×C418yes—
95#14273725C2×C418yes—
96#14273717C2×C418yes—
97#14273717C2×C418yes—
98#14273707C2×C418yes—
99#14273705C2×C418yes—
100#14273705C2×C418yes—
101#14273703C2×C418yes—
102C4×Dic118C2×C414yes—
103C4×Dic118C2×C414yes—
104C4×Dic118C2×C414yes—
105C4×Dic118C2314yes—
106C4×Dic118C2314yes—
107C4×Dic118C2314yes—
108#14273684C2×C414yes—
109#14273684C2×C414yes—
110#14273684C2314yes—
111#14273684C2314yes—
112C2×C4⋊Dic59C2×C411yescharacteristic
113C2×C4⋊Dic59C2×C411yescharacteristic
114C2×C4⋊Dic59C2×C411yescharacteristic
115C2×Dic59⋊C4C2×C411yescharacteristic
116C2×Dic59⋊C4C2×C411yescharacteristic
117C2×Dic59⋊C4C2×C411yescharacteristic
118C2×Dic59⋊C4C2×C411yescharacteristic
119C2×Dic59⋊C4C2×C411yescharacteristic
120C2×Dic59⋊C4C2×C411yescharacteristic
121C2×Dic59⋊C4C2×C411yescharacteristic
122C2×Dic59⋊C4C2×C411yescharacteristic
123C2×Dic59⋊C4C2×C411yescharacteristic
124C2×Dic59⋊C4C2×C411yescharacteristic
125C2×(C2×D59)⋊C4C2×C411yescharacteristic
126C2×(C2×D59)⋊C4C2×C411yescharacteristic
127C2×(C2×D59)⋊C4C2×C411yescharacteristic
128C2×(C2×D59)⋊C4C2×C411yescharacteristic
129C2×C4×Dic59C2×C411yescharacteristic
130C2×C4×Dic59C2×C411yescharacteristic
131C2×C4×Dic59C2311yescharacteristic
132C2×C4×Dic59C2311yescharacteristic
133C2×C4×Dic59C2311yescharacteristic
134C42×D59C2×C414yes—
135C42×D59C2314yes—
136C4⋊(C59⋊C8)C2314yes—
137C4⋊(C59⋊C8)C2314yes—
138C4⋊(C59⋊C8)C2314yes—
139Dic59⋊C8C2314yes—
140Dic59⋊C8C2314yes—
141Dic59⋊C8C2314yes—
142Dic59⋊C8C2314yes—
143Dic59⋊C8C2314yes—
144Dic59⋊C8C2314yes—
145#14273638C2314yes—
146#14273638C2314yes—
147#14273637C2314yes—
148#14273637C2314yes—
149#14273637C2314yes—
150#14273637C2314yes—
151C4×C59⋊C8C2314yes—
152C8×Dic59C2314yes—
153C8×Dic59C2314yes—
154C22×Q8×C59C2×C411yescharacteristic
155C22×C8×C59C2311yescharacteristic
156C22×C8×C59C2311yescharacteristic
157C22×C8×C59C2311yescharacteristic
158C22×C8×C59C2311yescharacteristic
159C4×Q8×C59C2×C414yes—
160C4×Q8×C59C2314yes—
161C2×C4⋊C4×C59C2×C411yescharacteristic
162C2×C4⋊C4×C59C2×C411yescharacteristic
163C2×C4⋊C4×C59C2×C411yescharacteristic
164C2×C42×C59C2311yescharacteristic
165C2×C42×C59C2311yescharacteristic
166C2×C42×C59C2311yescharacteristic
167C4⋊C8×C59C2314yes—
168C4⋊C8×C59C2314yes—
169C4⋊C8×C59C2314yes—
170#97×C59C2314yes—
171#97×C59C2314yes—
172C4×C8×C59C2314yes—
173C23×D59C22×C411yescharacteristic
174C2×Q8×C59—42no—
175C2×Q8×C59C22×C414yes—
176C22×C4×C59C22×C411yescharacteristic
177C22×C4×C59C22×C411yescharacteristic
178C22×C4×C59C22×C411yescharacteristic
179C22×C4×C59C22×C411yescharacteristic
180C22×C4×C59C22×C411yescharacteristic
181C22×C4×C59C22×C411yescharacteristic
182C22×C4×C59C2411yescharacteristic
183C22×Dic59C22×C411yescharacteristic
184C22×Dic59C22×C411yescharacteristic
185C22×Dic59C22×C411yescharacteristic
186C22×Dic59C22×C411yescharacteristic
187C22×Dic59C22×C411yescharacteristic
188C22×Dic59C22×C411yescharacteristic
189C22×Dic59C22×C411yescharacteristic
190C2×C4×D59—42no—
191C2×C4×D59—42no—
192C2×C4×D59C22×C414yes—
193C2×C4×D59C22×C414yes—
194C2×C4×D59C22×C412yes—
195C2×C4×D59C2×Q814yes—
196C2×C4×D59#4114yes—
197C2×C4×D59C2412yes—
198C2×Dic118—42no—
199C2×Dic118—42no—
200C2×Dic118—42no—
201C2×Dic118C22×C414yes—
202C2×Dic118C22×C414yes—
203C2×Dic118C22×C414yes—
204C2×C8×C59—22no—
205C2×C8×C59—22no—
206C2×C8×C59—22no—
207C2×C8×C59C2×Q814yes—
208C2×C8×C59C2412yes—
209C2×C8×C59C2412yes—
210C2×C8×C59C2412yes—
211C2×C8×C59C2412yes—
212C4⋊C4×C59C22×C414yes—
213C4⋊C4×C59C22×C414yes—
214C4⋊C4×C59C22×C414yes—
215C42×C59C22×C412yes—
216C42×C59C22×C412yes—
217C42×C59C22×C412yes—
218C42×C59C2412yes—
219C42×C59C2412yes—
220C42×C59C2412yes—
221(C2×D59)⋊C4C22×C414yes—
222(C2×D59)⋊C4C22×C414yes—
223(C2×D59)⋊C4C22×C414yes—
224(C2×D59)⋊C4C22×C414yes—
225C4⋊Dic59C22×C414yes—
226C4⋊Dic59C22×C414yes—
227C4⋊Dic59C22×C414yes—
228Dic59⋊C4C22×C414yes—
229Dic59⋊C4C22×C414yes—
230Dic59⋊C4C22×C414yes—
231Dic59⋊C4C22×C414yes—
232Dic59⋊C4C22×C414yes—
233Dic59⋊C4C22×C414yes—
234Dic59⋊C4C22×C414yes—
235Dic59⋊C4C22×C414yes—
236Dic59⋊C4C22×C414yes—
237Dic59⋊C4C22×C414yes—
238C4×Dic59C22×C412yes—
239C4×Dic59C22×C414yes—
240C4×Dic59C22×C414yes—
241C4×Dic59C22×C412yes—
242C4×Dic59C22×C412yes—
243C4×Dic59C2412yes—
244C4×Dic59C2412yes—
245C4×Dic59C2412yes—
246C2×C59⋊C8—22no—
247C2×C59⋊C8—22no—
248C2×C59⋊C8—22no—
249C2×C59⋊C8C2×Q814yes—
250C2×C59⋊C8C2412yes—
251C2×C59⋊C8C2412yes—
252C2×C59⋊C8C2412yes—
253C2×C59⋊C8C2412yes—
254#11745659—28no—
255#11745659—28no—
256C8×D59—28no—
257C8×D59C2×Q8116yescomplemented
258C23×C59C23×C411yescharacteristic
259C22×D59—22no—
260C22×D59—22no—
261C22×D59C4×Q814yes—
262C22×D59C23×C412yes—
263Q8×C59—44no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59C23×C412yes—
271C2×C4×C59C23×C412yes—
272C2×C4×C59C23×C412yes—
273C2×C4×C59C23×C412yes—
274C2×C4×C59C23×C412yes—
275C2×C4×C59C23×C412yes—
276C2×C4×C59C23×C411yescharacteristic
277C2×C4×C59C22×Q812yes—
278C2×C4×C59C2×#4112yes—
279C2×C4×C59C2511yescharacteristic
280C2×Dic59—22no—
281C2×Dic59—22no—
282C2×Dic59—22no—
283C2×Dic59—22no—
284C2×Dic59—22no—
285C2×Dic59—22no—
286C2×Dic59C4×Q814yes—
287C2×Dic59C23×C412yes—
288C2×Dic59C23×C412yes—
289C2×Dic59C23×C412yes—
290C2×Dic59C23×C412yes—
291C2×Dic59C23×C412yes—
292C2×Dic59C23×C412yes—
293C2×Dic59C23×C412yes—
294C4×D59—44no—
295C4×D59—44no—
296C4×D59C4×Q818yes—
297C4×D59C22×Q814yes—
298C4×D59C2×#4114yes—
299Dic118—44no—
300Dic118—44no—
301Dic118—44no—
302C8×C59—22no—
303C8×C59—22no—
304C8×C59—22no—
305C8×C59C22×Q814yes—
306C59⋊C8—22no—
307C59⋊C8—22no—
308C59⋊C8—22no—
309C59⋊C8C22×Q814yes—
310C2×#2961—591nomaximal, Sylow
311C22×C59C2×C4×Q812yes—
312C22×C59#56812yes—
313C22×C59#56812yes—
314C22×C59C24×C411yescharacteristic
315C2×D59—28no—
316C2×D59—22no—
317C2×D59—22no—
318C2×D59C2×C4×Q814yes—
319C4×C59—22no—
320C4×C59—22no—
321C4×C59—22no—
322C4×C59—22no—
323C4×C59—22no—
324C4×C59—22no—
325C4×C59C2×C4×Q812yes—
326C4×C59C23×Q811yescharacteristic
327C4×C59C22×#4111yescharacteristic
328Dic59—22no—
329Dic59—22no—
330Dic59—22no—
331Dic59—22no—
332Dic59—22no—
333Dic59—22no—
334Dic59C2×C4×Q814yes—
335C2×#533—591no—
336#2961—5916no—
337C2×#446—591no—
338C2×#446—591no—
339C2×#446—591no—
340C2×#446—591no—
341C2×#446—591no—
342C2×#446—591no—
343C2×#446—591no—
344C2×#446D5911yescharacteristic, complemented
345C2×#424—591no—
346C2×#424—591no—
347C2×#423—591no—
348C2×#405—591no—
349C2×#405—591no—
350C22×#97—591no—
351C2×C59#296114yescomplemented
352C2×C59C22×C4×Q811yescharacteristic
353C2×C59C2×#56811yescharacteristic
354C2×C59C2×#56811yescharacteristic
355D59—24no—
356C22×M16—591no—
357C22×M16—591no—
358C23×C8—591no—
359C23×C8—591no—
360#533—598no—
361#533—598no—
362C2×C4⋊Q8—591no—
363C2×C4⋊Q8—591no—
364C2×#125—591no—
365C2×#125—591no—
366C2×C22⋊Q8—591no—
367C2×C22⋊Q8—591no—
368C2×C22⋊Q8—591no—
369C2×C22⋊Q8—591no—
370C2×C4×Q8—591no—
371C2×C4×Q8—591no—
372C2×C4×Q8—591no—
373C2×C4×Q8C2×D5911yescharacteristic
374C2×#117—591no—
375C2×#117—591no—
376C22×C42—591no—
377#446—598no—
378#446—598no—
379#446—598no—
380#446—598no—
381#446—598no—
382#446—598no—
383#446—598no—
384#446C2×D5918yescomplemented
385#424—598no—
386#424—598no—
387#423—598no—
388C2×C4⋊C8—591no—
389C2×C4⋊C8—591no—
390C2×C4⋊C8—591no—
391C2×C4⋊C8—591no—
392C2×C4⋊C8—591no—
393C2×C4⋊C8—591no—
394C2×C4⋊C8—591no—
395C2×C4⋊C8—591no—
396C2×C4⋊C8—591no—
397C2×C4⋊C8C2×D5911yescharacteristic
398C2×C4⋊C8C2×D5911yescharacteristic
399C2×C4⋊C8C2×D5911yescharacteristic
400#405—598no—
401#405—598no—
402C2×#97—591no—
403C2×#97—591no—
404C2×#97—591no—
405C2×#97—591no—
406C2×#97—591no—
407C2×#97—591no—
408C2×#97—598no—
409C2×#97C2×D5911yescharacteristic
410C2×#97C2×D5911yescharacteristic
411C2×C4×C8—591no—
412C2×C4×C8—591no—
413C2×C4×C8—591no—
414C2×C4×C8C2×D5911yescharacteristic
415C59C2×#296111yescharacteristic, complemented, Sylow
416C22×Q8—591no—
417C22×Q8—591no—
418C22×Q8—591no—
419C22×Q8C4×D5911yescharacteristic
420C23×C4—591no—
421C23×C4—591no—
422C23×C4—591no—
423C2×M16—594no—
424C2×M16—594no—
425C2×M16—1184no—
426C2×M16—1184no—
427C22×C8—591no—
428C22×C8—598no—
429C22×C8—594no—
430C22×C8—591no—
431C22×C8—591no—
432C22×C8—591no—
433C22×C8—594no—
434C22×C8—1184no—
435C22×C8C22×D5911yescharacteristic
436C22×C8C22×D5911yescharacteristic
437C22×C8C22×D5911yescharacteristic
438C22×C8C22×D5911yescharacteristic
439C4⋊Q8—598no—
440C4⋊Q8—598no—
441#125—598no—
442#125—598no—
443C22⋊Q8—598no—
444C22⋊Q8—598no—
445C22⋊Q8—598no—
446C22⋊Q8—598no—
447C4×Q8—594no—
448C4×Q8—594no—
449C4×Q8—594no—
450C4×Q8—594no—
451C4×Q8—594no—
452C4×Q8—594no—
453C4×Q8C4×D5914yes—
454C4×Q8C22×D5914yes—
455#117—594no—
456#117—594no—
457#117—594no—
458#117—594no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—591no—
461C2×C4⋊C4—591no—
462C2×C4⋊C4—591no—
463C2×C4⋊C4—591no—
464C2×C4⋊C4—591no—
465C2×C4⋊C4—591no—
466C2×C4⋊C4—591no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—591no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4C4×D5911yescharacteristic
473C2×C4⋊C4C4×D5911yescharacteristic
474C2×C4⋊C4C4×D5911yescharacteristic
475C2×C22⋊C4—591no—
476C2×C22⋊C4—591no—
477C2×C22⋊C4—591no—
478C2×C22⋊C4—591no—
479C2×C42—591no—
480C2×C42—591no—
481C2×C42—591no—
482C2×C42—591no—
483C2×C42—591no—
484C2×C42—594no—
485C2×C42—594no—
486C2×C42C22×D5911yescharacteristic
487C2×C42C22×D5911yescharacteristic
488C2×C42C22×D5911yescharacteristic
489C4⋊C8—594no—
490C4⋊C8—594no—
491C4⋊C8—594no—
492C4⋊C8—594no—
493C4⋊C8—594no—
494C4⋊C8—594no—
495C4⋊C8—594no—
496C4⋊C8—594no—
497C4⋊C8—594no—
498C4⋊C8C22×D5914yes—
499C4⋊C8C22×D5914yes—
500C4⋊C8C22×D5914yes—
501#97—594no—
502#97—594no—
503#97—594no—
504#97—594no—
505#97—594no—
506#97—594no—
507#97C22×D5914yes—
508#97C22×D5914yes—
509C4×C8—594no—
510C4×C8—594no—
511C4×C8—594no—
512C4×C8C22×D5914yes—
513C24—591no—
514C2×Q8—42no—
515C2×Q8—594no—
516C2×Q8—594no—
517C2×Q8—594no—
518C2×Q8—2362no—
519C2×Q8—2362no—
520C2×Q8—2362no—
521C2×Q8C2×C4×D5914yes—
522C22×C4—591no—
523C22×C4—592no—
524C22×C4—594no—
525C22×C4—594no—
526C22×C4—592no—
527C22×C4—591no—
528C22×C4—591no—
529C22×C4—591no—
530C22×C4—591no—
531C22×C4—591no—
532C22×C4—591no—
533C22×C4—594no—
534C22×C4—594no—
535C22×C4—2362no—
536C22×C4—2362no—
537C22×C4C2×C4×D5911yescharacteristic
538C22×C4C2×C4×D5911yescharacteristic
539C22×C4C2×C4×D5911yescharacteristic
540C22×C4C2×C4×D5911yescharacteristic
541C22×C4C2×C4×D5911yescharacteristic
542C22×C4C2×C4×D5911yescharacteristic
543C22×C4C23×D5911yescharacteristic
544M16—1188no—
545M16—1188no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—594no—
550C2×C8—592no—
551C2×C8—5916no—
552C2×C8—592no—
553C2×C8—592no—
554C2×C8—592no—
555C2×C8—1188no—
556C2×C8—1182no—
557C2×C8—1182no—
558C2×C8—1182no—
559C2×C8Q8×D5914yes—
560C2×C8C23×D5912yes—
561C2×C8C23×D5912yes—
562C2×C8C23×D5912yes—
563C2×C8C23×D5912yes—
564C4⋊C4—594no—
565C4⋊C4—594no—
566C4⋊C4—594no—
567C4⋊C4—594no—
568C4⋊C4—594no—
569C4⋊C4—594no—
570C4⋊C4—594no—
571C4⋊C4—594no—
572C4⋊C4—594no—
573C4⋊C4—594no—
574C4⋊C4—594no—
575C4⋊C4—594no—
576C4⋊C4—594no—
577C4⋊C4C2×C4×D5914yes—
578C4⋊C4C2×C4×D5914yes—
579C4⋊C4C2×C4×D5914yes—
580C22⋊C4—594no—
581C22⋊C4—594no—
582C22⋊C4—594no—
583C22⋊C4—594no—
584C42—592no—
585C42—594no—
586C42—594no—
587C42—592no—
588C42—592no—
589C42—592no—
590C42—592no—
591C42—592no—
592C42C2×C4×D5912yes—
593C42C2×C4×D5912yes—
594C42C2×C4×D5912yes—
595C42C23×D5912yes—
596C42C23×D5912yes—
597C42C23×D5912yes—
598C23—592no—
599C23—594no—
600C23—1182no—
601C23—1182no—
602C23C22×C4×D5911yescharacteristic
603Q8—44no—
604Q8—2364no—
605Q8—2364no—
606Q8—2364no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—592no—
614C2×C4—594no—
615C2×C4—594no—
616C2×C4—594no—
617C2×C4—598no—
618C2×C4—592no—
619C2×C4—592no—
620C2×C4—592no—
621C2×C4—592no—
622C2×C4—592no—
623C2×C4—592no—
624C2×C4—1182no—
625C2×C4—1182no—
626C2×C4—1182no—
627C2×C4—1182no—
628C2×C4—1182no—
629C2×C4—1182no—
630C2×C4—2364no—
631C2×C4—2364no—
632C2×C4C22×C4×D5912yes—
633C2×C4C22×C4×D5912yes—
634C2×C4C22×C4×D5912yes—
635C2×C4C22×C4×D5912yes—
636C2×C4C22×C4×D5912yes—
637C2×C4C22×C4×D5912yes—
638C2×C4C22×C4×D5911yescharacteristic
639C2×C4C2×Q8×D5912yes—
640C2×C4#41×D5912yes—
641C2×C4C24×D5911yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—594no—
646C8—1182no—
647C8—1182no—
648C8—1182no—
649C8C2×Q8×D5914yes—
650C22—594no—
651C22—1182no—
652C22—1182no—
653C22—1188no—
654C22C4×Q8×D5912yes—
655C22#1683816712yes—
656C22#1683816812yes—
657C22C23×C4×D5911yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—594no—
665C4—1182no—
666C4—1182no—
667C4—1182no—
668C4—1182no—
669C4—1182no—
670C4—1182no—
671C4C4×Q8×D5912yes—
672C4C22×Q8×D5911yescharacteristic
673C4C2×#41×D5911yescharacteristic
674C2—1184no—
675C2#2143303214yesdirect product factor
676C2C2×C4×Q8×D5911yescharacteristic
677C2C2×#1683816711yescharacteristic
678C2C2×#1683816811yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#446C2
socleC23×C59C23×C4
prime radicalC23×D59C22×C4
cosocleC2×C4×C59C25
hypercenterC2×#446D59
hypocenterC59C2×#2961
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #21433032C2direct (N × H)
3. C2×#16837533C2semidirect
4. C2×#16837532C2semidirect
5. C2×#16837531C2semidirect
6. C2×#16837531C2semidirect
7. C2×#16837530C2semidirect
8. C2×#16837530C2semidirect
9. C2×#16837529C2semidirect
16. C2×C59×#446C2semidirect
37. #16837533C22semidirect
38. #16837532C22semidirect
39. #16837531C22semidirect
40. #16837531C22semidirect
41. #16837530C22semidirect
42. #16837530C22semidirect
43. #16837529C22semidirect
69. C59×#446C22semidirect
91. C2×C8×D59Q8semidirect
257. C8×D59C2×Q8semidirect
344. C2×#446D59semidirect
351. C2×C59#2961semidirect
384. #446C2×D59semidirect
415. C59C2×#2961semidirect
675. C2#21433032direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379562
#214330322
C2×#168375332
C2×#168375322
C2×#168375312
C2×#168375302
C2×#168375292
C2×#168374272
C2×#168374242
C2×#168373592
C2×#168373562
C2×#97×D592
C2×C59×#4462
C2×#296159