Finite Group Databasebeta

← C2×#20283705 #28248561

Subgroups — C2×#20283705 #28248561

Order 13568.

2026 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811151C211yesmaximal, characteristic
2#20283705C2116yesmaximal, direct product factor
3C2×#16810753C211yesmaximal, characteristic, complemented
4C2×#16810751C211yesmaximal, characteristic, complemented
5C2×#16810696C211yesmaximal, characteristic, complemented
6C2×#16810694C211yesmaximal, characteristic, complemented
7C2×#16810692C211yesmaximal, characteristic, complemented
8C2×#16810692C211yesmaximal, characteristic, complemented
9C2×C8×D212C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
11C2×#16810684C211yesmaximal, characteristic, complemented
12C2×#16810682C211yesmaximal, characteristic, complemented
13C2×#16810674C211yesmaximal, characteristic, complemented
14C2×#16810580C211yesmaximal, characteristic, complemented
15C2×#97×D53C211yesmaximal, characteristic, complemented
16C2×C53×#405C211yesmaximal, characteristic, complemented
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811151C418yes—
22#16811151C2218yes—
23C2×#13133212C411yescharacteristic
24C2×#13133210C411yescharacteristic
25C2×#13133207C411yescharacteristic
26C2×#13133203C411yescharacteristic
27C2×#13133202C411yescharacteristic
28C2×#13133199C411yescharacteristic
29C2×#13133195C411yescharacteristic
30C2×#13133190C411yescharacteristic
31C2×C4×Dic106C2211yescharacteristic
32C2×C4×D212C2211yescharacteristic
33C2×C4×C22⋊D53C2211yescharacteristic
34C2×C4×C22⋊D53C2211yescharacteristic
35C2×#13133174C2211yescharacteristic
36C2×C42×D53C2211yescharacteristic
37#16810753C2218yescomplemented
38#16810751C2218yescomplemented
39#16810696C2218yescomplemented
40#16810694C2218yescomplemented
41#16810692C2218yescomplemented
42#16810692C2218yescomplemented
43C8×D212C2218yescomplemented
44C8×C22⋊D53C2218yescomplemented
45#16810684C2218yescomplemented
46#16810682C2218yescomplemented
47#16810674C2218yescomplemented
48C2×C4⋊#88322C2211yescharacteristic
49C2×C4⋊#88322C2211yescharacteristic
50C2×#13133146C2211yescharacteristic
51C2×#13133146C2211yescharacteristic
52C2×#13133146C2211yescharacteristic
53C2×#13133146C2211yescharacteristic
54C2×C22⋊#88322C2211yescharacteristic
55C2×C22⋊#88322C2211yescharacteristic
56C2×#13133129C2211yescharacteristic
57C2×#13133129C2211yescharacteristic
58C2×#13133129C2211yescharacteristic
59C2×#13133129C2211yescharacteristic
60#16810580C2218yescomplemented
61C2×#13133128C2211yescharacteristic
62C2×#13133127C2211yescharacteristic
63C2×#13133127C2211yescharacteristic
64C2×#13133127C2211yescharacteristic
65#97×D53C2218yescomplemented
66C2×C4×#88322C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C22×M16×C53C2211yescharacteristic
69C23×C8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#405C2218yescomplemented
72C2×#97×C53C2211yescharacteristic
73C2×#97×C53C2211yescharacteristic
74C2×C4×C8×C53C2211yescharacteristic
75C2×C4×C8×C53C2211yescharacteristic
76C22×Dic106C2×C411yescharacteristic
77C22×D212C2×C411yescharacteristic
78C22×C22⋊D53C2×C411yescharacteristic
79C22×C22⋊D53C2×C411yescharacteristic
80C22×C4×D53C2×C411yescharacteristic
81C22×C4×D53C2×C411yescharacteristic
82C22×C4×D53C2311yescharacteristic
83C22×C4×D53C2311yescharacteristic
84C2×#11719912—24no—
85C2×#11719912C2314yes—
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C2×C8×D53—24no—
91C2×C8×D53—24no—
92C2×C8×D53—24no—
93C2×C8×D53C2314yes—
94C2×C8×D53C2314yes—
95C2×C8×D53C2314yes—
96#13133212C2×C418yes—
97#13133210C2×C418yes—
98#13133207C2×C418yes—
99#13133203C2×C418yes—
100#13133202C2×C418yes—
101#13133199C2×C418yes—
102#13133195C2×C418yes—
103#13133190C2×C418yes—
104C4×Dic106C2×C414yes—
105C4×Dic106C2314yes—
106C4×D212C2×C414yes—
107C4×D212C2314yes—
108C4×C22⋊D53C2×C414yes—
109C4×C22⋊D53C2×C414yes—
110C4×C22⋊D53C2314yes—
111C4×C22⋊D53C2314yes—
112#13133174C2×C414yes—
113#13133174C2314yes—
114C2×C4⋊Dic53C2×C411yescharacteristic
115C2×C4⋊Dic53C2×C411yescharacteristic
116C2×#11719919C2×C411yescharacteristic
117C2×#11719919C2×C411yescharacteristic
118C2×#11719919C2×C411yescharacteristic
119C2×#11719919C2×C411yescharacteristic
120C2×#11719919C2×C411yescharacteristic
121C2×#11719919C2×C411yescharacteristic
122C2×C22⋊Dic53C2×C411yescharacteristic
123C2×C22⋊Dic53C2×C411yescharacteristic
124C2×#11719921C2×C411yescharacteristic
125C2×#11719921C2×C411yescharacteristic
126C2×#11719921C2×C411yescharacteristic
127C2×#11719921C2×C411yescharacteristic
128C2×#11719921C2×C411yescharacteristic
129C2×#11719921C2×C411yescharacteristic
130C2×C4×Dic53C2×C411yescharacteristic
131C2×C4×Dic53C2×C411yescharacteristic
132C2×C4×Dic53C2311yescharacteristic
133C2×C4×Dic53C2311yescharacteristic
134C42×D53C2×C414yes—
135C42×D53C2314yes—
136C4⋊#88322C2314yes—
137C4⋊#88322C2314yes—
138#13133146C2314yes—
139#13133146C2314yes—
140#13133146C2314yes—
141#13133146C2314yes—
142C22⋊#88322C2314yes—
143C22⋊#88322C2314yes—
144#13133129C2314yes—
145#13133129C2314yes—
146#13133129C2314yes—
147#13133129C2314yes—
148#13133128C2314yes—
149#13133127C2314yes—
150#13133127C2314yes—
151#13133127C2314yes—
152C4×#88322C2314yes—
153C8×Dic53C2314yes—
154C23×C4×C53C2311yescharacteristic
155C2×M16×C53—24no—
156C2×M16×C53C2314yes—
157C22×C8×C53—24no—
158C22×C8×C53C2311yescharacteristic
159C22×C8×C53C2314yes—
160C22×C8×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163#117×C53C2×C414yes—
164#117×C53C2314yes—
165C2×C4⋊C4×C53C2×C411yescharacteristic
166C2×C4⋊C4×C53C2×C411yescharacteristic
167C2×C22⋊C4×C53C2×C411yescharacteristic
168C2×C22⋊C4×C53C2×C411yescharacteristic
169C2×C42×C53C2311yescharacteristic
170C2×C42×C53C2311yescharacteristic
171#97×C53C2314yes—
172#97×C53C2314yes—
173C4×C8×C53C2314yes—
174C4×C8×C53C2314yes—
175C24×C53C22×C411yescharacteristic
176C23×D53C22×C411yescharacteristic
177C23×D53C22×C411yescharacteristic
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53C22×C411yescharacteristic
181C22×C4×C53C22×C411yescharacteristic
182C22×C4×C53C22×C411yescharacteristic
183C22×C4×C53C22×C411yescharacteristic
184C22×C4×C53C22×C411yescharacteristic
185C22×C4×C53C22×C412yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2411yescharacteristic
188C2×C22⋊D53—24no—
189C2×C22⋊D53—42no—
190C2×C22⋊D53C22×C414yes—
191C2×C22⋊D53C22×C414yes—
192C22×Dic53C22×C411yescharacteristic
193C22×Dic53C22×C411yescharacteristic
194C22×Dic53C22×C411yescharacteristic
195C22×Dic53C22×C411yescharacteristic
196C22×Dic53C22×C411yescharacteristic
197C22×Dic53C22×C411yescharacteristic
198C2×D212—24no—
199C2×D212C22×C414yes—
200C2×C4×D53—24no—
201C2×C4×D53—22no—
202C2×C4×D53—22no—
203C2×C4×D53—22no—
204C2×C4×D53—22no—
205C2×C4×D53—42no—
206C2×C4×D53C22×C412yes—
207C2×C4×D53C22×C414yes—
208C2×C4×D53C22×C412yes—
209C2×C4×D53C22×C414yes—
210C2×C4×D53C2412yes—
211C2×C4×D53C2412yes—
212C2×Dic106—42no—
213C2×Dic106C22×C414yes—
214M16×C53—28no—
215C2×C8×C53—22no—
216C2×C8×C53—22no—
217C2×C8×C53—28no—
218C2×C8×C53#4114yes—
219C2×C8×C53#4114yes—
220C2×C8×C53C2412yes—
221C2×C8×C53C2412yes—
222C2×C8×C53C2412yes—
223C2×C8×C53C2412yes—
224C4⋊C4×C53C22×C414yes—
225C4⋊C4×C53C22×C414yes—
226C22⋊C4×C53C22×C414yes—
227C22⋊C4×C53C22×C414yes—
228C42×C53C22×C412yes—
229C42×C53C22×C412yes—
230C42×C53C2412yes—
231C42×C53C2412yes—
232C22⋊Dic53C22×C414yes—
233C22⋊Dic53C22×C414yes—
234#11719921C22×C414yes—
235#11719921C22×C414yes—
236#11719921C22×C414yes—
237#11719921C22×C414yes—
238#11719921C22×C414yes—
239#11719921C22×C414yes—
240C4⋊Dic53C22×C414yes—
241C4⋊Dic53C22×C414yes—
242#11719919C22×C414yes—
243#11719919C22×C414yes—
244#11719919C22×C414yes—
245#11719919C22×C414yes—
246#11719919C22×C414yes—
247#11719919C22×C414yes—
248C4×Dic53C22×C412yes—
249C4×Dic53C22×C414yes—
250C4×Dic53C22×C414yes—
251C4×Dic53C22×C412yes—
252C4×Dic53C2412yes—
253C4×Dic53C2412yes—
254C2×#88322—22no—
255C2×#88322—22no—
256C2×#88322—22no—
257C2×#88322—22no—
258C2×#88322C2412yes—
259C2×#88322C2412yes—
260C2×#88322C2412yes—
261C2×#88322C2412yes—
262#11719912—28no—
263C8×D53—28no—
264C8×D53—28no—
265C8×D53—28no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53C23×C412yes—
270C23×C53C23×C411yescharacteristic
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53#13114yes—
277C22×D53C23×C412yes—
278C22×D53C23×C412yes—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—24no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53C23×C412yes—
288C2×C4×C53C23×C412yes—
289C2×C4×C53C23×C412yes—
290C2×C4×C53C23×C412yes—
291C2×C4×C53C23×C412yes—
292C2×C4×C53C23×C411yescharacteristic
293C2×C4×C53C2×#4112yes—
294C2×C4×C53C2×#4112yes—
295C2×C4×C53C2511yescharacteristic
296C22⋊D53—28no—
297C22⋊D53—44no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53C23×C412yes—
305C2×Dic53C23×C412yes—
306C2×Dic53C23×C412yes—
307C2×Dic53C23×C412yes—
308C2×Dic53C23×C412yes—
309C2×Dic53C23×C412yes—
310D212—28no—
311C4×D53—28no—
312C4×D53—24no—
313C4×D53—24no—
314C4×D53—22no—
315C4×D53—22no—
316C4×D53—22no—
317C4×D53—22no—
318C4×D53—44no—
319Dic106—44no—
320C8×C53—22no—
321C8×C53—22no—
322C8×C53C2×#4114yes—
323C8×C53C2×#4114yes—
324#88322—22no—
325#88322—22no—
326#88322—22no—
327#88322—22no—
328C2×#2968—531nomaximal, Sylow
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—44no—
333C22×C53C4×#4112yes—
334C22×C53C2×#13112yes—
335C22×C53#56812yes—
336C22×C53C24×C411yescharacteristic
337C2×D53—22no—
338C2×D53—28no—
339C2×D53—22no—
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—44no—
344C2×D53C2×#13114yes—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—22no—
350C4×C53C4×#4112yes—
351C4×C53C22×#4111yescharacteristic
352C4×C53C22×#4111yescharacteristic
353Dic53—22no—
354Dic53—22no—
355Dic53—22no—
356Dic53—22no—
357Dic53—22no—
358Dic53—22no—
359C2×#529—531no—
360#2968—5316no—
361C2×#446—531no—
362C2×#446—531no—
363C2×#435—531no—
364C2×#435—531no—
365C2×#435—531no—
366C2×#435—531no—
367C2×C8×D4—531no—
368C2×C8×D4—531no—
369C2×#433—531no—
370C2×#433—531no—
371C2×#431—531no—
372C2×#405—531no—
373C2×#405D5311yescharacteristic, complemented
374C22×#97—531no—
375C2×C53—42no—
376C2×C53#296814yescomplemented
377C2×C53C2×C4×#4111yescharacteristic
378C2×C53C22×#13111yescharacteristic
379C2×C53C2×#56811yescharacteristic
380D53—24no—
381D53—42no—
382C22×M16—531no—
383C22×M16C2×D5311yescharacteristic
384C23×C8—531no—
385C23×C8—531no—
386C23×C8—531no—
387C23×C8C2×D5311yescharacteristic
388#529—538no—
389#529—538no—
390C2×#126—531no—
391C2×#126—531no—
392C2×#125—531no—
393C2×#124—531no—
394C2×#123—531no—
395C2×#123—531no—
396C2×C22⋊Q8—531no—
397C2×#121—531no—
398C2×C4×Q8—531no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×C4×D4—531no—
402C2×#117—531no—
403C2×#117C2×D5311yescharacteristic
404C22×C42—531no—
405#446—538no—
406#446—538no—
407#435—538no—
408#435—538no—
409#435—538no—
410#435—538no—
411C8×D4—538no—
412C8×D4—538no—
413#433—538no—
414#433—538no—
415#431—538no—
416C2×C4⋊C8—531no—
417C2×C4⋊C8—531no—
418C2×C4⋊C8—531no—
419C2×C4⋊C8—531no—
420C2×C4⋊C8—531no—
421C2×C4⋊C8—531no—
422C2×C22⋊C8—531no—
423C2×C22⋊C8—531no—
424C2×C22⋊C8—531no—
425C2×C22⋊C8—531no—
426C2×C22⋊C8—531no—
427C2×C22⋊C8—531no—
428#405—538no—
429#405C2×D5318yescomplemented
430C2×#97—531no—
431C2×#97—531no—
432C2×#97—531no—
433C2×#97—531no—
434C2×#97—538no—
435C2×#97C2×D5311yescharacteristic
436C2×#97C2×D5311yescharacteristic
437C2×C4×C8—531no—
438C2×C4×C8—531no—
439C2×C4×C8C2×D5311yescharacteristic
440C2×C4×C8C2×D5311yescharacteristic
441C53C2×#296811yescharacteristic, complemented, Sylow
442C22×Q8—531no—
443C22×D4—531no—
444C22×D4—531no—
445C22×D4—531no—
446C23×C4—531no—
447C23×C4—531no—
448C23×C4—531no—
449C23×C4—531no—
450C23×C4C22×D5311yescharacteristic
451C2×M16—24no—
452C2×M16—534no—
453C2×M16—1064no—
454C2×M16C22×D5314yes—
455C22×C8—24no—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—534no—
461C22×C8—534no—
462C22×C8—534no—
463C22×C8—1064no—
464C22×C8—1064no—
465C22×C8—1064no—
466C22×C8C22×D5314yes—
467C22×C8C22×D5311yescharacteristic
468C22×C8C22×D5311yescharacteristic
469C22×C8C22×D5311yescharacteristic
470C22×C8C22×D5311yescharacteristic
471#126—538no—
472#126—538no—
473#125—538no—
474#124—538no—
475#123—538no—
476#123—538no—
477C22⋊Q8—538no—
478#121—538no—
479C4×Q8—534no—
480C4×Q8—534no—
481C4×D4—534no—
482C4×D4—534no—
483C4×D4—534no—
484C4×D4—534no—
485C4×D4—534no—
486C4×D4—534no—
487#117—534no—
488#117—534no—
489#117C4×D5314yes—
490#117C22×D5314yes—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4C4×D5311yescharacteristic
500C2×C4⋊C4C4×D5311yescharacteristic
501C2×C22⋊C4—531no—
502C2×C22⋊C4—531no—
503C2×C22⋊C4—531no—
504C2×C22⋊C4—531no—
505C2×C22⋊C4—531no—
506C2×C22⋊C4—531no—
507C2×C22⋊C4—531no—
508C2×C22⋊C4—531no—
509C2×C22⋊C4C4×D5311yescharacteristic
510C2×C22⋊C4C4×D5311yescharacteristic
511C2×C42—531no—
512C2×C42—531no—
513C2×C42—531no—
514C2×C42—531no—
515C2×C42—534no—
516C2×C42—534no—
517C2×C42C22×D5311yescharacteristic
518C2×C42C22×D5311yescharacteristic
519C4⋊C8—534no—
520C4⋊C8—534no—
521C4⋊C8—534no—
522C4⋊C8—534no—
523C4⋊C8—534no—
524C4⋊C8—534no—
525C22⋊C8—534no—
526C22⋊C8—534no—
527C22⋊C8—534no—
528C22⋊C8—534no—
529C22⋊C8—534no—
530C22⋊C8—534no—
531#97—534no—
532#97—534no—
533#97—534no—
534#97—534no—
535#97C22×D5314yes—
536#97C22×D5314yes—
537C4×C8—534no—
538C4×C8—534no—
539C4×C8C22×D5314yes—
540C4×C8C22×D5314yes—
541C24—531no—
542C24—531no—
543C24C2×C4×D5311yescharacteristic
544C2×Q8—534no—
545C2×Q8—2122no—
546C2×D4—534no—
547C2×D4—534no—
548C2×D4—534no—
549C2×D4—1064no—
550C2×D4—1064no—
551C2×D4—2122no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—531no—
555C22×C4—531no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—531no—
559C22×C4—531no—
560C22×C4—532no—
561C22×C4—534no—
562C22×C4—532no—
563C22×C4—532no—
564C22×C4—532no—
565C22×C4—534no—
566C22×C4—1064no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—2122no—
572C22×C4C2×C4×D5311yescharacteristic
573C22×C4C2×C4×D5311yescharacteristic
574C22×C4C2×C4×D5311yescharacteristic
575C22×C4C2×C4×D5311yescharacteristic
576C22×C4C2×C4×D5311yescharacteristic
577C22×C4C2×C4×D5312yes—
578C22×C4C23×D5312yes—
579C22×C4C23×D5311yescharacteristic
580M16—28no—
581M16—1068no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—28no—
585C2×C8—532no—
586C2×C8—532no—
587C2×C8—532no—
588C2×C8—532no—
589C2×C8—1062no—
590C2×C8—1062no—
591C2×C8—1062no—
592C2×C8—1062no—
593C2×C8—1068no—
594C2×C8—1068no—
595C2×C8—1068no—
596C2×C8#1171994514yes—
597C2×C8#1171994514yes—
598C2×C8C23×D5312yes—
599C2×C8C23×D5312yes—
600C2×C8C23×D5312yes—
601C2×C8C23×D5312yes—
602C4⋊C4—534no—
603C4⋊C4—534no—
604C4⋊C4—534no—
605C4⋊C4—534no—
606C4⋊C4—534no—
607C4⋊C4—534no—
608C4⋊C4—534no—
609C4⋊C4—534no—
610C4⋊C4C2×C4×D5314yes—
611C4⋊C4C2×C4×D5314yes—
612C22⋊C4—534no—
613C22⋊C4—534no—
614C22⋊C4—534no—
615C22⋊C4—534no—
616C22⋊C4—534no—
617C22⋊C4—534no—
618C22⋊C4—534no—
619C22⋊C4—534no—
620C22⋊C4C2×C4×D5314yes—
621C22⋊C4C2×C4×D5314yes—
622C42—532no—
623C42—534no—
624C42—534no—
625C42—532no—
626C42—532no—
627C42—532no—
628C42C2×C4×D5312yes—
629C42C2×C4×D5312yes—
630C42C23×D5312yes—
631C42C23×D5312yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—534no—
636C23—532no—
637C23—532no—
638C23—1062no—
639C23—1062no—
640C23—1062no—
641C23—1062no—
642C23—1062no—
643C23C22×C4×D5312yes—
644C23C22×C4×D5311yescharacteristic
645Q8—2124no—
646D4—1068no—
647D4—1068no—
648D4—2124no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—532no—
658C2×C4—532no—
659C2×C4—532no—
660C2×C4—532no—
661C2×C4—532no—
662C2×C4—532no—
663C2×C4—1068no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1064no—
671C2×C4—1064no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—2124no—
677C2×C4C22×C4×D5312yes—
678C2×C4C22×C4×D5312yes—
679C2×C4C22×C4×D5312yes—
680C2×C4C22×C4×D5312yes—
681C2×C4C22×C4×D5312yes—
682C2×C4C22×C4×D5311yescharacteristic
683C2×C4C2×#1171994512yes—
684C2×C4C2×#1171994512yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1062no—
689C8—1062no—
690C8—1062no—
691C8—1062no—
692C8C2×#1171994514yes—
693C8C2×#1171994514yes—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—534no—
699C22—1068no—
700C22—1062no—
701C22—1062no—
702C22—1062no—
703C22—1062no—
704C22—1062no—
705C22—2124no—
706C22C4×#1171994512yes—
707C22#131×D5312yes—
708C22#1681138812yes—
709C22C23×C4×D5311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—1062no—
716C4—1062no—
717C4—1062no—
718C4—1062no—
719C4—1062no—
720C4—1062no—
721C4C4×#1171994512yes—
722C4C22×#1171994511yescharacteristic
723C4C22×#1171994511yescharacteristic
724C2—42no—
725C2—1064no—
726C2—2122no—
727C2#2028370514yesdirect product factor
728C2C2×C4×#1171994511yescharacteristic
729C2C2×#131×D5311yescharacteristic
730C2C2×#1681138811yescharacteristic
subgroupG/H
centerC22×C4C23×D53
commutatorC22×C53C24×C4
FrattiniC2×C4C24×D53
FittingC2×C53×#405C2
socleC23×C53C23×C4
prime radicalC2×#13133190C4
cosocleC2×C4×C53C25
hypercenterC2×#405D53
hypocenterC53C2×#2968
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #20283705C2direct (N × H)
3. C2×#16810753C2semidirect
4. C2×#16810751C2semidirect
5. C2×#16810696C2semidirect
6. C2×#16810694C2semidirect
7. C2×#16810692C2semidirect
8. C2×#16810692C2semidirect
9. C2×C8×D212C2semidirect
10. C2×C8×C22⋊D53C2semidirect
11. C2×#16810684C2semidirect
12. C2×#16810682C2semidirect
13. C2×#16810674C2semidirect
14. C2×#16810580C2semidirect
15. C2×#97×D53C2semidirect
16. C2×C53×#405C2semidirect
37. #16810753C22semidirect
38. #16810751C22semidirect
39. #16810696C22semidirect
40. #16810694C22semidirect
41. #16810692C22semidirect
42. #16810692C22semidirect
43. C8×D212C22semidirect
44. C8×C22⋊D53C22semidirect
45. #16810684C22semidirect
46. #16810682C22semidirect
47. #16810674C22semidirect
60. #16810580C22semidirect
65. #97×D53C22semidirect
71. C53×#405C22semidirect
373. C2×#405D53semidirect
376. C2×C53#2968semidirect
429. #405C2×D53semidirect
441. C53C2×#2968semidirect
727. C2#20283705direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111512
#202837052
C2×#168107532
C2×#168107512
C2×#168106962
C2×#168106942
C2×#168106922
C2×C8×D2122
C2×C8×C22⋊D532
C2×#168106842
C2×#168106822
C2×#168106742
C2×#168105802
C2×#97×D532
C2×C53×#4052
C2×#296853