Finite Group Databasebeta

← C2×#23774732 #35161069

Subgroups — C2×#23774732 #35161069

Order 20224.

1930 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099115C211yesmaximal, characteristic, complemented
2C2×#19099099C211yesmaximal, characteristic
3#23774732C2116yesmaximal, direct product factor
4C2×#19098869C211yesmaximal, characteristic, complemented
5C2×#19098868C211yesmaximal, characteristic, complemented
6C2×#19098846C211yesmaximal, characteristic, complemented
7C2×#19098842C211yesmaximal, characteristic, complemented
8C2×#19098802C211yesmaximal, characteristic, complemented
9C2×#19098794C211yesmaximal, characteristic
10C2×#19098792C211yesmaximal, characteristic
11C2×#19098788C211yesmaximal, characteristic, complemented
12C2×#19098787C211yesmaximal, characteristic, complemented
13C2×#19098771C211yesmaximal, characteristic, complemented
14C2×#19098767C211yesmaximal, characteristic, complemented
15C22×Dic79⋊C8C211yesmaximal, characteristic, complemented
16C2×#467×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929613C2211yescharacteristic
19C22×#11929611C2211yescharacteristic
20C23×C79⋊C8C2211yescharacteristic
21#19099115—24no—
22#19099115C2218yescomplemented
23C2×#14579160C2211yescharacteristic
24C2×#14579159C2211yescharacteristic
25#19099099—24no—
26#19099099C2218yes—
27C2×#14579156—21no—
28C2×#14579152C2211yescharacteristic
29C2×#14579151—21no—
30C2×#14579150C2211yescharacteristic
31C2×#14579145—21no—
32C2×#14579140C2211yescharacteristic
33C2×#14579138—21no—
34C2×#14579135C2211yescharacteristic
35C2×Q8×Dic79C2211yescharacteristic
36C2×Q8×Dic79C2211yescharacteristic
37C2×#14579126—21no—
38C2×#14579126C2211yescharacteristic
39C2×#14579123C2211yescharacteristic
40C2×(C22⋊D79)⋊C4—21no—
41C2×#14579119—21no—
42C2×#14579117—21no—
43C22×C4×Dic79C2211yescharacteristic
44#19098869C2218yescomplemented
45#19098868C2218yescomplemented
46#19098846C2218yescomplemented
47#19098842C2218yescomplemented
48#19098802C2218yescomplemented
49#19098794C2218yes—
50#19098792C2218yes—
51#19098788C2218yescomplemented
52#19098787C2218yescomplemented
53#19098771C2218yescomplemented
54#19098767C2218yescomplemented
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×Dic79⋊C8C2218yescomplemented
63C2×#14579086C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×#14579084C2211yescharacteristic
67C2×#14579083C2211yescharacteristic
68C2×#14579081C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73#467×C79C2218yescomplemented
74C2×#107×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C23×Dic79D411yescharacteristic
82C23×Dic79D411yescharacteristic
83C22×C4×D79—21no—
84C2×#11929614—42no—
85C2×#11929614C2314yes—
86C2×#11929613—42no—
87C2×#11929613C2314yes—
88C2×#11929611—42no—
89C2×#11929611C2314yes—
90C22×C79⋊C8—42no—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93C22×C79⋊C8C2314yes—
94#14579160—22no—
95#14579160C2314yes—
96#14579159—22no—
97#14579159C2314yes—
98#14579156—28no—
99#14579152—22no—
100#14579152C2314yes—
101#14579151—28no—
102#14579150—22no—
103#14579150C2314yes—
104#14579145—28no—
105#14579140—22no—
106#14579140C2314yes—
107#14579138—28no—
108#14579135—22no—
109#14579135C2314yes—
110Q8×Dic79—22no—
111Q8×Dic79—22no—
112Q8×Dic79C2314yes—
113Q8×Dic79C2314yes—
114#14579126—28no—
115#14579126—22no—
116#14579126C2314yes—
117#14579123—22no—
118#14579123C2314yes—
119(C22⋊D79)⋊C4—28no—
120#14579119—28no—
121#14579117—28no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×C22⋊Dic79—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79D411yescharacteristic
142C2×C4×Dic79D411yescharacteristic
143C2×C4×Dic79D414yes—
144C2×C4×Dic79C2311yescharacteristic
145C2×C4×Dic79C2311yescharacteristic
146C2×C4×Dic79C2314yes—
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150Dic79⋊C8C2314yes—
151Dic79⋊C8C2314yes—
152Dic79⋊C8C2314yes—
153Dic79⋊C8C2314yes—
154#14579086C2314yes—
155#14579085C2314yes—
156#14579085C2314yes—
157#14579084C2314yes—
158#14579083C2314yes—
159#14579081C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×Q8×C79C2311yescharacteristic
162C23×C4×C79C2311yescharacteristic
163C2×Q16×C79—42no—
164C2×Q16×C79C2314yes—
165C22×C8×C79—42no—
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2314yes—
169C22⋊Q8×C79—22no—
170C22⋊Q8×C79—22no—
171C22⋊Q8×C79C2314yes—
172C22⋊Q8×C79C2314yes—
173C2×C4⋊C4×C79—21no—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179#107×C79C2314yes—
180#103×C79C2314yes—
181#103×C79C2314yes—
182C23×D79—21no—
183C2×Dic158—24no—
184C2×Dic158—21no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—44no—
188C2×Dic158C2412yes—
189C2×D316—21no—
190C2×D316—22no—
191C2×D316—22no—
192C2×D316C2412yes—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—44no—
195C22×Dic79—24no—
196C22×Dic79—24no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D414yes—
204C22×Dic79C2×D414yes—
205C22×Dic79C2×D411yescharacteristic
206C2×C4×D79—24no—
207C2×C4×D79—44no—
208#11929614—44no—
209#11929613—44no—
210#11929611—44no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8—44no—
214C2×C79⋊C8C2412yes—
215C2×C79⋊C8C2412yes—
216C4⋊Dic79—24no—
217C4⋊Dic79—24no—
218C4⋊Dic79—24no—
219C4⋊Dic79—21no—
220C4⋊Dic79—21no—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229C22⋊Dic79—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79—24no—
237C4×Dic79C2×D414yes—
238C4×Dic79C2×D412yes—
239C4×Dic79C2×D412yes—
240C4×Dic79C2×D414yes—
241C4×Dic79C2412yes—
242C4×Dic79C2412yes—
243C24×C79C2×D411yescharacteristic
244C2×Q8×C79—21no—
245C2×Q8×C79—21no—
246C2×Q8×C79—22no—
247C2×Q8×C79—22no—
248C2×Q8×C79—22no—
249C2×Q8×C79—22no—
250C2×Q8×C79C2412yes—
251C2×Q8×C79C2412yes—
252C22×C4×C79—22no—
253C22×C4×C79—22no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2×D412yes—
260C22×C4×C79C2412yes—
261C22×C4×C79C2411yescharacteristic
262Q16×C79—44no—
263C2×C8×C79—22no—
264C2×C8×C79—22no—
265C2×C8×C79—44no—
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C4⋊C4×C79—24no—
269C4⋊C4×C79—24no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79C2412yes—
273C4⋊C4×C79C2412yes—
274C22⋊C4×C79—24no—
275C22⋊C4×C79—24no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79#13714yes—
279C23×C79C22×D412yes—
280C23×C79C22×D411yescharacteristic
281C22×D79—22no—
282C22×D79—42no—
283C22×D79—42no—
284C22×D79—42no—
285Q8×C79—22no—
286Q8×C79—22no—
287Q8×C79—22no—
288Q8×C79—22no—
289Q8×C79—42no—
290Q8×C79—42no—
291C2×C4×C79—22no—
292C2×C4×C79—24no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—42no—
300C2×C4×C79—42no—
301C2×C4×C79—42no—
302C2×C4×C79—42no—
303C2×C4×C79C22×D412yes—
304C2×C4×C79C22×D411yescharacteristic
305C2×C4×C79H(5,𝔽2)12yes—
306C2×C4×C792−1+412yes—
307C2×C4×C79C2511yescharacteristic
308C22⋊D79—48no—
309C2×Dic79—22no—
310C2×Dic79—28no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—28no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79#13514yes—
321C2×Dic79C22×D412yes—
322C2×Dic79C22×D412yes—
323C2×Dic79C22×D412yes—
324C2×Dic79C22×D412yes—
325D316—22no—
326D316—22no—
327D316—42no—
328C4×D79—48no—
329Dic158—22no—
330Dic158—22no—
331Dic158—42no—
332Dic158—48no—
333C8×C79—22no—
334C8×C79—22no—
335C79⋊C8—22no—
336C79⋊C8—22no—
337C22×C79—22no—
338C22×C79—28no—
339C22×C79—22no—
340C22×C79#53712yes—
341C22×C79C2×#13512yes—
342C22×C79C2×#13714yes—
343C22×C79C2×#13712yes—
344C22×C79C23×D411yescharacteristic
345C2×D79—42no—
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—84no—
349C4×C79—22no—
350C4×C79—42no—
351C4×C79—42no—
352C4×C79—42no—
353C4×C79—42no—
354C4×C79#53712yes—
355C4×C79C2×H(5,𝔽2)11yescharacteristic
356C4×C79C2×2−1+411yescharacteristic
357Dic79—22no—
358Dic79—22no—
359Dic79—22no—
360Dic79—42no—
361Dic79—42no—
362Dic79—42no—
363Dic79C2×#13514yes—
364C2×#3248—791nomaximal, Sylow
365C2×C79—24no—
366C2×C79#324814yescomplemented
367C2×C79C2×#53711yescharacteristic
368C2×C79C22×#13511yescharacteristic
369C2×C79C22×#13711yescharacteristic
370D79—82no—
371C2×#533—791no—
372C2×#529—791no—
373#3248—7916no—
374C2×#479—791no—
375C2×#479—791no—
376C2×#475—791no—
377C2×#474—791no—
378C2×#467—791no—
379C2×#467D7911yescharacteristic, complemented
380C2×#465—791no—
381C2×#465—791no—
382C2×#464—791no—
383C2×#464—791no—
384C2×#462—791no—
385C2×#461—791no—
386C22×C4⋊C8—791no—
387C79C2×#324811yescharacteristic, complemented, Sylow
388C22×Q16—791no—
389C22×Q16C2×D7911yescharacteristic
390C22×SD16—791no—
391C22×SD16—791no—
392C23×C8—791no—
393C23×C8C2×D7911yescharacteristic
394#533—798no—
395#533—1584no—
396C2×C4⋊Q8—791no—
397C2×C4⋊Q8—791no—
398#529—798no—
399#529—1584no—
400C2×#126—1581no—
401C2×#125—791no—
402C2×#125—1581no—
403C2×#124—791no—
404C2×#123—1581no—
405C2×C22⋊Q8—791no—
406C2×C22⋊Q8—1581no—
407C2×C22⋊Q8C2×D7911yescharacteristic
408C2×C22⋊Q8C2×D7911yescharacteristic
409C2×#121—791no—
410C2×C4×Q8—791no—
411C2×C4×Q8—791no—
412C2×C4×Q8—791no—
413C2×C4×Q8—1581no—
414C2×C4×D4—791no—
415C2×C4×D4—1581no—
416C2×#117—1581no—
417C2×#117—1581no—
418C22×C42—791no—
419#479—798no—
420#479—798no—
421#475—798no—
422#474—798no—
423#467—798no—
424#467C2×D7918yescomplemented
425#465—798no—
426#465—798no—
427#464—798no—
428#464—798no—
429#462—798no—
430#461—798no—
431C2×#107—791no—
432C2×#107C2×D7911yescharacteristic
433C2×#106—791no—
434C2×#106—791no—
435C2×C4⋊C8—791no—
436C2×C4⋊C8—791no—
437C2×C4⋊C8—791no—
438C2×C4⋊C8—798no—
439C2×C4⋊C8—791no—
440C2×#103—791no—
441C2×#103—791no—
442C2×#103—791no—
443C2×#103—791no—
444C2×#103C2×D7911yescharacteristic
445C2×#103C2×D7911yescharacteristic
446C2×#102—791no—
447C2×#102—791no—
448C22×Q8—791no—
449C22×Q8—1581no—
450C22×Q8C22×D7911yescharacteristic
451C22×Q8C22×D7911yescharacteristic
452C22×D4—791no—
453C22×D4—1581no—
454C23×C4—791no—
455C23×C4—791no—
456C23×C4—1581no—
457C23×C4C22×D7911yescharacteristic
458C2×Q16—42no—
459C2×Q16—3162no—
460C2×Q16—794no—
461C2×Q16C22×D7914yes—
462C2×SD16—3162no—
463C2×SD16—3162no—
464C2×SD16—794no—
465C2×SD16—794no—
466C22×C8—42no—
467C22×C8—3162no—
468C22×C8—794no—
469C22×C8—791no—
470C22×C8—791no—
471C22×C8C22×D7911yescharacteristic
472C22×C8C22×D7911yescharacteristic
473C22×C8C22×D7914yes—
474C4⋊Q8—794no—
475C4⋊Q8—794no—
476C4⋊Q8—1582no—
477C4⋊Q8—1582no—
478#126—1588no—
479#125—794no—
480#125—1582no—
481#125—1588no—
482#124—794no—
483#124—1582no—
484#123—1588no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—794no—
488C22⋊Q8—1588no—
489C22⋊Q8—1582no—
490C22⋊Q8C22×D7914yes—
491C22⋊Q8C22×D7914yes—
492#121—794no—
493#121—1582no—
494C4×Q8—794no—
495C4×Q8—794no—
496C4×Q8—794no—
497C4×Q8—1582no—
498C4×Q8—1588no—
499C4×Q8—1582no—
500C4×Q8—1582no—
501C4×D4—794no—
502C4×D4—1582no—
503C4×D4—1588no—
504#117—1588no—
505#117—1588no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1581no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4C22×D7911yescharacteristic
520C2×C4⋊C4C22×D7911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—791no—
529C2×C42—791no—
530C2×C42—794no—
531C2×C42—791no—
532C2×C42—791no—
533C2×C42—794no—
534C2×C42—1581no—
535C2×C42—1581no—
536C2×C42—1581no—
537#107—794no—
538#107C22×D7914yes—
539#106—794no—
540#106—794no—
541C4⋊C8—794no—
542C4⋊C8—794no—
543C4⋊C8—794no—
544C4⋊C8—794no—
545#103—794no—
546#103—794no—
547#103—794no—
548#103—794no—
549#103C22×D7914yes—
550#103C22×D7914yes—
551#102—794no—
552#102—794no—
553C24—1581no—
554C24D4×D7911yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—3164no—
562C2×Q8—792no—
563C2×Q8—1584no—
564C2×Q8—1582no—
565C2×Q8—1582no—
566C2×Q8—1581no—
567C2×Q8C23×D7912yes—
568C2×Q8C23×D7912yes—
569C2×D4—3164no—
570C2×D4—792no—
571C2×D4—1584no—
572C2×D4—1582no—
573C2×D4—1582no—
574C2×D4—1581no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—3164no—
582C22×C4—791no—
583C22×C4—794no—
584C22×C4—794no—
585C22×C4—791no—
586C22×C4—791no—
587C22×C4—791no—
588C22×C4—1584no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1584no—
593C22×C4—1584no—
594C22×C4D4×D7912yes—
595C22×C4D4×D7911yescharacteristic
596C22×C4C23×D7912yes—
597C22×C4C23×D7911yescharacteristic
598Q16—44no—
599Q16—3164no—
600SD16—3164no—
601SD16—3164no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—44no—
605C2×C8—3164no—
606C2×C8—792no—
607C2×C8—792no—
608C2×C8—1582no—
609C2×C8—1582no—
610C2×C8C23×D7912yes—
611C2×C8C23×D7912yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—792no—
617C4⋊C4—792no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1584no—
626C4⋊C4—1584no—
627C4⋊C4—1581no—
628C4⋊C4—1581no—
629C4⋊C4C23×D7912yes—
630C4⋊C4C23×D7912yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C42—792no—
639C42—792no—
640C42—794no—
641C42—792no—
642C42—792no—
643C42—794no—
644C42—1584no—
645C42—1584no—
646C42—1584no—
647C23—22no—
648C23—22no—
649C23—3162no—
650C23—3162no—
651C23—3162no—
652C23—1582no—
653C23#1457919314yes—
654C23C2×D4×D7912yes—
655C23C2×D4×D7911yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—3168no—
663Q8—3162no—
664Q8—1582no—
665Q8—1582no—
666D4—3168no—
667D4—3162no—
668D4—1582no—
669D4—1582no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—3168no—
683C2×C4—3162no—
684C2×C4—3162no—
685C2×C4—3162no—
686C2×C4—794no—
687C2×C4—792no—
688C2×C4—792no—
689C2×C4—792no—
690C2×C4—792no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1588no—
695C2×C4—1582no—
696C2×C4—1588no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4C2×D4×D7912yes—
700C2×C4C2×D4×D7911yescharacteristic
701C2×C4#1457920612yes—
702C2×C4#1457920812yes—
703C2×C4C24×D7911yescharacteristic
704C8—22no—
705C8—22no—
706C8—1582no—
707C8—1582no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—3162no—
712C22—3162no—
713C22—3162no—
714C22—6324no—
715C22#1909914012yes—
716C22#135×D7912yes—
717C22C2×#1457919314yes—
718C22C2×#1457919312yes—
719C22C22×D4×D7911yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—3162no—
726C4—3162no—
727C4—3162no—
728C4—794no—
729C4—1582no—
730C4—1582no—
731C4—1582no—
732C4#1909914012yes—
733C4C2×#1457920611yescharacteristic
734C4C2×#1457920811yescharacteristic
735C2—24no—
736C2—6322no—
737C2#2377473214yesdirect product factor
738C2C2×#1909914011yescharacteristic
739C2C2×#135×D7911yescharacteristic
740C2C22×#1457919311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#467×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
hypercenterC2×#467D79
hypocenterC79C2×#3248
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#19099115C2semidirect
3. #23774732C2direct (N × H)
4. C2×#19098869C2semidirect
5. C2×#19098868C2semidirect
6. C2×#19098846C2semidirect
7. C2×#19098842C2semidirect
8. C2×#19098802C2semidirect
11. C2×#19098788C2semidirect
12. C2×#19098787C2semidirect
13. C2×#19098771C2semidirect
14. C2×#19098767C2semidirect
15. C22×Dic79⋊C8C2semidirect
16. C2×#467×C79C2semidirect
22. #19099115C22semidirect
44. #19098869C22semidirect
45. #19098868C22semidirect
46. #19098846C22semidirect
47. #19098842C22semidirect
48. #19098802C22semidirect
51. #19098788C22semidirect
52. #19098787C22semidirect
53. #19098771C22semidirect
54. #19098767C22semidirect
62. C2×Dic79⋊C8C22semidirect
73. #467×C79C22semidirect
366. C2×C79#3248semidirect
379. C2×#467D79semidirect
387. C79C2×#3248semidirect
424. #467C2×D79semidirect
737. C2#23774732direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991152
C2×#190990992
#237747322
C2×#190988692
C2×#190988682
C2×#190988462
C2×#190988422
C2×#190988022
C2×#190987942
C2×#190987922
C2×#190987882
C2×#190987872
C2×#190987712
C2×#190987672
C22×Dic79⋊C82
C2×#467×C792
C2×#324879