Finite Group Databasebeta

← C2×#23774856 #35161229

Subgroups — C2×#23774856 #35161229

Order 20224.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099184C211yesmaximal, characteristic, complemented
2#23774856C2116yesmaximal, direct product factor
3C2×#19098858C211yesmaximal, characteristic, complemented
4C2×#19098855C211yesmaximal, characteristic, complemented
5C2×#19098843C211yesmaximal, characteristic, complemented
6C2×#19098840C211yesmaximal, characteristic, complemented
7C2×#19098811C211yesmaximal, characteristic, complemented
8C2×#19098807C211yesmaximal, characteristic, complemented
9C2×#19098802C211yesmaximal, characteristic, complemented
10C2×#19098797C211yesmaximal, characteristic
11C2×#19098785C211yesmaximal, characteristic, complemented
12C2×#19098782C211yesmaximal, characteristic, complemented
13C2×#19098778C211yesmaximal, characteristic, complemented
14C2×#19098775C211yesmaximal, characteristic, complemented
15C2×#19098590C211yesmaximal, characteristic, complemented
16C2×#542×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929612C2211yescharacteristic
19C22×#11929611C2211yescharacteristic
20C22×#11929609C2211yescharacteristic
21C22×#11929608C2211yescharacteristic
22C23×C79⋊C8C2211yescharacteristic
23#19099184—24no—
24#19099184C2218yescomplemented
25C2×#14579161C2211yescharacteristic
26C2×#14579156—21no—
27C2×#14579149C2211yescharacteristic
28C2×#14579147—21no—
29C2×#14579143—21no—
30C2×#14579140C2211yescharacteristic
31C2×#14579139—21no—
32C2×#14579135C2211yescharacteristic
33C2×C4×Dic158C2211yescharacteristic
34C2×C4×D316C2211yescharacteristic
35#19098858C2218yescomplemented
36#19098855C2218yescomplemented
37#19098843C2218yescomplemented
38#19098840C2218yescomplemented
39#19098811C2218yescomplemented
40#19098807C2218yescomplemented
41#19098802C2218yescomplemented
42#19098797C2218yes—
43#19098785C2218yescomplemented
44#19098782C2218yescomplemented
45#19098778C2218yescomplemented
46#19098775C2218yescomplemented
47C2×#14579094C2211yescharacteristic
48C2×#14579094C2211yescharacteristic
49C2×#14579094C2211yescharacteristic
50C2×#14579094C2211yescharacteristic
51#19098590C2218yescomplemented
52C2×C4⋊(C79⋊C8)C2211yescharacteristic
53C2×C4⋊(C79⋊C8)C2211yescharacteristic
54C2×C4⋊(C79⋊C8)C2211yescharacteristic
55C2×C4⋊(C79⋊C8)C2211yescharacteristic
56C2×#14579085C2211yescharacteristic
57C2×#14579085C2211yescharacteristic
58C2×#14579084C2211yescharacteristic
59C2×#14579084C2211yescharacteristic
60C2×#14579082C2211yescharacteristic
61C2×#14579082C2211yescharacteristic
62C2×#14579081C2211yescharacteristic
63C2×#14579081C2211yescharacteristic
64#542×C79—24no—
65#542×C79C2218yescomplemented
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#126×C79—21no—
68C2×#124×C79—21no—
69C2×#124×C79C2211yescharacteristic
70C2×#123×C79—21no—
71C2×C22⋊Q8×C79—21no—
72C2×C22⋊Q8×C79C2211yescharacteristic
73C2×#121×C79C2211yescharacteristic
74C2×C4×Q8×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C2×#117×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C22×C4×D79—21no—
82C2×#11929614—42no—
83C2×#11929614C2314yes—
84C2×#11929612—42no—
85C2×#11929612C2314yes—
86C2×#11929611—42no—
87C2×#11929611C2314yes—
88C2×#11929609—42no—
89C2×#11929609C2314yes—
90C2×#11929608—42no—
91C2×#11929608C2314yes—
92C22×C79⋊C8—42no—
93C22×C79⋊C8C2311yescharacteristic
94C22×C79⋊C8C2311yescharacteristic
95C22×C79⋊C8C2311yescharacteristic
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2314yes—
98#14579161—22no—
99#14579161C2314yes—
100#14579156—28no—
101#14579149—22no—
102#14579149C2314yes—
103#14579147—28no—
104#14579143—28no—
105#14579140—22no—
106#14579140C2314yes—
107#14579139—28no—
108#14579135—22no—
109#14579135C2314yes—
110C4×Dic158—22no—
111C4×Dic158C2314yes—
112C4×D316—22no—
113C4×D316C2314yes—
114C2×C4⋊Dic79—21no—
115C2×C4⋊Dic79C2311yescharacteristic
116C2×C4⋊Dic79C2311yescharacteristic
117C2×Dic79⋊C4—21no—
118C2×Dic79⋊C4—21no—
119C2×C22⋊Dic79—21no—
120C2×(C2×D79)⋊C4—21no—
121C2×(C2×D79)⋊C4—21no—
122C2×(C2×D79)⋊C4—21no—
123C2×(C2×D79)⋊C4—21no—
124C2×C4×Dic79—21no—
125#14579094C2314yes—
126#14579094C2314yes—
127#14579094C2314yes—
128#14579094C2314yes—
129C4⋊(C79⋊C8)C2314yes—
130C4⋊(C79⋊C8)C2314yes—
131C4⋊(C79⋊C8)C2314yes—
132C4⋊(C79⋊C8)C2314yes—
133#14579085C2314yes—
134#14579085C2314yes—
135#14579084C2314yes—
136#14579084C2314yes—
137#14579082C2314yes—
138#14579082C2314yes—
139#14579081C2314yes—
140#14579081C2314yes—
141C22×Q8×C79—21no—
142C22×Q8×C79C2311yescharacteristic
143C22×D4×C79—21no—
144C22×D4×C79C2311yescharacteristic
145C23×C4×C79—21no—
146C23×C4×C79C2311yescharacteristic
147C4⋊Q8×C79—22no—
148C4⋊Q8×C79C2314yes—
149#126×C79—28no—
150#124×C79—28no—
151#124×C79—22no—
152#124×C79C2314yes—
153#123×C79—28no—
154C22⋊Q8×C79—22no—
155C22⋊Q8×C79—28no—
156C22⋊Q8×C79C2314yes—
157#121×C79—22no—
158#121×C79C2314yes—
159C4×Q8×C79—22no—
160C4×Q8×C79C2314yes—
161C4×D4×C79—22no—
162C4×D4×C79C2314yes—
163#117×C79D414yes—
164#117×C79C2314yes—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—21no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79D411yescharacteristic
169C2×C4⋊C4×C79D411yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177C2×C22⋊C4×C79D411yescharacteristic
178C2×C22⋊C4×C79D411yescharacteristic
179C2×C42×C79—21no—
180C2×C42×C79C2311yescharacteristic
181C2×C42×C79C2311yescharacteristic
182C23×D79—21no—
183C2×Dic158—21no—
184C2×Dic158—24no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—82no—
188C2×Dic158C2412yes—
189C2×D316—21no—
190C2×D316—22no—
191C2×D316—22no—
192C2×D316C2412yes—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—82no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C2×C4×D79—24no—
199C2×C4×D79—82no—
200#11929614—44no—
201#11929612—44no—
202#11929611—44no—
203#11929609—44no—
204#11929608—44no—
205C2×C79⋊C8—22no—
206C2×C79⋊C8—22no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8—22no—
209C2×C79⋊C8—44no—
210C2×C79⋊C8C2412yes—
211C2×C79⋊C8C2412yes—
212C2×C79⋊C8C2412yes—
213C2×C79⋊C8C2412yes—
214C4⋊Dic79—24no—
215C4⋊Dic79—21no—
216C4⋊Dic79—21no—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221C22⋊Dic79—24no—
222(C2×D79)⋊C4—24no—
223(C2×D79)⋊C4—24no—
224(C2×D79)⋊C4—24no—
225(C2×D79)⋊C4—24no—
226C4×Dic79—24no—
227C24×C79—21no—
228C24×C79C2×D411yescharacteristic
229C2×Q8×C79—21no—
230C2×Q8×C79—24no—
231C2×Q8×C79—22no—
232C2×Q8×C79—22no—
233C2×Q8×C79—82no—
234C2×Q8×C79C2412yes—
235C2×D4×C79—24no—
236C2×D4×C79—21no—
237C2×D4×C79—22no—
238C2×D4×C79—22no—
239C2×D4×C79—82no—
240C2×D4×C79C2412yes—
241C22×C4×C79—22no—
242C22×C4×C79—22no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—24no—
247C22×C4×C79—82no—
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D412yes—
254C22×C4×C79C2412yes—
255C22×C4×C79C2411yescharacteristic
256C4⋊C4×C79—24no—
257C4⋊C4×C79—24no—
258C4⋊C4×C79—24no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79C2×D414yes—
262C4⋊C4×C79C2×D414yes—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C22⋊C4×C79—24no—
266C22⋊C4×C79—24no—
267C22⋊C4×C79—24no—
268C22⋊C4×C79—24no—
269C22⋊C4×C79—24no—
270C22⋊C4×C79C2×D414yes—
271C22⋊C4×C79C2×D414yes—
272C42×C79—24no—
273C42×C79C2×D412yes—
274C42×C79C2×D412yes—
275C42×C79C2412yes—
276C42×C79C2412yes—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—22no—
280C23×C79—22no—
281C23×C79—42no—
282C23×C79—42no—
283C23×C79—42no—
284C23×C79C22×D412yes—
285C23×C79C22×D411yescharacteristic
286C22×D79—22no—
287C22×D79—42no—
288C22×D79—42no—
289C22×D79—42no—
290Q8×C79—22no—
291Q8×C79—22no—
292Q8×C79—42no—
293Q8×C79—84no—
294D4×C79—22no—
295D4×C79—22no—
296D4×C79—42no—
297D4×C79—84no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—24no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—42no—
310C2×C4×C79—42no—
311C2×C4×C79—42no—
312C2×C4×C79—84no—
313C2×C4×C79C22×D412yes—
314C2×C4×C79C22×D412yes—
315C2×C4×C79C22×D412yes—
316C2×C4×C79C22×D412yes—
317C2×C4×C79C22×D412yes—
318C2×C4×C79C22×D411yescharacteristic
319C2×C4×C79H(5,𝔽2)12yes—
320C2×C4×C792−1+412yes—
321C2×C4×C79C2511yescharacteristic
322C22⋊D79—84no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—42no—
327C2×Dic79—42no—
328C2×Dic79—42no—
329D316—22no—
330D316—22no—
331D316—42no—
332C4×D79—84no—
333Dic158—22no—
334Dic158—22no—
335Dic158—42no—
336Dic158—84no—
337C79⋊C8—22no—
338C79⋊C8—22no—
339C79⋊C8—22no—
340C79⋊C8—22no—
341C22×C79—22no—
342C22×C79—22no—
343C22×C79—22no—
344C22×C79—44no—
345C22×C79—42no—
346C22×C79—42no—
347C22×C79—42no—
348C22×C79—84no—
349C22×C79#53712yes—
350C22×C79#57612yes—
351C22×C79#57812yes—
352C22×C79C23×D411yescharacteristic
353C2×D79—42no—
354C2×D79—42no—
355C2×D79—42no—
356C2×D79—84no—
357C4×C79—22no—
358C4×C79—22no—
359C4×C79—22no—
360C4×C79—22no—
361C4×C79—22no—
362C4×C79—42no—
363C4×C79—42no—
364C4×C79—42no—
365C4×C79#53712yes—
366C4×C79C2×H(5,𝔽2)11yescharacteristic
367C4×C79C2×2−1+411yescharacteristic
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371C2×#3262—791nomaximal, Sylow
372C2×C79—42no—
373C2×C79—82no—
374C2×C79#326214yescomplemented
375C2×C79C2×#53711yescharacteristic
376C2×C79C2×#57611yescharacteristic
377C2×C79C2×#57811yescharacteristic
378D79—82no—
379C2×#542—791no—
380C2×#542D7911yescharacteristic, complemented
381#3262—7916no—
382C2×#477—791no—
383C2×#477—791no—
384C2×#474—791no—
385C2×#474—791no—
386C2×#468—791no—
387C2×#468—791no—
388C2×#467—791no—
389C2×#466—791no—
390C2×#464—791no—
391C2×#464—791no—
392C2×#463—791no—
393C2×#463—791no—
394C2×#424—791no—
395C79C2×#326211yescharacteristic, complemented, Sylow
396C22×Q16—791no—
397C22×SD16—791no—
398C22×SD16—791no—
399C22×D8—791no—
400C22×M16—791no—
401C23×C8—791no—
402#542—24no—
403#542—798no—
404#542—1584no—
405#542C2×D7918yescomplemented
406C2×C4⋊Q8—791no—
407C2×C4⋊Q8C2×D7911yescharacteristic
408C2×#126—21no—
409C2×#126—1581no—
410C2×#124—21no—
411C2×#124—791no—
412C2×#124—1581no—
413C2×#124C2×D7911yescharacteristic
414C2×#123—21no—
415C2×#123—1581no—
416C2×C22⋊Q8—21no—
417C2×C22⋊Q8—791no—
418C2×C22⋊Q8—1581no—
419C2×C22⋊Q8C2×D7911yescharacteristic
420C2×#121—791no—
421C2×#121C2×D7911yescharacteristic
422C2×C4×Q8—791no—
423C2×C4×Q8C2×D7911yescharacteristic
424C2×C4×D4—791no—
425C2×C4×D4C2×D7911yescharacteristic
426C2×#117C2×D7911yescharacteristic
427#477—798no—
428#477—798no—
429#474—798no—
430#474—798no—
431#468—798no—
432#468—798no—
433#467—798no—
434#466—798no—
435#464—798no—
436#464—798no—
437#463—798no—
438#463—798no—
439C2×#107—791no—
440C2×#107—791no—
441C2×#107—791no—
442C2×#107—791no—
443#424—798no—
444C2×C4⋊C8—791no—
445C2×C4⋊C8—791no—
446C2×C4⋊C8—791no—
447C2×C4⋊C8—791no—
448C2×#103—791no—
449C2×#103—791no—
450C2×#103—791no—
451C2×#103—791no—
452C2×#102—791no—
453C2×#102—791no—
454C2×#102—791no—
455C2×#102—791no—
456C22×Q8—21no—
457C22×Q8—791no—
458C22×Q8—1581no—
459C22×Q8C22×D7911yescharacteristic
460C22×D4—21no—
461C22×D4—791no—
462C22×D4—1581no—
463C22×D4C22×D7911yescharacteristic
464C23×C4—21no—
465C23×C4—1581no—
466C23×C4C22×D7911yescharacteristic
467C2×Q16—3162no—
468C2×Q16—794no—
469C2×SD16—3162no—
470C2×SD16—3162no—
471C2×SD16—794no—
472C2×SD16—794no—
473C2×D8—3162no—
474C2×D8—794no—
475C2×M16—3162no—
476C2×M16—794no—
477C22×C8—3162no—
478C22×C8—794no—
479C22×C8—791no—
480C22×C8—791no—
481C22×C8—791no—
482C22×C8—791no—
483C4⋊Q8—22no—
484C4⋊Q8—794no—
485C4⋊Q8—1582no—
486C4⋊Q8C22×D7914yes—
487#126—28no—
488#126—1588no—
489#124—28no—
490#124—22no—
491#124—794no—
492#124—1588no—
493#124—1582no—
494#124C22×D7914yes—
495#123—28no—
496#123—1588no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8—794no—
500C22⋊Q8—1582no—
501C22⋊Q8—1588no—
502C22⋊Q8C22×D7914yes—
503#121—22no—
504#121—794no—
505#121—1582no—
506#121C22×D7914yes—
507C4×Q8—22no—
508C4×Q8—794no—
509C4×Q8—1582no—
510C4×Q8C22×D7914yes—
511C4×D4—22no—
512C4×D4—794no—
513C4×D4—1582no—
514C4×D4C22×D7914yes—
515#117C22⋊D7914yes—
516#117C22×D7914yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—791no—
522C2×C4⋊C4—1581no—
523C2×C4⋊C4—1581no—
524C2×C4⋊C4—1581no—
525C2×C4⋊C4C22⋊D7911yescharacteristic
526C2×C4⋊C4C22⋊D7911yescharacteristic
527C2×C4⋊C4C22×D7911yescharacteristic
528C2×C4⋊C4C22×D7911yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1581no—
535C2×C22⋊C4—1581no—
536C2×C22⋊C4—1581no—
537C2×C22⋊C4—1581no—
538C2×C22⋊C4—1581no—
539C2×C22⋊C4C22⋊D7911yescharacteristic
540C2×C22⋊C4C22⋊D7911yescharacteristic
541C2×C42—21no—
542C2×C42—1581no—
543C2×C42C22×D7911yescharacteristic
544C2×C42C22×D7911yescharacteristic
545#107—794no—
546#107—794no—
547#107—794no—
548#107—794no—
549C4⋊C8—794no—
550C4⋊C8—794no—
551C4⋊C8—794no—
552C4⋊C8—794no—
553#103—794no—
554#103—794no—
555#103—794no—
556#103—794no—
557#102—794no—
558#102—794no—
559#102—794no—
560#102—794no—
561C24—21no—
562C24—1581no—
563C24C2×C22⋊D7911yescharacteristic
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—792no—
570C2×Q8—6322no—
571C2×Q8—1582no—
572C2×Q8—1582no—
573C2×Q8—1581no—
574C2×Q8—1584no—
575C2×Q8C23×D7912yes—
576C2×D4—24no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—82no—
581C2×D4—792no—
582C2×D4—6322no—
583C2×D4—1584no—
584C2×D4—1582no—
585C2×D4—1582no—
586C2×D4—1581no—
587C2×D4C23×D7912yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—6322no—
596C22×C4—1581no—
597C22×C4—1581no—
598C22×C4—1581no—
599C22×C4—1584no—
600C22×C4C2×C22⋊D7912yes—
601C22×C4C2×C22⋊D7911yescharacteristic
602C22×C4C2×C22⋊D7911yescharacteristic
603C22×C4C2×C22⋊D7911yescharacteristic
604C22×C4C2×C22⋊D7911yescharacteristic
605C22×C4C2×C22⋊D7911yescharacteristic
606C22×C4C23×D7912yes—
607C22×C4C23×D7911yescharacteristic
608Q16—3164no—
609SD16—3164no—
610SD16—3164no—
611D8—3164no—
612M16—3164no—
613C2×C8—3164no—
614C2×C8—792no—
615C2×C8—792no—
616C2×C8—792no—
617C2×C8—792no—
618C2×C8—1582no—
619C2×C8—1582no—
620C2×C8—1582no—
621C2×C8—1582no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—792no—
628C4⋊C4—792no—
629C4⋊C4—1584no—
630C4⋊C4—1584no—
631C4⋊C4—1581no—
632C4⋊C4—1581no—
633C4⋊C4—1584no—
634C4⋊C4C2×C22⋊D7914yes—
635C4⋊C4C2×C22⋊D7914yes—
636C4⋊C4C23×D7912yes—
637C4⋊C4C23×D7912yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—1584no—
644C22⋊C4—1584no—
645C22⋊C4—1584no—
646C22⋊C4—1584no—
647C22⋊C4—1584no—
648C22⋊C4C2×C22⋊D7914yes—
649C22⋊C4C2×C22⋊D7914yes—
650C42—24no—
651C42—1584no—
652C42C2×C22⋊D7912yes—
653C42C2×C22⋊D7912yes—
654C42C23×D7912yes—
655C42C23×D7912yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—3162no—
664C23—3162no—
665C23—3162no—
666C23—1582no—
667C23C22×C22⋊D7912yes—
668C23C22×C22⋊D7911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—3162no—
674Q8—6324no—
675Q8—1582no—
676Q8—1582no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—3162no—
682D4—6324no—
683D4—1582no—
684D4—1582no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—3162no—
701C2×C4—3162no—
702C2×C4—3162no—
703C2×C4—6324no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4C22×C22⋊D7912yes—
708C2×C4C22×C22⋊D7912yes—
709C2×C4C22×C22⋊D7912yes—
710C2×C4C22×C22⋊D7912yes—
711C2×C4C22×C22⋊D7912yes—
712C2×C4C22×C22⋊D7911yescharacteristic
713C2×C4#1457920712yes—
714C2×C4#1457920812yes—
715C2×C4C24×D7911yescharacteristic
716C8—1582no—
717C8—1582no—
718C8—1582no—
719C8—1582no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—3162no—
729C22—3162no—
730C22—3162no—
731C22—6324no—
732C22#1909914112yes—
733C22#1909936612yes—
734C22#1909937812yes—
735C22C23×C22⋊D7911yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—3162no—
745C4—3162no—
746C4—3162no—
747C4#1909914112yes—
748C4C2×#1457920711yescharacteristic
749C4C2×#1457920811yescharacteristic
750C2—42no—
751C2—82no—
752C2—6322no—
753C2#2377485614yesdirect product factor
754C2C2×#1909914111yescharacteristic
755C2C2×#1909936611yescharacteristic
756C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#542×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098797C2
hypercenterC2×#542D79
hypocenterC79C2×#3262
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#19099184C2semidirect
2. #23774856C2direct (N × H)
3. C2×#19098858C2semidirect
4. C2×#19098855C2semidirect
5. C2×#19098843C2semidirect
6. C2×#19098840C2semidirect
7. C2×#19098811C2semidirect
8. C2×#19098807C2semidirect
9. C2×#19098802C2semidirect
11. C2×#19098785C2semidirect
12. C2×#19098782C2semidirect
13. C2×#19098778C2semidirect
14. C2×#19098775C2semidirect
15. C2×#19098590C2semidirect
16. C2×#542×C79C2semidirect
24. #19099184C22semidirect
35. #19098858C22semidirect
36. #19098855C22semidirect
37. #19098843C22semidirect
38. #19098840C22semidirect
39. #19098811C22semidirect
40. #19098807C22semidirect
41. #19098802C22semidirect
43. #19098785C22semidirect
44. #19098782C22semidirect
45. #19098778C22semidirect
46. #19098775C22semidirect
51. #19098590C22semidirect
65. #542×C79C22semidirect
374. C2×C79#3262semidirect
380. C2×#542D79semidirect
395. C79C2×#3262semidirect
405. #542C2×D79semidirect
753. C2#23774856direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991842
#237748562
C2×#190988582
C2×#190988552
C2×#190988432
C2×#190988402
C2×#190988112
C2×#190988072
C2×#190988022
C2×#190987972
C2×#190987852
C2×#190987822
C2×#190987782
C2×#190987752
C2×#190985902
C2×#542×C792
C2×#326279