Finite Group Databasebeta

← C2×#23777938 #35195631

Subgroups — C2×#23777938 #35195631

Order 20224.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777938C2132yesmaximal, direct product factor
2C2×#19099313C212yesmaximal, complemented
3C2×#19099307C212yesmaximal, complemented
4C2×#19099272C212yesmaximal, complemented
5C2×#19099265C212yesmaximal, complemented
6C2×#19099263C212yesmaximal, complemented
7C2×#19099213C212yesmaximal, complemented
8C2×#19099212C214yesmaximal, complemented
9C2×#19099190C212yesmaximal, complemented
10C2×#19099167C212yesmaximal, complemented
11C2×#19099158C212yesmaximal, complemented
12C2×#19099155C214yesmaximal, complemented
13C2×#19099140C212yesmaximal, complemented
14C2×#19099097C211yesmaximal, characteristic, complemented
15C22×#14579153C211yesmaximal, characteristic, complemented
16C2×#532×C79C211yesmaximal, characteristic, complemented
17C22×#11929623C2214yes—
18#19099313C22132yescomplemented
19#19099307C22132yescomplemented
20#19099272C22132yescomplemented
21#19099265C22132yescomplemented
22#19099263C22132yescomplemented
23#19099213C22132yescomplemented
24#19099212C22164yescomplemented
25#19099190C22132yescomplemented
26#19099167C22132yescomplemented
27#19099158C22132yescomplemented
28#19099155C22164yescomplemented
29#19099140C22132yescomplemented
30C2×#14579160C2212yes—
31C2×#14579159C2214yes—
32#19099097C22116yescomplemented
33C2×#14579155C2212yes—
34C2×#14579154C2214yes—
35C2×#14579154C2214yes—
36C2×#14579153C2212yes—
37C2×#14579153C2212yes—
38C2×#14579153C2212yes—
39C2×#14579153C2212yes—
40C2×#14579153C2211yescharacteristic
41C2×#14579153C22116yescomplemented
42C2×#14579152C2212yes—
43C2×#14579151C2214yes—
44C2×#14579149C2211yescharacteristic
45C2×#14579145C2214yes—
46C2×#14579144C2212yes—
47C2×#14579144C2214yes—
48C2×#14579143C2214yes—
49C2×#14579142C2214yes—
50C2×#14579142C2214yes—
51C2×#14579142C2214yes—
52C2×#14579140C2214yes—
53C2×#14579140C2211yescharacteristic
54C2×#14579139C2214yes—
55C2×#14579138C2214yes—
56C2×#14579138C2214yes—
57C2×#14579138C2214yes—
58C2×#14579137C2214yes—
59C2×#14579135C2211yescharacteristic
60C2×#14579134C2214yes—
61C2×#14579133C2214yes—
62C2×#14579133C2214yes—
63C2×#14579133C2214yes—
64C2×#14579132C2212yes—
65C2×#14579132C2212yes—
66C2×C4×Dic158C2211yescharacteristic
67C2×C4×D316C2211yescharacteristic
68C2×D4×Dic79C2214yes—
69C2×D4×Dic79C2212yes—
70C2×D4×Dic79C2212yes—
71C2×C4×C22⋊D79C2214yes—
72C2×C4×C22⋊D79C2212yes—
73C2×#14579119C2212yes—
74C2×#14579118C2212yes—
75C22×C4⋊Dic79C2211yescharacteristic
76C22×C4⋊Dic79C2211yescharacteristic
77C22×Dic79⋊C4C2212yes—
78C22×Dic79⋊C4C2214yes—
79C22×Dic79⋊C4C2212yes—
80C2×C4⋊C4×D79C2212yes—
81C22×#41×C79C2212yes—
82#532×C79C22116yescomplemented
83C2×C4⋊Q8×C79C2211yescharacteristic
84C2×#127×C79C2211yescharacteristic
85C2×#124×C79C2212yes—
86C2×#121×C79C2212yes—
87C2×#121×C79C2212yes—
88C2×C4×D4×C79C2212yes—
89C2×C4×D4×C79C2212yes—
90C22×C42×C79C2211yescharacteristic
91C2×#11929623—416no—
92C2×#11929623C23132yes—
93C22×Dic158C2311yescharacteristic
94C22×Dic158C2314yes—
95C22×D316C2311yescharacteristic
96C22×C22⋊D79C2312yes—
97C22×C22⋊D79C2314yes—
98C22×C22⋊D79C2314yes—
99C23×Dic79C2312yes—
100C23×Dic79C2312yes—
101C23×Dic79C2314yes—
102C23×Dic79C2314yes—
103C22×C4×D79C2312yes—
104C22×C4×D79C2314yes—
105#14579160C23116yes—
106#14579159C23132yes—
107#14579155C23116yes—
108#14579154C23132yes—
109#14579154C23132yes—
110#14579153C23116yes—
111#14579153C23116yes—
112#14579153C23116yes—
113#14579153C23116yes—
114#14579153C2318yes—
115#14579152C23116yes—
116#14579151C23132yes—
117#14579149C2318yes—
118#14579145C23132yes—
119#14579144C23132yes—
120#14579144C23116yes—
121#14579143C23132yes—
122#14579142C23132yes—
123#14579142C23132yes—
124#14579142C23132yes—
125#14579140C23132yes—
126#14579140C2318yes—
127#14579139C23132yes—
128#14579138C23132yes—
129#14579138C23132yes—
130#14579138C23132yes—
131#14579137C23132yes—
132#14579135C2318yes—
133#14579134C23132yes—
134#14579133C23132yes—
135#14579133C23132yes—
136#14579133C23132yes—
137#14579132C23116yes—
138#14579132C23116yes—
139C4×Dic158C2318yes—
140C4×D316C2318yes—
141D4×Dic79C23132yes—
142D4×Dic79C23116yes—
143D4×Dic79C23116yes—
144C4×C22⋊D79C23132yes—
145C4×C22⋊D79C23116yes—
146#14579119C23116yes—
147#14579118C23116yes—
148C2×C4⋊Dic79C2318yes—
149C2×C4⋊Dic79C2318yes—
150C2×C4⋊Dic79C2312yes—
151C2×C4⋊Dic79C2312yes—
152C2×C4⋊Dic79C2312yes—
153C2×C4⋊Dic79C2312yes—
154C2×C4⋊Dic79C2314yes—
155C2×C4⋊Dic79C2311yescharacteristic
156C2×C4⋊Dic79C2311yescharacteristic
157C2×Dic79⋊C4C23116yes—
158C2×Dic79⋊C4C23132yes—
159C2×Dic79⋊C4C23116yes—
160C2×Dic79⋊C4C2314yes—
161C2×Dic79⋊C4C2314yes—
162C2×Dic79⋊C4C2312yes—
163C2×Dic79⋊C4C2314yes—
164C2×Dic79⋊C4C2314yes—
165C2×Dic79⋊C4C2314yes—
166C2×Dic79⋊C4C2314yes—
167C2×Dic79⋊C4C2314yes—
168C2×Dic79⋊C4C2312yes—
169C2×Dic79⋊C4C2312yes—
170C2×Dic79⋊C4C2312yes—
171C4⋊C4×D79C23116yes—
172C2×C22⋊Dic79C2312yes—
173C2×C22⋊Dic79C2314yes—
174C2×C22⋊Dic79C2314yes—
175C2×C22⋊Dic79C2314yes—
176C2×C22⋊Dic79C2314yes—
177C2×(C2×D79)⋊C4C2312yes—
178C2×(C2×D79)⋊C4C2312yes—
179C2×(C2×D79)⋊C4C2314yes—
180C2×(C2×D79)⋊C4C2312yes—
181C2×(C2×D79)⋊C4C2312yes—
182C2×C4×Dic79C2312yes—
183C2×C4×Dic79C2314yes—
184C2×#41×C79—48no—
185C2×#41×C79C23116yes—
186C22×Q8×C79C2312yes—
187C22×D4×C79C2312yes—
188C22×D4×C79C2314yes—
189C22×D4×C79C2312yes—
190C22×D4×C79C2312yes—
191C23×C4×C79C2311yescharacteristic
192C23×C4×C79C2311yescharacteristic
193C23×C4×C79C2311yescharacteristic
194C23×C4×C79C2314yes—
195C4⋊Q8×C79C2318yes—
196#127×C79C2318yes—
197#124×C79C23116yes—
198#121×C79C23116yes—
199#121×C79C23116yes—
200C4×D4×C79C23116yes—
201C4×D4×C79C23116yes—
202C2×C4⋊C4×C79C2312yes—
203C2×C4⋊C4×C79C2312yes—
204C2×C22⋊C4×C79C2314yes—
205C2×C22⋊C4×C79C2314yes—
206C2×C42×C79C2311yescharacteristic
207C2×C42×C79C2311yescharacteristic
208C2×C42×C79C2311yescharacteristic
209C2×C42×C79C2311yescharacteristic
210C2×C42×C79C2318yes—
211C23×D79C2412yes—
212#11929623—464no—
213C2×Dic158—42no—
214C2×Dic158—48no—
215C2×Dic158C24116yes—
216C2×Dic158C2414yes—
217C2×D316—42no—
218C2×D316C2414yes—
219C2×C22⋊D79—28no—
220C2×C22⋊D79—48no—
221C2×C22⋊D79—48no—
222C2×C22⋊D79C2418yes—
223C2×C22⋊D79C24116yes—
224C2×C22⋊D79C24116yes—
225C22×Dic79—28no—
226C22×Dic79—48no—
227C22×Dic79—44no—
228C22×Dic79—48no—
229C22×Dic79C2412yes—
230C22×Dic79C2412yes—
231C22×Dic79C2414yes—
232C22×Dic79C2418yes—
233C22×Dic79C2412yes—
234C22×Dic79C2414yes—
235C22×Dic79C24116yes—
236C22×Dic79C2418yes—
237C22×Dic79C24116yes—
238C2×C4×D79—28no—
239C2×C4×D79—48no—
240C2×C4×D79C2418yes—
241C2×C4×D79C24116yes—
242C4⋊Dic79C2418yes—
243C4⋊Dic79C2418yes—
244C4⋊Dic79C2418yes—
245C4⋊Dic79C2418yes—
246C4⋊Dic79C24116yes—
247C4⋊Dic79C2414yes—
248C4⋊Dic79C2414yes—
249Dic79⋊C4C24116yes—
250Dic79⋊C4C24116yes—
251Dic79⋊C4C2418yes—
252Dic79⋊C4C24116yes—
253Dic79⋊C4C24116yes—
254Dic79⋊C4C24116yes—
255Dic79⋊C4C24116yes—
256Dic79⋊C4C24116yes—
257Dic79⋊C4C2418yes—
258Dic79⋊C4C2418yes—
259Dic79⋊C4C2418yes—
260C22⋊Dic79C2418yes—
261C22⋊Dic79C24116yes—
262C22⋊Dic79C24116yes—
263C22⋊Dic79C24116yes—
264C22⋊Dic79C24116yes—
265(C2×D79)⋊C4C2418yes—
266(C2×D79)⋊C4C2418yes—
267(C2×D79)⋊C4C24116yes—
268(C2×D79)⋊C4C2418yes—
269(C2×D79)⋊C4C2418yes—
270C4×Dic79C2418yes—
271C4×Dic79C24116yes—
272C24×C79C2414yes—
273C24×C79C2411yescharacteristic
274#41×C79—432no—
275C2×Q8×C79—44no—
276C2×Q8×C79C2418yes—
277C2×D4×C79—216no—
278C2×D4×C79—28no—
279C2×D4×C79—44no—
280C2×D4×C79—44no—
281C2×D4×C79C24116yes—
282C2×D4×C79C2418yes—
283C2×D4×C79C2418yes—
284C2×D4×C79C2418yes—
285C22×C4×C79—24no—
286C22×C4×C79—24no—
287C22×C4×C79—42no—
288C22×C4×C79—48no—
289C22×C4×C79C2411yescharacteristic
290C22×C4×C79C2414yes—
291C22×C4×C79C2411yescharacteristic
292C22×C4×C79C2411yescharacteristic
293C22×C4×C79C2414yes—
294C22×C4×C79C2411yescharacteristic
295C22×C4×C79C2411yescharacteristic
296C22×C4×C79C2414yes—
297C22×C4×C79C2414yes—
298C22×C4×C79C24116yes—
299C22×C4×C79C2411yescharacteristic
300C4⋊C4×C79C2418yes—
301C4⋊C4×C79C2418yes—
302C22⋊C4×C79C24116yes—
303C22⋊C4×C79C24116yes—
304C42×C79C2414yes—
305C42×C79C2414yes—
306C42×C79C2414yes—
307C42×C79C2414yes—
308C23×C79—22no—
309C23×C79—22no—
310C23×C79—28no—
311C23×C79—28no—
312C23×C79—28no—
313C23×C79H(5,𝔽2)14yes—
314C23×C79C2518yes—
315C23×C79C2512yes—
316C23×C79C2511yescharacteristic
317C22×D79—24no—
318C22×D79—24no—
319C22×D79—24no—
320C22×D79C2514yes—
321Q8×C79—48no—
322D4×C79—232no—
323D4×C79—216no—
324D4×C79—48no—
325D4×C79—48no—
326C2×C4×C79—28no—
327C2×C4×C79—22no—
328C2×C4×C79—22no—
329C2×C4×C79—28no—
330C2×C4×C79—22no—
331C2×C4×C79—22no—
332C2×C4×C79—22no—
333C2×C4×C79—28no—
334C2×C4×C79—44no—
335C2×C4×C79—416no—
336C2×C4×C792−1+414yes—
337C2×C4×C79C2518yes—
338C2×C4×C79C2512yes—
339C2×C4×C79C2512yes—
340C2×C4×C79C2512yes—
341C2×C4×C79C2512yes—
342C2×C4×C79C2512yes—
343C2×C4×C79C2512yes—
344C22⋊D79—216no—
345C22⋊D79—416no—
346C22⋊D79—416no—
347C2×Dic79—28no—
348C2×Dic79—216no—
349C2×Dic79—24no—
350C2×Dic79—24no—
351C2×Dic79—28no—
352C2×Dic79—24no—
353C2×Dic79—48no—
354C2×Dic79—416no—
355C2×Dic79—416no—
356C2×Dic79C2514yes—
357C2×Dic79C2514yes—
358C2×Dic79C2518yes—
359C2×Dic79C2514yes—
360C2×Dic79C2518yes—
361D316—44no—
362C4×D79—216no—
363C4×D79—416no—
364Dic158—44no—
365Dic158—416no—
366C22×C79—22no—
367C22×C79—22no—
368C22×C79—28no—
369C22×C79—28no—
370C22×C79—28no—
371C22×C79—28no—
372C22×C79—416no—
373C22×C79C2×H(5,𝔽2)14yes—
374C22×C79C2×H(5,𝔽2)12yes—
375C22×C79C2×2−1+412yes—
376C22×C79#58512yes—
377C22×C79C2611yescharacteristic
378C2×D79—24no—
379C2×D79—24no—
380C2×D79—24no—
381C2×D79—48no—
382C4×C79—22no—
383C4×C79—22no—
384C4×C79—28no—
385C4×C79—22no—
386C4×C79—22no—
387C4×C79—22no—
388C4×C79C2×2−1+414yes—
389Dic79—24no—
390Dic79—28no—
391Dic79—24no—
392Dic79—28no—
393Dic79—24no—
394C2×#3559—791nomaximal, Sylow
395C2×C79—24no—
396C2×C79—48no—
397C2×C79#355914yescomplemented
398C2×C79C22×H(5,𝔽2)11yescharacteristic
399C2×C79C22×2−1+411yescharacteristic
400C2×C79C2×#58511yescharacteristic
401D79—44no—
402#3559—7932no—
403C2×#563—792no—
404C2×#562—792no—
405C2×#554—792no—
406C2×#553—792no—
407C2×#553—792no—
408C2×#547—794no—
409C2×#547—792no—
410C2×#544—792no—
411C2×#540—792no—
412C2×#539—792no—
413C2×#539—794no—
414C2×#537—792no—
415C2×#532D7911yescharacteristic, complemented
416C2×#529—791no—
417C22×#125—791no—
418C79C2×#355911yescharacteristic, complemented, Sylow
419C22×#41—794no—
420C22×#41C2×D7912yes—
421#563—7932no—
422#562—7932no—
423#554—7932no—
424#553—7932no—
425#553—7932no—
426#547—7964no—
427#547—7932no—
428#544—7932no—
429#540—7932no—
430#539—7932no—
431#539—7964no—
432#537—7932no—
433#532C2×D79116yescomplemented
434C2×C4⋊Q8—794no—
435C2×C4⋊Q8—792no—
436C2×C4⋊Q8C2×D7911yescharacteristic
437C2×#127C2×D7911yescharacteristic
438#529—7916no—
439C2×#126—794no—
440C2×#126—794no—
441C2×#126—792no—
442C2×#125—794no—
443C2×#125—792no—
444C2×#125—792no—
445C2×#125—792no—
446C2×#125—792no—
447C2×#125—792no—
448C2×#125—7916no—
449C2×#125—791no—
450C2×#124—791no—
451C2×#124C2×D7912yes—
452C2×#123—794no—
453C2×#123—794no—
454C2×#123—794no—
455C2×#123—792no—
456C2×#123—794no—
457C2×#123—794no—
458C2×#123—794no—
459C2×C22⋊Q8—794no—
460C2×C22⋊Q8—791no—
461C2×C22⋊Q8—794no—
462C2×C22⋊Q8—794no—
463C2×C22⋊Q8—794no—
464C2×C22⋊Q8—794no—
465C2×C22⋊Q8—794no—
466C2×#121—794no—
467C2×#121—794no—
468C2×#121—792no—
469C2×#121—794no—
470C2×#121—792no—
471C2×#121—791no—
472C2×#121—794no—
473C2×#121C2×D7912yes—
474C2×#121C2×D7912yes—
475C2×C4×Q8—791no—
476C2×C4×D4—794no—
477C2×C4×D4—792no—
478C2×C4×D4—792no—
479C2×C4×D4—792no—
480C2×C4×D4—794no—
481C2×C4×D4—791no—
482C2×C4×D4C2×D7912yes—
483C2×C4×D4C2×D7912yes—
484C2×#117—792no—
485C2×#117—792no—
486C22×C4⋊C4—792no—
487C22×C4⋊C4—792no—
488C22×C4⋊C4—791no—
489C22×C4⋊C4—791no—
490C22×C4⋊C4—794no—
491C22×C4⋊C4—792no—
492C22×C42C2×D7911yescharacteristic
493C2×#41—48no—
494C2×#41—31616no—
495C2×#41—7932no—
496C2×#41C22×D79116yes—
497C22×Q8—791no—
498C22×Q8—794no—
499C22×Q8C22×D7912yes—
500C22×D4—794no—
501C22×D4—794no—
502C22×D4—792no—
503C22×D4—791no—
504C22×D4C22×D7912yes—
505C22×D4C22×D7914yes—
506C22×D4C22×D7912yes—
507C22×D4C22×D7912yes—
508C23×C4—792no—
509C23×C4—794no—
510C23×C4—794no—
511C23×C4—794no—
512C23×C4—792no—
513C23×C4—792no—
514C23×C4C22×D7911yescharacteristic
515C23×C4C22×D7911yescharacteristic
516C23×C4C22×D7911yescharacteristic
517C23×C4C22×D7914yes—
518C4⋊Q8—7932no—
519C4⋊Q8—7916no—
520C4⋊Q8C22×D7918yes—
521#127C22×D7918yes—
522#126—7932no—
523#126—7932no—
524#126—7916no—
525#125—7932no—
526#125—7916no—
527#125—7916no—
528#125—7916no—
529#125—7916no—
530#125—7916no—
531#125—798no—
532#124—798no—
533#124C22×D79116yes—
534#123—7932no—
535#123—7932no—
536#123—7932no—
537#123—7916no—
538#123—7932no—
539#123—7932no—
540#123—7932no—
541C22⋊Q8—7932no—
542C22⋊Q8—798no—
543C22⋊Q8—7932no—
544C22⋊Q8—7932no—
545C22⋊Q8—7932no—
546C22⋊Q8—7932no—
547C22⋊Q8—7932no—
548#121—7932no—
549#121—7932no—
550#121—7916no—
551#121—7932no—
552#121—7916no—
553#121—798no—
554#121—7932no—
555#121C22×D79116yes—
556#121C22×D79116yes—
557C4×Q8—798no—
558C4×D4—7932no—
559C4×D4—7916no—
560C4×D4—7916no—
561C4×D4—7916no—
562C4×D4—7932no—
563C4×D4—798no—
564C4×D4C22×D79116yes—
565C4×D4C22×D79116yes—
566#117—7916no—
567#117—7916no—
568C2×C4⋊C4—792no—
569C2×C4⋊C4—794no—
570C2×C4⋊C4—792no—
571C2×C4⋊C4—792no—
572C2×C4⋊C4—794no—
573C2×C4⋊C4—794no—
574C2×C4⋊C4—794no—
575C2×C4⋊C4—794no—
576C2×C4⋊C4—792no—
577C2×C4⋊C4—794no—
578C2×C4⋊C4—794no—
579C2×C4⋊C4—792no—
580C2×C4⋊C4—7916no—
581C2×C4⋊C4—7916no—
582C2×C4⋊C4—798no—
583C2×C4⋊C4—798no—
584C2×C4⋊C4—7932no—
585C2×C4⋊C4—792no—
586C2×C4⋊C4—792no—
587C2×C4⋊C4—794no—
588C2×C4⋊C4—792no—
589C2×C4⋊C4—791no—
590C2×C4⋊C4—791no—
591C2×C4⋊C4—7916no—
592C2×C4⋊C4C22×D7912yes—
593C2×C4⋊C4C22×D7912yes—
594C2×C22⋊C4—792no—
595C2×C22⋊C4—794no—
596C2×C22⋊C4—794no—
597C2×C22⋊C4—794no—
598C2×C22⋊C4—794no—
599C2×C22⋊C4—792no—
600C2×C22⋊C4—794no—
601C2×C22⋊C4—792no—
602C2×C22⋊C4—792no—
603C2×C22⋊C4—792no—
604C2×C22⋊C4C22×D7914yes—
605C2×C22⋊C4C22×D7914yes—
606C2×C42—792no—
607C2×C42—794no—
608C2×C42C22×D7911yescharacteristic
609C2×C42C22×D7911yescharacteristic
610C2×C42C22×D7911yescharacteristic
611C2×C42C22×D7911yescharacteristic
612C2×C42C22×D7918yes—
613C24—792no—
614C24C23×D7914yes—
615C24C23×D7911yescharacteristic
616#41—432no—
617#41—31664no—
618C2×Q8—44no—
619C2×Q8—3162no—
620C2×Q8—3168no—
621C2×Q8—794no—
622C2×Q8—7916no—
623C2×Q8C23×D7918yes—
624C2×D4—216no—
625C2×D4—28no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—3162no—
629C2×D4—3168no—
630C2×D4—3168no—
631C2×D4—7916no—
632C2×D4—7916no—
633C2×D4—798no—
634C2×D4—794no—
635C2×D4—1588no—
636C2×D4C23×D7918yes—
637C2×D4C23×D79116yes—
638C2×D4C23×D7918yes—
639C2×D4C23×D7918yes—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—48no—
643C22×C4—42no—
644C22×C4—3168no—
645C22×C4—3164no—
646C22×C4—3168no—
647C22×C4—3168no—
648C22×C4—798no—
649C22×C4—7916no—
650C22×C4—7916no—
651C22×C4—7916no—
652C22×C4—798no—
653C22×C4—792no—
654C22×C4—792no—
655C22×C4—794no—
656C22×C4—792no—
657C22×C4—794no—
658C22×C4—798no—
659C22×C4—1588no—
660C22×C4—1588no—
661C22×C4C23×D7914yes—
662C22×C4C23×D7914yes—
663C22×C4C23×D7914yes—
664C22×C4C23×D7911yescharacteristic
665C22×C4C23×D7911yescharacteristic
666C22×C4C23×D7911yescharacteristic
667C22×C4C23×D7911yescharacteristic
668C22×C4C23×D7911yescharacteristic
669C22×C4C23×D7914yes—
670C22×C4C23×D79116yes—
671C22×C4C23×D7911yescharacteristic
672C4⋊C4—7916no—
673C4⋊C4—798no—
674C4⋊C4—7916no—
675C4⋊C4—7916no—
676C4⋊C4—7916no—
677C4⋊C4—7916no—
678C4⋊C4—7916no—
679C4⋊C4—7916no—
680C4⋊C4—798no—
681C4⋊C4—798no—
682C4⋊C4—798no—
683C4⋊C4—798no—
684C4⋊C4—798no—
685C4⋊C4—798no—
686C4⋊C4—798no—
687C4⋊C4—7916no—
688C4⋊C4—794no—
689C4⋊C4—794no—
690C4⋊C4C23×D7918yes—
691C4⋊C4C23×D7918yes—
692C22⋊C4—798no—
693C22⋊C4—7916no—
694C22⋊C4—7916no—
695C22⋊C4—7916no—
696C22⋊C4—7916no—
697C22⋊C4—798no—
698C22⋊C4—7916no—
699C22⋊C4—798no—
700C22⋊C4—798no—
701C22⋊C4—798no—
702C22⋊C4C23×D79116yes—
703C22⋊C4C23×D79116yes—
704C42—798no—
705C42—7916no—
706C42C23×D7914yes—
707C42C23×D7914yes—
708C42C23×D7914yes—
709C42C23×D7914yes—
710C23—22no—
711C23—22no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—794no—
716C23—1584no—
717C23—1584no—
718C23—1584no—
719C23#1457920614yes—
720C23C24×D7918yes—
721C23C24×D7912yes—
722C23C24×D7911yescharacteristic
723Q8—48no—
724Q8—31616no—
725Q8—3164no—
726D4—232no—
727D4—216no—
728D4—48no—
729D4—48no—
730D4—3164no—
731D4—31616no—
732D4—31616no—
733D4—15816no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—28no—
742C2×C4—44no—
743C2×C4—416no—
744C2×C4—31616no—
745C2×C4—31616no—
746C2×C4—3168no—
747C2×C4—31616no—
748C2×C4—794no—
749C2×C4—794no—
750C2×C4—798no—
751C2×C4—794no—
752C2×C4—798no—
753C2×C4—1588no—
754C2×C4—1584no—
755C2×C4—15816no—
756C2×C4—1584no—
757C2×C4—1588no—
758C2×C4—1584no—
759C2×C4—15816no—
760C2×C4#1457920814yes—
761C2×C4C24×D7918yes—
762C2×C4C24×D7912yes—
763C2×C4C24×D7912yes—
764C2×C4C24×D7912yes—
765C2×C4C24×D7912yes—
766C2×C4C24×D7912yes—
767C2×C4C24×D7912yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—416no—
775C22—3168no—
776C22—1584no—
777C22—1584no—
778C22—1584no—
779C22C2×#1457920614yes—
780C22C2×#1457920612yes—
781C22C2×#1457920812yes—
782C22#1909939912yes—
783C22C25×D7911yescharacteristic
784C4—22no—
785C4—22no—
786C4—28no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—1588no—
791C4—1584no—
792C4—1584no—
793C4—1588no—
794C4—1584no—
795C4C2×#1457920814yes—
796C2—24no—
797C2—48no—
798C2—3164no—
799C2#2377793814yesdirect product factor
800C2C22×#1457920611yescharacteristic
801C2C22×#1457920811yescharacteristic
802C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#532×C79C2
socleC23×C79C25
hypercenterC2×#532D79
hypocenterC79C2×#3559
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #23777938C2direct (N × H)
2. C2×#19099313C2semidirect
3. C2×#19099307C2semidirect
4. C2×#19099272C2semidirect
5. C2×#19099265C2semidirect
6. C2×#19099263C2semidirect
7. C2×#19099213C2semidirect
8. C2×#19099212C2semidirect
9. C2×#19099190C2semidirect
10. C2×#19099167C2semidirect
11. C2×#19099158C2semidirect
12. C2×#19099155C2semidirect
13. C2×#19099140C2semidirect
14. C2×#19099097C2semidirect
15. C22×#14579153C2semidirect
16. C2×#532×C79C2semidirect
18. #19099313C22semidirect
19. #19099307C22semidirect
20. #19099272C22semidirect
21. #19099265C22semidirect
22. #19099263C22semidirect
23. #19099213C22semidirect
24. #19099212C22semidirect
25. #19099190C22semidirect
26. #19099167C22semidirect
27. #19099158C22semidirect
28. #19099155C22semidirect
29. #19099140C22semidirect
32. #19099097C22semidirect
41. C2×#14579153C22semidirect
82. #532×C79C22semidirect
397. C2×C79#3559semidirect
415. C2×#532D79semidirect
418. C79C2×#3559semidirect
433. #532C2×D79semidirect
799. C2#23777938direct (N × H)

Maximal subgroups

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

subgroupindex
#237779382
C2×#190993132
C2×#190993072
C2×#190992722
C2×#190992652
C2×#190992632
C2×#190992132
C2×#190992122
C2×#190991902
C2×#190991672
C2×#190991582
C2×#190991552
C2×#190991402
C2×#190990972
C22×#145791532
C2×#532×C792
C2×#355979