Finite Group Databasebeta

← C2×#20286888 #28260716

Subgroups — C2×#20286888 #28260716

Order 13568.

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×#16811319C211yesmaximal, characteristic
2C2×D4×Dic106C211yesmaximal, characteristic, complemented
3#20286888C2116yesmaximal, direct product factor
4C2×#16810992C211yesmaximal, characteristic, complemented
5C2×#16810959C211yesmaximal, characteristic, complemented
6C2×#16810965C211yesmaximal, characteristic, complemented
7C2×#16810931C211yesmaximal, characteristic, complemented
8C2×#16810869C211yesmaximal, characteristic, complemented
9C2×#16810852C211yesmaximal, characteristic, complemented
10C2×#16810829C211yesmaximal, characteristic, complemented
11C2×#16810764C211yesmaximal, characteristic, complemented
12C2×#16810764C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810633C211yesmaximal, characteristic, complemented
15C22×#13133142C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22#16811319—24no—
23#16811319C2218yes—
24D4×Dic106—24no—
25D4×Dic106C2218yescomplemented
26C2×#13133217C2211yescharacteristic
27C2×#13133216—21no—
28C2×#13133212—21no—
29C2×#13133209C2211yescharacteristic
30C2×#13133199—21no—
31C2×#13133196C2211yescharacteristic
32C2×#13133196C2211yescharacteristic
33C2×#13133194—21no—
34C2×#13133194—21no—
35C2×#13133191C2211yescharacteristic
36C2×#13133191C2211yescharacteristic
37C2×#13133189—21no—
38C2×C4×Dic106C2211yescharacteristic
39C2×C4×D212C2211yescharacteristic
40C2×D4×Dic53—21no—
41C2×#13133177—21no—
42C2×#13133176C2211yescharacteristic
43C22×C4⋊Dic53C2211yescharacteristic
44#16810992C2218yescomplemented
45#16810965C2218yescomplemented
46#16810959C2218yescomplemented
47#16810931C2218yescomplemented
48#16810869C2218yescomplemented
49#16810852C2218yescomplemented
50#16810829C2218yescomplemented
51#16810764C2218yescomplemented
52#16810764C2218yescomplemented
53#16810725C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57#16810633C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133142C2211yescharacteristic
67C2×#13133142C2218yescomplemented
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#435C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—24no—
78C22×Dic106—24no—
79C22×Dic106—22no—
80C22×Dic106—22no—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×Dic106—42no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2314yes—
88C22×Dic106C2314yes—
89C22×Dic106C2311yescharacteristic
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C23×Dic53—21no—
94C23×Dic53—21no—
95C23×Dic53—21no—
96C22×C4×D53—21no—
97C2×#11719913—24no—
98C2×#11719913—42no—
99C2×#11719913—42no—
100C2×#11719913C2314yes—
101C2×#11719913C2314yes—
102C2×#11719913C2314yes—
103#13133217—22no—
104#13133217C2314yes—
105#13133216—28no—
106#13133212—28no—
107#13133209—22no—
108#13133209C2314yes—
109#13133199—28no—
110#13133196—22no—
111#13133196—22no—
112#13133196C2314yes—
113#13133196C2314yes—
114#13133194—28no—
115#13133194—28no—
116#13133191—22no—
117#13133191—22no—
118#13133191C2314yes—
119#13133191C2314yes—
120#13133189—28no—
121C4×Dic106—22no—
122C4×Dic106C2314yes—
123C4×D212—22no—
124C4×D212C2314yes—
125D4×Dic53—28no—
126#13133177—28no—
127#13133176—22no—
128#13133176C2314yes—
129C2×C4⋊Dic53—22no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53C2314yes—
134C2×C4⋊Dic53C2311yescharacteristic
135C2×C4⋊Dic53C2311yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×C22⋊Dic53—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151#13133151C2314yes—
152#13133151C2314yes—
153#13133149C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133142C2314yes—
159#13133142C2314yes—
160#13133142C2314yes—
161#13133142C2314yes—
162#13133142C2314yes—
163#13133139C2314yes—
164C22×D4×C53D411yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C2×M16×C53—42no—
168C2×M16×C53C2314yes—
169C22×C8×C53—42no—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2314yes—
175C4×D4×C53D414yes—
176C4×D4×C53C2314yes—
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C4⋊C8×C53C2314yes—
182C22⋊C8×C53C2314yes—
183C22⋊C8×C53C2314yes—
184#97×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C2×D4×C53—24no—
189C2×D4×C53C2×D414yes—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—44no—
206C2×C22⋊D53—82no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—24no—
216C22×Dic53—24no—
217C22×Dic53—44no—
218C22×Dic53—44no—
219C22×Dic53—82no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—21no—
223C2×D212C2412yes—
224C2×C4×D53—24no—
225C2×C4×D53—82no—
226C2×Dic106—21no—
227C2×Dic106—22no—
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—28no—
233C2×Dic106—28no—
234C2×Dic106—24no—
235C2×Dic106—24no—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—44no—
239C2×Dic106—44no—
240C2×Dic106—48no—
241C2×Dic106—48no—
242C2×Dic106—44no—
243C2×Dic106—44no—
244C2×Dic106#4114yes—
245C2×Dic106C2412yes—
246C2×Dic106C2412yes—
247C2×Dic106C2412yes—
248M16×C53—44no—
249C2×C8×C53—22no—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53—22no—
253C2×C8×C53—44no—
254C2×C8×C53C2412yes—
255C2×C8×C53C2412yes—
256C2×C8×C53C2412yes—
257C2×C8×C53C2412yes—
258C4⋊C4×C53C2×D414yes—
259C22⋊C4×C53C2×D414yes—
260C22⋊C4×C53C2×D414yes—
261C42×C53C2×D412yes—
262C42×C53C2412yes—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265C22⋊Dic53—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—24no—
272C4⋊Dic53—24no—
273C4⋊Dic53—24no—
274C4⋊Dic53—21no—
275C4⋊Dic53—21no—
276C4⋊Dic53C2412yes—
277C4⋊Dic53C2412yes—
278C4⋊Dic53C2412yes—
279C4⋊Dic53C2412yes—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283#11719919—24no—
284#11719919—24no—
285C4×Dic53—24no—
286C4×Dic53—24no—
287#11719913—28no—
288#11719913—44no—
289#11719913—44no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53#13714yes—
296C23×C53C22×D412yes—
297C23×C53C22×D412yes—
298C23×C53C22×D411yescharacteristic
299C22×D53—22no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303D4×C53—28no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—24no—
309C2×C4×C53—24no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53C2×#4112yes—
320C2×C4×C53H(5,𝔽2)12yes—
321C2×C4×C53C2511yescharacteristic
322C22⋊D53—48no—
323C22⋊D53—84no—
324C2×Dic53—24no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—48no—
333C2×Dic53—48no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—84no—
341D212—22no—
342D212—22no—
343D212—42no—
344C4×D53—84no—
345Dic106—24no—
346Dic106—22no—
347Dic106—22no—
348Dic106—22no—
349Dic106—22no—
350Dic106—22no—
351Dic106—48no—
352Dic106—48no—
353Dic106—42no—
354Dic106—42no—
355Dic106C2×#4114yes—
356C8×C53—22no—
357C8×C53—22no—
358C8×C53—22no—
359C8×C53—22no—
360C2×#3320—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—28no—
363C22×C53—22no—
364C22×C53—22no—
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—44no—
368C22×C53#54612yes—
369C22×C53C2×#13714yes—
370C22×C53C2×#13712yes—
371C22×C53#57712yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—84no—
377C4×C53—22no—
378C4×C53—22no—
379C4×C53—22no—
380C4×C53—22no—
381C4×C53#54612yes—
382C4×C53C22×#4111yescharacteristic
383C4×C53C2×H(5,𝔽2)11yescharacteristic
384Dic53—24no—
385Dic53—42no—
386Dic53—42no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391C2×#553—531no—
392C2×D4×Q8—531no—
393#3320—5316no—
394C2×#491—531no—
395C2×#484—531no—
396C2×#485—531no—
397C2×#479—531no—
398C2×#468—531no—
399C2×#465—531no—
400C2×#461—531no—
401C2×#448—531no—
402C2×#448—531no—
403C2×#440—531no—
404C2×#435D5311yescharacteristic, complemented
405C2×#419—531no—
406C22×#103—531no—
407C2×C53—24no—
408C2×C53—42no—
409C2×C53#332014yescomplemented
410C2×C53C2×#54611yescharacteristic
411C2×C53C22×#13711yescharacteristic
412C2×C53C2×#57711yescharacteristic
413D53—82no—
414C23×Q8—531no—
415C23×Q8—531no—
416C22×SD16—531no—
417C22×SD16—531no—
418C22×SD16—531no—
419C22×M16C2×D5311yescharacteristic
420C23×C8C2×D5311yescharacteristic
421#553—538no—
422#553—1064no—
423D4×Q8—538no—
424D4×Q8—1064no—
425C2×C4⋊Q8—531no—
426C2×C4⋊Q8—1061no—
427C2×#126—1061no—
428C2×#125—531no—
429C2×#123—1061no—
430C2×C22⋊Q8—531no—
431C2×C22⋊Q8—531no—
432C2×C22⋊Q8—1061no—
433C2×C22⋊Q8—1061no—
434C2×#121—531no—
435C2×#121—531no—
436C2×#121—1061no—
437C2×C4×Q8—531no—
438C2×C4×D4—531no—
439C2×C4×D4—1061no—
440C2×C4×D4—1061no—
441C2×C4×D4C2×D5311yescharacteristic
442C2×#117—531no—
443C22×C4⋊C4—531no—
444#491—538no—
445#485—538no—
446#484—538no—
447#479—538no—
448#468—538no—
449#465—538no—
450#461—538no—
451#448—538no—
452#448—538no—
453#440—538no—
454#435C2×D5318yescomplemented
455C2×#107—531no—
456C2×#107—531no—
457C2×#106—531no—
458C2×C4⋊C8C2×D5311yescharacteristic
459#419—538no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103—531no—
469C2×#103—538no—
470C2×#102—531no—
471C2×C22⋊C8C2×D5311yescharacteristic
472C2×C22⋊C8C2×D5311yescharacteristic
473C2×#97C2×D5311yescharacteristic
474C53C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—531no—
476C22×Q8—531no—
477C22×Q8—531no—
478C22×Q8—534no—
479C22×Q8—534no—
480C22×Q8—1064no—
481C22×Q8—1064no—
482C22×Q8—1061no—
483C22×Q8—1061no—
484C22×Q8—1062no—
485C22×Q8—1062no—
486C22×Q8—2122no—
487C22×Q8—2122no—
488C22×D4—531no—
489C22×D4—1061no—
490C22×D4—1061no—
491C22×D4D21211yescharacteristic
492C23×C4—1061no—
493C23×C4—1061no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4C22×D5311yescharacteristic
497C23×C4C22×D5311yescharacteristic
498C2×SD16—534no—
499C2×SD16—534no—
500C2×SD16—534no—
501C2×SD16—1064no—
502C2×SD16—2122no—
503C2×SD16—2122no—
504C2×M16—42no—
505C2×M16C22×D5314yes—
506C22×C8—42no—
507C22×C8C22×D5311yescharacteristic
508C22×C8C22×D5311yescharacteristic
509C22×C8C22×D5311yescharacteristic
510C22×C8C22×D5311yescharacteristic
511C22×C8C22×D5314yes—
512C4⋊Q8—534no—
513C4⋊Q8—1068no—
514C4⋊Q8—1062no—
515#126—1068no—
516#125—534no—
517#125—1062no—
518#123—1068no—
519C22⋊Q8—534no—
520C22⋊Q8—534no—
521C22⋊Q8—1062no—
522C22⋊Q8—1062no—
523C22⋊Q8—1068no—
524C22⋊Q8—1068no—
525#121—534no—
526#121—534no—
527#121—1068no—
528#121—1062no—
529#121—1062no—
530C4×Q8—534no—
531C4×Q8—1062no—
532C4×D4—534no—
533C4×D4—1068no—
534C4×D4—1068no—
535C4×D4—1062no—
536C4×D4D21214yes—
537C4×D4C22×D5314yes—
538#117—534no—
539#117—1062no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—534no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1062no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4—1061no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4D21211yescharacteristic
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4D21211yescharacteristic
562C2×C22⋊C4D21211yescharacteristic
563C2×C42—1061no—
564C2×C42—1061no—
565C2×C42C22×D5311yescharacteristic
566#107—534no—
567#107—534no—
568#106—534no—
569C4⋊C8C22×D5314yes—
570#103—534no—
571#103—534no—
572#103—534no—
573#103—534no—
574#103—534no—
575#103—534no—
576#103—534no—
577#103—534no—
578#103—534no—
579#102—534no—
580C22⋊C8C22×D5314yes—
581C22⋊C8C22×D5314yes—
582#97C22×D5314yes—
583C24—1061no—
584C24C2×D21211yescharacteristic
585C24C2×D21211yescharacteristic
586C2×Q8—534no—
587C2×Q8—532no—
588C2×Q8—532no—
589C2×Q8—532no—
590C2×Q8—1068no—
591C2×Q8—1068no—
592C2×Q8—1061no—
593C2×Q8—1064no—
594C2×Q8—1064no—
595C2×Q8—1061no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8—1062no—
600C2×Q8—1062no—
601C2×Q8—1062no—
602C2×Q8—2124no—
603C2×Q8—2124no—
604C2×Q8—2124no—
605C2×Q8—2124no—
606C2×Q8—2128no—
607C2×Q8—2128no—
608C2×D4—24no—
609C2×D4—532no—
610C2×D4—1064no—
611C2×D4—1064no—
612C2×D4—1061no—
613C2×D4—1062no—
614C2×D4—1062no—
615C2×D4—4242no—
616C2×D4—2124no—
617C2×D4C2×D21214yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—1061no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1064no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—1064no—
633C22×C4—4242no—
634C22×C4—4242no—
635C22×C4—2124no—
636C22×C4—2124no—
637C22×C4C2×D21212yes—
638C22×C4C2×D21212yes—
639C22×C4C2×D21211yescharacteristic
640C22×C4C2×D21211yescharacteristic
641C22×C4C2×D21211yescharacteristic
642C22×C4C2×D21211yescharacteristic
643C22×C4C23×D5312yes—
644C22×C4C23×D5312yes—
645C22×C4C23×D5311yescharacteristic
646SD16—1068no—
647SD16—2124no—
648SD16—2124no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—44no—
655C2×C8C23×D5312yes—
656C2×C8C23×D5312yes—
657C2×C8C23×D5312yes—
658C2×C8C23×D5312yes—
659C4⋊C4—532no—
660C4⋊C4—532no—
661C4⋊C4—532no—
662C4⋊C4—532no—
663C4⋊C4—1061no—
664C4⋊C4—1061no—
665C4⋊C4—1064no—
666C4⋊C4—1061no—
667C4⋊C4—1061no—
668C4⋊C4—1064no—
669C4⋊C4—1064no—
670C4⋊C4—1064no—
671C4⋊C4—1064no—
672C4⋊C4—1064no—
673C4⋊C4—1064no—
674C4⋊C4—1064no—
675C4⋊C4C2×D21214yes—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4C2×D21214yes—
683C22⋊C4C2×D21214yes—
684C42—1064no—
685C42—1064no—
686C42C2×D21212yes—
687C42C23×D5312yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—1062no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23#1313325014yes—
698C23C22×D21212yes—
699C23C22×D21212yes—
700C23C22×D21211yescharacteristic
701Q8—534no—
702Q8—1064no—
703Q8—1062no—
704Q8—1062no—
705Q8—1062no—
706Q8—1062no—
707Q8—1062no—
708Q8—2128no—
709Q8—2128no—
710Q8—2122no—
711Q8—2122no—
712D4—28no—
713D4—1062no—
714D4—1062no—
715D4—4244no—
716D4—2128no—
717D4—2122no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—1064no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—4244no—
737C2×C4—4244no—
738C2×C4—2128no—
739C2×C4—2128no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4C22×D21212yes—
747C2×C4C22×D21212yes—
748C2×C4C22×D21212yes—
749C2×C4C22×D21212yes—
750C2×C4C22×D21211yescharacteristic
751C2×C4#41×D5312yes—
752C2×C4#1313326212yes—
753C2×C4C24×D5311yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—4244no—
766C22—2122no—
767C22—2122no—
768C22—2122no—
769C22#1681126812yes—
770C22C2×#1313325014yes—
771C22C2×#1313325012yes—
772C22#1681143512yes—
773C22C23×D21211yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—1064no—
779C4—2122no—
780C4—2122no—
781C4—2122no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C4#1681126812yes—
786C4C2×#41×D5311yescharacteristic
787C4C2×#1313326211yescharacteristic
788C2—24no—
789C2—42no—
790C2—4242no—
791C2#2028688814yesdirect product factor
792C2C2×#1681126811yescharacteristic
793C2C22×#1313325011yescharacteristic
794C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811319C2
hypercenterC2×#435D53
hypocenterC53C2×#3320
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic106C2semidirect
3. #20286888C2direct (N × H)
4. C2×#16810992C2semidirect
5. C2×#16810959C2semidirect
6. C2×#16810965C2semidirect
7. C2×#16810931C2semidirect
8. C2×#16810869C2semidirect
9. C2×#16810852C2semidirect
10. C2×#16810829C2semidirect
11. C2×#16810764C2semidirect
12. C2×#16810764C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810633C2semidirect
15. C22×#13133142C2semidirect
16. C2×C53×#435C2semidirect
25. D4×Dic106C22semidirect
44. #16810992C22semidirect
45. #16810965C22semidirect
46. #16810959C22semidirect
47. #16810931C22semidirect
48. #16810869C22semidirect
49. #16810852C22semidirect
50. #16810829C22semidirect
51. #16810764C22semidirect
52. #16810764C22semidirect
53. #16810725C22semidirect
57. #16810633C22semidirect
67. C2×#13133142C22semidirect
72. C53×#435C22semidirect
404. C2×#435D53semidirect
409. C2×C53#3320semidirect
454. #435C2×D53semidirect
474. C53C2×#3320semidirect
791. C2#20286888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113192
C2×D4×Dic1062
#202868882
C2×#168109922
C2×#168109592
C2×#168109652
C2×#168109312
C2×#168108692
C2×#168108522
C2×#168108292
C2×#168107642
C2×#168107252
C2×#168106332
C22×#131331422
C2×C53×#4352
C2×#332053