Finite Group Databasebeta

← C2×#23774595 #35160409

Subgroups — C2×#23774595 #35160409

Order 20224.

2038 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099116C211yesmaximal, characteristic, complemented
2C2×#19099108C211yesmaximal, characteristic
3#23774595C2116yesmaximal, direct product factor
4C2×#19098971C211yesmaximal, characteristic, complemented
5C2×#19098970C211yesmaximal, characteristic, complemented
6C2×#19098926C211yesmaximal, characteristic, complemented
7C2×#19098926C211yesmaximal, characteristic, complemented
8C2×#19098888C211yesmaximal, characteristic, complemented
9C2×#19098887C211yesmaximal, characteristic, complemented
10C2×#19098884C211yesmaximal, characteristic, complemented
11C2×#19098852C211yesmaximal, characteristic, complemented
12C2×#19098851C211yesmaximal, characteristic, complemented
13C2×#19098842C211yesmaximal, characteristic, complemented
14C2×#19098841C211yesmaximal, characteristic, complemented
15C2×#19098617C211yesmaximal, characteristic, complemented
16C2×#482×C79C211yesmaximal, characteristic, complemented
17C22×#11929623—21no—
18#19099116—24no—
19#19099116C2218yescomplemented
20#19099108—24no—
21#19099108C2218yes—
22C2×#14579160C2211yescharacteristic
23C2×#14579160C2211yescharacteristic
24C2×#14579160C2211yescharacteristic
25C2×#14579157C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579152C2211yescharacteristic
28C2×#14579147—21no—
29C2×#14579138—21no—
30C2×#14579138—21no—
31C2×#14579135C2211yescharacteristic
32C2×#14579133—21no—
33C2×C4×Dic158—21no—
34C2×C4×Dic158—21no—
35C2×D4×Dic79C2211yescharacteristic
36C2×#14579123C2211yescharacteristic
37C2×(C22⋊D79)⋊C4—21no—
38C2×#14579120C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40#19098971C2218yescomplemented
41#19098970C2218yescomplemented
42#19098926C2218yescomplemented
43#19098926C2218yescomplemented
44#19098888C2218yescomplemented
45#19098887C2218yescomplemented
46#19098884C2218yescomplemented
47#19098852C2218yescomplemented
48#19098851C2218yescomplemented
49#19098842C2218yescomplemented
50#19098841C2218yescomplemented
51#19098617C2218yescomplemented
52C2×#14579095C2211yescharacteristic
53C2×#14579094C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579083C2211yescharacteristic
61C2×#14579083C2211yescharacteristic
62C2×#14579082C2211yescharacteristic
63C2×#14579082C2211yescharacteristic
64C2×#14579081C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×#14579071C2211yescharacteristic
69C2×#121×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71#482×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C2×#11929623—28no—
78C2×#11929623—48no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×Dic158—21no—
82C22×D316C2311yescharacteristic
83C22×C22⋊D79—21no—
84C22×C22⋊D79—21no—
85C22×C22⋊D79—21no—
86C23×Dic79—21no—
87C23×Dic79D411yescharacteristic
88C23×Dic79D411yescharacteristic
89C22×C4×D79—21no—
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92#14579160—22no—
93#14579160—22no—
94#14579160—22no—
95#14579160C2314yes—
96#14579160C2314yes—
97#14579160C2314yes—
98#14579157—22no—
99#14579157C2314yes—
100#14579152—22no—
101#14579152—22no—
102#14579152C2314yes—
103#14579152C2314yes—
104#14579147—28no—
105#14579138—28no—
106#14579138—28no—
107#14579135—22no—
108#14579135C2314yes—
109#14579133—28no—
110C4×Dic158—28no—
111C4×Dic158—28no—
112D4×Dic79—22no—
113D4×Dic79C2314yes—
114#14579123—22no—
115#14579123C2314yes—
116(C22⋊D79)⋊C4—28no—
117#14579120—22no—
118#14579120C2314yes—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×C22⋊Dic79—21no—
130C2×C22⋊Dic79—21no—
131C2×(C2×D79)⋊C4—21no—
132C2×(C2×D79)⋊C4—21no—
133C2×C4×Dic79—21no—
134C2×C4×Dic79D411yescharacteristic
135C2×C4×Dic79D411yescharacteristic
136C2×C4×Dic79D414yes—
137C2×C4×Dic79C2311yescharacteristic
138C2×C4×Dic79C2311yescharacteristic
139C2×C4×Dic79C2314yes—
140#14579095C2314yes—
141#14579094C2314yes—
142#14579094C2314yes—
143#14579093C2314yes—
144#14579092C2314yes—
145#14579092C2314yes—
146Dic79⋊C8C2314yes—
147Dic79⋊C8C2314yes—
148#14579083C2314yes—
149#14579083C2314yes—
150#14579082C2314yes—
151#14579082C2314yes—
152#14579081C2314yes—
153#14579081C2314yes—
154C22⋊(C79⋊C8)C2314yes—
155#14579071C2314yes—
156#14579071C2314yes—
157C22×D4×C79—21no—
158C22×D4×C79C2311yescharacteristic
159C23×C4×C79C2311yescharacteristic
160C22×C8×C79C2311yescharacteristic
161C22×C8×C79C2311yescharacteristic
162#121×C79—22no—
163#121×C79C2314yes—
164#117×C79—22no—
165#117×C79C2314yes—
166C2×C4⋊C4×C79C2311yescharacteristic
167C2×C4⋊C4×C79C2311yescharacteristic
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C22⋊C4×C79—21no—
170C2×C22⋊C4×C79—21no—
171C2×C42×C79—21no—
172#107×C79C2314yes—
173#106×C79C2314yes—
174#102×C79C2314yes—
175#102×C79C2314yes—
176C22⋊C8×C79C2314yes—
177C23×D79—21no—
178#11929623—432no—
179C2×Dic158—24no—
180C2×Dic158—24no—
181C2×Dic158—24no—
182C2×Dic158—44no—
183C2×Dic158—44no—
184C2×Dic158—44no—
185C2×D316—21no—
186C2×D316—22no—
187C2×D316—22no—
188C2×D316C2412yes—
189C2×C22⋊D79—24no—
190C2×C22⋊D79—24no—
191C2×C22⋊D79—24no—
192C2×C22⋊D79—44no—
193C2×C22⋊D79—44no—
194C2×C22⋊D79—44no—
195C22×Dic79—24no—
196C22×Dic79—24no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—42no—
201C22×Dic79—44no—
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D414yes—
205C22×Dic79C2×D411yescharacteristic
206C22×Dic79C2×D414yes—
207C22×Dic79C2×D411yescharacteristic
208C2×C4×D79—24no—
209C2×C4×D79—44no—
210C2×C79⋊C8—22no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8C2412yes—
213C2×C79⋊C8C2412yes—
214C4⋊Dic79—24no—
215C4⋊Dic79—24no—
216C4⋊Dic79—21no—
217C4⋊Dic79—21no—
218C4⋊Dic79—21no—
219C4⋊Dic79C2412yes—
220C4⋊Dic79C2412yes—
221C4⋊Dic79C2412yes—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227C22⋊Dic79—24no—
228C22⋊Dic79—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231C4×Dic79—24no—
232C4×Dic79C2×D414yes—
233C4×Dic79C2×D412yes—
234C4×Dic79C2×D414yes—
235C4×Dic79C2×D412yes—
236C4×Dic79C2412yes—
237C4×Dic79C2412yes—
238C24×C79—21no—
239C24×C79C2×D411yescharacteristic
240C2×D4×C79—24no—
241C2×D4×C79—21no—
242C2×D4×C79—22no—
243C2×D4×C79—22no—
244C2×D4×C79—44no—
245C2×D4×C79C2412yes—
246C22×C4×C79—22no—
247C22×C4×C79—22no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D412yes—
253C22×C4×C79C2412yes—
254C22×C4×C79C2411yescharacteristic
255C2×C8×C79—22no—
256C2×C8×C79—22no—
257C2×C8×C79C2412yes—
258C2×C8×C79C2412yes—
259C4⋊C4×C79—21no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79C2412yes—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C22⋊C4×C79—24no—
266C22⋊C4×C79—24no—
267C42×C79—24no—
268C23×C79—22no—
269C23×C79—22no—
270C23×C79—22no—
271C23×C79—22no—
272C23×C79—42no—
273C23×C79—42no—
274C23×C79—42no—
275C23×C79C22×D412yes—
276C23×C79C22×D411yescharacteristic
277C22×D79—22no—
278C22×D79—42no—
279C22×D79—42no—
280C22×D79—42no—
281D4×C79—22no—
282D4×C79—22no—
283D4×C79—48no—
284D4×C79—42no—
285C2×C4×C79—22no—
286C2×C4×C79—24no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—42no—
293C2×C4×C79—42no—
294C2×C4×C79—42no—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D411yescharacteristic
297C2×C4×C792−1+412yes—
298C2×C4×C792−1+412yes—
299C2×C4×C79C2511yescharacteristic
300C22⋊D79—48no—
301C22⋊D79—48no—
302C22⋊D79—48no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—28no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—44no—
311C2×Dic79—42no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314C2×Dic79—48no—
315C2×Dic79AGL(1,ℤ/8)14yes—
316C2×Dic79C22×D412yes—
317C2×Dic79C22×D412yes—
318C2×Dic79C22×D412yes—
319C2×Dic79C22×D412yes—
320D316—22no—
321D316—22no—
322D316—42no—
323C4×D79—48no—
324Dic158—48no—
325Dic158—48no—
326Dic158—48no—
327C8×C79—22no—
328C8×C79—22no—
329C79⋊C8—22no—
330C79⋊C8—22no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—22no—
334C22×C79—44no—
335C22×C79—42no—
336C22×C79—42no—
337C22×C79—42no—
338C22×C79—84no—
339C22×C79#53612yes—
340C22×C79C2×AGL(1,ℤ/8)12yes—
341C22×C79#57512yes—
342C22×C79C23×D411yescharacteristic
343C2×D79—42no—
344C2×D79—42no—
345C2×D79—42no—
346C2×D79—84no—
347C4×C79—22no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79—42no—
351C4×C79#53612yes—
352C4×C79C2×2−1+411yescharacteristic
353C4×C79C2×2−1+411yescharacteristic
354Dic79—22no—
355Dic79—22no—
356Dic79—22no—
357Dic79—42no—
358Dic79—42no—
359Dic79—42no—
360Dic79C2×AGL(1,ℤ/8)14yes—
361C2×#3235—791nomaximal, Sylow
362C2×C79—42no—
363C2×C79—82no—
364C2×C79#323514yescomplemented
365C2×C79C2×#53611yescharacteristic
366C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
367C2×C79C2×#57511yescharacteristic
368D79—82no—
369C2×#533—791no—
370C2×#532—791no—
371#3235—7916no—
372C2×#501—791no—
373C2×#501—791no—
374C2×#490—791no—
375C2×#490—791no—
376C2×#482—791no—
377C2×#482—791no—
378C2×#482—791no—
379C2×#482D7911yescharacteristic, complemented
380C2×#476—791no—
381C2×#476—791no—
382C2×#474—791no—
383C2×#474—791no—
384C2×#432—791no—
385C79C2×#323511yescharacteristic, complemented, Sylow
386C22×#41—1581no—
387#533—798no—
388#533—1584no—
389#532—798no—
390#532—1584no—
391C2×C4⋊Q8—791no—
392C2×C4⋊Q8—791no—
393C2×C4⋊Q8—791no—
394C2×#127—791no—
395C2×#125—791no—
396C2×#125—791no—
397C2×#124—1581no—
398C2×C22⋊Q8—1581no—
399C2×C22⋊Q8—1581no—
400C2×#121—791no—
401C2×#121—1581no—
402C2×#121C2×D7911yescharacteristic
403C2×C4×Q8—1581no—
404C2×C4×Q8—1581no—
405C2×C4×D4—791no—
406C2×C4×D4—791no—
407C2×C4×D4—1581no—
408C2×#117—791no—
409C2×#117C2×D7911yescharacteristic
410C22×C42—791no—
411#501—798no—
412#501—798no—
413#490—798no—
414#490—798no—
415#482—798no—
416#482—798no—
417#482—798no—
418#482C2×D7918yescomplemented
419#476—798no—
420#476—798no—
421#474—798no—
422#474—798no—
423#432—798no—
424C2×#107—791no—
425C2×#107—791no—
426C2×#107—791no—
427C2×#107C2×D7911yescharacteristic
428C2×#106—791no—
429C2×#106—791no—
430C2×#106—791no—
431C2×#106C2×D7911yescharacteristic
432C2×C4⋊C8—791no—
433C2×C4⋊C8—791no—
434C2×#102—791no—
435C2×#102—791no—
436C2×#102—791no—
437C2×#102—791no—
438C2×#102—791no—
439C2×#102—791no—
440C2×#102C2×D7911yescharacteristic
441C2×#102C2×D7911yescharacteristic
442C2×C22⋊C8—791no—
443C2×C22⋊C8C2×D7911yescharacteristic
444C2×#97—791no—
445C2×#97—791no—
446C2×#41—3168no—
447C2×#41—1588no—
448C22×Q8—1581no—
449C22×Q8—1581no—
450C22×Q8—1581no—
451C22×D4—21no—
452C22×D4—791no—
453C22×D4—1581no—
454C22×D4—1581no—
455C22×D4—1581no—
456C22×D4C22×D7911yescharacteristic
457C23×C4—791no—
458C23×C4—791no—
459C23×C4—1581no—
460C23×C4—1581no—
461C23×C4C22×D7911yescharacteristic
462C22×C8—791no—
463C22×C8—791no—
464C22×C8C22×D7911yescharacteristic
465C22×C8C22×D7911yescharacteristic
466C4⋊Q8—794no—
467C4⋊Q8—794no—
468C4⋊Q8—794no—
469C4⋊Q8—1582no—
470C4⋊Q8—1582no—
471C4⋊Q8—1582no—
472#127—794no—
473#127—1582no—
474#125—794no—
475#125—794no—
476#125—1582no—
477#125—1582no—
478#124—1588no—
479C22⋊Q8—1588no—
480C22⋊Q8—1588no—
481#121—22no—
482#121—794no—
483#121—1588no—
484#121—1582no—
485#121C22×D7914yes—
486C4×Q8—1588no—
487C4×Q8—1588no—
488C4×D4—794no—
489C4×D4—794no—
490C4×D4—1588no—
491C4×D4—1582no—
492C4×D4—1582no—
493#117—22no—
494#117—794no—
495#117—1582no—
496#117C22×D7914yes—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—791no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4C22×D7911yescharacteristic
508C2×C4⋊C4C22×D7911yescharacteristic
509C2×C4⋊C4C22×D7911yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C22⋊C4—1581no—
515C2×C22⋊C4—1581no—
516C2×C42—21no—
517C2×C42—791no—
518C2×C42—791no—
519C2×C42—794no—
520C2×C42—791no—
521C2×C42—791no—
522C2×C42—794no—
523C2×C42—1581no—
524#107—794no—
525#107—794no—
526#107—794no—
527#107C22×D7914yes—
528#106—794no—
529#106—794no—
530#106—794no—
531#106C22×D7914yes—
532C4⋊C8—794no—
533C4⋊C8—794no—
534#102—794no—
535#102—794no—
536#102—794no—
537#102—794no—
538#102—794no—
539#102—794no—
540#102C22×D7914yes—
541#102C22×D7914yes—
542C22⋊C8—794no—
543C22⋊C8C22×D7914yes—
544#97—794no—
545#97—794no—
546C24—21no—
547C24—1581no—
548C24D4×D7911yescharacteristic
549#41—31632no—
550C2×Q8—3164no—
551C2×Q8—3164no—
552C2×Q8—3164no—
553C2×Q8—1584no—
554C2×Q8—1584no—
555C2×Q8—1584no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—44no—
561C2×D4—3164no—
562C2×D4—3164no—
563C2×D4—3164no—
564C2×D4—792no—
565C2×D4—1584no—
566C2×D4—1584no—
567C2×D4—1584no—
568C2×D4—1582no—
569C2×D4—1582no—
570C2×D4—1581no—
571C2×D4C23×D7912yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—3164no—
578C22×C4—3164no—
579C22×C4—3162no—
580C22×C4—794no—
581C22×C4—791no—
582C22×C4—794no—
583C22×C4—791no—
584C22×C4—791no—
585C22×C4—791no—
586C22×C4—1584no—
587C22×C4—1584no—
588C22×C4—1581no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1584no—
592C22×C4D4×D7912yes—
593C22×C4D4×D7911yescharacteristic
594C22×C4C23×D7912yes—
595C22×C4C23×D7911yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—792no—
599C2×C8—792no—
600C2×C8—1582no—
601C2×C8—1582no—
602C2×C8C23×D7912yes—
603C2×C8C23×D7912yes—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—792no—
608C4⋊C4—792no—
609C4⋊C4—792no—
610C4⋊C4—1584no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1584no—
616C4⋊C4—1584no—
617C4⋊C4—1581no—
618C4⋊C4—1581no—
619C4⋊C4—1581no—
620C4⋊C4C23×D7912yes—
621C4⋊C4C23×D7912yes—
622C4⋊C4C23×D7912yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—1584no—
626C22⋊C4—1584no—
627C22⋊C4—1584no—
628C22⋊C4—1584no—
629C42—24no—
630C42—792no—
631C42—792no—
632C42—794no—
633C42—792no—
634C42—794no—
635C42—792no—
636C42—1584no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—3162no—
645C23—3162no—
646C23—3162no—
647C23—1582no—
648C23C2×D4×D7912yes—
649C23C2×D4×D7911yescharacteristic
650Q8—3168no—
651Q8—3168no—
652Q8—3168no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—3168no—
658D4—3168no—
659D4—3168no—
660D4—3162no—
661D4—1582no—
662D4—1582no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—3168no—
674C2×C4—3162no—
675C2×C4—3162no—
676C2×C4—3162no—
677C2×C4—3168no—
678C2×C4—3164no—
679C2×C4—794no—
680C2×C4—792no—
681C2×C4—792no—
682C2×C4—792no—
683C2×C4—792no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1588no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4C2×D4×D7912yes—
692C2×C4C2×D4×D7911yescharacteristic
693C2×C4#1457920812yes—
694C2×C4#1457920812yes—
695C2×C4C24×D7911yescharacteristic
696C8—22no—
697C8—22no—
698C8—1582no—
699C8—1582no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22—3162no—
709C22—3162no—
710C22—3162no—
711C22—6324no—
712C22#1909913512yes—
713C22AGL(1,ℤ/8)×D7912yes—
714C22#1909936012yes—
715C22C22×D4×D7911yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—3162no—
721C4—3162no—
722C4—3162no—
723C4—794no—
724C4—1582no—
725C4—1582no—
726C4—1582no—
727C4#1909913512yes—
728C4C2×#1457920811yescharacteristic
729C4C2×#1457920811yescharacteristic
730C2—42no—
731C2—82no—
732C2—6322no—
733C2#2377459514yesdirect product factor
734C2C2×#1909913511yescharacteristic
735C2C2×AGL(1,ℤ/8)×D7911yescharacteristic
736C2C2×#1909936011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#482×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099108C2
hypercenterC2×#482D79
hypocenterC79C2×#3235
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#19099116C2semidirect
3. #23774595C2direct (N × H)
4. C2×#19098971C2semidirect
5. C2×#19098970C2semidirect
6. C2×#19098926C2semidirect
7. C2×#19098926C2semidirect
8. C2×#19098888C2semidirect
9. C2×#19098887C2semidirect
10. C2×#19098884C2semidirect
11. C2×#19098852C2semidirect
12. C2×#19098851C2semidirect
13. C2×#19098842C2semidirect
14. C2×#19098841C2semidirect
15. C2×#19098617C2semidirect
16. C2×#482×C79C2semidirect
19. #19099116C22semidirect
40. #19098971C22semidirect
41. #19098970C22semidirect
42. #19098926C22semidirect
43. #19098926C22semidirect
44. #19098888C22semidirect
45. #19098887C22semidirect
46. #19098884C22semidirect
47. #19098852C22semidirect
48. #19098851C22semidirect
49. #19098842C22semidirect
50. #19098841C22semidirect
51. #19098617C22semidirect
71. #482×C79C22semidirect
364. C2×C79#3235semidirect
379. C2×#482D79semidirect
385. C79C2×#3235semidirect
418. #482C2×D79semidirect
733. C2#23774595direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991162
C2×#190991082
#237745952
C2×#190989712
C2×#190989702
C2×#190989262
C2×#190988882
C2×#190988872
C2×#190988842
C2×#190988522
C2×#190988512
C2×#190988422
C2×#190988412
C2×#190986172
C2×#482×C792
C2×#323579