Finite Group Databasebeta

← C2×#21436550 #29467235

Subgroups — C2×#21436550 #29467235

Order 15104.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838113C211yesmaximal, characteristic
2C2×#16838090C211yesmaximal, characteristic
3#21436550C2116yesmaximal, direct product factor
4C2×#16837739C211yesmaximal, characteristic, complemented
5C2×#16837745C211yesmaximal, characteristic, complemented
6C2×#16837734C211yesmaximal, characteristic, complemented
7C2×#16837734C211yesmaximal, characteristic, complemented
8C2×#16837706C211yesmaximal, characteristic, complemented
9C2×#16837684C211yesmaximal, characteristic, complemented
10C2×#16837661C211yesmaximal, characteristic, complemented
11C2×#16837644C211yesmaximal, characteristic, complemented
12C2×#16837510C211yesmaximal, characteristic, complemented
13C2×#16837475C211yesmaximal, characteristic
14C2×#16837443C211yesmaximal, characteristic, complemented
15C2×#106×D59C211yesmaximal, characteristic, complemented
16C2×C59×#501C211yesmaximal, characteristic, complemented
17C22×Dic236C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838113—24no—
21#16838113C2218yes—
22#16838090—24no—
23#16838090C2218yes—
24C2×#14273722—21no—
25C2×#14273718—21no—
26C2×#14273718—21no—
27C2×#14273712—21no—
28C2×#14273707C2211yescharacteristic
29C2×#14273707C2211yescharacteristic
30C2×#14273707C2211yescharacteristic
31C2×#14273707C2211yescharacteristic
32C2×#14273703—21no—
33C2×#14273703—21no—
34C2×C4×Dic118C2211yescharacteristic
35C2×C4×Dic118C2211yescharacteristic
36C2×C4×D236C2211yescharacteristic
37C2×#14273689—21no—
38C2×#14273685—21no—
39C2×#14273685C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837745C2218yescomplemented
44#16837739C2218yescomplemented
45#16837734C2218yescomplemented
46#16837734C2218yescomplemented
47#16837706C2218yescomplemented
48#16837684C2218yescomplemented
49#16837661C2218yescomplemented
50#16837644C2218yescomplemented
51#16837510C2218yescomplemented
52#16837475C2218yes—
53#16837443C2218yescomplemented
54C2×#14273660C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59#106×D59C2218yescomplemented
60C2×C4⋊(C59⋊C8)C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×#14273650C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×#125×C59C2211yescharacteristic
71C59×#501C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#106×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C22×Dic118C2311yescharacteristic
79C22×D236D411yescharacteristic
80C22×C4×D59—21no—
81C22×C4×D59—21no—
82C22×C4×D59—21no—
83C22×C4×D59C2311yescharacteristic
84C22×C4×D59C2311yescharacteristic
85C2×Dic236—24no—
86C2×Dic236C2314yes—
87C2×#11745659—24no—
88C2×#11745659C2314yes—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C2×C8×D59—24no—
92C2×C8×D59C2314yes—
93#14273722—28no—
94#14273718—28no—
95#14273718—28no—
96#14273712—28no—
97#14273707—22no—
98#14273707—22no—
99#14273707—22no—
100#14273707—22no—
101#14273707C2314yes—
102#14273707C2314yes—
103#14273707C2314yes—
104#14273707C2314yes—
105#14273703—28no—
106#14273703—28no—
107C4×Dic118—22no—
108C4×Dic118—22no—
109C4×Dic118C2314yes—
110C4×Dic118C2314yes—
111C4×D236D414yes—
112C4×D236C2314yes—
113#14273689—28no—
114#14273685—22no—
115#14273685—28no—
116#14273685C2314yes—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59D411yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C4⋊C4×D59—22no—
130C4⋊C4×D59—22no—
131C4⋊C4×D59—22no—
132C4⋊C4×D59C2314yes—
133C4⋊C4×D59C2314yes—
134C4⋊C4×D59C2314yes—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4D411yescharacteristic
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145#14273660C2314yes—
146#14273659C2314yes—
147#14273658C2314yes—
148#14273658C2314yes—
149#14273658C2314yes—
150C4⋊(C59⋊C8)C2314yes—
151#14273652C2314yes—
152#14273652C2314yes—
153#14273650C2314yes—
154#14273650C2314yes—
155#14273650C2314yes—
156#14273650C2314yes—
157(C2×D59)⋊C8C2314yes—
158(C2×D59)⋊C8C2314yes—
159C22×Q8×C59—21no—
160C22×C8×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162C4⋊Q8×C59—22no—
163C4⋊Q8×C59C2314yes—
164#125×C59—22no—
165#125×C59C2314yes—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C42×C59C2311yescharacteristic
174#107×C59C2314yes—
175#107×C59C2314yes—
176#106×C59C2314yes—
177#106×C59C2314yes—
178#97×C59C2314yes—
179C23×D59C2×D411yescharacteristic
180C23×D59C2×D411yescharacteristic
181C2×Q8×C59—24no—
182C2×Q8×C59—82no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2411yescharacteristic
190C22×Dic59—21no—
191C22×Dic59—21no—
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59C2×D411yescharacteristic
195C22×Dic59C2×D411yescharacteristic
196C2×D236—24no—
197C2×D236C2×D414yes—
198C2×C4×D59—22no—
199C2×C4×D59—22no—
200C2×C4×D59—22no—
201C2×C4×D59—22no—
202C2×C4×D59—24no—
203C2×C4×D59—24no—
204C2×C4×D59—24no—
205C2×C4×D59—44no—
206C2×C4×D59—82no—
207C2×C4×D59—82no—
208C2×C4×D59C2×D412yes—
209C2×C4×D59C2×D412yes—
210C2×C4×D59C2412yes—
211C2×C4×D59C2412yes—
212C2×Dic118—22no—
213C2×Dic118—22no—
214C2×Dic118—22no—
215C2×Dic118—22no—
216C2×Dic118—21no—
217C2×Dic118—21no—
218C2×Dic118C2412yes—
219C2×Dic118C2412yes—
220C2×C8×C59—22no—
221C2×C8×C59#4114yes—
222C2×C8×C59C2412yes—
223C2×C8×C59C2412yes—
224C4⋊C4×C59—24no—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59C2412yes—
232C4⋊C4×C59C2412yes—
233C4⋊C4×C59C2412yes—
234C4⋊C4×C59C2412yes—
235C42×C59C2×D412yes—
236C42×C59C2412yes—
237(C2×D59)⋊C4—24no—
238(C2×D59)⋊C4—24no—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4C2×D414yes—
243(C2×D59)⋊C4C2×D414yes—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—24no—
247C4⋊Dic59—24no—
248C4⋊Dic59—24no—
249C4⋊Dic59—24no—
250C4⋊Dic59C2×D414yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—22no—
263C2×C59⋊C8C2412yes—
264C2×C59⋊C8C2412yes—
265Dic236—28no—
266#11745659—28no—
267C8×D59—28no—
268C23×C59C22×D411yescharacteristic
269C22×D59—22no—
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59#13714yes—
275C22×D59C22×D412yes—
276C22×D59C22×D412yes—
277Q8×C59—84no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—42no—
285C2×C4×C59—42no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C59C2×#4112yes—
292C2×C4×C592−1+412yes—
293C2×C4×C59C2511yescharacteristic
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—42no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59C22×D412yes—
305C2×Dic59C22×D412yes—
306D236—28no—
307C4×D59—24no—
308C4×D59—24no—
309C4×D59—22no—
310C4×D59—22no—
311C4×D59—22no—
312C4×D59—22no—
313C4×D59—48no—
314C4×D59—84no—
315C4×D59—84no—
316Dic118—22no—
317Dic118—22no—
318Dic118—22no—
319Dic118—22no—
320Dic118—42no—
321Dic118—42no—
322C8×C59—22no—
323C8×C59C2×#4114yes—
324C59⋊C8—22no—
325C59⋊C8—22no—
326C2×#3344—591nomaximal, Sylow
327C22×C59#54712yes—
328C22×C59C2×#13712yes—
329C22×C59#57712yes—
330C22×C59C23×D411yescharacteristic
331C2×D59—28no—
332C2×D59—22no—
333C2×D59—22no—
334C2×D59—22no—
335C2×D59—22no—
336C2×D59—22no—
337C2×D59—44no—
338C2×D59C2×#13714yes—
339C4×C59—22no—
340C4×C59—22no—
341C4×C59—42no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59#54712yes—
346C4×C59C22×#4111yescharacteristic
347C4×C59C2×2−1+411yescharacteristic
348Dic59—22no—
349Dic59—22no—
350Dic59—42no—
351Dic59—42no—
352Dic59—42no—
353Dic59—42no—
354C2×#554—591no—
355C2×#552—591no—
356#3344—5916no—
357C2×#501D5911yescharacteristic, complemented
358C2×#484—591no—
359C2×#485—591no—
360C2×#483—591no—
361C2×#483—591no—
362C2×#479—591no—
363C2×#475—591no—
364C2×#470—591no—
365C2×#467—591no—
366C2×#441—591no—
367C2×#435—591no—
368C2×#428—591no—
369C22×#106—591no—
370C2×C59#334414yescomplemented
371C2×C59C2×#54711yescharacteristic
372C2×C59C22×#13711yescharacteristic
373C2×C59C2×#57711yescharacteristic
374D59—24no—
375D59—42no—
376C22×Q16—591no—
377C22×M16—591no—
378C23×C8—591no—
379#554—598no—
380#554—1184no—
381#552—598no—
382#552—1184no—
383C2×C4⋊Q8C2×D5911yescharacteristic
384C2×#126—1181no—
385C2×#125—1181no—
386C2×#125—1181no—
387C2×#125C2×D5911yescharacteristic
388C2×#123—1181no—
389C2×C22⋊Q8—591no—
390C2×C22⋊Q8—591no—
391C2×C22⋊Q8—591no—
392C2×C22⋊Q8—591no—
393C2×C22⋊Q8—1181no—
394C2×C22⋊Q8—1181no—
395C2×C4×Q8—591no—
396C2×C4×Q8—591no—
397C2×C4×D4—591no—
398C2×C4×D4—1181no—
399C2×#117—591no—
400C2×#117—1181no—
401C22×C4⋊C4—591no—
402C22×C4⋊C4—591no—
403C22×C4⋊C4—591no—
404#501C2×D5918yescomplemented
405#485—598no—
406#484—598no—
407#483—598no—
408#483—598no—
409#479—598no—
410#475—598no—
411#470—598no—
412#467—598no—
413#441—598no—
414#435—598no—
415#428—598no—
416C2×#107—591no—
417C2×#107C2×D5911yescharacteristic
418C2×#107C2×D5911yescharacteristic
419C2×#106—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×#106—591no—
423C2×#106—598no—
424C2×#106C2×D5911yescharacteristic
425C2×#106C2×D5911yescharacteristic
426C2×C4⋊C8—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103—591no—
430C2×#103—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×C22⋊C8—591no—
434C2×C22⋊C8—591no—
435C2×#97C2×D5911yescharacteristic
436C59C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—21no—
438C22×Q8—591no—
439C22×Q8—591no—
440C22×D4—591no—
441C23×C4—591no—
442C23×C4—591no—
443C23×C4—1181no—
444C23×C4—1181no—
445C23×C4—1181no—
446C2×Q16—594no—
447C2×Q16—1184no—
448C2×M16—594no—
449C2×M16—1184no—
450C22×C8—591no—
451C22×C8—591no—
452C22×C8—594no—
453C22×C8—1184no—
454C22×C8C22×D5911yescharacteristic
455C22×C8C22×D5911yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8C22×D5914yes—
458#126—1188no—
459#125—22no—
460#125—1188no—
461#125—1188no—
462#125C22×D5914yes—
463#123—1188no—
464C22⋊Q8—594no—
465C22⋊Q8—594no—
466C22⋊Q8—594no—
467C22⋊Q8—594no—
468C22⋊Q8—1188no—
469C22⋊Q8—1188no—
470C22⋊Q8—1182no—
471C22⋊Q8—1182no—
472C22⋊Q8—1182no—
473C22⋊Q8—1182no—
474C4×Q8—594no—
475C4×Q8—594no—
476C4×Q8—1182no—
477C4×Q8—1182no—
478C4×D4—594no—
479C4×D4—594no—
480C4×D4—1188no—
481#117—594no—
482#117—1188no—
483#117—1182no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—591no—
490C2×C4⋊C4—594no—
491C2×C4⋊C4—594no—
492C2×C4⋊C4—594no—
493C2×C4⋊C4—1182no—
494C2×C4⋊C4—1182no—
495C2×C4⋊C4—1182no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C4⋊C4C22×D5911yescharacteristic
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C22⋊C4—591no—
510C2×C22⋊C4—591no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C42—1181no—
517C2×C42—1181no—
518C2×C42—1181no—
519C2×C42C22×D5911yescharacteristic
520#107—594no—
521#107C22×D5914yes—
522#107C22×D5914yes—
523#106—594no—
524#106—594no—
525#106—594no—
526#106—594no—
527#106C22×D5914yes—
528#106C22×D5914yes—
529C4⋊C8—594no—
530#103—594no—
531#103—594no—
532#103—594no—
533#103—594no—
534#103—594no—
535#103—594no—
536C22⋊C8—594no—
537C22⋊C8—594no—
538#97C22×D5914yes—
539C24—591no—
540C24—591no—
541C2×Q8—24no—
542C2×Q8—82no—
543C2×Q8—592no—
544C2×Q8—592no—
545C2×Q8—1181no—
546C2×Q8—1181no—
547C2×Q8—1182no—
548C2×Q8—1182no—
549C2×Q8—1182no—
550C2×Q8—1182no—
551C2×D4—594no—
552C2×D4—1184no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—591no—
558C22×C4—591no—
559C22×C4—592no—
560C22×C4—592no—
561C22×C4—592no—
562C22×C4—592no—
563C22×C4—1184no—
564C22×C4—1184no—
565C22×C4—1184no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4—1181no—
574C22×C4—4722no—
575C22×C4—4722no—
576C22×C4—2364no—
577C22×C4D4×D5911yescharacteristic
578C22×C4D4×D5911yescharacteristic
579C22×C4C23×D5911yescharacteristic
580Q16—1188no—
581M16—1188no—
582C2×C8—22no—
583C2×C8—592no—
584C2×C8—592no—
585C2×C8—1182no—
586C2×C8—1182no—
587C2×C8—1188no—
588C2×C8#1174568914yes—
589C2×C8C23×D5912yes—
590C2×C8C23×D5912yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—594no—
599C4⋊C4—592no—
600C4⋊C4—592no—
601C4⋊C4—1184no—
602C4⋊C4—1184no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1181no—
609C4⋊C4—1181no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4C23×D5912yes—
613C4⋊C4C23×D5912yes—
614C4⋊C4C23×D5912yes—
615C4⋊C4C23×D5912yes—
616C22⋊C4—594no—
617C22⋊C4—594no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—1184no—
624C42—1184no—
625C42—1184no—
626C42D4×D5912yes—
627C42C23×D5912yes—
628C23—594no—
629C23—592no—
630C23—592no—
631C23—1182no—
632C23—1182no—
633C23—1182no—
634C23—1182no—
635C23—1182no—
636C23C2×D4×D5911yescharacteristic
637Q8—84no—
638Q8—1182no—
639Q8—1182no—
640Q8—1182no—
641Q8—1182no—
642Q8—2362no—
643Q8—2362no—
644D4—1188no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—592no—
656C2×C4—592no—
657C2×C4—1182no—
658C2×C4—1182no—
659C2×C4—1182no—
660C2×C4—1182no—
661C2×C4—1182no—
662C2×C4—1182no—
663C2×C4—1184no—
664C2×C4—1184no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—4724no—
670C2×C4—4724no—
671C2×C4—2368no—
672C2×C4—2362no—
673C2×C4—2362no—
674C2×C4—2362no—
675C2×C4—2362no—
676C2×C4C2×D4×D5912yes—
677C2×C4C2×D4×D5912yes—
678C2×C4C2×D4×D5911yescharacteristic
679C2×C4C2×#1174568912yes—
680C2×C4#1427377512yes—
681C2×C4C24×D5911yescharacteristic
682C8—22no—
683C8—1182no—
684C8—1182no—
685C8C2×#1174568914yes—
686C22—594no—
687C22—1182no—
688C22—1188no—
689C22—1182no—
690C22—1182no—
691C22—1182no—
692C22—1182no—
693C22—2364no—
694C22#1683805512yes—
695C22#137×D5912yes—
696C22#1683821212yes—
697C22C22×D4×D5911yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—1182no—
705C4—1182no—
706C4—2362no—
707C4—2362no—
708C4—2362no—
709C4—2362no—
710C4#1683805512yes—
711C4C22×#1174568911yescharacteristic
712C4C2×#1427377511yescharacteristic
713C2—1184no—
714C2—2362no—
715C2#2143655014yesdirect product factor
716C2C2×#1683805511yescharacteristic
717C2C2×#137×D5911yescharacteristic
718C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#501C2
socleC23×C59C22×D4
prime radicalC22×D236D4
hypercenterC2×#501D59
hypocenterC59C2×#3344
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #21436550C2direct (N × H)
4. C2×#16837739C2semidirect
5. C2×#16837745C2semidirect
6. C2×#16837734C2semidirect
7. C2×#16837734C2semidirect
8. C2×#16837706C2semidirect
9. C2×#16837684C2semidirect
10. C2×#16837661C2semidirect
11. C2×#16837644C2semidirect
12. C2×#16837510C2semidirect
14. C2×#16837443C2semidirect
15. C2×#106×D59C2semidirect
16. C2×C59×#501C2semidirect
43. #16837745C22semidirect
44. #16837739C22semidirect
45. #16837734C22semidirect
46. #16837734C22semidirect
47. #16837706C22semidirect
48. #16837684C22semidirect
49. #16837661C22semidirect
50. #16837644C22semidirect
51. #16837510C22semidirect
53. #16837443C22semidirect
59. #106×D59C22semidirect
71. C59×#501C22semidirect
357. C2×#501D59semidirect
370. C2×C59#3344semidirect
404. #501C2×D59semidirect
436. C59C2×#3344semidirect
715. C2#21436550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381132
C2×#168380902
#214365502
C2×#168377392
C2×#168377452
C2×#168377342
C2×#168377062
C2×#168376842
C2×#168376612
C2×#168376442
C2×#168375102
C2×#168374752
C2×#168374432
C2×#106×D592
C2×C59×#5012
C2×#334459