Finite Group Databasebeta

← C2×#21427228 #28748405

Subgroups — C2×#21427228 #28748405

Order 15104.

3094 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
1C22×#14273712C211yesmaximal, characteristic
2#21427228C2116yesmaximal, direct product factor
3C2×#16837303C211yesmaximal, characteristic
4C2×#16837294C211yesmaximal, characteristic, complemented
5C2×#16837294C211yesmaximal, characteristic, complemented
6C2×#16837291C211yesmaximal, characteristic, complemented
7C2×#16837291C211yesmaximal, characteristic, complemented
8C2×#16837283C211yesmaximal, characteristic, complemented
9C2×#16837280C211yesmaximal, characteristic
10C2×C4⋊C4×Dic59C211yesmaximal, characteristic, complemented
11C2×#16837253C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
14C2×#16837249C211yesmaximal, characteristic, complemented
15C2×#16837249C211yesmaximal, characteristic, complemented
16C2×C59×#387C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C2×#14273712C4116yescomplemented
21C2×#14273712C2218yes—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×(C2×D59)⋊C4C2211yescharacteristic
33C22×(C2×D59)⋊C4C2211yescharacteristic
34C22×(C2×D59)⋊C4C2211yescharacteristic
35C22×C4×Dic59C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37C22×C4×Dic59C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39C22×C4×Dic59C2211yescharacteristic
40C22×C4×Dic59C2211yescharacteristic
41#16837303C2218yes—
42#16837294C2218yescomplemented
43#16837294C2218yescomplemented
44#16837291C2218yescomplemented
45#16837291C2218yescomplemented
46#16837283C2218yescomplemented
47#16837280C2218yes—
48C4⋊C4×Dic59C2218yescomplemented
49#16837253C2218yescomplemented
50C4×(C2×D59)⋊C4C2218yescomplemented
51C4×(C2×D59)⋊C4C2218yescomplemented
52#16837249C2218yescomplemented
53#16837249C2218yescomplemented
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C22×C4⋊C4×C59C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C42×C59C2211yescharacteristic
63C59×#387C2218yescomplemented
64C2×#95×C59C2211yescharacteristic
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C24×D59C2311yescharacteristic
69C24×D59C2311yescharacteristic
70C22×D236—42no—
71C22×D236—42no—
72C22×D236C2×C418yes—
73C22×D236C2314yes—
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C22×C4×D59—24no—
81C22×C4×D59—24no—
82C22×C4×D59—42no—
83C22×C4×D59—42no—
84C22×C4×D59—42no—
85C22×C4×D59C2×C418yescomplemented
86C22×C4×D59C2314yes—
87C22×C4×D59C2314yes—
88#14273712C2×C4164yescomplemented
89C2×C4⋊Dic59—24no—
90C2×C4⋊Dic59C2314yes—
91C2×Dic59⋊C4—24no—
92C2×Dic59⋊C4C2×C418yescomplemented
93C2×Dic59⋊C4C2314yes—
94C2×Dic59⋊C4C2314yes—
95C2×(C2×D59)⋊C4—24no—
96C2×(C2×D59)⋊C4—24no—
97C2×(C2×D59)⋊C4—24no—
98C2×(C2×D59)⋊C4—24no—
99C2×(C2×D59)⋊C4—24no—
100C2×(C2×D59)⋊C4—24no—
101C2×(C2×D59)⋊C4—42no—
102C2×(C2×D59)⋊C4C2×C418yes—
103C2×(C2×D59)⋊C4C2×C418yes—
104C2×(C2×D59)⋊C4C2×C418yescomplemented
105C2×(C2×D59)⋊C4C2314yes—
106C2×(C2×D59)⋊C4C2314yes—
107C2×(C2×D59)⋊C4C2314yes—
108C2×(C2×D59)⋊C4C2314yes—
109C2×(C2×D59)⋊C4C2314yes—
110C2×(C2×D59)⋊C4C2314yes—
111C2×(C2×D59)⋊C4C2314yes—
112C2×(C2×D59)⋊C4C2314yes—
113C2×(C2×D59)⋊C4C2314yes—
114C2×(C2×D59)⋊C4C2314yes—
115C2×C4×Dic59—24no—
116C2×C4×Dic59—24no—
117C2×C4×Dic59—42no—
118C2×C4×Dic59—42no—
119C2×C4×Dic59—42no—
120C2×C4×Dic59—42no—
121C2×C4×Dic59C2314yes—
122C2×C4×Dic59C2314yes—
123C2×C4×Dic59C2314yes—
124C2×C4×Dic59C2314yes—
125C2×C4×Dic59C2314yes—
126C2×C4×Dic59C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C59⋊#95C2314yes—
132C59⋊#95C2314yes—
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59—42no—
141C2×C4⋊C4×C59C2×C418yescomplemented
142C2×C4⋊C4×C59C2314yes—
143C2×C4⋊C4×C59C2314yes—
144C2×C42×C59—42no—
145C2×C42×C59C2314yes—
146#95×C59C2314yes—
147#95×C59C2314yes—
148#95×C59C2314yes—
149#95×C59C2314yes—
150C24×C59C2411yescharacteristic
151C23×D59—22no—
152C23×D59—22no—
153C23×D59—22no—
154C23×D59—22no—
155C23×D59—22no—
156C23×D59—22no—
157C23×D59—22no—
158C23×D59—22no—
159C23×D59—22no—
160C23×D59—22no—
161C23×D59—22no—
162C23×D59—22no—
163C23×D59C22×C414yes—
164C23×D59C22×C414yes—
165C23×D59C2412yes—
166C23×D59C2412yes—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59C22×C414yes—
185C22×C4×C59C22×C414yes—
186C22×C4×C59C22×C414yes—
187C22×C4×C59#4114yes—
188C22×C4×C59C2412yes—
189C22×C4×C59C2412yes—
190C22×C4×C59C2412yes—
191C22×C4×C59C2412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2412yes—
195C22×Dic59—22no—
196C22×Dic59—22no—
197C22×Dic59—22no—
198C22×Dic59—22no—
199C22×Dic59—22no—
200C22×Dic59—22no—
201C22×Dic59—22no—
202C22×Dic59—22no—
203C22×Dic59—22no—
204C22×Dic59—22no—
205C22×Dic59—22no—
206C22×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59C22×C414yes—
209C22×Dic59C22×C414yes—
210C22×Dic59#4114yes—
211C22×Dic59#4114yes—
212C22×Dic59#4114yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C2×D236—416no—
220C2×D236—44no—
221C2×D236—44no—
222C2×D236C22×C4116yes—
223C2×C4×D59—28no—
224C2×C4×D59—28no—
225C2×C4×D59—416no—
226C2×C4×D59—44no—
227C2×C4×D59—44no—
228C2×C4×D59—44no—
229C2×C4×D59—416no—
230C2×C4×D59C22×C4116yescomplemented
231C4⋊C4×C59—44no—
232C4⋊C4×C59C22×C4116yescomplemented
233C42×C59—44no—
234(C2×D59)⋊C4—28no—
235(C2×D59)⋊C4—28no—
236(C2×D59)⋊C4—28no—
237(C2×D59)⋊C4—28no—
238(C2×D59)⋊C4—28no—
239(C2×D59)⋊C4—28no—
240(C2×D59)⋊C4—44no—
241(C2×D59)⋊C4C22×C4116yes—
242(C2×D59)⋊C4C22×C4116yes—
243(C2×D59)⋊C4C22×C4116yescomplemented
244C4⋊Dic59—28no—
245Dic59⋊C4—28no—
246Dic59⋊C4C22×C4116yescomplemented
247C4×Dic59—28no—
248C4×Dic59—28no—
249C4×Dic59—44no—
250C4×Dic59—44no—
251C4×Dic59—44no—
252C4×Dic59—44no—
253C23×C59C23×C412yes—
254C23×C59C2×#4112yes—
255C23×C59C2×#4112yes—
256C23×C59C2×#4112yes—
257C23×C59C2×#4112yes—
258C23×C59H(5,𝔽2)12yes—
259C23×C59H(5,𝔽2)12yes—
260C23×C59C2511yescharacteristic
261C22×D59—28no—
262C22×D59—28no—
263C22×D59—28no—
264C22×D59—28no—
265C22×D59—28no—
266C22×D59—28no—
267C22×D59—22no—
268C22×D59—22no—
269C22×D59—22no—
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—44no—
280C22×D59—44no—
281C22×D59—44no—
282C22×D59—44no—
283C22×D59—44no—
284C22×D59—44no—
285C22×D59—44no—
286C22×D59—44no—
287C22×D59C23×C414yes—
288C22×D59C23×C414yes—
289C2×C4×C59—28no—
290C2×C4×C59—28no—
291C2×C4×C59—28no—
292C2×C4×C59—28no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—44no—
311C2×C4×C59—44no—
312C2×C4×C59—44no—
313C2×C4×C59C23×C414yes—
314C2×C4×C59C23×C414yes—
315C2×C4×C59C23×C414yes—
316C2×C4×C59C2×#4114yes—
317C2×Dic59—28no—
318C2×Dic59—28no—
319C2×Dic59—28no—
320C2×Dic59—28no—
321C2×Dic59—28no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—44no—
336C2×Dic59C23×C414yes—
337C2×Dic59C23×C414yes—
338C2×Dic59C2×#4114yes—
339C2×Dic59C2×#4114yes—
340C2×Dic59C2×#4114yes—
341D236—416no—
342C4×D59—416no—
343C4×D59—416no—
344C2×#2374—591nomaximal, Sylow
345C22×C59C4×#4114yes—
346C22×C59C4×#4114yes—
347C22×C59#51814yes—
348C22×C59#55114yes—
349C22×C59#55314yes—
350C22×C59#55314yes—
351C22×C59#55914yes—
352C22×C59C24×C411yescharacteristic
353C22×C59C22×#4111yescharacteristic
354C22×C59C22×#4111yescharacteristic
355C22×C59C22×#4111yescharacteristic
356C22×C59C22×#4111yescharacteristic
357C22×C59C2×H(5,𝔽2)11yescharacteristic
358C22×C59C2×H(5,𝔽2)11yescharacteristic
359C2×D59—24no—
360C2×D59—24no—
361C2×D59—24no—
362C2×D59—24no—
363C2×D59—24no—
364C2×D59—24no—
365C2×D59—416no—
366C2×D59—416no—
367C2×D59—42no—
368C2×D59—42no—
369C2×D59—42no—
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C4×C59—24no—
376C4×C59—24no—
377C4×C59—24no—
378C4×C59—24no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59—42no—
382Dic59—24no—
383Dic59—24no—
384Dic59—24no—
385Dic59—24no—
386Dic59—24no—
387Dic59—42no—
388C22×#123—591no—
389#2374—5916no—
390C2×#390—591no—
391C2×#388—591no—
392C2×#388—591no—
393C2×#388—591no—
394C2×#388—591no—
395C2×#387—591no—
396C2×#387D5911yescharacteristic, complemented
397C2×#386—591no—
398C2×C4×C4⋊C4—591no—
399C2×C4×C4⋊C4—591no—
400C2×C4×C22⋊C4—591no—
401C2×C4×C22⋊C4—591no—
402C2×C4×C22⋊C4—591no—
403C2×C4×C22⋊C4—591no—
404C2×C59#237418yescomplemented
405C2×C59C2×C4×#4111yescharacteristic
406C2×C59C2×C4×#4111yescharacteristic
407C2×C59C2×#51811yescharacteristic
408C2×C59C2×#55111yescharacteristic
409C2×C59C2×#55311yescharacteristic
410C2×C59C2×#55311yescharacteristic
411C2×C59C2×#55911yescharacteristic
412D59—44no—
413D59—44no—
414C23×D4—591no—
415C24×C4—591no—
416C24×C4—591no—
417C2×#123—5916no—
418C2×#123—598no—
419C22×C4⋊C4—591no—
420C22×C4⋊C4—591no—
421C22×C4⋊C4—591no—
422C22×C4⋊C4C2×D5911yescharacteristic
423C22×C4⋊C4C2×D5911yescharacteristic
424C22×C22⋊C4—591no—
425C22×C22⋊C4—591no—
426C22×C22⋊C4—591no—
427C22×C22⋊C4—591no—
428C22×C22⋊C4—591no—
429C22×C22⋊C4—591no—
430C22×C22⋊C4—591no—
431C22×C22⋊C4—591no—
432C22×C22⋊C4—591no—
433C22×C22⋊C4—591no—
434C22×C42—591no—
435C22×C42—591no—
436C22×C42—591no—
437C22×C42—591no—
438C22×C42—591no—
439C22×C42—591no—
440C22×C42C2×D5911yescharacteristic
441#390—598no—
442#388—598no—
443#388—598no—
444#388—598no—
445#388—598no—
446#387—598no—
447#387C2×D5918yescomplemented
448#386—598no—
449C4×C4⋊C4—598no—
450C4×C4⋊C4—598no—
451C4×C22⋊C4—598no—
452C4×C22⋊C4—598no—
453C4×C22⋊C4—598no—
454C4×C22⋊C4—598no—
455C2×#95—591no—
456C2×#95—591no—
457C2×#95—591no—
458C2×#95—591no—
459C2×#95—591no—
460C2×#95—591no—
461C2×#95C2×D5911yescharacteristic
462C2×#95C2×D5911yescharacteristic
463C2×#95C2×D5911yescharacteristic
464C2×#95C2×D5911yescharacteristic
465C59C2×#237411yescharacteristic, complemented, Sylow
466C25—591no—
467C25—591no—
468C22×D4—598no—
469C22×D4—594no—
470C22×D4—2362no—
471C22×D4—2362no—
472C23×C4—591no—
473C23×C4—591no—
474C23×C4—591no—
475C23×C4—591no—
476C23×C4—591no—
477C23×C4—598no—
478C23×C4—594no—
479C23×C4—591no—
480C23×C4—594no—
481C23×C4—1184no—
482C23×C4—1184no—
483C23×C4—2362no—
484C23×C4—2362no—
485C23×C4—2362no—
486C23×C4C22×D5911yescharacteristic
487C23×C4C22×D5911yescharacteristic
488C23×C4C22×D5911yescharacteristic
489C23×C4C22×D5911yescharacteristic
490C23×C4C22×D5911yescharacteristic
491C23×C4C22×D5911yescharacteristic
492C23×C4C22×D5911yescharacteristic
493#123—5964no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—598no—
496C2×C4⋊C4—594no—
497C2×C4⋊C4—594no—
498C2×C4⋊C4—594no—
499C2×C4⋊C4—1184no—
500C2×C4⋊C4—1184no—
501C2×C4⋊C4C4×D5918yescomplemented
502C2×C4⋊C4C22×D5914yes—
503C2×C4⋊C4C22×D5914yes—
504C2×C22⋊C4—598no—
505C2×C22⋊C4—598no—
506C2×C22⋊C4—598no—
507C2×C22⋊C4—594no—
508C2×C22⋊C4—594no—
509C2×C22⋊C4—594no—
510C2×C22⋊C4—594no—
511C2×C22⋊C4—594no—
512C2×C22⋊C4—594no—
513C2×C22⋊C4—594no—
514C2×C22⋊C4—594no—
515C2×C22⋊C4—594no—
516C2×C22⋊C4—594no—
517C2×C22⋊C4—1184no—
518C2×C22⋊C4—1184no—
519C2×C22⋊C4—1184no—
520C2×C22⋊C4—1184no—
521C2×C22⋊C4—1184no—
522C2×C22⋊C4—1184no—
523C2×C22⋊C4—2362no—
524C2×C42—42no—
525C2×C42—594no—
526C2×C42—594no—
527C2×C42—594no—
528C2×C42—594no—
529C2×C42—594no—
530C2×C42—594no—
531C2×C42—1184no—
532C2×C42—1184no—
533C2×C42—2362no—
534C2×C42—2362no—
535C2×C42—2362no—
536C2×C42—2362no—
537C2×C42C22×D5914yes—
538#95—594no—
539#95—594no—
540#95—594no—
541#95—594no—
542#95—594no—
543#95—594no—
544#95C22×D5914yes—
545#95C22×D5914yes—
546#95C22×D5914yes—
547#95C22×D5914yes—
548C24—594no—
549C24—594no—
550C24—592no—
551C24—592no—
552C24—1182no—
553C24—1182no—
554C24—1182no—
555C24—1182no—
556C24—1182no—
557C24—1182no—
558C24—1182no—
559C24—1182no—
560C24—1182no—
561C24—1182no—
562C24—1182no—
563C24—1182no—
564C24C23×D5911yescharacteristic
565C2×D4—5916no—
566C2×D4—2364no—
567C2×D4—2364no—
568C2×D4—23616no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—594no—
587C22×C4—594no—
588C22×C4—594no—
589C22×C4—594no—
590C22×C4—594no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—592no—
594C22×C4—592no—
595C22×C4—592no—
596C22×C4—5916no—
597C22×C4—592no—
598C22×C4—1188no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—1182no—
605C22×C4—1182no—
606C22×C4—1182no—
607C22×C4—1182no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—1182no—
611C22×C4—1182no—
612C22×C4—1188no—
613C22×C4—2364no—
614C22×C4—2364no—
615C22×C4—2364no—
616C22×C4—23616no—
617C22×C4—23616no—
618C22×C4C2×C4×D5914yes—
619C22×C4C2×C4×D5914yes—
620C22×C4C2×C4×D5914yes—
621C22×C4#1174568914yes—
622C22×C4C23×D5912yes—
623C22×C4C23×D5912yes—
624C22×C4C23×D5912yes—
625C22×C4C23×D5912yes—
626C22×C4C23×D5912yes—
627C22×C4C23×D5912yes—
628C22×C4C23×D5912yes—
629C4⋊C4—44no—
630C4⋊C4—5916no—
631C4⋊C4—1188no—
632C4⋊C4—1188no—
633C4⋊C4C2×C4×D59116yescomplemented
634C22⋊C4—5916no—
635C22⋊C4—5916no—
636C22⋊C4—5916no—
637C22⋊C4—1188no—
638C22⋊C4—1188no—
639C22⋊C4—1188no—
640C22⋊C4—1188no—
641C22⋊C4—1188no—
642C22⋊C4—1188no—
643C22⋊C4—2364no—
644C42—44no—
645C42—1188no—
646C42—1188no—
647C42—2364no—
648C42—2364no—
649C42—2364no—
650C42—2364no—
651C23—594no—
652C23—594no—
653C23—1182no—
654C23—1182no—
655C23—1182no—
656C23—1182no—
657C23—1182no—
658C23—1182no—
659C23—1182no—
660C23—1182no—
661C23—1182no—
662C23—1182no—
663C23—1182no—
664C23—1182no—
665C23—1188no—
666C23—1188no—
667C23—1188no—
668C23—1188no—
669C23—1188no—
670C23—1188no—
671C23—2364no—
672C23—2364no—
673C23—2364no—
674C23—2364no—
675C23—2364no—
676C23—2364no—
677C23—2364no—
678C23—2364no—
679C23C22×C4×D5912yes—
680C23#41×D5912yes—
681C23#41×D5912yes—
682C23#41×D5912yes—
683C23C2×#1174568912yes—
684C23#1427377212yes—
685C23#1427377312yes—
686C23C24×D5911yescharacteristic
687D4—23616no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—594no—
713C2×C4—594no—
714C2×C4—594no—
715C2×C4—594no—
716C2×C4—594no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1188no—
728C2×C4—1188no—
729C2×C4—1188no—
730C2×C4—1188no—
731C2×C4—1188no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—23616no—
736C2×C4—23616no—
737C2×C4—2364no—
738C2×C4C22×C4×D5914yes—
739C2×C4C22×C4×D5914yes—
740C2×C4C22×C4×D5914yes—
741C2×C4C2×#1174568914yes—
742C22—1184no—
743C22—1184no—
744C22—1184no—
745C22—1184no—
746C22—1184no—
747C22—1184no—
748C22—23616no—
749C22—23616no—
750C22—2362no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22—2362no—
755C22—2362no—
756C22—2362no—
757C22—2362no—
758C22#1683787014yes—
759C22C4×#1174568914yes—
760C22#1683787414yes—
761C22#1683807914yes—
762C22#1683810314yes—
763C22#1683810514yes—
764C22#1683813614yes—
765C22C23×C4×D5911yescharacteristic
766C22C2×#41×D5911yescharacteristic
767C22C2×#41×D5911yescharacteristic
768C22C2×#41×D5911yescharacteristic
769C22C22×#1174568911yescharacteristic
770C22C2×#1427377211yescharacteristic
771C22C2×#1427377311yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—1184no—
780C4—1184no—
781C4—1184no—
782C4—1184no—
783C4—1184no—
784C4—2362no—
785C2—2364no—
786C2—2364no—
787C2#2142722818yesdirect product factor
788C2C2×#1683787011yescharacteristic
789C2C2×C4×#1174568911yescharacteristic
790C2C2×#1683787411yescharacteristic
791C2C2×#1683807911yescharacteristic
792C2C2×#1683810311yescharacteristic
793C2C2×#1683810511yescharacteristic
794C2C2×#1683813611yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#387C2
socleC24×C59C24
prime radicalC23×D236C22
cosocleC23×C59C25
hypercenterC2×#387D59
hypocenterC59C2×#2374
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #21427228C2direct (N × H)
4. C2×#16837294C2semidirect
5. C2×#16837294C2semidirect
6. C2×#16837291C2semidirect
7. C2×#16837291C2semidirect
8. C2×#16837283C2semidirect
10. C2×C4⋊C4×Dic59C2semidirect
11. C2×#16837253C2semidirect
12. C2×C4×(C2×D59)⋊C4C2semidirect
13. C2×C4×(C2×D59)⋊C4C2semidirect
14. C2×#16837249C2semidirect
15. C2×#16837249C2semidirect
16. C2×C59×#387C2semidirect
20. C2×#14273712C4semidirect
42. #16837294C22semidirect
43. #16837294C22semidirect
44. #16837291C22semidirect
45. #16837291C22semidirect
46. #16837283C22semidirect
48. C4⋊C4×Dic59C22semidirect
49. #16837253C22semidirect
50. C4×(C2×D59)⋊C4C22semidirect
51. C4×(C2×D59)⋊C4C22semidirect
52. #16837249C22semidirect
53. #16837249C22semidirect
63. C59×#387C22semidirect
85. C22×C4×D59C2×C4semidirect
88. #14273712C2×C4semidirect
92. C2×Dic59⋊C4C2×C4semidirect
104. C2×(C2×D59)⋊C4C2×C4semidirect
141. C2×C4⋊C4×C59C2×C4semidirect
230. C2×C4×D59C22×C4semidirect
232. C4⋊C4×C59C22×C4semidirect
243. (C2×D59)⋊C4C22×C4semidirect
246. Dic59⋊C4C22×C4semidirect
396. C2×#387D59semidirect
404. C2×C59#2374semidirect
447. #387C2×D59semidirect
465. C59C2×#2374semidirect
501. C2×C4⋊C4C4×D59semidirect
633. C4⋊C4C2×C4×D59semidirect
787. C2#21427228direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737122
#214272282
C2×#168373032
C2×#168372942
C2×#168372912
C2×#168372832
C2×#168372802
C2×C4⋊C4×Dic592
C2×#168372532
C2×C4×(C2×D59)⋊C42
C2×#168372492
C2×C59×#3872
C2×#237459