Finite Group Databasebeta

← C2×#21434133 #29456725

Subgroups — C2×#21434133 #29456725

Order 15104.

2138 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×#16837956C211yesmaximal, characteristic
2C2×C4×Q8×D59C211yesmaximal, characteristic
3#21434133C2116yesmaximal, direct product factor
4C2×#16837739C211yesmaximal, characteristic
5C2×#16837736C211yesmaximal, characteristic
6C2×#16837696C211yesmaximal, characteristic, complemented
7C2×#16837695C211yesmaximal, characteristic, complemented
8C2×#16837611C211yesmaximal, characteristic, complemented
9C2×#16837610C211yesmaximal, characteristic, complemented
10C2×#16837559C211yesmaximal, characteristic
11C2×#16837556C211yesmaximal, characteristic
12C2×C4×Dic236C211yesmaximal, characteristic, complemented
13C2×C4×#11745672C211yesmaximal, characteristic, complemented
14C2×C4×#11745672C211yesmaximal, characteristic, complemented
15C2×#16837453C211yesmaximal, characteristic
16C2×C4×Q16×C59C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745672C2211yescharacteristic
21#16837956—24no—
22#16837956C2218yes—
23C2×#14273726C2211yescharacteristic
24C2×#14273725C2211yescharacteristic
25C2×#14273717—21no—
26C2×#14273707C2211yescharacteristic
27C2×#14273705—21no—
28C2×#14273703C2211yescharacteristic
29C2×Q8×Dic59C2211yescharacteristic
30C2×C4×Dic118—21no—
31C2×C4×Dic118—21no—
32C2×C4×Dic118C2211yescharacteristic
33C2×C4×Dic118C2211yescharacteristic
34C2×#14273692—21no—
35C2×#14273692C2211yescharacteristic
36C4×Q8×D59—24no—
37C4×Q8×D59C2218yes—
38C2×#14273684—21no—
39C2×C4⋊C4×D59—21no—
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C42×D59—21no—
42C2×C42×D59C2211yescharacteristic
43#16837739C2218yes—
44#16837736C2218yes—
45#16837696C2218yescomplemented
46#16837695C2218yescomplemented
47#16837611C2218yescomplemented
48#16837610C2218yescomplemented
49#16837559C2218yes—
50#16837556C2218yes—
51C4×Dic236C2218yescomplemented
52C4×#11745672C2218yescomplemented
53C4×#11745672C2218yescomplemented
54#16837453C2218yes—
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C4×Q16×C59C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×Dic118C2311yescharacteristic
81C2×Q8×D59—24no—
82C2×Q8×D59—22no—
83C2×Q8×D59—24no—
84C2×Q8×D59C2314yes—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59D411yescharacteristic
88C22×C4×D59D411yescharacteristic
89C22×C4×D59C2311yescharacteristic
90C2×Dic236—24no—
91C2×Dic236C2314yes—
92C2×#11745672—24no—
93C2×#11745672—24no—
94C2×#11745672C2314yes—
95C2×#11745672C2314yes—
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98#14273726—22no—
99#14273726C2314yes—
100#14273725—22no—
101#14273725C2314yes—
102#14273717—28no—
103#14273707—22no—
104#14273707C2314yes—
105#14273705—28no—
106#14273703—22no—
107#14273703C2314yes—
108Q8×Dic59—22no—
109Q8×Dic59C2314yes—
110C4×Dic118—22no—
111C4×Dic118—22no—
112C4×Dic118—28no—
113C4×Dic118—28no—
114C4×Dic118C2314yes—
115C4×Dic118C2314yes—
116#14273692—22no—
117#14273692—28no—
118#14273692C2314yes—
119#14273684—28no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
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—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C4⋊C4×D59—28no—
133C4⋊C4×D59—22no—
134C4⋊C4×D59C2314yes—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59D411yescharacteristic
142C2×C4×Dic59D411yescharacteristic
143C2×C4×Dic59C2311yescharacteristic
144C42×D59—28no—
145C42×D59D414yes—
146C42×D59C2314yes—
147#14273661C2314yes—
148#14273660C2314yes—
149#14273660C2314yes—
150Dic59⋊C8C2314yes—
151Dic59⋊C8C2314yes—
152#14273652C2314yes—
153#14273652C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157#14273650C2314yes—
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160C4×C59⋊C8C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×Q8×C59C2311yescharacteristic
163C2×Q16×C59—24no—
164C2×Q16×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C4×Q8×C59—22no—
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C4×Q8×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C42×C59—21no—
176C2×C42×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#107×C59C2314yes—
179#103×C59C2314yes—
180#103×C59C2314yes—
181C4×C8×C59C2314yes—
182C23×D59C2×D411yescharacteristic
183C2×Q8×C59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59#4114yes—
189C2×Q8×C59C2412yes—
190C2×Q8×C59C2412yes—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2411yescharacteristic
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205Q8×D59—216no—
206Q8×D59—28no—
207Q8×D59—28no—
208C2×C4×D59—28no—
209C2×C4×D59—24no—
210C2×C4×D59—22no—
211C2×C4×D59—22no—
212C2×C4×D59—24no—
213C2×C4×D59—42no—
214C2×C4×D59—44no—
215C2×C4×D59Q1618yescomplemented
216C2×C4×D59C2×D412yes—
217C2×C4×D59C2×D414yes—
218C2×C4×D59C2×D414yes—
219C2×C4×D59C2412yes—
220C2×Dic118—28no—
221C2×Dic118—21no—
222C2×Dic118—22no—
223C2×Dic118—24no—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—21no—
227C2×Dic118—24no—
228C2×Dic118—44no—
229C2×Dic118#4114yes—
230C2×Dic118C2412yes—
231C2×Dic118C2412yes—
232Q16×C59—28no—
233C2×C8×C59—22no—
234C2×C8×C59—22no—
235C2×C8×C59C2412yes—
236C2×C8×C59C2412yes—
237C4⋊C4×C59—24no—
238C4⋊C4×C59—24no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59C2412yes—
242C4⋊C4×C59C2412yes—
243C42×C59—24no—
244C42×C59—24no—
245C42×C59C2×D412yes—
246C42×C59C2412yes—
247#11745672—28no—
248#11745672—28no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4—24no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—24no—
254C4⋊Dic59—24no—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59C2×D412yes—
270C4×Dic59C2×D414yes—
271C4×Dic59C2×D414yes—
272C4×Dic59C2412yes—
273C2×C59⋊C8—22no—
274C2×C59⋊C8—22no—
275C2×C59⋊C8C2412yes—
276C2×C59⋊C8C2412yes—
277Dic236—28no—
278C23×C59C22×D411yescharacteristic
279C22×D59—22no—
280C22×D59—22no—
281C22×D59C2×Q1614yes—
282C22×D59C22×D412yes—
283Q8×C59—24no—
284Q8×C59—22no—
285Q8×C59—22no—
286Q8×C59—22no—
287Q8×C59—42no—
288Q8×C59C2×#4114yes—
289C2×C4×C59—24no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59C2×Q1614yes—
299C2×C4×C59C22×D412yes—
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C22×D412yes—
302C2×C4×C59C2×#4112yes—
303C2×C4×C59C2×#4112yes—
304C2×C4×C59C2511yescharacteristic
305C2×Dic59—22no—
306C2×Dic59—24no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—42no—
313C2×Dic59—42no—
314C2×Dic59—42no—
315C2×Dic59C2×Q1614yes—
316C2×Dic59C22×D412yes—
317C2×Dic59C22×D412yes—
318C2×Dic59C22×D412yes—
319C4×D59—216no—
320C4×D59—24no—
321C4×D59—22no—
322C4×D59—22no—
323C4×D59—44no—
324C4×D59—48no—
325C4×D59C2×Q16116yescomplemented
326Dic118—216no—
327Dic118—24no—
328Dic118—22no—
329Dic118—22no—
330Dic118—22no—
331Dic118—48no—
332Dic118—42no—
333Dic118C2×#4114yes—
334C8×C59—22no—
335C8×C59—22no—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C2×#3104—591nomaximal, Sylow
339C22×C59#52512yes—
340C22×C59C22×Q1612yes—
341C22×C59#57512yes—
342C22×C59C23×D411yescharacteristic
343C2×D59—28no—
344C2×D59—22no—
345C2×D59—22no—
346C2×D59C22×Q1614yes—
347C4×C59—24no—
348C4×C59—22no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59#52512yes—
353C4×C59C22×Q1614yes—
354C4×C59C22×#4111yescharacteristic
355C4×C59C22×#4111yescharacteristic
356Dic59—22no—
357Dic59—24no—
358Dic59—22no—
359Dic59—42no—
360Dic59—42no—
361Dic59—42no—
362Dic59C22×Q1614yes—
363C2×#533—591no—
364C22×C4×Q8—591no—
365#3104—5916no—
366C2×#484—591no—
367C2×#484—591no—
368C2×#477—591no—
369C2×#477—591no—
370C2×#462—591no—
371C2×#462—591no—
372C2×#451—591no—
373C2×#451—591no—
374C2×C4×Q16—591no—
375C2×C4×Q16—591no—
376C2×C4×Q16—591no—
377C2×C4×Q16D5911yescharacteristic, complemented
378C2×#431—591no—
379C2×C59#310414yescomplemented
380C2×C59C2×#52511yescharacteristic
381C2×C59C23×Q1611yescharacteristic
382C2×C59C2×#57511yescharacteristic
383D59—24no—
384C23×Q8—591no—
385C22×Q16—591no—
386C22×Q16—591no—
387C22×Q16—591no—
388C22×Q16C2×D5911yescharacteristic
389#533—598no—
390#533—1184no—
391C2×C4⋊Q8—591no—
392C2×C4⋊Q8—591no—
393C2×#125—1181no—
394C2×C22⋊Q8—591no—
395C2×C22⋊Q8—591no—
396C2×C22⋊Q8—1181no—
397C2×C4×Q8—591no—
398C2×C4×Q8—598no—
399C2×C4×Q8—591no—
400C2×C4×Q8—591no—
401C2×C4×Q8—591no—
402C2×C4×Q8—1181no—
403C2×C4×Q8—1181no—
404C2×C4×Q8—1181no—
405C2×C4×Q8—1184no—
406C2×C4×Q8C2×D5911yescharacteristic
407C2×C4×Q8C2×D5911yescharacteristic
408C2×#117—1181no—
409C22×C4⋊C4—591no—
410C22×C4⋊C4—1181no—
411C22×C42—591no—
412C22×C42—1181no—
413#484—598no—
414#484—598no—
415#477—598no—
416#477—598no—
417#462—598no—
418#462—598no—
419#451—598no—
420#451—598no—
421C4×Q16—598no—
422C4×Q16—598no—
423C4×Q16—598no—
424C4×Q16C2×D5918yescomplemented
425#431—598no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#107—591no—
429C2×#107C2×D5911yescharacteristic
430C2×C4⋊C8—591no—
431C2×C4⋊C8—591no—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#103C2×D5911yescharacteristic
439C2×#103C2×D5911yescharacteristic
440C2×C22⋊C8—591no—
441C2×C22⋊C8—591no—
442C2×C4×C8—591no—
443C2×C4×C8C2×D5911yescharacteristic
444C59C2×#310411yescharacteristic, complemented, Sylow
445C22×Q8—594no—
446C22×Q8—591no—
447C22×Q8—591no—
448C22×Q8—1181no—
449C22×Q8—1181no—
450C22×Q8—1182no—
451C22×Q8—1184no—
452C22×Q8—1184no—
453C22×Q8C22×D5911yescharacteristic
454C22×Q8C22×D5911yescharacteristic
455C23×C4—591no—
456C23×C4—591no—
457C23×C4—591no—
458C23×C4—1181no—
459C23×C4—1181no—
460C2×Q16—24no—
461C2×Q16—594no—
462C2×Q16—594no—
463C2×Q16—594no—
464C2×Q16—1184no—
465C2×Q16—1184no—
466C2×Q16—1184no—
467C2×Q16C22×D5914yes—
468C22×C8—591no—
469C22×C8—591no—
470C22×C8C22×D5911yescharacteristic
471C22×C8C22×D5911yescharacteristic
472C4⋊Q8—594no—
473C4⋊Q8—594no—
474C4⋊Q8—1182no—
475C4⋊Q8—1182no—
476#125—1188no—
477C22⋊Q8—594no—
478C22⋊Q8—594no—
479C22⋊Q8—1182no—
480C22⋊Q8—1188no—
481C22⋊Q8—1182no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—594no—
485C4×Q8—594no—
486C4×Q8—594no—
487C4×Q8—594no—
488C4×Q8—1188no—
489C4×Q8—1188no—
490C4×Q8—1188no—
491C4×Q8—1182no—
492C4×Q8—1182no—
493C4×Q8—1182no—
494C4×Q8—1182no—
495C4×Q8C22×D5914yes—
496C4×Q8C22×D5914yes—
497#117—1188no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—594no—
503C2×C4⋊C4—1182no—
504C2×C4⋊C4—1188no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4C22×D5911yescharacteristic
516C2×C4⋊C4C22×D5911yescharacteristic
517C2×C22⋊C4—1181no—
518C2×C22⋊C4—1181no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—591no—
522C2×C42—591no—
523C2×C42—591no—
524C2×C42—594no—
525C2×C42—594no—
526C2×C42—1188no—
527C2×C42—1181no—
528C2×C42—1181no—
529C2×C42—1181no—
530C2×C42—1181no—
531C2×C42C22×D5911yescharacteristic
532#107—594no—
533#107—594no—
534#107—594no—
535#107C22×D5914yes—
536C4⋊C8—594no—
537C4⋊C8—594no—
538#103—594no—
539#103—594no—
540#103—594no—
541#103—594no—
542#103—594no—
543#103—594no—
544#103C22×D5914yes—
545#103C22×D5914yes—
546C22⋊C8—594no—
547C22⋊C8—594no—
548C4×C8—594no—
549C4×C8C22×D5914yes—
550C24—591no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—594no—
557C2×Q8—592no—
558C2×Q8—592no—
559C2×Q8—1184no—
560C2×Q8—1184no—
561C2×Q8—1188no—
562C2×Q8—1188no—
563C2×Q8—11816no—
564C2×Q8—1188no—
565C2×Q8—1181no—
566C2×Q8—1181no—
567C2×Q8—1182no—
568C2×Q8—1182no—
569C2×Q8—1182no—
570C2×Q8—2364no—
571C2×Q8#1174568514yes—
572C2×Q8C23×D5912yes—
573C2×Q8C23×D5912yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—591no—
579C22×C4—598no—
580C22×C4—594no—
581C22×C4—591no—
582C22×C4—591no—
583C22×C4—592no—
584C22×C4—592no—
585C22×C4—594no—
586C22×C4—1184no—
587C22×C4—1188no—
588C22×C4—1184no—
589C22×C4—1181no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—2362no—
596C22×C4—2364no—
597C22×C4D4×D5911yescharacteristic
598C22×C4D4×D5911yescharacteristic
599C22×C4C23×D5911yescharacteristic
600Q16—28no—
601Q16—1188no—
602Q16—1188no—
603Q16—1188no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—592no—
607C2×C8—592no—
608C2×C8—1182no—
609C2×C8—1182no—
610C2×C8C23×D5912yes—
611C2×C8C23×D5912yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—592no—
617C4⋊C4—592no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1184no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1181no—
627C4⋊C4—1181no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4C23×D5912yes—
631C4⋊C4C23×D5912yes—
632C22⋊C4—1184no—
633C22⋊C4—1184no—
634C42—24no—
635C42—24no—
636C42—594no—
637C42—594no—
638C42—592no—
639C42—592no—
640C42—1184no—
641C42—1184no—
642C42—1184no—
643C42—1184no—
644C42D4×D5912yes—
645C42C23×D5912yes—
646C23—594no—
647C23—592no—
648C23—1182no—
649C23—1182no—
650C23C2×D4×D5911yescharacteristic
651Q8—24no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—594no—
657Q8—11816no—
658Q8—1184no—
659Q8—1182no—
660Q8—1182no—
661Q8—1182no—
662Q8—2368no—
663Q8—2362no—
664Q8C2×#1174568514yes—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—594no—
675C2×C4—592no—
676C2×C4—5916no—
677C2×C4—592no—
678C2×C4—592no—
679C2×C4—11816no—
680C2×C4—1182no—
681C2×C4—1184no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1184no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—2364no—
691C2×C4—2368no—
692C2×C4—2362no—
693C2×C4—2362no—
694C2×C4—2362no—
695C2×C4Q16×D5914yes—
696C2×C4C2×D4×D5912yes—
697C2×C4C2×D4×D5911yescharacteristic
698C2×C4C2×D4×D5912yes—
699C2×C4#41×D5912yes—
700C2×C4C2×#1174568512yes—
701C2×C4C24×D5911yescharacteristic
702C8—22no—
703C8—22no—
704C8—1182no—
705C8—1182no—
706C22—594no—
707C22—1188no—
708C22—1182no—
709C22—1182no—
710C22#1683791112yes—
711C22C2×Q16×D5912yes—
712C22#1683819912yes—
713C22C22×D4×D5911yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—594no—
720C4—1182no—
721C4—1182no—
722C4—1184no—
723C4—2362no—
724C4—2362no—
725C4—2362no—
726C4#1683791112yes—
727C4C2×Q16×D5914yes—
728C4C2×#41×D5911yescharacteristic
729C4C22×#1174568511yescharacteristic
730C2—1184no—
731C2#2143413314yesdirect product factor
732C2C2×#1683791111yescharacteristic
733C2C22×Q16×D5911yescharacteristic
734C2C2×#1683819911yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×Q16×C59C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenterC2×C4×Q16D59
hypocenterC59C2×#3104
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #21434133C2direct (N × H)
6. C2×#16837696C2semidirect
7. C2×#16837695C2semidirect
8. C2×#16837611C2semidirect
9. C2×#16837610C2semidirect
12. C2×C4×Dic236C2semidirect
13. C2×C4×#11745672C2semidirect
14. C2×C4×#11745672C2semidirect
16. C2×C4×Q16×C59C2semidirect
45. #16837696C22semidirect
46. #16837695C22semidirect
47. #16837611C22semidirect
48. #16837610C22semidirect
51. C4×Dic236C22semidirect
52. C4×#11745672C22semidirect
53. C4×#11745672C22semidirect
72. C4×Q16×C59C22semidirect
215. C2×C4×D59Q16semidirect
325. C4×D59C2×Q16semidirect
377. C2×C4×Q16D59semidirect
379. C2×C59#3104semidirect
424. C4×Q16C2×D59semidirect
444. C59C2×#3104semidirect
731. C2#21434133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379562
C2×C4×Q8×D592
#214341332
C2×#168377392
C2×#168377362
C2×#168376962
C2×#168376952
C2×#168376112
C2×#168376102
C2×#168375592
C2×#168375562
C2×C4×Dic2362
C2×C4×#117456722
C2×#168374532
C2×C4×Q16×C592
C2×#310459