Finite Group Databasebeta

← C2×#21435388 #29460920

Subgroups — C2×#21435388 #29460920

Order 15104.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838030C211yesmaximal, characteristic, complemented
2#21435388C2116yesmaximal, direct product factor
3C2×#16837808C211yesmaximal, characteristic, complemented
4C2×#16837798C211yesmaximal, characteristic, complemented
5C2×#16837761C211yesmaximal, characteristic, complemented
6C2×#16837756C211yesmaximal, characteristic, complemented
7C2×#16837718C211yesmaximal, characteristic
8C2×#16837740C211yesmaximal, characteristic, complemented
9C2×#16837723C211yesmaximal, characteristic
10C2×#16837730C211yesmaximal, characteristic, complemented
11C2×#16837709C211yesmaximal, characteristic, complemented
12C2×#16837687C211yesmaximal, characteristic, complemented
13C2×#16837702C211yesmaximal, characteristic, complemented
14C2×#16837692C211yesmaximal, characteristic, complemented
15C2×#16837463C211yesmaximal, characteristic, complemented
16C2×C59×#542C211yesmaximal, characteristic
17#16838030—24no—
18#16838030C2218yescomplemented
19C2×#14273727C2211yescharacteristic
20C2×#14273727C2211yescharacteristic
21C2×#14273726—21no—
22C2×#14273719C2211yescharacteristic
23C2×#14273719C2211yescharacteristic
24C2×#14273718—21no—
25C2×#14273704—21no—
26C2×#14273704—21no—
27C2×#14273686C2211yescharacteristic
28C22×C4⋊Dic59C2211yescharacteristic
29#16837808C2218yescomplemented
30#16837798C2218yescomplemented
31#16837761C2218yescomplemented
32#16837756C2218yescomplemented
33#16837740C2218yescomplemented
34#16837730C2218yescomplemented
35#16837723C2218yes—
36#16837718C2218yes—
37#16837709C2218yescomplemented
38#16837702C2218yescomplemented
39#16837692C2218yescomplemented
40#16837687C2218yescomplemented
41#16837463C2218yescomplemented
42C2×#14273660C2211yescharacteristic
43C2×#14273660C2211yescharacteristic
44C2×#14273658C2211yescharacteristic
45C2×#14273658C2211yescharacteristic
46C2×#14273658C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×#14273658C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×C4⋊(C59⋊C8)C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273651C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273648C2211yescharacteristic
57C2×#14273648C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#542—24no—
65C59×#542C2218yes—
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#126×C59—21no—
68C2×#124×C59—21no—
69C2×#124×C59C2211yescharacteristic
70C2×#123×C59—21no—
71C2×C22⋊Q8×C59—21no—
72C2×C22⋊Q8×C59C2211yescharacteristic
73C2×#121×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C2×#117×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C23×Dic59—21no—
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84#14273727—22no—
85#14273727—22no—
86#14273727C2314yes—
87#14273727C2314yes—
88#14273726—28no—
89#14273719—22no—
90#14273719—22no—
91#14273719C2314yes—
92#14273719C2314yes—
93#14273718—28no—
94#14273704—28no—
95#14273704—28no—
96#14273686—22no—
97#14273686C2314yes—
98C2×C4⋊Dic59—21no—
99C2×C4⋊Dic59—21no—
100C2×C4⋊Dic59—21no—
101C2×C4⋊Dic59—22no—
102C2×C4⋊Dic59C2311yescharacteristic
103C2×C4⋊Dic59C2311yescharacteristic
104C2×C4⋊Dic59C2311yescharacteristic
105C2×C4⋊Dic59C2311yescharacteristic
106C2×C4⋊Dic59C2314yes—
107C2×Dic59⋊C4—21no—
108C2×Dic59⋊C4—21no—
109C2×Dic59⋊C4—21no—
110C2×Dic59⋊C4—21no—
111C2×C22⋊Dic59—21no—
112C2×C4×Dic59—21no—
113#14273660C2314yes—
114#14273660C2314yes—
115#14273658C2314yes—
116#14273658C2314yes—
117#14273658C2314yes—
118#14273658C2314yes—
119#14273658C2314yes—
120#14273658C2314yes—
121C4⋊(C59⋊C8)C2314yes—
122C4⋊(C59⋊C8)C2314yes—
123#14273651C2314yes—
124#14273651C2314yes—
125#14273651C2314yes—
126#14273651C2314yes—
127#14273648C2314yes—
128#14273648C2314yes—
129#14273648C2314yes—
130#14273648C2314yes—
131C22⋊(C59⋊C8)C2314yes—
132C22⋊(C59⋊C8)C2314yes—
133#14273638C2314yes—
134C4×C59⋊C8C2314yes—
135C22×Q8×C59—21no—
136C22×Q8×C59C2311yescharacteristic
137C22×D4×C59—21no—
138C22×D4×C59C2311yescharacteristic
139C23×C4×C59—21no—
140C23×C4×C59C2311yescharacteristic
141C4⋊Q8×C59—22no—
142C4⋊Q8×C59C2314yes—
143#126×C59—28no—
144#124×C59—28no—
145#124×C59—22no—
146#124×C59C2314yes—
147#123×C59—28no—
148C22⋊Q8×C59—22no—
149C22⋊Q8×C59—28no—
150C22⋊Q8×C59C2314yes—
151#121×C59—22no—
152#121×C59C2314yes—
153C4×Q8×C59—22no—
154C4×Q8×C59C2314yes—
155C4×D4×C59—22no—
156C4×D4×C59C2314yes—
157#117×C59D414yes—
158#117×C59C2314yes—
159C2×C4⋊C4×C59—21no—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59D411yescharacteristic
163C2×C4⋊C4×C59D411yescharacteristic
164C2×C4⋊C4×C59C2311yescharacteristic
165C2×C4⋊C4×C59C2311yescharacteristic
166C2×C22⋊C4×C59—21no—
167C2×C22⋊C4×C59—21no—
168C2×C22⋊C4×C59—21no—
169C2×C22⋊C4×C59—21no—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175C2×C42×C59C2311yescharacteristic
176C24×C59—21no—
177C24×C59C2×D411yescharacteristic
178C2×Q8×C59—21no—
179C2×Q8×C59—24no—
180C2×Q8×C59—22no—
181C2×Q8×C59—22no—
182C2×Q8×C59—82no—
183C2×Q8×C59C2412yes—
184C2×D4×C59—24no—
185C2×D4×C59—21no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59—82no—
189C2×D4×C59C2412yes—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—24no—
196C22×C4×C59—82no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D412yes—
203C22×C4×C59C2412yes—
204C22×C4×C59C2411yescharacteristic
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—24no—
210C22×Dic59—82no—
211C2×Dic118—24no—
212C2×Dic118—24no—
213C2×Dic118—82no—
214C2×Dic118—82no—
215C4⋊C4×C59—24no—
216C4⋊C4×C59—24no—
217C4⋊C4×C59—24no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—21no—
220C4⋊C4×C59C2×D414yes—
221C4⋊C4×C59C2×D414yes—
222C4⋊C4×C59C2412yes—
223C4⋊C4×C59C2412yes—
224C22⋊C4×C59—24no—
225C22⋊C4×C59—24no—
226C22⋊C4×C59—24no—
227C22⋊C4×C59—24no—
228C22⋊C4×C59—24no—
229C22⋊C4×C59C2×D414yes—
230C22⋊C4×C59C2×D414yes—
231C42×C59—24no—
232C42×C59C2×D412yes—
233C42×C59C2×D412yes—
234C42×C59C2412yes—
235C42×C59C2412yes—
236C22⋊Dic59—24no—
237C4⋊Dic59—24no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—24no—
241C4⋊Dic59—24no—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59C2412yes—
245C4⋊Dic59C2412yes—
246C4⋊Dic59C2412yes—
247C4⋊Dic59C2412yes—
248Dic59⋊C4—24no—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252C4×Dic59—24no—
253C2×C59⋊C8—22no—
254C2×C59⋊C8—22no—
255C2×C59⋊C8—22no—
256C2×C59⋊C8—22no—
257C2×C59⋊C8C2412yes—
258C2×C59⋊C8C2412yes—
259C2×C59⋊C8C2412yes—
260C2×C59⋊C8C2412yes—
261C23×C59—22no—
262C23×C59—22no—
263C23×C59—22no—
264C23×C59—22no—
265C23×C59—42no—
266C23×C59—42no—
267C23×C59—42no—
268C23×C59C22×D412yes—
269C23×C59C22×D411yescharacteristic
270Q8×C59—22no—
271Q8×C59—22no—
272Q8×C59—42no—
273Q8×C59—84no—
274D4×C59—22no—
275D4×C59—22no—
276D4×C59—42no—
277D4×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—24no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—42no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59—84no—
293C2×C4×C59C22×D412yes—
294C2×C4×C59C22×D412yes—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D412yes—
297C2×C4×C59C22×D412yes—
298C2×C4×C59C22×D411yescharacteristic
299C2×C4×C592−1+412yes—
300C2×C4×C592−1+412yes—
301C2×C4×C59C2511yescharacteristic
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—84no—
311Dic118—84no—
312Dic118—84no—
313C59⋊C8—22no—
314C59⋊C8—22no—
315C59⋊C8—22no—
316C59⋊C8—22no—
317C2×#3244—591nomaximal, Sylow
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—22no—
321C22×C59—44no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—42no—
325C22×C59—84no—
326C22×C59#53612yes—
327C22×C59#57712yes—
328C22×C59#57712yes—
329C22×C59C23×D411yescharacteristic
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59#53612yes—
339C4×C59C2×2−1+411yescharacteristic
340C4×C59C2×2−1+411yescharacteristic
341Dic59—42no—
342Dic59—42no—
343Dic59—42no—
344Dic59—42no—
345C2×#544—591no—
346C2×#542D5911yescharacteristic
347#3244—5916no—
348C2×#501—591no—
349C2×#498—591no—
350C2×#489—591no—
351C2×#488—591no—
352C2×#481—591no—
353C2×#485—591no—
354C2×#482—591no—
355C2×#483—591no—
356C2×#479—591no—
357C2×#475—591no—
358C2×#478—591no—
359C2×#476—591no—
360C2×#433—591no—
361C2×C59—42no—
362C2×C59—82no—
363C2×C59#324414yescomplemented
364C2×C59C2×#53611yescharacteristic
365C2×C59C2×#57711yescharacteristic
366C2×C59C2×#57711yescharacteristic
367#544—598no—
368#544—1184no—
369#542—24no—
370#542C2×D5918yes—
371C2×C4⋊Q8—591no—
372C2×C4⋊Q8—591no—
373C2×C4⋊Q8—1181no—
374C2×C4⋊Q8C2×D5911yescharacteristic
375C2×#126—21no—
376C2×#125—591no—
377C2×#125—591no—
378C2×#125—1181no—
379C2×#124—21no—
380C2×#124C2×D5911yescharacteristic
381C2×#123—21no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—1181no—
384C2×C22⋊Q8—1181no—
385C2×C22⋊Q8C2×D5911yescharacteristic
386C2×#121C2×D5911yescharacteristic
387C2×C4×Q8C2×D5911yescharacteristic
388C2×C4×D4C2×D5911yescharacteristic
389C2×#117—591no—
390C2×#117C2×D5911yescharacteristic
391C22×C4⋊C4—591no—
392#501—598no—
393#498—598no—
394#489—598no—
395#488—598no—
396#485—598no—
397#483—598no—
398#482—598no—
399#481—598no—
400#479—598no—
401#478—598no—
402#476—598no—
403#475—598no—
404#433—598no—
405C2×#107—591no—
406C2×#107—591no—
407C2×#106—591no—
408C2×#106—591no—
409C2×#106—591no—
410C2×#106—591no—
411C2×#106—591no—
412C2×#106—591no—
413C2×C4⋊C8—591no—
414C2×C4⋊C8—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103—591no—
418C2×#103—591no—
419C2×#102—591no—
420C2×#102—591no—
421C2×#102—591no—
422C2×#102—591no—
423C2×C22⋊C8—591no—
424C2×C22⋊C8—591no—
425C2×#97—591no—
426C2×C4×C8—591no—
427C59C2×#324411yescharacteristic, complemented, Sylow
428C22×Q8—21no—
429C22×Q8—1181no—
430C22×Q8—1181no—
431C22×Q8C22×D5911yescharacteristic
432C22×D4—21no—
433C22×D4C22×D5911yescharacteristic
434C23×C4—21no—
435C23×C4—1181no—
436C23×C4C22×D5911yescharacteristic
437C22×C8—591no—
438C22×C8—591no—
439C22×C8—591no—
440C22×C8—591no—
441C4⋊Q8—22no—
442C4⋊Q8—594no—
443C4⋊Q8—594no—
444C4⋊Q8—1188no—
445C4⋊Q8—1182no—
446C4⋊Q8—1182no—
447C4⋊Q8C22×D5914yes—
448#126—28no—
449#125—594no—
450#125—594no—
451#125—1188no—
452#125—1182no—
453#125—1182no—
454#124—28no—
455#124—22no—
456#124C22×D5914yes—
457#123—28no—
458C22⋊Q8—22no—
459C22⋊Q8—28no—
460C22⋊Q8—1188no—
461C22⋊Q8—1188no—
462C22⋊Q8C22×D5914yes—
463#121—22no—
464#121C22×D5914yes—
465C4×Q8—22no—
466C4×Q8C22×D5914yes—
467C4×D4—22no—
468C4×D4C22×D5914yes—
469#117—594no—
470#117—1182no—
471#117C22⋊D5914yes—
472#117C22×D5914yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—594no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—591no—
481C2×C4⋊C4—1181no—
482C2×C4⋊C4—1182no—
483C2×C4⋊C4—1181no—
484C2×C4⋊C4—1181no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4—1181no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4C22⋊D5911yescharacteristic
490C2×C4⋊C4C22⋊D5911yescharacteristic
491C2×C4⋊C4C22×D5911yescharacteristic
492C2×C4⋊C4C22×D5911yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—1181no—
499C2×C22⋊C4C22⋊D5911yescharacteristic
500C2×C22⋊C4C22⋊D5911yescharacteristic
501C2×C42—21no—
502C2×C42—1181no—
503C2×C42C22×D5911yescharacteristic
504C2×C42C22×D5911yescharacteristic
505#107—594no—
506#107—594no—
507#106—594no—
508#106—594no—
509#106—594no—
510#106—594no—
511#106—594no—
512#106—594no—
513C4⋊C8—594no—
514C4⋊C8—594no—
515#103—594no—
516#103—594no—
517#103—594no—
518#103—594no—
519#102—594no—
520#102—594no—
521#102—594no—
522#102—594no—
523C22⋊C8—594no—
524C22⋊C8—594no—
525#97—594no—
526C4×C8—594no—
527C24—21no—
528C24C2×C22⋊D5911yescharacteristic
529C2×Q8—21no—
530C2×Q8—24no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—82no—
534C2×Q8—1184no—
535C2×Q8—1184no—
536C2×Q8—4722no—
537C2×Q8—4722no—
538C2×Q8C23×D5912yes—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—82no—
544C2×D4C23×D5912yes—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—82no—
552C22×C4—1184no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—4722no—
558C22×C4C2×C22⋊D5912yes—
559C22×C4C2×C22⋊D5911yescharacteristic
560C22×C4C2×C22⋊D5911yescharacteristic
561C22×C4C2×C22⋊D5911yescharacteristic
562C22×C4C2×C22⋊D5911yescharacteristic
563C22×C4C2×C22⋊D5911yescharacteristic
564C22×C4C23×D5912yes—
565C22×C4C23×D5911yescharacteristic
566C2×C8—592no—
567C2×C8—592no—
568C2×C8—592no—
569C2×C8—592no—
570C2×C8—1182no—
571C2×C8—1182no—
572C2×C8—1182no—
573C2×C8—1182no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—592no—
580C4⋊C4—592no—
581C4⋊C4—592no—
582C4⋊C4—592no—
583C4⋊C4—1184no—
584C4⋊C4—1181no—
585C4⋊C4—1181no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—1184no—
589C4⋊C4—1184no—
590C4⋊C4—1184no—
591C4⋊C4—1184no—
592C4⋊C4—1184no—
593C4⋊C4—1184no—
594C4⋊C4C2×C22⋊D5914yes—
595C4⋊C4C2×C22⋊D5914yes—
596C4⋊C4C23×D5912yes—
597C4⋊C4C23×D5912yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—1184no—
604C22⋊C4C2×C22⋊D5914yes—
605C22⋊C4C2×C22⋊D5914yes—
606C42—24no—
607C42—1184no—
608C42C2×C22⋊D5912yes—
609C42C2×C22⋊D5912yes—
610C42C23×D5912yes—
611C42C23×D5912yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C22×C22⋊D5912yes—
620C23C22×C22⋊D5911yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—84no—
625Q8—4724no—
626Q8—4724no—
627D4—22no—
628D4—22no—
629D4—42no—
630D4—84no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—84no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—4724no—
651C2×C4—2362no—
652C2×C4—2362no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4C22×C22⋊D5912yes—
656C2×C4C22×C22⋊D5912yes—
657C2×C4C22×C22⋊D5912yes—
658C2×C4C22×C22⋊D5912yes—
659C2×C4C22×C22⋊D5912yes—
660C2×C4C22×C22⋊D5911yescharacteristic
661C2×C4#1427377412yes—
662C2×C4#1427377412yes—
663C2×C4C24×D5911yescharacteristic
664C8—1182no—
665C8—1182no—
666C8—1182no—
667C8—1182no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—84no—
676C22#1683797312yes—
677C22#1683821012yes—
678C22#1683821312yes—
679C22C23×C22⋊D5911yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2362no—
689C4—2362no—
690C4—2362no—
691C4—2362no—
692C4#1683797312yes—
693C4C2×#1427377411yescharacteristic
694C4C2×#1427377411yescharacteristic
695C2—42no—
696C2—82no—
697C2#2143538814yesdirect product factor
698C2C2×#1683797311yescharacteristic
699C2C2×#1683821011yescharacteristic
700C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#542C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
hypercenterC2×#542D59
hypocenterC59C2×#3244
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16838030C2semidirect
2. #21435388C2direct (N × H)
3. C2×#16837808C2semidirect
4. C2×#16837798C2semidirect
5. C2×#16837761C2semidirect
6. C2×#16837756C2semidirect
8. C2×#16837740C2semidirect
10. C2×#16837730C2semidirect
11. C2×#16837709C2semidirect
12. C2×#16837687C2semidirect
13. C2×#16837702C2semidirect
14. C2×#16837692C2semidirect
15. C2×#16837463C2semidirect
18. #16838030C22semidirect
29. #16837808C22semidirect
30. #16837798C22semidirect
31. #16837761C22semidirect
32. #16837756C22semidirect
33. #16837740C22semidirect
34. #16837730C22semidirect
37. #16837709C22semidirect
38. #16837702C22semidirect
39. #16837692C22semidirect
40. #16837687C22semidirect
41. #16837463C22semidirect
363. C2×C59#3244semidirect
427. C59C2×#3244semidirect
697. C2#21435388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380302
#214353882
C2×#168378082
C2×#168377982
C2×#168377612
C2×#168377562
C2×#168377182
C2×#168377402
C2×#168377232
C2×#168377302
C2×#168377092
C2×#168376872
C2×#168377022
C2×#168376922
C2×#168374632
C2×C59×#5422
C2×#324459