Finite Group Databasebeta

← C2×#21433199 #29453655

Subgroups — C2×#21433199 #29453655

Order 15104.

1706 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837956C211yesmaximal, characteristic
2#21433199C2116yesmaximal, 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×#16837464C211yesmaximal, characteristic
11C2×#16837462C211yesmaximal, characteristic
12C2×#16837462C211yesmaximal, characteristic
13C2×#16837461C211yesmaximal, characteristic
14C2×#16837458C211yesmaximal, characteristic
15C2×#16837457C211yesmaximal, characteristic
16C2×C59×#446C211yesmaximal, characteristic, complemented
17#16837956C418yes—
18#16837956C2218yes—
19C2×#14273726C411yescharacteristic
20C2×#14273725C411yescharacteristic
21C2×#14273717C411yescharacteristic
22C2×#14273717C411yescharacteristic
23C2×#14273707C411yescharacteristic
24C2×#14273705C411yescharacteristic
25C2×#14273705C411yescharacteristic
26C2×#14273703C411yescharacteristic
27C2×C4×Dic118C2211yescharacteristic
28C2×C4×Dic118C2211yescharacteristic
29C2×C4×Dic118C2211yescharacteristic
30C2×#14273684C2211yescharacteristic
31C2×#14273684C2211yescharacteristic
32C2×C42×D59C2211yescharacteristic
33#16837533C2218yescomplemented
34#16837532C2218yescomplemented
35#16837531C2218yescomplemented
36#16837531C2218yescomplemented
37#16837530C2218yescomplemented
38#16837530C2218yescomplemented
39#16837529C2218yescomplemented
40#16837464C2218yes—
41#16837462C2218yes—
42#16837462C2218yes—
43#16837461C2218yes—
44#16837458C2218yes—
45#16837457C2218yes—
46C2×C4⋊(C59⋊C8)C2211yescharacteristic
47C2×C4⋊(C59⋊C8)C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49C2×Dic59⋊C8C2211yescharacteristic
50C2×Dic59⋊C8C2211yescharacteristic
51C2×Dic59⋊C8C2211yescharacteristic
52C2×Dic59⋊C8C2211yescharacteristic
53C2×Dic59⋊C8C2211yescharacteristic
54C2×Dic59⋊C8C2211yescharacteristic
55C2×(C2×D59)⋊C8C2211yescharacteristic
56C2×(C2×D59)⋊C8C2211yescharacteristic
57C2×(C2×D59)⋊C8C2211yescharacteristic
58C2×(C2×D59)⋊C8C2211yescharacteristic
59C2×#14273638C2211yescharacteristic
60C2×#14273638C2211yescharacteristic
61C2×#14273637C2211yescharacteristic
62C2×#14273637C2211yescharacteristic
63C2×#14273637C2211yescharacteristic
64C2×#14273637C2211yescharacteristic
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
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86#14273726C2×C418yes—
87#14273725C2×C418yes—
88#14273717C2×C418yes—
89#14273717C2×C418yes—
90#14273707C2×C418yes—
91#14273705C2×C418yes—
92#14273705C2×C418yes—
93#14273703C2×C418yes—
94C4×Dic118C2×C414yes—
95C4×Dic118C2×C414yes—
96C4×Dic118C2×C414yes—
97C4×Dic118C2314yes—
98C4×Dic118C2314yes—
99C4×Dic118C2314yes—
100#14273684C2×C414yes—
101#14273684C2×C414yes—
102#14273684C2314yes—
103#14273684C2314yes—
104C2×C4⋊Dic59C2×C411yescharacteristic
105C2×C4⋊Dic59C2×C411yescharacteristic
106C2×C4⋊Dic59C2×C411yescharacteristic
107C2×Dic59⋊C4C2×C411yescharacteristic
108C2×Dic59⋊C4C2×C411yescharacteristic
109C2×Dic59⋊C4C2×C411yescharacteristic
110C2×Dic59⋊C4C2×C411yescharacteristic
111C2×Dic59⋊C4C2×C411yescharacteristic
112C2×Dic59⋊C4C2×C411yescharacteristic
113C2×Dic59⋊C4C2×C411yescharacteristic
114C2×Dic59⋊C4C2×C411yescharacteristic
115C2×Dic59⋊C4C2×C411yescharacteristic
116C2×Dic59⋊C4C2×C411yescharacteristic
117C2×(C2×D59)⋊C4C2×C411yescharacteristic
118C2×(C2×D59)⋊C4C2×C411yescharacteristic
119C2×(C2×D59)⋊C4C2×C411yescharacteristic
120C2×(C2×D59)⋊C4C2×C411yescharacteristic
121C2×C4×Dic59C2×C411yescharacteristic
122C2×C4×Dic59C2×C411yescharacteristic
123C2×C4×Dic59C2311yescharacteristic
124C2×C4×Dic59C2311yescharacteristic
125C2×C4×Dic59C2311yescharacteristic
126C42×D59C2×C414yes—
127C42×D59C2314yes—
128C4⋊(C59⋊C8)C2314yes—
129C4⋊(C59⋊C8)C2314yes—
130C4⋊(C59⋊C8)C2314yes—
131Dic59⋊C8C2314yes—
132Dic59⋊C8C2314yes—
133Dic59⋊C8C2314yes—
134Dic59⋊C8C2314yes—
135Dic59⋊C8C2314yes—
136Dic59⋊C8C2314yes—
137(C2×D59)⋊C8C2314yes—
138(C2×D59)⋊C8C2314yes—
139(C2×D59)⋊C8C2314yes—
140(C2×D59)⋊C8C2314yes—
141#14273638C2314yes—
142#14273638C2314yes—
143#14273637C2314yes—
144#14273637C2314yes—
145#14273637C2314yes—
146#14273637C2314yes—
147C4×C59⋊C8C2314yes—
148C8×Dic59C2314yes—
149C8×Dic59C2314yes—
150C22×Q8×C59C2×C411yescharacteristic
151C22×C8×C59C2311yescharacteristic
152C22×C8×C59C2311yescharacteristic
153C22×C8×C59C2311yescharacteristic
154C22×C8×C59C2311yescharacteristic
155C4×Q8×C59C2×C414yes—
156C4×Q8×C59C2314yes—
157C2×C4⋊C4×C59C2×C411yescharacteristic
158C2×C4⋊C4×C59C2×C411yescharacteristic
159C2×C4⋊C4×C59C2×C411yescharacteristic
160C2×C42×C59C2311yescharacteristic
161C2×C42×C59C2311yescharacteristic
162C2×C42×C59C2311yescharacteristic
163C4⋊C8×C59C2314yes—
164C4⋊C8×C59C2314yes—
165C4⋊C8×C59C2314yes—
166#97×C59C2314yes—
167#97×C59C2314yes—
168C4×C8×C59C2314yes—
169C23×D59C22×C411yescharacteristic
170C2×Q8×C59—42no—
171C2×Q8×C59C22×C414yes—
172C22×C4×C59C22×C411yescharacteristic
173C22×C4×C59C22×C411yescharacteristic
174C22×C4×C59C22×C411yescharacteristic
175C22×C4×C59C22×C411yescharacteristic
176C22×C4×C59C22×C411yescharacteristic
177C22×C4×C59C22×C411yescharacteristic
178C22×C4×C59C2411yescharacteristic
179C22×Dic59C22×C411yescharacteristic
180C22×Dic59C22×C411yescharacteristic
181C22×Dic59C22×C411yescharacteristic
182C22×Dic59C22×C411yescharacteristic
183C22×Dic59C22×C411yescharacteristic
184C22×Dic59C22×C411yescharacteristic
185C22×Dic59C22×C411yescharacteristic
186C2×C4×D59—22no—
187C2×C4×D59—22no—
188C2×C4×D59—42no—
189C2×C4×D59—42no—
190C2×C4×D59C22×C412yes—
191C2×C4×D59C22×C414yes—
192C2×C4×D59C22×C414yes—
193C2×C4×D59C2412yes—
194C2×Dic118—42no—
195C2×Dic118—42no—
196C2×Dic118—42no—
197C2×Dic118C22×C414yes—
198C2×Dic118C22×C414yes—
199C2×Dic118C22×C414yes—
200C2×C8×C59—22no—
201C2×C8×C59—22no—
202C2×C8×C59—22no—
203C2×C8×C59—22no—
204C2×C8×C59C2412yes—
205C2×C8×C59C2412yes—
206C2×C8×C59C2412yes—
207C2×C8×C59C2412yes—
208C4⋊C4×C59C22×C414yes—
209C4⋊C4×C59C22×C414yes—
210C4⋊C4×C59C22×C414yes—
211C42×C59C22×C412yes—
212C42×C59C22×C412yes—
213C42×C59C22×C412yes—
214C42×C59C2412yes—
215C42×C59C2412yes—
216C42×C59C2412yes—
217(C2×D59)⋊C4C22×C414yes—
218(C2×D59)⋊C4C22×C414yes—
219(C2×D59)⋊C4C22×C414yes—
220(C2×D59)⋊C4C22×C414yes—
221C4⋊Dic59C22×C414yes—
222C4⋊Dic59C22×C414yes—
223C4⋊Dic59C22×C414yes—
224Dic59⋊C4C22×C414yes—
225Dic59⋊C4C22×C414yes—
226Dic59⋊C4C22×C414yes—
227Dic59⋊C4C22×C414yes—
228Dic59⋊C4C22×C414yes—
229Dic59⋊C4C22×C414yes—
230Dic59⋊C4C22×C414yes—
231Dic59⋊C4C22×C414yes—
232Dic59⋊C4C22×C414yes—
233Dic59⋊C4C22×C414yes—
234C4×Dic59C22×C412yes—
235C4×Dic59C22×C414yes—
236C4×Dic59C22×C414yes—
237C4×Dic59C22×C412yes—
238C4×Dic59C22×C412yes—
239C4×Dic59C2412yes—
240C4×Dic59C2412yes—
241C4×Dic59C2412yes—
242C2×C59⋊C8—22no—
243C2×C59⋊C8—22no—
244C2×C59⋊C8—22no—
245C2×C59⋊C8—22no—
246C2×C59⋊C8C2412yes—
247C2×C59⋊C8C2412yes—
248C2×C59⋊C8C2412yes—
249C2×C59⋊C8C2412yes—
250C23×C59C23×C411yescharacteristic
251C22×D59—22no—
252C22×D59—22no—
253C22×D59—22no—
254C22×D59C23×C412yes—
255Q8×C59—44no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59C23×C412yes—
263C2×C4×C59C23×C412yes—
264C2×C4×C59C23×C412yes—
265C2×C4×C59C23×C412yes—
266C2×C4×C59C23×C412yes—
267C2×C4×C59C23×C412yes—
268C2×C4×C59C23×C411yescharacteristic
269C2×C4×C592−1+412yes—
270C2×C4×C592−1+412yes—
271C2×C4×C59C2511yescharacteristic
272C2×Dic59—22no—
273C2×Dic59—22no—
274C2×Dic59—22no—
275C2×Dic59—22no—
276C2×Dic59—22no—
277C2×Dic59—22no—
278C2×Dic59—22no—
279C2×Dic59C23×C412yes—
280C2×Dic59C23×C412yes—
281C2×Dic59C23×C412yes—
282C2×Dic59C23×C412yes—
283C2×Dic59C23×C412yes—
284C2×Dic59C23×C412yes—
285C2×Dic59C23×C412yes—
286C4×D59—24no—
287C4×D59—22no—
288C4×D59—22no—
289C4×D59—44no—
290C4×D59—44no—
291Dic118—44no—
292Dic118—44no—
293Dic118—44no—
294C8×C59—22no—
295C8×C59—22no—
296C8×C59—22no—
297C8×C59—22no—
298C59⋊C8—22no—
299C59⋊C8—22no—
300C59⋊C8—22no—
301C59⋊C8—22no—
302C2×#2987—591nomaximal, Sylow
303C22×C59#51912yes—
304C22×C59#56812yes—
305C22×C59#56812yes—
306C22×C59C24×C411yescharacteristic
307C2×D59—22no—
308C2×D59—22no—
309C2×D59—22no—
310C2×D59—44no—
311C4×C59—22no—
312C4×C59—22no—
313C4×C59—22no—
314C4×C59—22no—
315C4×C59—22no—
316C4×C59—22no—
317C4×C59#51912yes—
318C4×C59C2×2−1+411yescharacteristic
319C4×C59C2×2−1+411yescharacteristic
320Dic59—22no—
321Dic59—22no—
322Dic59—22no—
323Dic59—22no—
324Dic59—22no—
325Dic59—22no—
326Dic59—22no—
327C2×#533—591no—
328#2987—5916no—
329C2×#446—591no—
330C2×#446—591no—
331C2×#446—591no—
332C2×#446—591no—
333C2×#446—591no—
334C2×#446—591no—
335C2×#446—591no—
336C2×#446D5911yescharacteristic, complemented
337C2×#433—591no—
338C2×#433—591no—
339C2×#433—591no—
340C2×#433—591no—
341C2×#432—591no—
342C2×#432—591no—
343C2×C59#298714yescomplemented
344C2×C59C2×#51911yescharacteristic
345C2×C59C2×#56811yescharacteristic
346C2×C59C2×#56811yescharacteristic
347D59—42no—
348#533—598no—
349#533—598no—
350C2×C4⋊Q8—591no—
351C2×C4⋊Q8—591no—
352C2×#125—591no—
353C2×#125—591no—
354C2×C22⋊Q8—591no—
355C2×C22⋊Q8—591no—
356C2×C22⋊Q8—591no—
357C2×C22⋊Q8—591no—
358C2×C4×Q8—591no—
359C2×C4×Q8—591no—
360C2×C4×Q8—591no—
361C2×C4×Q8C2×D5911yescharacteristic
362C2×#117—591no—
363C2×#117—591no—
364C22×C42—591no—
365#446—598no—
366#446—598no—
367#446—598no—
368#446—598no—
369#446—598no—
370#446—598no—
371#446—598no—
372#446C2×D5918yescomplemented
373#433—598no—
374#433—598no—
375#433—598no—
376#433—598no—
377#432—598no—
378#432—598no—
379C2×C4⋊C8—591no—
380C2×C4⋊C8—591no—
381C2×C4⋊C8—591no—
382C2×C4⋊C8—591no—
383C2×C4⋊C8—591no—
384C2×C4⋊C8—591no—
385C2×C4⋊C8—591no—
386C2×C4⋊C8—591no—
387C2×C4⋊C8—591no—
388C2×C4⋊C8C2×D5911yescharacteristic
389C2×C4⋊C8C2×D5911yescharacteristic
390C2×C4⋊C8C2×D5911yescharacteristic
391C2×C22⋊C8—591no—
392C2×C22⋊C8—591no—
393C2×C22⋊C8—591no—
394C2×C22⋊C8—591no—
395C2×#97—591no—
396C2×#97—591no—
397C2×#97—591no—
398C2×#97—591no—
399C2×#97—591no—
400C2×#97—591no—
401C2×#97C2×D5911yescharacteristic
402C2×#97C2×D5911yescharacteristic
403C2×C4×C8—591no—
404C2×C4×C8—591no—
405C2×C4×C8—591no—
406C2×C4×C8C2×D5911yescharacteristic
407C59C2×#298711yescharacteristic, complemented, Sylow
408C22×Q8—591no—
409C22×Q8—591no—
410C22×Q8—591no—
411C22×Q8C4×D5911yescharacteristic
412C23×C4—591no—
413C23×C4—591no—
414C23×C4—591no—
415C22×C8—591no—
416C22×C8—591no—
417C22×C8—591no—
418C22×C8—591no—
419C22×C8C22×D5911yescharacteristic
420C22×C8C22×D5911yescharacteristic
421C22×C8C22×D5911yescharacteristic
422C22×C8C22×D5911yescharacteristic
423C4⋊Q8—598no—
424C4⋊Q8—598no—
425#125—598no—
426#125—598no—
427C22⋊Q8—598no—
428C22⋊Q8—598no—
429C22⋊Q8—598no—
430C22⋊Q8—598no—
431C4×Q8—594no—
432C4×Q8—594no—
433C4×Q8—594no—
434C4×Q8—594no—
435C4×Q8—594no—
436C4×Q8—594no—
437C4×Q8C4×D5914yes—
438C4×Q8C22×D5914yes—
439#117—594no—
440#117—594no—
441#117—594no—
442#117—594no—
443C2×C4⋊C4—591no—
444C2×C4⋊C4—591no—
445C2×C4⋊C4—591no—
446C2×C4⋊C4—591no—
447C2×C4⋊C4—591no—
448C2×C4⋊C4—591no—
449C2×C4⋊C4—591no—
450C2×C4⋊C4—591no—
451C2×C4⋊C4—591no—
452C2×C4⋊C4—591no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4C4×D5911yescharacteristic
457C2×C4⋊C4C4×D5911yescharacteristic
458C2×C4⋊C4C4×D5911yescharacteristic
459C2×C22⋊C4—591no—
460C2×C22⋊C4—591no—
461C2×C22⋊C4—591no—
462C2×C22⋊C4—591no—
463C2×C42—591no—
464C2×C42—591no—
465C2×C42—591no—
466C2×C42—591no—
467C2×C42—591no—
468C2×C42—594no—
469C2×C42—594no—
470C2×C42C22×D5911yescharacteristic
471C2×C42C22×D5911yescharacteristic
472C2×C42C22×D5911yescharacteristic
473C4⋊C8—594no—
474C4⋊C8—594no—
475C4⋊C8—594no—
476C4⋊C8—594no—
477C4⋊C8—594no—
478C4⋊C8—594no—
479C4⋊C8—594no—
480C4⋊C8—594no—
481C4⋊C8—594no—
482C4⋊C8C22×D5914yes—
483C4⋊C8C22×D5914yes—
484C4⋊C8C22×D5914yes—
485C22⋊C8—594no—
486C22⋊C8—594no—
487C22⋊C8—594no—
488C22⋊C8—594no—
489#97—594no—
490#97—594no—
491#97—594no—
492#97—594no—
493#97—594no—
494#97—594no—
495#97C22×D5914yes—
496#97C22×D5914yes—
497C4×C8—594no—
498C4×C8—594no—
499C4×C8—594no—
500C4×C8C22×D5914yes—
501C24—591no—
502C2×Q8—42no—
503C2×Q8—594no—
504C2×Q8—594no—
505C2×Q8—594no—
506C2×Q8—2362no—
507C2×Q8—2362no—
508C2×Q8—2362no—
509C2×Q8C2×C4×D5914yes—
510C22×C4—591no—
511C22×C4—591no—
512C22×C4—591no—
513C22×C4—591no—
514C22×C4—591no—
515C22×C4—591no—
516C22×C4—591no—
517C22×C4—592no—
518C22×C4—592no—
519C22×C4—594no—
520C22×C4—594no—
521C22×C4—1182no—
522C22×C4—1182no—
523C22×C4—2362no—
524C22×C4—2362no—
525C22×C4C2×C4×D5911yescharacteristic
526C22×C4C2×C4×D5911yescharacteristic
527C22×C4C2×C4×D5911yescharacteristic
528C22×C4C2×C4×D5911yescharacteristic
529C22×C4C2×C4×D5911yescharacteristic
530C22×C4C2×C4×D5911yescharacteristic
531C22×C4C23×D5911yescharacteristic
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—592no—
537C2×C8—592no—
538C2×C8—592no—
539C2×C8—592no—
540C2×C8—1182no—
541C2×C8—1182no—
542C2×C8—1182no—
543C2×C8—1182no—
544C2×C8C23×D5912yes—
545C2×C8C23×D5912yes—
546C2×C8C23×D5912yes—
547C2×C8C23×D5912yes—
548C4⋊C4—594no—
549C4⋊C4—594no—
550C4⋊C4—594no—
551C4⋊C4—594no—
552C4⋊C4—594no—
553C4⋊C4—594no—
554C4⋊C4—594no—
555C4⋊C4—594no—
556C4⋊C4—594no—
557C4⋊C4—594no—
558C4⋊C4—594no—
559C4⋊C4—594no—
560C4⋊C4—594no—
561C4⋊C4C2×C4×D5914yes—
562C4⋊C4C2×C4×D5914yes—
563C4⋊C4C2×C4×D5914yes—
564C22⋊C4—594no—
565C22⋊C4—594no—
566C22⋊C4—594no—
567C22⋊C4—594no—
568C42—592no—
569C42—594no—
570C42—594no—
571C42—592no—
572C42—592no—
573C42—592no—
574C42—592no—
575C42—592no—
576C42C2×C4×D5912yes—
577C42C2×C4×D5912yes—
578C42C2×C4×D5912yes—
579C42C23×D5912yes—
580C42C23×D5912yes—
581C42C23×D5912yes—
582C23—592no—
583C23—1182no—
584C23—1182no—
585C23—1182no—
586C23C22×C4×D5911yescharacteristic
587Q8—44no—
588Q8—2364no—
589Q8—2364no—
590Q8—2364no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—592no—
598C2×C4—592no—
599C2×C4—592no—
600C2×C4—592no—
601C2×C4—592no—
602C2×C4—592no—
603C2×C4—592no—
604C2×C4—1182no—
605C2×C4—1182no—
606C2×C4—1182no—
607C2×C4—1182no—
608C2×C4—1182no—
609C2×C4—1182no—
610C2×C4—1182no—
611C2×C4—1182no—
612C2×C4—1182no—
613C2×C4—1184no—
614C2×C4—2364no—
615C2×C4—2364no—
616C2×C4C22×C4×D5912yes—
617C2×C4C22×C4×D5912yes—
618C2×C4C22×C4×D5912yes—
619C2×C4C22×C4×D5912yes—
620C2×C4C22×C4×D5912yes—
621C2×C4C22×C4×D5912yes—
622C2×C4C22×C4×D5911yescharacteristic
623C2×C4#1427377412yes—
624C2×C4#1427377512yes—
625C2×C4C24×D5911yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—22no—
630C8—1182no—
631C8—1182no—
632C8—1182no—
633C8—1182no—
634C22—1182no—
635C22—1182no—
636C22—1182no—
637C22—2364no—
638C22#1683787812yes—
639C22#1683816712yes—
640C22#1683816812yes—
641C22C23×C4×D5911yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—1182no—
649C4—1182no—
650C4—1182no—
651C4—1182no—
652C4—1182no—
653C4—1182no—
654C4—1182no—
655C4#1683787812yes—
656C4C2×#1427377411yescharacteristic
657C4C2×#1427377511yescharacteristic
658C2—2362no—
659C2#2143319914yesdirect product factor
660C2C2×#1683787811yescharacteristic
661C2C2×#1683816711yescharacteristic
662C2C2×#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×#2987
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #21433199C2direct (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
33. #16837533C22semidirect
34. #16837532C22semidirect
35. #16837531C22semidirect
36. #16837531C22semidirect
37. #16837530C22semidirect
38. #16837530C22semidirect
39. #16837529C22semidirect
69. C59×#446C22semidirect
336. C2×#446D59semidirect
343. C2×C59#2987semidirect
372. #446C2×D59semidirect
407. C59C2×#2987semidirect
659. C2#21433199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379562
#214331992
C2×#168375332
C2×#168375322
C2×#168375312
C2×#168375302
C2×#168375292
C2×#168374642
C2×#168374622
C2×#168374612
C2×#168374582
C2×#168374572
C2×C59×#4462
C2×#298759