Finite Group Databasebeta

← C2×#21436407 #29465605

Subgroups — C2×#21436407 #29465605

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838110C211yesmaximal, characteristic, complemented
2C2×#16838054C211yesmaximal, characteristic
3#21436407C2116yesmaximal, direct product factor
4C2×#16837751C211yesmaximal, characteristic, complemented
5C2×#16837734C211yesmaximal, characteristic, complemented
6C2×#16837730C211yesmaximal, characteristic, complemented
7C2×#16837691C211yesmaximal, characteristic, complemented
8C2×#16837659C211yesmaximal, characteristic, complemented
9C2×#16837610C211yesmaximal, characteristic, complemented
10C2×#16837563C211yesmaximal, characteristic, complemented
11C2×#16837562C211yesmaximal, characteristic, complemented
12C2×#16837487C211yesmaximal, characteristic, complemented
13C2×#16837478C211yesmaximal, characteristic, complemented
14C2×#16837404C211yesmaximal, characteristic, complemented
15C2×#16837402C211yesmaximal, characteristic, complemented
16C2×C59×#470C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745685C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22#16838110—24no—
23#16838110C2218yescomplemented
24#16838054—24no—
25#16838054C2218yes—
26C2×#14273726C2211yescharacteristic
27C2×#14273725C2211yescharacteristic
28C2×#14273717—21no—
29C2×#14273712—21no—
30C2×#14273709—21no—
31C2×#14273707—21no—
32C2×#14273707C2211yescharacteristic
33C2×#14273704—21no—
34C2×#14273703C2211yescharacteristic
35C2×#14273700—21no—
36C2×Q8×Dic59C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×(C22⋊D59)⋊C4—21no—
40C22×C4⋊Dic59C2211yescharacteristic
41C2×C4⋊C4×D59—21no—
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837751C2218yescomplemented
44#16837734C2218yescomplemented
45#16837730C2218yescomplemented
46#16837691C2218yescomplemented
47#16837659C2218yescomplemented
48#16837610C2218yescomplemented
49#16837563C2218yescomplemented
50#16837562C2218yescomplemented
51#16837487C2218yescomplemented
52#16837478C2218yescomplemented
53C2×#14273658C2211yescharacteristic
54C2×#14273658C2211yescharacteristic
55C2×Dic59⋊C8C2211yescharacteristic
56#16837404C2218yescomplemented
57#16837402C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#470C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C2×#11745689—22no—
78C2×#11745689—24no—
79C2×#11745689—42no—
80C2×#11745689C2314yes—
81C2×#11745685—22no—
82C2×#11745685—24no—
83C2×#11745685—42no—
84C2×#11745685C2314yes—
85C22×Dic118—21no—
86C22×Dic118C2311yescharacteristic
87C22×D236—21no—
88C22×D236C2311yescharacteristic
89C22×C22⋊D59—21no—
90C22×C22⋊D59D411yescharacteristic
91C23×Dic59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C22×C4×D59C2311yescharacteristic
97C2×#11745672—42no—
98C2×#11745672C2314yes—
99C2×#11745671—24no—
100C2×#11745671C2314yes—
101C2×#11745659—42no—
102C2×#11745659C2314yes—
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105#14273726—22no—
106#14273726C2314yes—
107#14273725—22no—
108#14273725C2314yes—
109#14273717—28no—
110#14273712—28no—
111#14273709—28no—
112#14273707—22no—
113#14273707—28no—
114#14273707C2314yes—
115#14273704—28no—
116#14273703—22no—
117#14273703C2314yes—
118#14273700—28no—
119Q8×Dic59—22no—
120Q8×Dic59C2314yes—
121#14273689—22no—
122#14273689C2314yes—
123C4×C22⋊D59D414yes—
124C4×C22⋊D59C2314yes—
125(C22⋊D59)⋊C4—28no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59—22no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59C2311yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2314yes—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4D411yescharacteristic
139C4⋊C4×D59—22no—
140C4⋊C4×D59—28no—
141C4⋊C4×D59C2314yes—
142C2×C22⋊Dic59D411yescharacteristic
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4D411yescharacteristic
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273658C2314yes—
150#14273658C2314yes—
151Dic59⋊C8C2314yes—
152#14273652C2314yes—
153#14273652C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157#14273649C2314yes—
158#14273649C2314yes—
159#14273647C2314yes—
160C22⋊(C59⋊C8)C2314yes—
161(C2×D59)⋊C8C2314yes—
162C8×Dic59C2314yes—
163C22×Q8×C59C2311yescharacteristic
164C22×Q8×C59C2311yescharacteristic
165C23×C4×C59C2311yescharacteristic
166C2×Q16×C59—42no—
167C2×Q16×C59C2314yes—
168C2×M16×C59—42no—
169C2×M16×C59C2314yes—
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22⋊Q8×C59—22no—
173C22⋊Q8×C59—22no—
174C22⋊Q8×C59C2314yes—
175C22⋊Q8×C59C2314yes—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59—21no—
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182#106×C59C2314yes—
183#103×C59C2314yes—
184#103×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C23×D59—21no—
187C23×D59C2×D411yescharacteristic
188C2×Q8×C59—21no—
189C2×Q8×C59—21no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59—22no—
193C2×Q8×C59—22no—
194C2×Q8×C59C2412yes—
195C2×Q8×C59C2412yes—
196C22×C4×C59—22no—
197C22×C4×C59—22no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2412yes—
205C22×C4×C59C2411yescharacteristic
206C2×C22⋊D59—24no—
207C2×C22⋊D59—24no—
208C2×C22⋊D59—44no—
209C2×C22⋊D59C2×D414yes—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—24no—
214C22×Dic59—82no—
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218#11745689—28no—
219#11745689—44no—
220#11745689—48no—
221#11745685—28no—
222#11745685—44no—
223#11745685—48no—
224C2×D236—21no—
225C2×D236—22no—
226C2×D236—24no—
227C2×D236—44no—
228C2×D236#4114yes—
229C2×D236C2412yes—
230C2×C4×D59—22no—
231C2×C4×D59—22no—
232C2×C4×D59—24no—
233C2×C4×D59—24no—
234C2×C4×D59—24no—
235C2×C4×D59—24no—
236C2×C4×D59—44no—
237C2×C4×D59—44no—
238C2×C4×D59—44no—
239C2×C4×D59—82no—
240C2×C4×D59C2×D412yes—
241C2×C4×D59C2412yes—
242C2×Dic118—22no—
243C2×Dic118—22no—
244C2×Dic118—21no—
245C2×Dic118—24no—
246C2×Dic118—82no—
247C2×Dic118C2412yes—
248Q16×C59—44no—
249M16×C59—44no—
250C2×C8×C59—22no—
251C2×C8×C59—22no—
252C2×C8×C59C2412yes—
253C2×C8×C59C2412yes—
254C4⋊C4×C59—24no—
255C4⋊C4×C59—24no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59C2412yes—
259C4⋊C4×C59C2412yes—
260C22⋊C4×C59—24no—
261C22⋊C4×C59—24no—
262C22⋊Dic59C2×D414yes—
263#11745672—44no—
264#11745671—28no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4C2×D414yes—
269C4⋊Dic59—21no—
270C4⋊Dic59—21no—
271C4⋊Dic59—24no—
272C4⋊Dic59—24no—
273C4⋊Dic59—24no—
274C4⋊Dic59C2412yes—
275C4⋊Dic59C2412yes—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4—24no—
280Dic59⋊C4—24no—
281Dic59⋊C4C2×D414yes—
282C4×Dic59—24no—
283C4×Dic59C2×D412yes—
284C4×Dic59C2412yes—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—22no—
287C2×C59⋊C8C2412yes—
288C2×C59⋊C8C2412yes—
289#11745659—44no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59C22×D412yes—
294C23×C59C22×D411yescharacteristic
295C22×D59—22no—
296C22×D59—24no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—42no—
301C22×D59—42no—
302C22×D59C22×D412yes—
303Q8×C59—22no—
304Q8×C59—22no—
305Q8×C59—22no—
306Q8×C59—22no—
307Q8×C59—42no—
308Q8×C59—42no—
309C2×C4×C59—22no—
310C2×C4×C59—24no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59C22×D412yes—
322C2×C4×C59C22×D411yescharacteristic
323C2×C4×C59C2×#4112yes—
324C2×C4×C59H(5,𝔽2)12yes—
325C2×C4×C59C2511yescharacteristic
326C22⋊D59—28no—
327C22⋊D59—48no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—84no—
337C2×Dic59#13714yes—
338C2×Dic59C22×D412yes—
339C2×Dic59C22×D412yes—
340C2×Dic59C22×D412yes—
341D236—24no—
342D236—22no—
343D236—48no—
344D236C2×#4114yes—
345C4×D59—24no—
346C4×D59—22no—
347C4×D59—22no—
348C4×D59—48no—
349C4×D59—48no—
350C4×D59—48no—
351C4×D59—84no—
352Dic118—22no—
353Dic118—22no—
354Dic118—42no—
355Dic118—84no—
356C8×C59—22no—
357C8×C59—22no—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C2×#3331—591nomaximal, Sylow
361C22×C59—22no—
362C22×C59—22no—
363C22×C59—22no—
364C22×C59—44no—
365C22×C59#54612yes—
366C22×C59C2×#13712yes—
367C22×C59#57712yes—
368C22×C59C23×D411yescharacteristic
369C2×D59—22no—
370C2×D59—24no—
371C2×D59—22no—
372C2×D59—22no—
373C2×D59—44no—
374C2×D59—48no—
375C2×D59—42no—
376C2×D59—42no—
377C4×C59—22no—
378C4×C59—42no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59#54612yes—
383C4×C59C22×#4111yescharacteristic
384C4×C59C2×H(5,𝔽2)11yescharacteristic
385Dic59—22no—
386Dic59—22no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390Dic59C2×#13714yes—
391C2×#554—591no—
392C2×#547—591no—
393#3331—5916no—
394C2×#487—591no—
395C2×#483—591no—
396C2×#483—591no—
397C2×#476—591no—
398C2×#470—591no—
399C2×#470D5911yescharacteristic, complemented
400C2×#462—591no—
401C2×#452—591no—
402C2×#452—591no—
403C2×C4×SD16—591no—
404C2×#436—591no—
405C2×#417—591no—
406C2×#417—591no—
407C2×C59—42no—
408C2×C59#333114yescomplemented
409C2×C59C2×#54611yescharacteristic
410C2×C59C22×#13711yescharacteristic
411C2×C59C2×#57711yescharacteristic
412D59—42no—
413D59—44no—
414C22×#41—591no—
415C22×#41—591no—
416C22×Q16—591no—
417C22×Q16C2×D5911yescharacteristic
418C22×SD16—591no—
419C22×M16—591no—
420C22×M16C2×D5911yescharacteristic
421#554—598no—
422#554—1184no—
423#547—598no—
424#547—1184no—
425C2×C4⋊Q8—591no—
426C2×C4⋊Q8—591no—
427C2×#125—1181no—
428C2×#123—1181no—
429C2×#123—1181no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8—591no—
432C2×C22⋊Q8—1181no—
433C2×C22⋊Q8—1181no—
434C2×C22⋊Q8C2×D5911yescharacteristic
435C2×C22⋊Q8C2×D5911yescharacteristic
436C2×#121—1181no—
437C2×C4×Q8—591no—
438C2×C4×D4—591no—
439C2×C4×D4—591no—
440C2×C4×D4—1181no—
441C22×C4⋊C4—591no—
442C22×C4⋊C4—591no—
443C22×C4⋊C4—1181no—
444#487—598no—
445#483—598no—
446#483—598no—
447#476—598no—
448#470—598no—
449#470C2×D5918yescomplemented
450#462—598no—
451#452—598no—
452#452—598no—
453C4×SD16—598no—
454#436—598no—
455C2×#106—591no—
456C2×#106—591no—
457C2×#106C2×D5911yescharacteristic
458C2×C4⋊C8—591no—
459#417—598no—
460#417—598no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103C2×D5911yescharacteristic
467C2×#103C2×D5911yescharacteristic
468C2×#102—591no—
469C2×#102—591no—
470C2×#102—591no—
471C2×C22⋊C8—591no—
472C2×C22⋊C8—591no—
473C2×C4×C8—591no—
474C59C2×#333111yescharacteristic, complemented, Sylow
475C2×#41—594no—
476C2×#41—594no—
477C2×#41—1184no—
478C2×#41—1182no—
479C2×#41—1182no—
480C2×#41—1184no—
481C2×#41—2362no—
482C2×#41—2362no—
483C22×Q8—591no—
484C22×Q8—1181no—
485C22×Q8C22×D5911yescharacteristic
486C22×Q8C22×D5911yescharacteristic
487C22×D4—591no—
488C22×D4—591no—
489C22×D4—1181no—
490C22×D4—1181no—
491C23×C4—591no—
492C23×C4—1181no—
493C23×C4—1181no—
494C23×C4—1181no—
495C23×C4—1181no—
496C23×C4—1181no—
497C23×C4C22×D5911yescharacteristic
498C2×Q16—42no—
499C2×Q16—594no—
500C2×Q16—2362no—
501C2×Q16C22×D5914yes—
502C2×SD16—594no—
503C2×SD16—1184no—
504C2×M16—42no—
505C2×M16—594no—
506C2×M16—2362no—
507C2×M16C22×D5914yes—
508C22×C8—591no—
509C22×C8—591no—
510C22×C8C22×D5911yescharacteristic
511C22×C8C22×D5911yescharacteristic
512C4⋊Q8—594no—
513C4⋊Q8—594no—
514C4⋊Q8—1182no—
515C4⋊Q8—1182no—
516#125—1188no—
517#123—1188no—
518#123—1188no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—594no—
522C22⋊Q8—594no—
523C22⋊Q8—1188no—
524C22⋊Q8—1188no—
525C22⋊Q8—1182no—
526C22⋊Q8—1182no—
527C22⋊Q8C22×D5914yes—
528C22⋊Q8C22×D5914yes—
529#121—1188no—
530C4×Q8—594no—
531C4×Q8—1182no—
532C4×D4—594no—
533C4×D4—594no—
534C4×D4—594no—
535C4×D4—1182no—
536C4×D4—1188no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—591no—
541C2×C4⋊C4—591no—
542C2×C4⋊C4—594no—
543C2×C4⋊C4—594no—
544C2×C4⋊C4—1188no—
545C2×C4⋊C4—1182no—
546C2×C4⋊C4—1181no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4—1181no—
550C2×C4⋊C4—1181no—
551C2×C4⋊C4—1181no—
552C2×C4⋊C4—1181no—
553C2×C4⋊C4—1181no—
554C2×C4⋊C4—1182no—
555C2×C4⋊C4C22×D5911yescharacteristic
556C2×C4⋊C4C22×D5911yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—591no—
560C2×C22⋊C4—591no—
561C2×C22⋊C4—1181no—
562C2×C22⋊C4—1181no—
563C2×C22⋊C4—1181no—
564C2×C42—591no—
565C2×C42—1181no—
566#106—594no—
567#106—594no—
568#106C22×D5914yes—
569C4⋊C8—594no—
570#103—594no—
571#103—594no—
572#103—594no—
573#103—594no—
574#103—594no—
575#103C22×D5914yes—
576#103C22×D5914yes—
577#102—594no—
578#102—594no—
579#102—594no—
580C22⋊C8—594no—
581C22⋊C8—594no—
582C4×C8—594no—
583C24—591no—
584C24—1181no—
585C24D4×D5911yescharacteristic
586#41—1188no—
587#41—1188no—
588#41—2364no—
589#41—2368no—
590#41—2364no—
591#41—2368no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—592no—
599C2×Q8—1184no—
600C2×Q8—1181no—
601C2×Q8—1182no—
602C2×Q8—1182no—
603C2×Q8—4722no—
604C2×Q8C23×D5912yes—
605C2×Q8C23×D5912yes—
606C2×D4—594no—
607C2×D4—594no—
608C2×D4—592no—
609C2×D4—1184no—
610C2×D4—1184no—
611C2×D4—1184no—
612C2×D4—1181no—
613C2×D4—1182no—
614C2×D4—2364no—
615C2×D4—2364no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—591no—
623C22×C4—591no—
624C22×C4—591no—
625C22×C4—592no—
626C22×C4—592no—
627C22×C4—1184no—
628C22×C4—1184no—
629C22×C4—1184no—
630C22×C4—1182no—
631C22×C4—1182no—
632C22×C4—1184no—
633C22×C4—1181no—
634C22×C4—1181no—
635C22×C4—1181no—
636C22×C4—1184no—
637C22×C4—4722no—
638C22×C4—4722no—
639C22×C4—2364no—
640C22×C4—2364no—
641C22×C4—2364no—
642C22×C4D4×D5912yes—
643C22×C4D4×D5911yescharacteristic
644C22×C4C23×D5912yes—
645C22×C4C23×D5911yescharacteristic
646Q16—44no—
647Q16—2364no—
648SD16—1188no—
649M16—44no—
650M16—2364no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—592no—
654C2×C8—592no—
655C2×C8—1182no—
656C2×C8—1182no—
657C2×C8C23×D5912yes—
658C2×C8C23×D5912yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—594no—
664C4⋊C4—592no—
665C4⋊C4—592no—
666C4⋊C4—1184no—
667C4⋊C4—1184no—
668C4⋊C4—1184no—
669C4⋊C4—1184no—
670C4⋊C4—1184no—
671C4⋊C4—1184no—
672C4⋊C4—1184no—
673C4⋊C4—1181no—
674C4⋊C4—1184no—
675C4⋊C4—1181no—
676C4⋊C4C23×D5912yes—
677C4⋊C4C23×D5912yes—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—594no—
681C22⋊C4—594no—
682C22⋊C4—1184no—
683C22⋊C4—1184no—
684C22⋊C4—1184no—
685C42—592no—
686C42—592no—
687C42—1184no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—592no—
692C23—1182no—
693C23—1182no—
694C23—1182no—
695C23—1182no—
696C23—1184no—
697C23—2362no—
698C23—2362no—
699C23C2×D4×D5912yes—
700C23C2×D4×D5911yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—42no—
707Q8—1182no—
708Q8—1182no—
709Q8—4724no—
710Q8—2362no—
711D4—594no—
712D4—1188no—
713D4—1182no—
714D4—1184no—
715D4—2368no—
716D4—2368no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—594no—
730C2×C4—592no—
731C2×C4—592no—
732C2×C4—592no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1184no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—4724no—
742C2×C4—4724no—
743C2×C4—2368no—
744C2×C4—2368no—
745C2×C4—2368no—
746C2×C4—2362no—
747C2×C4—2362no—
748C2×C4—2362no—
749C2×C4C2×D4×D5912yes—
750C2×C4C2×D4×D5911yescharacteristic
751C2×C4#41×D5912yes—
752C2×C4#1427377212yes—
753C2×C4C24×D5911yescharacteristic
754C8—22no—
755C8—22no—
756C8—1182no—
757C8—1182no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—1182no—
763C22—1184no—
764C22—1182no—
765C22—1182no—
766C22—2362no—
767C22—2362no—
768C22—2364no—
769C22—2368no—
770C22#1683804112yes—
771C22#137×D5912yes—
772C22#1683821112yes—
773C22C22×D4×D5911yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—594no—
780C4—1182no—
781C4—1182no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C4#1683804112yes—
786C4C2×#41×D5911yescharacteristic
787C4C2×#1427377211yescharacteristic
788C2—42no—
789C2—2362no—
790C2—2364no—
791C2#2143640714yesdirect product factor
792C2C2×#1683804111yescharacteristic
793C2C2×#137×D5911yescharacteristic
794C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#470C2
socleC23×C59C22×D4
prime radicalC2×#16838054C2
hypercenterC2×#470D59
hypocenterC59C2×#3331
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#16838110C2semidirect
3. #21436407C2direct (N × H)
4. C2×#16837751C2semidirect
5. C2×#16837734C2semidirect
6. C2×#16837730C2semidirect
7. C2×#16837691C2semidirect
8. C2×#16837659C2semidirect
9. C2×#16837610C2semidirect
10. C2×#16837563C2semidirect
11. C2×#16837562C2semidirect
12. C2×#16837487C2semidirect
13. C2×#16837478C2semidirect
14. C2×#16837404C2semidirect
15. C2×#16837402C2semidirect
16. C2×C59×#470C2semidirect
23. #16838110C22semidirect
43. #16837751C22semidirect
44. #16837734C22semidirect
45. #16837730C22semidirect
46. #16837691C22semidirect
47. #16837659C22semidirect
48. #16837610C22semidirect
49. #16837563C22semidirect
50. #16837562C22semidirect
51. #16837487C22semidirect
52. #16837478C22semidirect
56. #16837404C22semidirect
57. #16837402C22semidirect
73. C59×#470C22semidirect
399. C2×#470D59semidirect
408. C2×C59#3331semidirect
449. #470C2×D59semidirect
474. C59C2×#3331semidirect
791. C2#21436407direct (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×#168380542
#214364072
C2×#168377512
C2×#168377342
C2×#168377302
C2×#168376912
C2×#168376592
C2×#168376102
C2×#168375632
C2×#168375622
C2×#168374872
C2×#168374782
C2×#168374042
C2×#168374022
C2×C59×#4702
C2×#333159