Finite Group Databasebeta

← C2×#21436147 #29465295

Subgroups — C2×#21436147 #29465295

Order 15104.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838092C211yesmaximal, characteristic
2#21436147C2116yesmaximal, direct product factor
3C2×#16837770C211yesmaximal, characteristic, complemented
4C2×#16837740C211yesmaximal, characteristic, complemented
5C2×#16837730C211yesmaximal, characteristic, complemented
6C2×#16837709C211yesmaximal, characteristic, complemented
7C2×#16837658C211yesmaximal, characteristic, complemented
8C2×#16837641C211yesmaximal, characteristic, complemented
9C2×#16837609C211yesmaximal, characteristic, complemented
10C2×#16837558C211yesmaximal, characteristic, complemented
11C2×#16837558C211yesmaximal, characteristic, complemented
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic
14C2×#16837411C211yesmaximal, characteristic, complemented
15C22×#14273651C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C59C211yesmaximal, characteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745664C2211yescharacteristic
21C23×C59⋊C8C2211yescharacteristic
22#16838092—24no—
23#16838092C2218yes—
24C2×#14273720—21no—
25C2×#14273719C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273708—21no—
28C2×#14273706C2211yescharacteristic
29C2×#14273706C2211yescharacteristic
30C2×C4×Dic118C2211yescharacteristic
31C2×#14273686C2211yescharacteristic
32C2×#14273683—21no—
33C22×C4⋊Dic59C2211yescharacteristic
34#16837770C2218yescomplemented
35#16837740C2218yescomplemented
36#16837730C2218yescomplemented
37#16837709C2218yescomplemented
38#16837658C2218yescomplemented
39#16837641C2218yescomplemented
40#16837609C2218yescomplemented
41#16837558C2218yescomplemented
42#16837558C2218yescomplemented
43#16837507C2218yescomplemented
44#16837474C2218yes—
45C2×#14273660C2211yescharacteristic
46C2×#14273658C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49#16837411C2218yescomplemented
50C2×#14273651C2211yescharacteristic
51C2×#14273651C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273651C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273651C2211yescharacteristic
58C2×#14273651C2211yescharacteristic
59C2×#14273651C2218yescomplemented
60C2×#14273650C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C23×Q8×C59C2211yescharacteristic
65C23×Q8×C59C2211yescharacteristic
66D4×Q8×C59—24no—
67D4×Q8×C59C2218yes—
68C2×C4⋊Q8×C59—21no—
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×C22⋊Q8×C59—21no—
71C2×C22⋊Q8×C59—21no—
72C2×C22⋊Q8×C59C2211yescharacteristic
73C2×C22⋊Q8×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59—21no—
76C2×C4×D4×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C23×Dic59—21no—
79C2×#11745672—24no—
80C2×#11745672—42no—
81C2×#11745672—42no—
82C2×#11745672C2314yes—
83C2×#11745672C2314yes—
84C2×#11745672C2314yes—
85C2×#11745664—42no—
86C2×#11745664C2314yes—
87C22×C59⋊C8—42no—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2314yes—
93#14273720—28no—
94#14273719—22no—
95#14273719C2314yes—
96#14273717—28no—
97#14273708—28no—
98#14273706—22no—
99#14273706—22no—
100#14273706C2314yes—
101#14273706C2314yes—
102C4×Dic118—22no—
103C4×Dic118C2314yes—
104#14273686—22no—
105#14273686C2314yes—
106#14273683—28no—
107C2×C4⋊Dic59—21no—
108C2×C4⋊Dic59—22no—
109C2×C4⋊Dic59C2311yescharacteristic
110C2×C4⋊Dic59C2311yescharacteristic
111C2×C4⋊Dic59C2311yescharacteristic
112C2×C4⋊Dic59C2314yes—
113C2×Dic59⋊C4—21no—
114C2×Dic59⋊C4—21no—
115C2×Dic59⋊C4—21no—
116C2×Dic59⋊C4—21no—
117C2×Dic59⋊C4—21no—
118C2×C22⋊Dic59—21no—
119C2×C22⋊Dic59—21no—
120C2×C22⋊Dic59—21no—
121C2×C4×Dic59—21no—
122C2×C4×Dic59—21no—
123#14273660C2314yes—
124#14273658C2314yes—
125#14273658C2314yes—
126C4⋊(C59⋊C8)C2314yes—
127#14273651C2314yes—
128#14273651C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273651C2314yes—
132#14273651C2314yes—
133#14273651C2314yes—
134#14273651C2314yes—
135#14273651C2314yes—
136#14273650C2314yes—
137C22⋊(C59⋊C8)C2314yes—
138C22⋊(C59⋊C8)C2314yes—
139#14273638C2314yes—
140C22×Q8×C59—21no—
141C22×Q8×C59—21no—
142C22×Q8×C59—22no—
143C22×Q8×C59—22no—
144C22×Q8×C59—24no—
145C22×Q8×C59—24no—
146C22×Q8×C59—42no—
147C22×Q8×C59—42no—
148C22×Q8×C59C2311yescharacteristic
149C22×Q8×C59C2311yescharacteristic
150C22×Q8×C59C2314yes—
151C22×Q8×C59C2314yes—
152C22×Q8×C59C2311yescharacteristic
153C22×D4×C59D411yescharacteristic
154C23×C4×C59—21no—
155C23×C4×C59—21no—
156C23×C4×C59C2311yescharacteristic
157C23×C4×C59C2311yescharacteristic
158C4⋊Q8×C59—28no—
159C4⋊Q8×C59—22no—
160C4⋊Q8×C59C2314yes—
161C22⋊Q8×C59—22no—
162C22⋊Q8×C59—22no—
163C22⋊Q8×C59—28no—
164C22⋊Q8×C59—28no—
165C22⋊Q8×C59C2314yes—
166C22⋊Q8×C59C2314yes—
167C4×Q8×C59—22no—
168C4×Q8×C59C2314yes—
169C4×D4×C59—28no—
170C4×D4×C59D414yes—
171C4×D4×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59—21no—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59D411yescharacteristic
182C2×C22⋊C4×C59D411yescharacteristic
183C2×C42×C59—21no—
184C2×C42×C59C2311yescharacteristic
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—24no—
189C2×Q8×C59—24no—
190C2×Q8×C59—21no—
191C2×Q8×C59—21no—
192C2×Q8×C59—22no—
193C2×Q8×C59—28no—
194C2×Q8×C59—28no—
195C2×Q8×C59—22no—
196C2×Q8×C59—22no—
197C2×Q8×C59—22no—
198C2×Q8×C59—22no—
199C2×Q8×C59—44no—
200C2×Q8×C59—44no—
201C2×Q8×C59—44no—
202C2×Q8×C59—44no—
203C2×Q8×C59—48no—
204C2×Q8×C59—48no—
205C2×Q8×C59#4114yes—
206C2×Q8×C59C2412yes—
207C2×Q8×C59C2412yes—
208C2×Q8×C59C2412yes—
209C2×D4×C59—24no—
210C2×D4×C59C2×D414yes—
211C22×C4×C59—21no—
212C22×C4×C59—22no—
213C22×C4×C59—22no—
214C22×C4×C59—22no—
215C22×C4×C59—22no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—24no—
220C22×C4×C59—24no—
221C22×C4×C59—44no—
222C22×C4×C59—44no—
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D412yes—
228C22×C4×C59C2×D412yes—
229C22×C4×C59C2412yes—
230C22×C4×C59C2412yes—
231C22×C4×C59C2411yescharacteristic
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—24no—
237C22×Dic59—44no—
238C2×Dic118—22no—
239C2×Dic118—22no—
240C2×Dic118—21no—
241C2×Dic118C2412yes—
242C4⋊C4×C59—24no—
243C4⋊C4×C59—24no—
244C4⋊C4×C59—24no—
245C4⋊C4×C59—24no—
246C4⋊C4×C59—24no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59C2×D414yes—
249C4⋊C4×C59C2412yes—
250C22⋊C4×C59—24no—
251C22⋊C4×C59—24no—
252C22⋊C4×C59C2×D414yes—
253C22⋊C4×C59C2×D414yes—
254C42×C59—24no—
255C42×C59C2×D412yes—
256C42×C59C2412yes—
257C22⋊Dic59—24no—
258C22⋊Dic59—24no—
259C22⋊Dic59—24no—
260#11745672—28no—
261#11745672—44no—
262#11745672—44no—
263C4⋊Dic59—21no—
264C4⋊Dic59—21no—
265C4⋊Dic59—24no—
266C4⋊Dic59—21no—
267C4⋊Dic59C2412yes—
268C4⋊Dic59C2412yes—
269C4⋊Dic59C2412yes—
270Dic59⋊C4—24no—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275C4×Dic59—24no—
276C4×Dic59—24no—
277#11745664—44no—
278C2×C59⋊C8—22no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—44no—
283C2×C59⋊C8C2412yes—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286C2×C59⋊C8C2412yes—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59#13714yes—
293C23×C59C22×D412yes—
294C23×C59C22×D412yes—
295C23×C59C22×D411yescharacteristic
296Q8×C59—24no—
297Q8×C59—22no—
298Q8×C59—22no—
299Q8×C59—22no—
300Q8×C59—22no—
301Q8×C59—22no—
302Q8×C59—48no—
303Q8×C59—48no—
304Q8×C59—42no—
305Q8×C59—42no—
306Q8×C59C2×#4114yes—
307D4×C59—28no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—24no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—24no—
315C2×C4×C59—24no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—48no—
324C2×C4×C59—48no—
325C2×C4×C59—42no—
326C2×C4×C59—42no—
327C2×C4×C59—42no—
328C2×C4×C59C22×D412yes—
329C2×C4×C59C22×D412yes—
330C2×C4×C59C22×D412yes—
331C2×C4×C59C22×D412yes—
332C2×C4×C59C22×D411yescharacteristic
333C2×C4×C59C2×#4112yes—
334C2×C4×C59H(5,𝔽2)12yes—
335C2×C4×C59C2511yescharacteristic
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—42no—
341C2×Dic59—48no—
342C2×Dic59—42no—
343C2×Dic59—42no—
344C2×Dic59—42no—
345Dic118—22no—
346Dic118—22no—
347Dic118—42no—
348C59⋊C8—22no—
349C59⋊C8—22no—
350C59⋊C8—22no—
351C59⋊C8—22no—
352C2×#3312—591nomaximal, Sylow
353C22×C59—22no—
354C22×C59—28no—
355C22×C59—22no—
356C22×C59—22no—
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—44no—
360C22×C59#54612yes—
361C22×C59C2×#13714yes—
362C22×C59C2×#13712yes—
363C22×C59#57812yes—
364C22×C59C23×D411yescharacteristic
365C4×C59—22no—
366C4×C59—22no—
367C4×C59—24no—
368C4×C59—22no—
369C4×C59—22no—
370C4×C59—42no—
371C4×C59—42no—
372C4×C59—42no—
373C4×C59#54612yes—
374C4×C59C22×#4111yescharacteristic
375C4×C59C2×H(5,𝔽2)11yescharacteristic
376Dic59—42no—
377Dic59—42no—
378Dic59—42no—
379Dic59—42no—
380C2×#552—591no—
381C2×D4×Q8D5911yescharacteristic
382#3312—5916no—
383C2×#491—591no—
384C2×#485—591no—
385C2×#483—591no—
386C2×#479—591no—
387C2×#470—591no—
388C2×#467—591no—
389C2×#462—591no—
390C2×#451—591no—
391C2×#451—591no—
392C2×#441—591no—
393C2×#435—591no—
394C2×#419—591no—
395C22×#103—591no—
396C2×C59—24no—
397C2×C59—42no—
398C2×C59#331214yescomplemented
399C2×C59C2×#54611yescharacteristic
400C2×C59C22×#13711yescharacteristic
401C2×C59C2×#57811yescharacteristic
402C23×Q8C2×D5911yescharacteristic
403C23×Q8C2×D5911yescharacteristic
404C22×Q16—591no—
405C22×Q16—591no—
406C22×Q16—591no—
407C22×M16—591no—
408C23×C8—591no—
409#552—598no—
410#552—1184no—
411D4×Q8—24no—
412D4×Q8C2×D5918yes—
413C2×C4⋊Q8—21no—
414C2×C4⋊Q8C2×D5911yescharacteristic
415C2×#126—1181no—
416C2×#125—591no—
417C2×#125—1181no—
418C2×#123—1181no—
419C2×C22⋊Q8—21no—
420C2×C22⋊Q8—21no—
421C2×C22⋊Q8—591no—
422C2×C22⋊Q8—591no—
423C2×C22⋊Q8C2×D5911yescharacteristic
424C2×C22⋊Q8C2×D5911yescharacteristic
425C2×C4×Q8—591no—
426C2×C4×Q8C2×D5911yescharacteristic
427C2×C4×D4—21no—
428C2×C4×D4C2×D5911yescharacteristic
429C2×#117—591no—
430C2×#117—1181no—
431C22×C4⋊C4—591no—
432#491—598no—
433#485—598no—
434#483—598no—
435#479—598no—
436#470—598no—
437#467—598no—
438#462—598no—
439#451—598no—
440#451—598no—
441#441—598no—
442#435—598no—
443C2×#107—591no—
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8—591no—
447#419—598no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#103—591no—
454C2×#103—591no—
455C2×#103—591no—
456C2×#103—591no—
457C2×#103—598no—
458C2×#103—591no—
459C2×C22⋊C8—591no—
460C2×C22⋊C8—591no—
461C2×#97—591no—
462C59C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—21no—
464C22×Q8—21no—
465C22×Q8—22no—
466C22×Q8—22no—
467C22×Q8—24no—
468C22×Q8—24no—
469C22×Q8—42no—
470C22×Q8—42no—
471C22×Q8—591no—
472C22×Q8C22×D5911yescharacteristic
473C22×Q8C22×D5911yescharacteristic
474C22×Q8C22×D5914yes—
475C22×Q8C22×D5914yes—
476C22×Q8C22×D5911yescharacteristic
477C22×D4C22⋊D5911yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—1181no—
481C23×C4C22×D5911yescharacteristic
482C23×C4C22×D5911yescharacteristic
483C2×Q16—594no—
484C2×Q16—594no—
485C2×Q16—594no—
486C2×Q16—1184no—
487C2×Q16—2362no—
488C2×Q16—2362no—
489C2×M16—594no—
490C2×M16—2362no—
491C22×C8—591no—
492C22×C8—591no—
493C22×C8—591no—
494C22×C8—591no—
495C22×C8—594no—
496C22×C8—2362no—
497C4⋊Q8—28no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D5914yes—
500#126—1188no—
501#125—594no—
502#125—1188no—
503#125—1182no—
504#123—1188no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—28no—
508C22⋊Q8—28no—
509C22⋊Q8—594no—
510C22⋊Q8—594no—
511C22⋊Q8—1182no—
512C22⋊Q8—1182no—
513C22⋊Q8C22×D5914yes—
514C22⋊Q8C22×D5914yes—
515C4×Q8—22no—
516C4×Q8—594no—
517C4×Q8—1182no—
518C4×Q8C22×D5914yes—
519C4×D4—28no—
520C4×D4C22⋊D5914yes—
521C4×D4C22×D5914yes—
522#117—594no—
523#117—1182no—
524#117—1188no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—591no—
531C2×C4⋊C4—591no—
532C2×C4⋊C4—594no—
533C2×C4⋊C4—591no—
534C2×C4⋊C4—1181no—
535C2×C4⋊C4—1182no—
536C2×C4⋊C4—1181no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4C22⋊D5911yescharacteristic
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—1181no—
546C2×C22⋊C4—1181no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4C22⋊D5911yescharacteristic
549C2×C22⋊C4C22⋊D5911yescharacteristic
550C2×C42—21no—
551C2×C42—1181no—
552C2×C42—1181no—
553C2×C42C22×D5911yescharacteristic
554#107—594no—
555#106—594no—
556#106—594no—
557C4⋊C8—594no—
558#103—594no—
559#103—594no—
560#103—594no—
561#103—594no—
562#103—594no—
563#103—594no—
564#103—594no—
565#103—594no—
566#103—594no—
567#103—594no—
568C22⋊C8—594no—
569C22⋊C8—594no—
570#97—594no—
571C24C2×C22⋊D5911yescharacteristic
572C24C2×C22⋊D5911yescharacteristic
573C2×Q8—21no—
574C2×Q8—24no—
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—28no—
580C2×Q8—28no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—48no—
590C2×Q8—48no—
591C2×Q8—592no—
592C2×Q8—1181no—
593C2×Q8—1182no—
594C2×Q8—1182no—
595C2×Q8#1174568714yes—
596C2×Q8C23×D5912yes—
597C2×Q8C23×D5912yes—
598C2×Q8C23×D5912yes—
599C2×D4—24no—
600C2×D4C2×C22⋊D5914yes—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—1184no—
614C22×C4—1181no—
615C22×C4—1181no—
616C22×C4—1181no—
617C22×C4—1181no—
618C22×C4—2364no—
619C22×C4C2×C22⋊D5912yes—
620C22×C4C2×C22⋊D5912yes—
621C22×C4C2×C22⋊D5911yescharacteristic
622C22×C4C2×C22⋊D5911yescharacteristic
623C22×C4C2×C22⋊D5911yescharacteristic
624C22×C4C2×C22⋊D5911yescharacteristic
625C22×C4C23×D5912yes—
626C22×C4C23×D5912yes—
627C22×C4C23×D5911yescharacteristic
628Q16—1188no—
629Q16—2364no—
630Q16—2364no—
631M16—2364no—
632C2×C8—592no—
633C2×C8—592no—
634C2×C8—592no—
635C2×C8—592no—
636C2×C8—1182no—
637C2×C8—1182no—
638C2×C8—1182no—
639C2×C8—1182no—
640C2×C8—2364no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—592no—
648C4⋊C4—592no—
649C4⋊C4—592no—
650C4⋊C4—1181no—
651C4⋊C4—1181no—
652C4⋊C4—1184no—
653C4⋊C4—1181no—
654C4⋊C4—1184no—
655C4⋊C4—1184no—
656C4⋊C4—1184no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4C2×C22⋊D5914yes—
660C4⋊C4C23×D5912yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—1184no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C22⋊C4C2×C22⋊D5914yes—
667C22⋊C4C2×C22⋊D5914yes—
668C42—24no—
669C42—1184no—
670C42—1184no—
671C42C2×C22⋊D5912yes—
672C42C23×D5912yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1427375814yes—
679C23C22×C22⋊D5912yes—
680C23C22×C22⋊D5912yes—
681C23C22×C22⋊D5911yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—48no—
690Q8—42no—
691Q8—42no—
692Q8—1182no—
693Q8—1182no—
694Q8—2362no—
695Q8C2×#1174568714yes—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—48no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—2368no—
722C2×C4—2362no—
723C2×C4—2362no—
724C2×C4—2362no—
725C2×C4—2362no—
726C2×C4C22×C22⋊D5912yes—
727C2×C4C22×C22⋊D5912yes—
728C2×C4C22×C22⋊D5912yes—
729C2×C4C22×C22⋊D5912yes—
730C2×C4C22×C22⋊D5911yescharacteristic
731C2×C4C2×#1174568712yes—
732C2×C4#1427377212yes—
733C2×C4C24×D5911yescharacteristic
734C8—1182no—
735C8—1182no—
736C8—1182no—
737C8—1182no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1683804612yes—
746C22C2×#1427375814yes—
747C22C2×#1427375812yes—
748C22#1683821712yes—
749C22C23×C22⋊D5911yescharacteristic
750C4—22no—
751C4—22no—
752C4—24no—
753C4—22no—
754C4—22no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—2362no—
759C4—2362no—
760C4—2362no—
761C4—2362no—
762C4#1683804612yes—
763C4C22×#1174568711yescharacteristic
764C4C2×#1427377211yescharacteristic
765C2—24no—
766C2—42no—
767C2#2143614714yesdirect product factor
768C2C2×#1683804611yescharacteristic
769C2C22×#1427375811yescharacteristic
770C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×D4×Q8×C59C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
hypercenterC2×D4×Q8D59
hypocenterC59C2×#3312
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #21436147C2direct (N × H)
3. C2×#16837770C2semidirect
4. C2×#16837740C2semidirect
5. C2×#16837730C2semidirect
6. C2×#16837709C2semidirect
7. C2×#16837658C2semidirect
8. C2×#16837641C2semidirect
9. C2×#16837609C2semidirect
10. C2×#16837558C2semidirect
11. C2×#16837558C2semidirect
12. C2×#16837507C2semidirect
14. C2×#16837411C2semidirect
15. C22×#14273651C2semidirect
34. #16837770C22semidirect
35. #16837740C22semidirect
36. #16837730C22semidirect
37. #16837709C22semidirect
38. #16837658C22semidirect
39. #16837641C22semidirect
40. #16837609C22semidirect
41. #16837558C22semidirect
42. #16837558C22semidirect
43. #16837507C22semidirect
49. #16837411C22semidirect
59. C2×#14273651C22semidirect
398. C2×C59#3312semidirect
462. C59C2×#3312semidirect
767. C2#21436147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380922
#214361472
C2×#168377702
C2×#168377402
C2×#168377302
C2×#168377092
C2×#168376582
C2×#168376412
C2×#168376092
C2×#168375582
C2×#168375072
C2×#168374742
C2×#168374112
C22×#142736512
C2×D4×Q8×C592
C2×#331259