Finite Group Databasebeta

← C2×#21436471 #29467132

Subgroups — C2×#21436471 #29467132

Order 15104.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838100C211yesmaximal, characteristic
2C2×#16838087C211yesmaximal, characteristic, complemented
3#21436471C2116yesmaximal, direct product factor
4C2×#16837802C211yesmaximal, characteristic, complemented
5C2×#16837737C211yesmaximal, characteristic, complemented
6C2×#16837746C211yesmaximal, characteristic, complemented
7C2×#16837728C211yesmaximal, characteristic, complemented
8C2×#16837715C211yesmaximal, characteristic, complemented
9C2×#16837712C211yesmaximal, characteristic, complemented
10C2×#16837701C211yesmaximal, characteristic, complemented
11C2×#16837632C211yesmaximal, characteristic, complemented
12C2×#16837631C211yesmaximal, characteristic, complemented
13C2×#16837489C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D59C211yesmaximal, characteristic, complemented
15C2×#16837437C211yesmaximal, characteristic, complemented
16C22×#106×C59C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16838100—24no—
20#16838100C2218yes—
21#16838087—24no—
22#16838087C2218yescomplemented
23C2×#14273722—21no—
24C2×#14273722—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273717—21no—
28C2×#14273712—21no—
29C2×#14273710—21no—
30C2×#14273707C2211yescharacteristic
31C2×#14273706C2211yescharacteristic
32C2×#14273702C2211yescharacteristic
33C2×#14273701—21no—
34C2×#14273701C2211yescharacteristic
35C2×#14273692C2211yescharacteristic
36C2×#14273689C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273686—21no—
40C2×#14273685C2211yescharacteristic
41C2×#14273685C2211yescharacteristic
42#16837802C2218yescomplemented
43#16837746C2218yescomplemented
44#16837737C2218yescomplemented
45#16837728C2218yescomplemented
46#16837715C2218yescomplemented
47#16837712C2218yescomplemented
48#16837701C2218yescomplemented
49#16837632C2218yescomplemented
50#16837631C2218yescomplemented
51#16837489C2218yescomplemented
52C8×C22⋊D59C2218yescomplemented
53#16837437C2218yescomplemented
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C23×C8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C22×C4⋊C4×C59C2211yescharacteristic
72C2×#106×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#106×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#106×C59C2218yescomplemented
77C22×Dic118C2311yescharacteristic
78C22×D236—21no—
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C22⋊D59D411yescharacteristic
82C22×C4×D59—21no—
83C22×C4×D59C2311yescharacteristic
84C2×#11745660—24no—
85C2×#11745660C2314yes—
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2311yescharacteristic
88C2×C8×D59—24no—
89C2×C8×D59C2314yes—
90#14273722—28no—
91#14273722—28no—
92#14273718—22no—
93#14273718—22no—
94#14273718C2314yes—
95#14273718C2314yes—
96#14273717—28no—
97#14273712—28no—
98#14273710—28no—
99#14273707—22no—
100#14273707C2314yes—
101#14273706—22no—
102#14273706C2314yes—
103#14273702—22no—
104#14273702C2314yes—
105#14273701—22no—
106#14273701—28no—
107#14273701C2314yes—
108#14273692—22no—
109#14273692C2314yes—
110#14273689—22no—
111#14273689C2314yes—
112C4×C22⋊D59—28no—
113C4×C22⋊D59D414yes—
114C4×C22⋊D59C2314yes—
115#14273686—28no—
116#14273685—22no—
117#14273685—22no—
118#14273685C2314yes—
119#14273685C2314yes—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4D411yescharacteristic
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59D411yescharacteristic
132C2×(C2×D59)⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4D411yescharacteristic
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143#14273660C2314yes—
144#14273660C2314yes—
145#14273660C2314yes—
146#14273660C2314yes—
147#14273659C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273650C2314yes—
151#14273650C2314yes—
152#14273649C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156(C2×D59)⋊C8C2314yes—
157C8×Dic59C2314yes—
158C23×C4×C59—21no—
159C23×C4×C59—21no—
160C23×C4×C59C2311yescharacteristic
161C22×C8×C59—24no—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2314yes—
164C22×C8×C59C2311yescharacteristic
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—22no—
168C2×C4⋊C4×C59—22no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2314yes—
174C2×C4⋊C4×C59C2314yes—
175#106×C59C2314yes—
176#106×C59C2314yes—
177#106×C59C2314yes—
178#106×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C23×D59—21no—
181C23×D59C2×D411yescharacteristic
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—24no—
189C22×C4×C59—24no—
190C22×C4×C59—44no—
191C22×C4×C59—82no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2411yescharacteristic
196C2×C22⋊D59—24no—
197C2×C22⋊D59—24no—
198C2×C22⋊D59—44no—
199C2×C22⋊D59C2×D414yes—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C2×D236—22no—
207C2×D236—22no—
208C2×D236—21no—
209C2×D236—24no—
210C2×D236—82no—
211C2×D236C2412yes—
212C2×C4×D59—22no—
213C2×C4×D59—22no—
214C2×C4×D59—24no—
215C2×C4×D59—82no—
216C2×C4×D59C2×D412yes—
217C2×C4×D59C2412yes—
218C2×Dic118—22no—
219C2×Dic118—22no—
220C2×Dic118—21no—
221C2×Dic118C2412yes—
222C2×C8×C59—22no—
223C2×C8×C59—28no—
224C2×C8×C59#4114yes—
225C2×C8×C59C2412yes—
226C2×C8×C59C2412yes—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59C2412yes—
234C4⋊C4×C59C2412yes—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C22⋊Dic59—24no—
238C22⋊Dic59C2×D414yes—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4C2×D414yes—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—24no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4C2×D414yes—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267#11745660—28no—
268C8×D59—28no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59#13514yes—
272C23×C59C22×D412yes—
273C23×C59C22×D411yescharacteristic
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—42no—
279C22×D59—42no—
280C22×D59—42no—
281C22×D59C22×D412yes—
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—22no—
290C2×C4×C59—48no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59—84no—
296C2×C4×C59C22×D412yes—
297C2×C4×C59C22×D411yescharacteristic
298C2×C4×C59C2×#4112yes—
299C2×C4×C592−1+412yes—
300C2×C4×C59C2511yescharacteristic
301C22⋊D59—28no—
302C22⋊D59—48no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315D236—22no—
316D236—22no—
317D236—42no—
318D236—84no—
319C4×D59—24no—
320C4×D59—22no—
321C4×D59—22no—
322C4×D59—84no—
323Dic118—22no—
324Dic118—22no—
325Dic118—42no—
326C8×C59—22no—
327C8×C59C2×#4114yes—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C2×#3337—591nomaximal, Sylow
331C22×C59—28no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59#54712yes—
335C22×C59C2×#13514yes—
336C22×C59C2×#13512yes—
337C22×C59#57712yes—
338C22×C59C23×D411yescharacteristic
339C2×D59—22no—
340C2×D59—22no—
341C2×D59—22no—
342C2×D59—44no—
343C2×D59—42no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—84no—
347C4×C59—22no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59#54712yes—
353C4×C59C22×#4111yescharacteristic
354C4×C59C2×2−1+411yescharacteristic
355Dic59—22no—
356Dic59—22no—
357Dic59—22no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361C2×#553—591no—
362C2×#552—591no—
363#3337—5916no—
364C2×#499—591no—
365C2×#484—591no—
366C2×#485—591no—
367C2×#482—591no—
368C2×#480—591no—
369C2×#479—591no—
370C2×#478—591no—
371C2×#465—591no—
372C2×#465—591no—
373C2×C4×SD16—591no—
374C2×C8×D4—591no—
375C2×#427—591no—
376C22×#106D5911yescharacteristic, complemented
377C2×C59—24no—
378C2×C59#333714yescomplemented
379C2×C59C2×#54711yescharacteristic
380C2×C59C22×#13511yescharacteristic
381C2×C59C2×#57711yescharacteristic
382D59—42no—
383D59—82no—
384C22×SD16—591no—
385C23×C8—591no—
386C23×C8C2×D5911yescharacteristic
387#553—598no—
388#553—1184no—
389#552—598no—
390#552—1184no—
391C2×#126—1181no—
392C2×#126—1181no—
393C2×#125—591no—
394C2×#125—591no—
395C2×#125—1181no—
396C2×#123—1181no—
397C2×#123—1181no—
398C2×C22⋊Q8—591no—
399C2×C22⋊Q8—591no—
400C2×#121—591no—
401C2×#121—591no—
402C2×#121—1181no—
403C2×C4×Q8—591no—
404C2×C4×D4—591no—
405C2×C4×D4—591no—
406C2×C4×D4—1181no—
407C2×#117—591no—
408C2×#117—591no—
409C2×#117—1181no—
410C22×C4⋊C4C2×D5911yescharacteristic
411C22×C4⋊C4C2×D5911yescharacteristic
412#499—598no—
413#485—598no—
414#484—598no—
415#482—598no—
416#480—598no—
417#479—598no—
418#478—598no—
419#465—598no—
420#465—598no—
421C4×SD16—598no—
422C8×D4—598no—
423#427—598no—
424C2×#107—591no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#106—591no—
429C2×#106C2×D5911yescharacteristic
430C2×#106C2×D5911yescharacteristic
431C2×#106C2×D5911yescharacteristic
432C2×#106C2×D5911yescharacteristic
433C2×#106C2×D5918yescomplemented
434C2×C4⋊C8—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#102—591no—
439C2×#102—591no—
440C2×#102—591no—
441C2×C22⋊C8—591no—
442C2×C22⋊C8—591no—
443C2×C4×C8—591no—
444C59C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8—591no—
446C22×D4—591no—
447C22×D4—591no—
448C22×D4—1181no—
449C22×D4—1181no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—591no—
453C23×C4—1181no—
454C23×C4C22×D5911yescharacteristic
455C2×SD16—594no—
456C2×SD16—1184no—
457C22×C8—24no—
458C22×C8—591no—
459C22×C8—591no—
460C22×C8—594no—
461C22×C8—1184no—
462C22×C8C22×D5911yescharacteristic
463C22×C8C22×D5914yes—
464C22×C8C22×D5911yescharacteristic
465#126—1188no—
466#126—1188no—
467#125—594no—
468#125—594no—
469#125—1182no—
470#125—1182no—
471#125—1188no—
472#123—1188no—
473#123—1188no—
474C22⋊Q8—594no—
475C22⋊Q8—594no—
476C22⋊Q8—1182no—
477C22⋊Q8—1182no—
478#121—594no—
479#121—594no—
480#121—1182no—
481#121—1188no—
482#121—1182no—
483C4×Q8—594no—
484C4×Q8—1182no—
485C4×D4—594no—
486C4×D4—594no—
487C4×D4—594no—
488C4×D4—1182no—
489C4×D4—1188no—
490#117—594no—
491#117—594no—
492#117—1188no—
493#117—1182no—
494#117—1182no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4C22×D5911yescharacteristic
510C2×C4⋊C4C22×D5911yescharacteristic
511C2×C4⋊C4C22×D5911yescharacteristic
512C2×C4⋊C4C22×D5911yescharacteristic
513C2×C4⋊C4C22×D5914yes—
514C2×C4⋊C4C22×D5914yes—
515C2×C22⋊C4—591no—
516C2×C22⋊C4—591no—
517C2×C22⋊C4—1181no—
518C2×C22⋊C4—1181no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C42—591no—
525C2×C42—1181no—
526C2×C42—1181no—
527C2×C42—1181no—
528#107—594no—
529#107—594no—
530#107—594no—
531#107—594no—
532#106—594no—
533#106C22×D5914yes—
534#106C22×D5914yes—
535#106C22×D5914yes—
536#106C22×D5914yes—
537C4⋊C8—594no—
538#103—594no—
539#103—594no—
540#103—594no—
541#102—594no—
542#102—594no—
543#102—594no—
544C22⋊C8—594no—
545C22⋊C8—594no—
546C4×C8—594no—
547C24—591no—
548C24—1181no—
549C24D4×D5911yescharacteristic
550C2×Q8—592no—
551C2×Q8—1181no—
552C2×Q8—1182no—
553C2×Q8—1182no—
554C2×D4—594no—
555C2×D4—592no—
556C2×D4—1184no—
557C2×D4—1184no—
558C2×D4—1184no—
559C2×D4—1181no—
560C2×D4—1182no—
561C2×D4—1182no—
562C2×D4—4722no—
563C2×D4—2364no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—82no—
574C22×C4—591no—
575C22×C4—591no—
576C22×C4—591no—
577C22×C4—592no—
578C22×C4—592no—
579C22×C4—1184no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—4722no—
586C22×C4D4×D5912yes—
587C22×C4D4×D5911yescharacteristic
588C22×C4C23×D5912yes—
589C22×C4C23×D5911yescharacteristic
590SD16—1188no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—592no—
594C2×C8—592no—
595C2×C8—1182no—
596C2×C8—1182no—
597C2×C8—1188no—
598C2×C8#1174568514yes—
599C2×C8C23×D5912yes—
600C2×C8C23×D5912yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—594no—
608C4⋊C4—592no—
609C4⋊C4—592no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4—1181no—
617C4⋊C4—1181no—
618C4⋊C4—1184no—
619C4⋊C4C23×D5912yes—
620C4⋊C4C23×D5912yes—
621C4⋊C4C23×D5912yes—
622C4⋊C4C23×D5912yes—
623C22⋊C4—594no—
624C22⋊C4—594no—
625C22⋊C4—1184no—
626C22⋊C4—1184no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C42—592no—
633C42—592no—
634C42—1184no—
635C42—1184no—
636C42—1184no—
637C23—22no—
638C23—22no—
639C23—592no—
640C23—1182no—
641C23—1182no—
642C23—1182no—
643C23—1182no—
644C23—2362no—
645C23—2362no—
646C23—2362no—
647C23#1427374814yes—
648C23C2×D4×D5912yes—
649C23C2×D4×D5911yescharacteristic
650Q8—1182no—
651Q8—1182no—
652Q8—2362no—
653D4—1188no—
654D4—1182no—
655D4—1182no—
656D4—4724no—
657D4—2368no—
658D4—2362no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—48no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—592no—
674C2×C4—592no—
675C2×C4—592no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1184no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—4724no—
686C2×C4—2362no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4C2×D4×D5912yes—
690C2×C4C2×D4×D5911yescharacteristic
691C2×C4C2×#1174568512yes—
692C2×C4#1427377512yes—
693C2×C4C24×D5911yescharacteristic
694C8—22no—
695C8—1182no—
696C8—1182no—
697C8C2×#1174568514yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—1182no—
702C22—1182no—
703C22—1182no—
704C22—4724no—
705C22—2362no—
706C22—2362no—
707C22—2362no—
708C22—2364no—
709C22#1683805312yes—
710C22C2×#1427374814yes—
711C22C2×#1427374812yes—
712C22#1683820812yes—
713C22C22×D4×D5911yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—1182no—
720C4—1182no—
721C4—1182no—
722C4—2362no—
723C4—2362no—
724C4—2362no—
725C4#1683805312yes—
726C4C22×#1174568511yescharacteristic
727C4C2×#1427377511yescharacteristic
728C2—24no—
729C2—4722no—
730C2—2362no—
731C2#2143647114yesdirect product factor
732C2C2×#1683805311yescharacteristic
733C2C22×#1427374811yescharacteristic
734C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#106×C59C2
socleC23×C59C22×D4
prime radicalC2×#16838100C2
hypercenterC22×#106D59
hypocenterC59C2×#3337
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#16838087C2semidirect
3. #21436471C2direct (N × H)
4. C2×#16837802C2semidirect
5. C2×#16837737C2semidirect
6. C2×#16837746C2semidirect
7. C2×#16837728C2semidirect
8. C2×#16837715C2semidirect
9. C2×#16837712C2semidirect
10. C2×#16837701C2semidirect
11. C2×#16837632C2semidirect
12. C2×#16837631C2semidirect
13. C2×#16837489C2semidirect
14. C2×C8×C22⋊D59C2semidirect
15. C2×#16837437C2semidirect
16. C22×#106×C59C2semidirect
22. #16838087C22semidirect
42. #16837802C22semidirect
43. #16837746C22semidirect
44. #16837737C22semidirect
45. #16837728C22semidirect
46. #16837715C22semidirect
47. #16837712C22semidirect
48. #16837701C22semidirect
49. #16837632C22semidirect
50. #16837631C22semidirect
51. #16837489C22semidirect
52. C8×C22⋊D59C22semidirect
53. #16837437C22semidirect
76. C2×#106×C59C22semidirect
376. C22×#106D59semidirect
378. C2×C59#3337semidirect
433. C2×#106C2×D59semidirect
444. C59C2×#3337semidirect
731. C2#21436471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381002
C2×#168380872
#214364712
C2×#168378022
C2×#168377372
C2×#168377462
C2×#168377282
C2×#168377152
C2×#168377122
C2×#168377012
C2×#168376322
C2×#168376312
C2×#168374892
C2×C8×C22⋊D592
C2×#168374372
C22×#106×C592
C2×#333759