Finite Group Databasebeta

← C2×#23777400 #35196522

Subgroups — C2×#23777400 #35196522

Order 20224.

7854 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777400C2132yesmaximal, direct product factor
2C2×#19099289C211yesmaximal, characteristic, complemented
3C2×#19099263C213yesmaximal, complemented
4C2×#19099261C213yesmaximal, complemented
5C2×#19099235C211yesmaximal, characteristic, complemented
6C2×#19099234C213yesmaximal, complemented
7C2×#19099232C211yesmaximal, characteristic, complemented
8C2×#19099232C211yesmaximal, characteristic, complemented
9C2×#19099214C213yesmaximal, complemented
10C2×#19099168C213yesmaximal, complemented
11C2×#19099164C213yesmaximal, complemented
12C2×#19099110C213yesmaximal, complemented
13C2×#19099091C213yesmaximal, complemented
14C2×#19099045C211yesmaximal, characteristic, complemented
15C2×C4×#11929625C211yesmaximal, characteristic, complemented
16C2×#520×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18C22×#11929625C2211yescharacteristic
19C22×#11929624C2216yes—
20#19099289C22116yescomplemented
21#19099263C22148yescomplemented
22#19099261C22148yescomplemented
23#19099235C22116yescomplemented
24#19099234C22148yescomplemented
25#19099232C22116yescomplemented
26#19099232C22116yescomplemented
27#19099214C22148yescomplemented
28#19099168C22148yescomplemented
29#19099164C22148yescomplemented
30#19099110C22148yescomplemented
31C2×#14579160C2213yes—
32C2×#14579158C2213yes—
33C2×#14579157C2213yes—
34C2×#14579157C2213yes—
35#19099091C22148yescomplemented
36C2×#14579156C2213yes—
37C2×#14579154C2213yes—
38C2×#14579153C2213yes—
39C2×#14579152C2213yes—
40C2×#14579151C2211yescharacteristic
41C2×#14579147C2213yes—
42C2×#14579146C2216yes—
43C2×#14579146C2213yes—
44C2×#14579144C2216yes—
45C2×#14579143C2213yes—
46C2×#14579139C2213yes—
47C2×#14579136C2213yes—
48C2×#14579136C2213yes—
49C2×#14579135C2213yes—
50C2×#14579135C2213yes—
51C2×#14579135C2216yes—
52C2×#14579134C2213yes—
53C2×#14579134C2216yes—
54C2×#14579134C2216yes—
55C2×#14579132C2213yes—
56C2×#14579132C2213yes—
57#19099045C22116yescomplemented
58C4×#11929625C22116yescomplemented
59C2×Q8×Dic79C2211yescharacteristic
60C2×Q8×Dic79C2211yescharacteristic
61C2×C4×Dic158C2213yes—
62C2×C4×D316C2213yes—
63C2×C4×D316C2213yes—
64C2×C4×D316C2213yes—
65C2×#14579123C2213yes—
66C2×#14579123C2213yes—
67C2×C4×C22⋊D79C2213yes—
68C2×C4×C22⋊D79C2213yes—
69C2×C4×C22⋊D79C2216yes—
70C2×#14579119C2213yes—
71C2×#14579118C2213yes—
72C2×C4⋊C4×D79C2213yes—
73C2×C42×D79C2213yes—
74C22×#41×C79C2211yescharacteristic
75#520×C79C22116yescomplemented
76C2×C4×Q8×C79C2211yescharacteristic
77C2×C4×Q8×C79C2211yescharacteristic
78C2×C4×D4×C79C2213yes—
79C2×C4×D4×C79C2213yes—
80C2×#117×C79C2213yes—
81C22×C4⋊C4×C79C2213yes—
82C2×#11929625—28no—
83C2×#11929625—28no—
84C2×#11929625C2318yes—
85C2×#11929625C2318yes—
86C2×#11929624—424no—
87C2×#11929624C23148yes—
88C22×Dic158C2313yes—
89C22×D316C2313yes—
90C22×D316C2313yes—
91C22×D316C2313yes—
92C22×D316C2316yes—
93C22×C22⋊D79C2313yes—
94C22×C22⋊D79C2316yes—
95C22×C22⋊D79C2313yes—
96C22×C22⋊D79C2316yes—
97C22×C4×D79C2313yes—
98C22×C4×D79C2313yes—
99C22×C4×D79C2313yes—
100C22×C4×D79C2313yes—
101C22×C4×D79C2316yes—
102#14579160C23124yes—
103#14579158C23124yes—
104#14579157C23124yes—
105#14579157C23124yes—
106#14579156C23124yes—
107#14579154C23124yes—
108#14579153C23124yes—
109#14579152C23124yes—
110#14579151C2318yes—
111#14579147C23124yes—
112#14579146C23124yes—
113#14579146C23148yes—
114#14579144C23148yes—
115#14579143C23124yes—
116#14579139C23124yes—
117#14579136C23124yes—
118#14579136C23124yes—
119#14579135C23148yes—
120#14579135C23124yes—
121#14579135C23124yes—
122#14579134C23148yes—
123#14579134C23148yes—
124#14579134C23124yes—
125#14579132C23124yes—
126#14579132C23124yes—
127Q8×Dic79C2318yes—
128Q8×Dic79C2318yes—
129C4×Dic158C23124yes—
130C4×D316C23124yes—
131C4×D316C23124yes—
132C4×D316C23124yes—
133#14579123C23124yes—
134#14579123C23124yes—
135C4×C22⋊D79C23124yes—
136C4×C22⋊D79C23124yes—
137C4×C22⋊D79C23148yes—
138#14579119C23124yes—
139#14579118C23124yes—
140C2×C4⋊Dic79C2313yes—
141C2×C4⋊Dic79C2313yes—
142C2×C4⋊Dic79C2311yescharacteristic
143C2×C4⋊Dic79C2313yes—
144C2×Dic79⋊C4C2313yes—
145C2×Dic79⋊C4C2311yescharacteristic
146C2×Dic79⋊C4C2311yescharacteristic
147C2×Dic79⋊C4C2311yescharacteristic
148C2×Dic79⋊C4C2316yes—
149C2×Dic79⋊C4C2311yescharacteristic
150C2×Dic79⋊C4C2313yes—
151C4⋊C4×D79C23124yes—
152C2×C22⋊Dic79C2313yes—
153C2×C22⋊Dic79C2313yes—
154C2×(C2×D79)⋊C4C2313yes—
155C2×(C2×D79)⋊C4C2313yes—
156C2×(C2×D79)⋊C4C2316yes—
157C2×(C2×D79)⋊C4C2313yes—
158C2×(C2×D79)⋊C4C2313yes—
159C2×(C2×D79)⋊C4C2313yes—
160C2×(C2×D79)⋊C4C2313yes—
161C2×C4×Dic79C2311yescharacteristic
162C2×C4×Dic79C2313yes—
163C2×C4×Dic79C2313yes—
164C2×C4×Dic79C2313yes—
165C42×D79C23124yes—
166C2×#41×C79—28no—
167C2×#41×C79C2318yes—
168C22×Q8×C79C2311yescharacteristic
169C22×D4×C79C2313yes—
170C23×C4×C79C2313yes—
171C23×C4×C79C2316yes—
172C4×Q8×C79C2318yes—
173C4×Q8×C79C2318yes—
174C4×D4×C79C23124yes—
175C4×D4×C79C23124yes—
176#117×C79C23124yes—
177C2×C4⋊C4×C79C23124yes—
178C2×C4⋊C4×C79C2313yes—
179C2×C4⋊C4×C79C2313yes—
180C2×C4⋊C4×C79C2313yes—
181C2×C4⋊C4×C79C2311yescharacteristic
182C2×C22⋊C4×C79C2313yes—
183C2×C22⋊C4×C79C2313yes—
184C2×C42×C79C2313yes—
185C2×C42×C79C2313yes—
186C23×D79C2413yes—
187C23×D79C2413yes—
188#11929625—232no—
189#11929625—232no—
190#11929624—496no—
191C2×Dic158—212no—
192C2×Dic158C24112yes—
193C2×D316—212no—
194C2×D316—212no—
195C2×D316—412no—
196C2×D316—46no—
197C2×D316C24112yes—
198C2×D316C24112yes—
199C2×D316C24124yes—
200C2×D316C24112yes—
201C2×C22⋊D79—212no—
202C2×C22⋊D79—412no—
203C2×C22⋊D79—46no—
204C2×C22⋊D79—412no—
205C2×C22⋊D79C24112yes—
206C2×C22⋊D79C24124yes—
207C2×C22⋊D79C24124yes—
208C2×C22⋊D79C24112yes—
209C22×Dic79C2413yes—
210C22×Dic79C2411yescharacteristic
211C22×Dic79C2411yescharacteristic
212C22×Dic79C2413yes—
213C22×Dic79C2411yescharacteristic
214C22×Dic79C2411yescharacteristic
215C2×C4×D79—212no—
216C2×C4×D79—212no—
217C2×C4×D79—212no—
218C2×C4×D79—412no—
219C2×C4×D79—46no—
220C2×C4×D79C24112yes—
221C2×C4×D79C24112yes—
222C2×C4×D79C24112yes—
223C2×C4×D79C24124yes—
224C2×C4×D79C24112yes—
225C4⋊Dic79C24112yes—
226C4⋊Dic79C24112yes—
227C4⋊Dic79C2414yes—
228C4⋊Dic79C24112yes—
229Dic79⋊C4C24112yes—
230Dic79⋊C4C2414yes—
231Dic79⋊C4C2414yes—
232Dic79⋊C4C2414yes—
233Dic79⋊C4C24124yes—
234Dic79⋊C4C2414yes—
235Dic79⋊C4C24112yes—
236C22⋊Dic79C24112yes—
237C22⋊Dic79C24112yes—
238(C2×D79)⋊C4C24112yes—
239(C2×D79)⋊C4C24112yes—
240(C2×D79)⋊C4C24124yes—
241(C2×D79)⋊C4C24112yes—
242(C2×D79)⋊C4C24112yes—
243(C2×D79)⋊C4C24112yes—
244(C2×D79)⋊C4C24112yes—
245C4×Dic79C2414yes—
246C4×Dic79C24112yes—
247C4×Dic79C24112yes—
248C4×Dic79C24112yes—
249C24×C79C2413yes—
250#41×C79—232no—
251C2×Q8×C79#4118yescomplemented
252C2×Q8×C79C2414yes—
253C2×D4×C79—212no—
254C2×D4×C79C24112yes—
255C22×C4×C79—212no—
256C22×C4×C79—412no—
257C22×C4×C79C2413yes—
258C22×C4×C79C2411yescharacteristic
259C22×C4×C79C2411yescharacteristic
260C22×C4×C79C2413yes—
261C22×C4×C79C2411yescharacteristic
262C22×C4×C79C24112yes—
263C22×C4×C79C24124yes—
264C22×C4×C79C2413yes—
265C4⋊C4×C79C24112yes—
266C4⋊C4×C79C24112yes—
267C4⋊C4×C79C24112yes—
268C4⋊C4×C79C2414yes—
269C22⋊C4×C79C24112yes—
270C22⋊C4×C79C24112yes—
271C42×C79C24112yes—
272C42×C79C24112yes—
273C23×C79—26no—
274C23×C79—26no—
275C23×C79—26no—
276C23×C79C2516yes—
277C23×C79C2511yescharacteristic
278C22×D79—26no—
279C22×D79—26no—
280C22×D79—26no—
281C22×D79—26no—
282C22×D79—26no—
283C22×D79—26no—
284C22×D79C2516yes—
285C22×D79C2516yes—
286Q8×C79C2×#41116yescomplemented
287D4×C79—224no—
288C2×C4×C79—22no—
289C2×C4×C79—26no—
290C2×C4×C79—26no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—224no—
294C2×C4×C79—424no—
295C2×C4×C79C2×#41112yes—
296C2×C4×C79C2512yes—
297C2×C4×C79C2516yes—
298C2×C4×C79C2512yes—
299C2×C4×C79C2516yes—
300C2×C4×C79C2512yes—
301C2×C4×C79C2516yes—
302C22⋊D79—224no—
303C22⋊D79—412no—
304C22⋊D79—424no—
305C22⋊D79—424no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—26no—
309C2×Dic79—26no—
310C2×Dic79—22no—
311C2×Dic79H(5,𝔽2)14yes—
312C2×Dic79C2512yes—
313C2×Dic79C2512yes—
314C2×Dic79C2516yes—
315C2×Dic79C2516yes—
316C2×Dic79C2512yes—
317C2×Dic79C2512yes—
318D316—224no—
319D316—224no—
320D316—412no—
321D316—424no—
322C4×D79—224no—
323C4×D79—224no—
324C4×D79—224no—
325C4×D79—412no—
326C4×D79—424no—
327Dic158—224no—
328C22×C79—26no—
329C22×C79—26no—
330C22×C79—26no—
331C22×C79—412no—
332C22×C79C22×#4112yes—
333C22×C79C2×H(5,𝔽2)12yes—
334C22×C79#58512yes—
335C22×C79C2611yescharacteristic
336C2×D79—26no—
337C2×D79—26no—
338C2×D79—26no—
339C2×D79—26no—
340C2×D79—26no—
341C2×D79—26no—
342C2×D79—412no—
343C2×D79—412no—
344C4×C79—22no—
345C4×C79—26no—
346C4×C79—26no—
347C4×C79—22no—
348C4×C79—22no—
349C4×C79C22×#41112yes—
350Dic79—22no—
351Dic79—22no—
352Dic79—26no—
353Dic79—22no—
354Dic79—26no—
355Dic79C2×H(5,𝔽2)14yes—
356C2×#3517—791nomaximal, Sylow
357C2×C79—46no—
358C2×C79#351714yescomplemented
359C2×C79C23×#4111yescharacteristic
360C2×C79C22×H(5,𝔽2)11yescharacteristic
361C2×C79C2×#58511yescharacteristic
362D79—46no—
363D79—46no—
364#3517—7932no—
365C2×#557—791no—
366C2×#553—793no—
367C2×#553—793no—
368C2×#550—791no—
369C2×#550—791no—
370C2×#550—791no—
371C2×#550—793no—
372C2×#547—793no—
373C2×#540—793no—
374C2×#540—793no—
375C2×#532—793no—
376C2×#529—793no—
377C2×#520—791no—
378C2×#520D7911yescharacteristic, complemented
379C2×C4×#41—791no—
380C79C2×#351711yescharacteristic, complemented, Sylow
381C22×#41—791no—
382C22×#41—791no—
383C22×#41—796no—
384C22×#41C2×D7911yescharacteristic
385#557—7916no—
386#553—7948no—
387#553—7948no—
388#550—7916no—
389#550—7916no—
390#550—7916no—
391#550—7948no—
392#547—7948no—
393#540—7948no—
394#540—7948no—
395#532—7948no—
396C2×C4⋊Q8—793no—
397C2×#127—793no—
398C2×#127—793no—
399C2×#127—793no—
400#529—7948no—
401C2×#126—793no—
402C2×#126—793no—
403C2×#125—791no—
404C2×#125—793no—
405C2×#125—793no—
406C2×#124—793no—
407C2×#123—796no—
408C2×#123—793no—
409C2×#123—796no—
410C2×#123—793no—
411C2×C22⋊Q8—793no—
412C2×#121—793no—
413C2×#121—793no—
414C2×#121—793no—
415C2×#121—796no—
416C2×#121—793no—
417C2×#121—793no—
418C2×#121—793no—
419C2×#121—793no—
420C2×#121—796no—
421C2×#121—796no—
422#520—7916no—
423#520C2×D79116yescomplemented
424C4×#41—7916no—
425C2×C4×Q8—791no—
426C2×C4×Q8—791no—
427C2×C4×Q8—793no—
428C2×C4×Q8C2×D7911yescharacteristic
429C2×C4×Q8C2×D7911yescharacteristic
430C2×C4×D4—793no—
431C2×C4×D4—793no—
432C2×C4×D4—796no—
433C2×C4×D4—793no—
434C2×C4×D4—793no—
435C2×C4×D4—793no—
436C2×C4×D4—793no—
437C2×C4×D4—793no—
438C2×C4×D4C2×D7913yes—
439C2×C4×D4C2×D7913yes—
440C2×#117—793no—
441C2×#117—793no—
442C2×#117C2×D7913yes—
443C22×C4⋊C4—793no—
444C22×C4⋊C4C2×D7913yes—
445C22×C42—793no—
446C2×#41—28no—
447C2×#41—31624no—
448C2×#41—798no—
449C2×#41—798no—
450C2×#41—7948no—
451C2×#41—1588no—
452C2×#41—1588no—
453C2×#41C22×D7918yes—
454C22×Q8—793no—
455C22×Q8C22×D7911yescharacteristic
456C22×D4—796no—
457C22×D4—793no—
458C22×D4—796no—
459C22×D4—793no—
460C22×D4—793no—
461C22×D4—796no—
462C22×D4—793no—
463C22×D4—793no—
464C22×D4C22×D7913yes—
465C23×C4—796no—
466C23×C4—793no—
467C23×C4—793no—
468C23×C4—793no—
469C23×C4—793no—
470C23×C4C22×D7913yes—
471C23×C4C22×D7916yes—
472C4⋊Q8—7924no—
473#127—7924no—
474#127—7924no—
475#127—7924no—
476#126—7924no—
477#126—7924no—
478#125—798no—
479#125—7924no—
480#125—7924no—
481#124—7924no—
482#123—7948no—
483#123—7924no—
484#123—7948no—
485#123—7924no—
486C22⋊Q8—7924no—
487#121—7924no—
488#121—7924no—
489#121—7924no—
490#121—7948no—
491#121—7924no—
492#121—7924no—
493#121—7924no—
494#121—7924no—
495#121—7948no—
496#121—7948no—
497C4×Q8—798no—
498C4×Q8—798no—
499C4×Q8—7924no—
500C4×Q8C22×D7918yes—
501C4×Q8C22×D7918yes—
502C4×D4—7924no—
503C4×D4—7924no—
504C4×D4—7948no—
505C4×D4—7924no—
506C4×D4—7924no—
507C4×D4—7924no—
508C4×D4—7924no—
509C4×D4—7924no—
510C4×D4C22×D79124yes—
511C4×D4C22×D79124yes—
512#117—7924no—
513#117—7924no—
514#117C22×D79124yes—
515C2×C4⋊C4—793no—
516C2×C4⋊C4—793no—
517C2×C4⋊C4—791no—
518C2×C4⋊C4—793no—
519C2×C4⋊C4—791no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—791no—
522C2×C4⋊C4—796no—
523C2×C4⋊C4—791no—
524C2×C4⋊C4—793no—
525C2×C4⋊C4—793no—
526C2×C4⋊C4—7924no—
527C2×C4⋊C4C22×D7913yes—
528C2×C4⋊C4C22×D7913yes—
529C2×C4⋊C4C22×D7913yes—
530C2×C4⋊C4C22×D79124yes—
531C2×C4⋊C4C22×D7911yescharacteristic
532C2×C22⋊C4—793no—
533C2×C22⋊C4—793no—
534C2×C22⋊C4—793no—
535C2×C22⋊C4—796no—
536C2×C22⋊C4—793no—
537C2×C22⋊C4—793no—
538C2×C22⋊C4—793no—
539C2×C22⋊C4—793no—
540C2×C22⋊C4—793no—
541C2×C22⋊C4C22×D7913yes—
542C2×C22⋊C4C22×D7913yes—
543C2×C42—793no—
544C2×C42—793no—
545C2×C42—793no—
546C2×C42—791no—
547C2×C42—7924no—
548C2×C42C22×D7913yes—
549C2×C42C22×D7913yes—
550C24—793no—
551C24—793no—
552C24C23×D7913yes—
553#41—232no—
554#41—31696no—
555#41—15832no—
556#41—15832no—
557C2×Q8—7912no—
558C2×Q8—15812no—
559C2×Q8#1192962418yescomplemented
560C2×Q8C23×D7914yes—
561C2×D4—212no—
562C2×D4—3166no—
563C2×D4—31612no—
564C2×D4—31612no—
565C2×D4—3166no—
566C2×D4—31612no—
567C2×D4—7924no—
568C2×D4—7912no—
569C2×D4—7924no—
570C2×D4—7912no—
571C2×D4—7912no—
572C2×D4—7924no—
573C2×D4—7912no—
574C2×D4—7912no—
575C2×D4—15812no—
576C2×D4—15812no—
577C2×D4—15812no—
578C2×D4C23×D79112yes—
579C22×C4—212no—
580C22×C4—412no—
581C22×C4—3166no—
582C22×C4—31612no—
583C22×C4—7912no—
584C22×C4—7924no—
585C22×C4—791no—
586C22×C4—791no—
587C22×C4—791no—
588C22×C4—793no—
589C22×C4—793no—
590C22×C4—791no—
591C22×C4—7912no—
592C22×C4—7912no—
593C22×C4—7912no—
594C22×C4—15812no—
595C22×C4—15812no—
596C22×C4—15812no—
597C22×C4C23×D79112yes—
598C22×C4C23×D7911yescharacteristic
599C22×C4C23×D7913yes—
600C22×C4C23×D7911yescharacteristic
601C22×C4C23×D7913yes—
602C22×C4C23×D7911yescharacteristic
603C22×C4C23×D79124yes—
604C22×C4C23×D7913yes—
605C4⋊C4—7912no—
606C4⋊C4—794no—
607C4⋊C4—794no—
608C4⋊C4—794no—
609C4⋊C4—7924no—
610C4⋊C4—794no—
611C4⋊C4—7912no—
612C4⋊C4—7912no—
613C4⋊C4—7912no—
614C4⋊C4—794no—
615C4⋊C4—7912no—
616C4⋊C4C23×D79112yes—
617C4⋊C4C23×D79112yes—
618C4⋊C4C23×D79112yes—
619C4⋊C4C23×D7914yes—
620C22⋊C4—7912no—
621C22⋊C4—7912no—
622C22⋊C4—7912no—
623C22⋊C4—7924no—
624C22⋊C4—7912no—
625C22⋊C4—7912no—
626C22⋊C4—7912no—
627C22⋊C4—7912no—
628C22⋊C4—7912no—
629C22⋊C4C23×D79112yes—
630C22⋊C4C23×D79112yes—
631C42—794no—
632C42—7912no—
633C42—7912no—
634C42—7912no—
635C42C23×D79112yes—
636C42C23×D79112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—796no—
641C23—796no—
642C23—1586no—
643C23—1586no—
644C23—1586no—
645C23—1586no—
646C23—1586no—
647C23—1586no—
648C23C24×D7916yes—
649C23C24×D7911yescharacteristic
650Q8—15824no—
651Q8C2×#11929624116yescomplemented
652D4—224no—
653D4—31624no—
654D4—31612no—
655D4—31624no—
656D4—31612no—
657D4—31624no—
658D4—15824no—
659D4—15824no—
660D4—15824no—
661C2×C4—26no—
662C2×C4—26no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—224no—
667C2×C4—424no—
668C2×C4—31624no—
669C2×C4—31612no—
670C2×C4—794no—
671C2×C4—792no—
672C2×C4—792no—
673C2×C4—792no—
674C2×C4—796no—
675C2×C4—796no—
676C2×C4—792no—
677C2×C4—15824no—
678C2×C4—1586no—
679C2×C4—1586no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—15824no—
684C2×C4—15824no—
685C2×C4C2×#11929624112yes—
686C2×C4C24×D7912yes—
687C2×C4C24×D7916yes—
688C2×C4C24×D7912yes—
689C2×C4C24×D7916yes—
690C2×C4C24×D7912yes—
691C2×C4C24×D7916yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—31612no—
697C22—31612no—
698C22—1586no—
699C22—1586no—
700C22—1586no—
701C22—1586no—
702C22—1586no—
703C22—1586no—
704C22C22×#1192962412yes—
705C22H(5,𝔽2)×D7912yes—
706C22#1909940012yes—
707C22C25×D7911yescharacteristic
708C4—22no—
709C4—26no—
710C4—26no—
711C4—22no—
712C4—22no—
713C4—794no—
714C4—1582no—
715C4—1582no—
716C4—1586no—
717C4—1586no—
718C4—1582no—
719C4C22×#11929624112yes—
720C2—46no—
721C2—3166no—
722C2—3166no—
723C2#2377740014yesdirect product factor
724C2C23×#1192962411yescharacteristic
725C2C2×H(5,𝔽2)×D7911yescharacteristic
726C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#520×C79C2
socleC23×C79C25
hypercenterC2×#520D79
hypocenterC79C2×#3517
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #23777400C2direct (N × H)
2. C2×#19099289C2semidirect
3. C2×#19099263C2semidirect
4. C2×#19099261C2semidirect
5. C2×#19099235C2semidirect
6. C2×#19099234C2semidirect
7. C2×#19099232C2semidirect
8. C2×#19099232C2semidirect
9. C2×#19099214C2semidirect
10. C2×#19099168C2semidirect
11. C2×#19099164C2semidirect
12. C2×#19099110C2semidirect
13. C2×#19099091C2semidirect
14. C2×#19099045C2semidirect
15. C2×C4×#11929625C2semidirect
16. C2×#520×C79C2semidirect
20. #19099289C22semidirect
21. #19099263C22semidirect
22. #19099261C22semidirect
23. #19099235C22semidirect
24. #19099234C22semidirect
25. #19099232C22semidirect
26. #19099232C22semidirect
27. #19099214C22semidirect
28. #19099168C22semidirect
29. #19099164C22semidirect
30. #19099110C22semidirect
35. #19099091C22semidirect
57. #19099045C22semidirect
58. C4×#11929625C22semidirect
75. #520×C79C22semidirect
251. C2×Q8×C79#41semidirect
286. Q8×C79C2×#41semidirect
358. C2×C79#3517semidirect
378. C2×#520D79semidirect
380. C79C2×#3517semidirect
423. #520C2×D79semidirect
559. C2×Q8#11929624semidirect
651. Q8C2×#11929624semidirect
723. C2#23777400direct (N × H)

Maximal subgroups

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

subgroupindex
#237774002
C2×#190992892
C2×#190992632
C2×#190992612
C2×#190992352
C2×#190992342
C2×#190992322
C2×#190992142
C2×#190991682
C2×#190991642
C2×#190991102
C2×#190990912
C2×#190990452
C2×C4×#119296252
C2×#520×C792
C2×#351779