Finite Group Databasebeta

← C2×#21436483 #29467145

Subgroups — C2×#21436483 #29467145

Order 15104.

1942 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838110C211yesmaximal, characteristic
2C2×#16838107C211yesmaximal, characteristic
3#21436483C2116yesmaximal, direct product factor
4C2×#16837806C211yesmaximal, characteristic, complemented
5C2×#16837739C211yesmaximal, characteristic, complemented
6C2×#16837738C211yesmaximal, characteristic, complemented
7C2×#16837736C211yesmaximal, characteristic, complemented
8C2×#16837696C211yesmaximal, characteristic, complemented
9C2×#16837695C211yesmaximal, characteristic, complemented
10C2×#16837642C211yesmaximal, characteristic, complemented
11C2×#16837641C211yesmaximal, characteristic, complemented
12C2×#16837494C211yesmaximal, characteristic, complemented
13C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic
14C22×#14273660C211yesmaximal, characteristic, complemented
15C2×#107×D59C211yesmaximal, characteristic, complemented
16C2×C59×#484C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838110—24no—
21#16838110C2218yes—
22#16838107—24no—
23#16838107C2218yes—
24C2×#14273726C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273717—21no—
28C2×#14273707—21no—
29C2×#14273707C2211yescharacteristic
30C2×#14273706—21no—
31C2×#14273706C2211yescharacteristic
32C2×#14273705—21no—
33C2×#14273704—21no—
34C2×#14273703C2211yescharacteristic
35C2×Q8×Dic59C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×(C22⋊D59)⋊C4—21no—
40C22×C4⋊Dic59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837806C2218yescomplemented
44#16837739C2218yescomplemented
45#16837738C2218yescomplemented
46#16837736C2218yescomplemented
47#16837696C2218yescomplemented
48#16837695C2218yescomplemented
49#16837642C2218yescomplemented
50#16837641C2218yescomplemented
51#16837494C2218yescomplemented
52(C22⋊D59)⋊C8C2218yes—
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273660C2211yescharacteristic
59C2×#14273660C2211yescharacteristic
60C2×#14273660C2218yescomplemented
61#107×D59C2218yescomplemented
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273651C2211yescharacteristic
66C2×#14273650C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#484C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×C22⋊D59D411yescharacteristic
81C23×Dic59—21no—
82C22×C4×D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59C2311yescharacteristic
85C2×#11745672—24no—
86C2×#11745672C2314yes—
87C22×C59⋊C8—24no—
88C22×C59⋊C8C2314yes—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C2×C8×D59—24no—
92C2×C8×D59C2314yes—
93#14273726—22no—
94#14273726—22no—
95#14273726C2314yes—
96#14273726C2314yes—
97#14273717—28no—
98#14273717—28no—
99#14273707—22no—
100#14273707—28no—
101#14273707C2314yes—
102#14273706—22no—
103#14273706—28no—
104#14273706C2314yes—
105#14273705—28no—
106#14273704—28no—
107#14273703—22no—
108#14273703C2314yes—
109Q8×Dic59—22no—
110Q8×Dic59C2314yes—
111#14273692—22no—
112#14273692C2314yes—
113C4×C22⋊D59—28no—
114C4×C22⋊D59D414yes—
115C4×C22⋊D59C2314yes—
116(C22⋊D59)⋊C4—28no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—22no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2314yes—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4D411yescharacteristic
133C4⋊C4×D59—22no—
134C4⋊C4×D59—22no—
135C4⋊C4×D59C2314yes—
136C4⋊C4×D59C2314yes—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59D411yescharacteristic
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145#14273661C2314yes—
146#14273661C2314yes—
147#14273660C2314yes—
148#14273660C2314yes—
149#14273660C2314yes—
150#14273660C2314yes—
151#14273660C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157(C2×D59)⋊C8C2314yes—
158C8×Dic59C2314yes—
159C22×Q8×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C23×C4×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C22⋊Q8×C59—22no—
165C22⋊Q8×C59C2314yes—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—22no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2314yes—
173C2×C22⋊C4×C59—21no—
174#107×C59C2314yes—
175#107×C59C2314yes—
176#103×C59C2314yes—
177#103×C59C2314yes—
178C22⋊C8×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C23×D59C2×D411yescharacteristic
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59—22no—
184C2×Q8×C59C2412yes—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—24no—
192C22×C4×C59—82no—
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2411yescharacteristic
197C2×C22⋊D59Q1618yescomplemented
198C2×C22⋊D59C2×D414yes—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—24no—
204C22×Dic59—82no—
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C2×C4×D59—22no—
209C2×C4×D59—22no—
210C2×C4×D59—24no—
211C2×C4×D59—24no—
212C2×C4×D59—82no—
213C2×C4×D59—82no—
214C2×C4×D59C2×D412yes—
215C2×C4×D59C2412yes—
216C2×Dic118—22no—
217C2×Dic118—22no—
218C2×Dic118—21no—
219C2×Dic118—24no—
220C2×Dic118—24no—
221C2×Dic118—82no—
222C2×Dic118—82no—
223C2×Dic118C2412yes—
224C2×C8×C59—22no—
225C2×C8×C59—22no—
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59C2412yes—
234C4⋊C4×C59C2412yes—
235C4⋊C4×C59C2412yes—
236C22⋊C4×C59—24no—
237C22⋊Dic59—24no—
238C22⋊Dic59C2×D414yes—
239#11745672—28no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4C2×D414yes—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—24no—
247C4⋊Dic59—24no—
248C4⋊Dic59—24no—
249C4⋊Dic59C2412yes—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4C2×D414yes—
260C4×Dic59—24no—
261C4×Dic59—24no—
262C4×Dic59C2×D412yes—
263C4×Dic59C2412yes—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—28no—
266C2×C59⋊C8#4114yes—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269C8×D59—28no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59C2×Q1614yes—
273C23×C59C22×D412yes—
274C23×C59C22×D411yescharacteristic
275C22×D59—22no—
276C22×D59—22no—
277C22×D59C2×Q1614yes—
278C22×D59C22×D412yes—
279Q8×C59—22no—
280Q8×C59—22no—
281Q8×C59—42no—
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—42no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—84no—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C2×#4112yes—
298C2×C4×C592−1+412yes—
299C2×C4×C59C2511yescharacteristic
300C22⋊D59C2×Q16116yescomplemented
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59—84no—
312C2×Dic59C2×Q1614yes—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315C2×Dic59C22×D412yes—
316C4×D59—24no—
317C4×D59—22no—
318C4×D59—22no—
319C4×D59—84no—
320C4×D59—84no—
321Dic118—22no—
322Dic118—22no—
323Dic118—42no—
324Dic118—84no—
325Dic118—84no—
326C8×C59—22no—
327C8×C59—22no—
328C59⋊C8—22no—
329C59⋊C8C2×#4114yes—
330C2×#3338—591nomaximal, Sylow
331C22×C59—28no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59#54712yes—
335C22×C59C22×Q1614yes—
336C22×C59C22×Q1612yes—
337C22×C59#57612yes—
338C22×C59C23×D411yescharacteristic
339C2×D59—28no—
340C2×D59—22no—
341C2×D59—22no—
342C2×D59C22×Q1614yes—
343C4×C59—22no—
344C4×C59—42no—
345C4×C59—42no—
346C4×C59—42no—
347C4×C59—42no—
348C4×C59#54712yes—
349C4×C59C22×#4111yescharacteristic
350C4×C59C2×2−1+411yescharacteristic
351Dic59—22no—
352Dic59—22no—
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356Dic59—42no—
357Dic59C22×Q1614yes—
358C2×#554—591no—
359C2×#554—591no—
360#3338—5916no—
361C2×#500—591no—
362C2×#484—591no—
363C2×#484—591no—
364C2×#484—591no—
365C2×#484D5911yescharacteristic, complemented
366C2×#477—591no—
367C2×#477—591no—
368C2×#467—591no—
369C2×#467—591no—
370C2×C4×Q16—591no—
371C2×C8×D4—591no—
372C22×#107—591no—
373C22×#107—591no—
374C2×C59—24no—
375C2×C59#333814yescomplemented
376C2×C59C2×#54711yescharacteristic
377C2×C59C23×Q1611yescharacteristic
378C2×C59C2×#57611yescharacteristic
379D59—24no—
380C22×Q16—591no—
381C23×C8—591no—
382C23×C8—591no—
383#554—598no—
384#554—598no—
385#554—1184no—
386#554—1184no—
387C2×C4⋊Q8—591no—
388C2×C4⋊Q8—591no—
389C2×#125—1181no—
390C2×#125—1181no—
391C2×C22⋊Q8—591no—
392C2×C22⋊Q8—591no—
393C2×C22⋊Q8—591no—
394C2×C22⋊Q8—1181no—
395C2×C22⋊Q8—1181no—
396C2×C22⋊Q8—1181no—
397C2×C22⋊Q8—1181no—
398C2×C22⋊Q8C2×D5911yescharacteristic
399C2×C4×Q8—591no—
400C2×C4×Q8—591no—
401C2×C4×D4—591no—
402C2×C4×D4—1181no—
403C2×C4×D4—1181no—
404C22×C4⋊C4—591no—
405C22×C4⋊C4—591no—
406C22×C4⋊C4—591no—
407C22×C4⋊C4C2×D5911yescharacteristic
408#500—598no—
409#484—598no—
410#484—598no—
411#484—598no—
412#484C2×D5918yescomplemented
413#477—598no—
414#477—598no—
415#467—598no—
416#467—598no—
417C4×Q16—598no—
418C8×D4—598no—
419C2×#107—591no—
420C2×#107—591no—
421C2×#107—591no—
422C2×#107—591no—
423C2×#107—598no—
424C2×#107—591no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#107—598no—
428C2×#107C2×D5911yescharacteristic
429C2×#107C2×D5911yescharacteristic
430C2×C4⋊C8—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103—591no—
435C2×#103C2×D5911yescharacteristic
436C2×#103C2×D5911yescharacteristic
437C2×C22⋊C8—591no—
438C2×C22⋊C8C2×D5911yescharacteristic
439C2×C4×C8—591no—
440C59C2×#333811yescharacteristic, complemented, Sylow
441C22×Q8—591no—
442C22×Q8—1181no—
443C22×Q8—1181no—
444C22×Q8C22×D5911yescharacteristic
445C22×D4—591no—
446C23×C4—21no—
447C23×C4—591no—
448C23×C4—1181no—
449C23×C4—1181no—
450C23×C4—1181no—
451C23×C4C22×D5911yescharacteristic
452C2×Q16—594no—
453C2×Q16—1184no—
454C22×C8—591no—
455C22×C8—591no—
456C22×C8—594no—
457C22×C8—594no—
458C22×C8—1184no—
459C22×C8—1184no—
460C22×C8C22×D5911yescharacteristic
461C22×C8C22×D5911yescharacteristic
462C4⋊Q8—594no—
463C4⋊Q8—594no—
464C4⋊Q8—1182no—
465C4⋊Q8—1182no—
466#125—1188no—
467#125—1188no—
468C22⋊Q8—22no—
469C22⋊Q8—594no—
470C22⋊Q8—594no—
471C22⋊Q8—594no—
472C22⋊Q8—1188no—
473C22⋊Q8—1188no—
474C22⋊Q8—1188no—
475C22⋊Q8—1188no—
476C22⋊Q8—1182no—
477C22⋊Q8—1182no—
478C22⋊Q8—1182no—
479C22⋊Q8C22×D5914yes—
480C4×Q8—594no—
481C4×Q8—594no—
482C4×Q8—1182no—
483C4×Q8—1182no—
484C4×D4—594no—
485C4×D4—594no—
486C4×D4—1188no—
487C4×D4—1188no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—591no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—594no—
496C2×C4⋊C4—594no—
497C2×C4⋊C4—594no—
498C2×C4⋊C4—1182no—
499C2×C4⋊C4—1182no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
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⋊C4—1182no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4C22×D5911yescharacteristic
512C2×C4⋊C4C22×D5911yescharacteristic
513C2×C4⋊C4C22×D5911yescharacteristic
514C2×C4⋊C4C22×D5914yes—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—591no—
517C2×C22⋊C4—591no—
518C2×C22⋊C4—1181no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C42—591no—
522C2×C42—1181no—
523C2×C42—1181no—
524#107—594no—
525#107—594no—
526#107—594no—
527#107—594no—
528#107—594no—
529#107—594no—
530#107—594no—
531#107C22×D5914yes—
532#107C22×D5914yes—
533C4⋊C8—594no—
534#103—594no—
535#103—594no—
536#103—594no—
537#103—594no—
538#103C22×D5914yes—
539#103C22×D5914yes—
540C22⋊C8—594no—
541C22⋊C8C22×D5914yes—
542C4×C8—594no—
543C24—591no—
544C24D4×D5911yescharacteristic
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—592no—
549C2×Q8—1184no—
550C2×Q8—1184no—
551C2×Q8—1181no—
552C2×Q8—1182no—
553C2×Q8—1182no—
554C2×Q8—4722no—
555C2×Q8—4722no—
556C2×Q8C23×D5912yes—
557C2×D4—598no—
558C2×D4—594no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—591no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—592no—
571C22×C4—592no—
572C22×C4—1184no—
573C22×C4—1184no—
574C22×C4—1182no—
575C22×C4—1182no—
576C22×C4—1184no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—4722no—
582C22×C4—4722no—
583C22×C4—4722no—
584C22×C4D4×D5912yes—
585C22×C4D4×D5911yescharacteristic
586C22×C4C23×D5912yes—
587C22×C4C23×D5911yescharacteristic
588Q16—1188no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—594no—
592C2×C8—592no—
593C2×C8—592no—
594C2×C8—1188no—
595C2×C8—1188no—
596C2×C8—1182no—
597C2×C8C23×D5912yes—
598C2×C8C23×D5912yes—
599C4⋊C4—21no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—594no—
605C4⋊C4—592no—
606C4⋊C4—592no—
607C4⋊C4—592no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4—1181no—
617C4⋊C4—1184no—
618C4⋊C4—1181no—
619C4⋊C4—1181no—
620C4⋊C4—1184no—
621C4⋊C4C23×D5912yes—
622C4⋊C4C23×D5912yes—
623C4⋊C4C23×D5912yes—
624C22⋊C4—24no—
625C22⋊C4—594no—
626C22⋊C4—594no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C42—592no—
631C42—592no—
632C42—1184no—
633C42—1184no—
634C23—22no—
635C23—22no—
636C23—594no—
637C23—592no—
638C23—1182no—
639C23—1182no—
640C23Q16×D5914yes—
641C23C2×D4×D5912yes—
642C23C2×D4×D5911yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—1182no—
647Q8—1182no—
648Q8—4724no—
649Q8—4724no—
650Q8—2362no—
651D4—5916no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—594no—
666C2×C4—592no—
667C2×C4—592no—
668C2×C4—592no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1184no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—4724no—
679C2×C4—4724no—
680C2×C4—4724no—
681C2×C4—2362no—
682C2×C4—2362no—
683C2×C4—2362no—
684C2×C4—2362no—
685C2×C4C2×D4×D5912yes—
686C2×C4C2×D4×D5911yescharacteristic
687C2×C4#41×D5912yes—
688C2×C4#1427377412yes—
689C2×C4C24×D5911yescharacteristic
690C8—22no—
691C8—22no—
692C8—594no—
693C8—1182no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—594no—
698C22—1188no—
699C22—1182no—
700C22—1182no—
701C22#1683805012yes—
702C22C2×Q16×D5914yes—
703C22C2×Q16×D5912yes—
704C22#1683820612yes—
705C22C22×D4×D5911yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—594no—
712C4—1182no—
713C4—1182no—
714C4—2362no—
715C4—2362no—
716C4—2362no—
717C4—2362no—
718C4#1683805012yes—
719C4C2×#41×D5911yescharacteristic
720C4C2×#1427377411yescharacteristic
721C2—24no—
722C2—1184no—
723C2#2143648314yesdirect product factor
724C2C2×#1683805011yescharacteristic
725C2C22×Q16×D5911yescharacteristic
726C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#484C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC2×#484D59
hypocenterC59C2×#3338
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #21436483C2direct (N × H)
4. C2×#16837806C2semidirect
5. C2×#16837739C2semidirect
6. C2×#16837738C2semidirect
7. C2×#16837736C2semidirect
8. C2×#16837696C2semidirect
9. C2×#16837695C2semidirect
10. C2×#16837642C2semidirect
11. C2×#16837641C2semidirect
12. C2×#16837494C2semidirect
14. C22×#14273660C2semidirect
15. C2×#107×D59C2semidirect
16. C2×C59×#484C2semidirect
43. #16837806C22semidirect
44. #16837739C22semidirect
45. #16837738C22semidirect
46. #16837736C22semidirect
47. #16837696C22semidirect
48. #16837695C22semidirect
49. #16837642C22semidirect
50. #16837641C22semidirect
51. #16837494C22semidirect
60. C2×#14273660C22semidirect
61. #107×D59C22semidirect
71. C59×#484C22semidirect
197. C2×C22⋊D59Q16semidirect
300. C22⋊D59C2×Q16semidirect
365. C2×#484D59semidirect
375. C2×C59#3338semidirect
412. #484C2×D59semidirect
440. C59C2×#3338semidirect
723. C2#21436483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381102
C2×#168381072
#214364832
C2×#168378062
C2×#168377392
C2×#168377382
C2×#168377362
C2×#168376962
C2×#168376952
C2×#168376422
C2×#168376412
C2×#168374942
C2×(C22⋊D59)⋊C82
C22×#142736602
C2×#107×D592
C2×C59×#4842
C2×#333859