Finite Group Databasebeta

← C2×#23773627 #35156546

Subgroups — C2×#23773627 #35156546

Order 20224.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099178C211yesmaximal, characteristic
2C2×#19099039C211yesmaximal, characteristic, complemented
3#23773627C2116yesmaximal, direct product factor
4C2×#19098906C211yesmaximal, characteristic, complemented
5C2×#19098886C211yesmaximal, characteristic
6C2×#19098857C211yesmaximal, characteristic, complemented
7C2×#19098846C211yesmaximal, characteristic, complemented
8C2×#19098784C211yesmaximal, characteristic, complemented
9C2×#19098783C211yesmaximal, characteristic, complemented
10C2×#19098720C211yesmaximal, characteristic, complemented
11C2×#19098700C211yesmaximal, characteristic
12C2×#19098671C211yesmaximal, characteristic, complemented
13C2×C4×#11929614C211yesmaximal, characteristic, complemented
14C2×C4×#11929612C211yesmaximal, characteristic, complemented
15C2×#19098625C211yesmaximal, characteristic, complemented
16C2×#440×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×Dic316C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20C22×#11929612C2211yescharacteristic
21#19099178—24no—
22#19099178C2218yes—
23C2×#14579160C2211yescharacteristic
24C2×#14579154—21no—
25C2×#14579148C2211yescharacteristic
26C2×#14579147—21no—
27C2×#14579144—21no—
28C2×#14579141C2211yescharacteristic
29C2×#14579140—21no—
30C2×#14579132C2211yescharacteristic
31#19099039—24no—
32#19099039C2218yescomplemented
33C2×Q8×Dic79C2211yescharacteristic
34C2×C4×Dic158—21no—
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×Dic158C2211yescharacteristic
37C2×#14579126—21no—
38C2×#14579126C2211yescharacteristic
39C2×#14579119—21no—
40C2×#14579119C2211yescharacteristic
41C2×#14579118—21no—
42C2×#14579118C2211yescharacteristic
43#19098906C2218yescomplemented
44#19098886C2218yes—
45#19098857C2218yescomplemented
46#19098846C2218yescomplemented
47#19098784C2218yescomplemented
48#19098783C2218yescomplemented
49#19098720C2218yescomplemented
50#19098700C2218yes—
51#19098671C2218yescomplemented
52C4×#11929614C2218yescomplemented
53C4×#11929612C2218yescomplemented
54#19098625C2218yescomplemented
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C4×C79⋊C8C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#440×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158C2311yescharacteristic
80C22×Dic158C2311yescharacteristic
81C2×Q8×D79—24no—
82C2×Q8×D79—24no—
83C2×Q8×D79—22no—
84C2×Q8×D79C2314yes—
85C22×C22⋊D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79C2311yescharacteristic
88C2×Dic316—24no—
89C2×Dic316C2314yes—
90C2×#11929614—24no—
91C2×#11929614C2314yes—
92C2×#11929612—24no—
93C2×#11929612C2314yes—
94C22×C79⋊C8C2311yescharacteristic
95C22×C79⋊C8C2311yescharacteristic
96#14579160—22no—
97#14579160C2314yes—
98#14579154—28no—
99#14579148—22no—
100#14579148C2314yes—
101#14579147—28no—
102#14579144—28no—
103#14579141—22no—
104#14579141C2314yes—
105#14579140—28no—
106#14579132—22no—
107#14579132C2314yes—
108Q8×Dic79—22no—
109Q8×Dic79C2314yes—
110C4×Dic158—22no—
111C4×Dic158—22no—
112C4×Dic158—28no—
113C4×Dic158C2314yes—
114C4×Dic158C2314yes—
115#14579126—28no—
116#14579126—22no—
117#14579126C2314yes—
118#14579119—22no—
119#14579119—28no—
120#14579119C2314yes—
121#14579118—28no—
122#14579118D414yes—
123#14579118C2314yes—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4D411yescharacteristic
133C2×Dic79⋊C4D411yescharacteristic
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×(C2×D79)⋊C4D411yescharacteristic
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79—21no—
145C2×C4×Dic79—21no—
146C2×C4×Dic79C2311yescharacteristic
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150Dic79⋊C8C2314yes—
151Dic79⋊C8C2314yes—
152#14579086C2314yes—
153#14579086C2314yes—
154#14579085C2314yes—
155#14579084C2314yes—
156#14579084C2314yes—
157#14579082C2314yes—
158(C2×D79)⋊C8C2314yes—
159(C2×D79)⋊C8C2314yes—
160C4×C79⋊C8C2314yes—
161C22×Q8×C79C2311yescharacteristic
162C22×D4×C79C2311yescharacteristic
163C23×C4×C79—21no—
164C2×SD16×C79—24no—
165C2×SD16×C79C2314yes—
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168C4×Q8×C79—22no—
169C4×Q8×C79C2314yes—
170C4×D4×C79—22no—
171C4×D4×C79C2314yes—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C22⋊C4×C79—21no—
176C2×C42×C79—21no—
177C2×C42×C79C2311yescharacteristic
178#107×C79C2314yes—
179#103×C79C2314yes—
180#102×C79C2314yes—
181#97×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183C2×Dic158—28no—
184C2×Dic158—24no—
185C2×Dic158—24no—
186C2×Dic158—21no—
187C2×Dic158—21no—
188C2×Dic158—22no—
189C2×Dic158—22no—
190C2×Dic158—22no—
191C2×Dic158—82no—
192C2×Dic158#4114yes—
193C2×Dic158C2412yes—
194C2×Dic158C2412yes—
195Q8×D79—216no—
196Q8×D79—28no—
197Q8×D79—28no—
198C2×C22⋊D79—24no—
199C2×C22⋊D79—82no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79—21no—
204C22×Dic79C2×D411yescharacteristic
205C22×Dic79C2×D411yescharacteristic
206C22×Dic79C2×D411yescharacteristic
207C2×C4×D79—28no—
208C2×C4×D79—24no—
209C2×C4×D79—22no—
210C2×C4×D79—22no—
211C2×C4×D79C2×D412yes—
212C2×C4×D79C2412yes—
213Dic316—28no—
214#11929614—28no—
215#11929612—28no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8—22no—
218C2×C79⋊C8C2412yes—
219C2×C79⋊C8C2412yes—
220C4⋊Dic79—24no—
221C4⋊Dic79—24no—
222C4⋊Dic79—21no—
223C4⋊Dic79—21no—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4C2×D414yes—
231Dic79⋊C4C2×D414yes—
232C22⋊Dic79—24no—
233C22⋊Dic79—24no—
234C22⋊Dic79—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4C2×D414yes—
238(C2×D79)⋊C4C2×D414yes—
239C4×Dic79—24no—
240C4×Dic79—24no—
241C4×Dic79—24no—
242C4×Dic79—24no—
243C4×Dic79—24no—
244C4×Dic79C2×D412yes—
245C4×Dic79C2412yes—
246C24×C79—21no—
247C2×Q8×C79—21no—
248C2×Q8×C79—22no—
249C2×Q8×C79#4114yes—
250C2×Q8×C79C2412yes—
251C2×D4×C79—21no—
252C2×D4×C79—22no—
253C2×D4×C79—22no—
254C2×D4×C79C2412yes—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79—24no—
259C22×C4×C79—82no—
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D411yescharacteristic
262C22×C4×C79C2411yescharacteristic
263SD16×C79—28no—
264C2×C8×C79—22no—
265C2×C8×C79—22no—
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C4⋊C4×C79—24no—
269C4⋊C4×C79—21no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79C2412yes—
272C4⋊C4×C79C2412yes—
273C22⋊C4×C79—24no—
274C42×C79—24no—
275C42×C79C2×D412yes—
276C42×C79C2412yes—
277C23×C79—22no—
278C23×C79—42no—
279C23×C79—42no—
280C23×C79—42no—
281C23×C79C22×D411yescharacteristic
282C22×D79—22no—
283C22×D79—22no—
284C22×D79—22no—
285C22×D79C22×D412yes—
286Q8×C79—24no—
287Q8×C79—22no—
288Q8×C79C2×#4114yes—
289D4×C79—22no—
290D4×C79—22no—
291D4×C79—42no—
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—42no—
299C2×C4×C79—42no—
300C2×C4×C79—84no—
301C2×C4×C79C22×D412yes—
302C2×C4×C79C22×D412yes—
303C2×C4×C79C22×D411yescharacteristic
304C2×C4×C79C2×#4112yes—
305C2×C4×C79C2×#4112yes—
306C2×C4×C79C2511yescharacteristic
307C22⋊D79—84no—
308C2×Dic79—24no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—42no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79C22×D412yes—
320C2×Dic79C22×D412yes—
321C2×Dic79C22×D412yes—
322C4×D79—216no—
323C4×D79—24no—
324C4×D79—22no—
325C4×D79—22no—
326Dic158—216no—
327Dic158—24no—
328Dic158—22no—
329Dic158—22no—
330Dic158—22no—
331Dic158—42no—
332Dic158—84no—
333Dic158C2×#4114yes—
334C8×C79—22no—
335C8×C79—22no—
336C79⋊C8—22no—
337C79⋊C8—22no—
338C22×C79—42no—
339C22×C79—42no—
340C22×C79—42no—
341C22×C79—84no—
342C22×C79#52512yes—
343C22×C79#57712yes—
344C22×C79#57812yes—
345C22×C79C23×D411yescharacteristic
346C2×D79—22no—
347C2×D79—22no—
348C2×D79—22no—
349C2×D79—44no—
350C4×C79—24no—
351C4×C79—22no—
352C4×C79—22no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79#52512yes—
356C4×C79C22×#4111yescharacteristic
357C4×C79C22×#4111yescharacteristic
358Dic79—22no—
359Dic79—24no—
360Dic79—22no—
361Dic79—22no—
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365C2×#3121—791nomaximal, Sylow
366C2×C79—82no—
367C2×C79#312114yescomplemented
368C2×C79C2×#52511yescharacteristic
369C2×C79C2×#57711yescharacteristic
370C2×C79C2×#57811yescharacteristic
371D79—42no—
372C2×#542—791no—
373C2×#519—791no—
374#3121—7916no—
375C2×#485—791no—
376C2×#482—791no—
377C2×#477—791no—
378C2×#475—791no—
379C2×#464—791no—
380C2×#464—791no—
381C2×#451—791no—
382C2×#448—791no—
383C2×#441—791no—
384C2×#440D7911yescharacteristic, complemented
385C2×C4×Q16—791no—
386C2×C4×SD16—791no—
387C2×#433—791no—
388C79C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8—791no—
390C22×Q16—791no—
391C22×Q16—791no—
392C22×SD16—791no—
393C22×SD16C2×D7911yescharacteristic
394#542—798no—
395#542—1584no—
396C2×C4⋊Q8—791no—
397C2×#126—1581no—
398C2×#124—791no—
399C2×#124—1581no—
400C2×#123—1581no—
401C2×C22⋊Q8—791no—
402C2×C22⋊Q8—1581no—
403C2×#121—791no—
404#519—798no—
405#519—1584no—
406C2×C4×Q8—791no—
407C2×C4×Q8—791no—
408C2×C4×Q8—791no—
409C2×C4×Q8—791no—
410C2×C4×Q8—1581no—
411C2×C4×Q8—1581no—
412C2×C4×Q8C2×D7911yescharacteristic
413C2×C4×D4C2×D7911yescharacteristic
414C2×#117—791no—
415C2×#117—791no—
416C2×#117—1581no—
417C2×#117—1581no—
418#485—798no—
419#482—798no—
420#477—798no—
421#475—798no—
422#464—798no—
423#464—798no—
424#451—798no—
425#448—798no—
426#441—798no—
427#440C2×D7918yescomplemented
428C4×Q16—798no—
429C4×SD16—798no—
430#433—798no—
431C2×#107—791no—
432C2×#107C2×D7911yescharacteristic
433C2×#106—791no—
434C2×#106—791no—
435C2×C4⋊C8—791no—
436C2×C4⋊C8—791no—
437C2×#103—791no—
438C2×#103—791no—
439C2×#103—791no—
440C2×#103—791no—
441C2×#103—791no—
442C2×#103C2×D7911yescharacteristic
443C2×#102—791no—
444C2×#102C2×D7911yescharacteristic
445C2×C22⋊C8—791no—
446C2×C22⋊C8—791no—
447C2×#97C2×D7911yescharacteristic
448C2×C4×C8—791no—
449C22×Q8—794no—
450C22×Q8—791no—
451C22×Q8—791no—
452C22×Q8—1581no—
453C22×Q8—1581no—
454C22×Q8—1582no—
455C22×Q8—1584no—
456C22×Q8—1584no—
457C22×Q8C22×D7911yescharacteristic
458C22×D4—1581no—
459C22×D4C22×D7911yescharacteristic
460C23×C4—21no—
461C23×C4—791no—
462C23×C4—1581no—
463C2×Q16—794no—
464C2×Q16—794no—
465C2×Q16—1584no—
466C2×Q16—1584no—
467C2×SD16—24no—
468C2×SD16—794no—
469C2×SD16—1584no—
470C2×SD16C22×D7914yes—
471C22×C8—791no—
472C22×C8—791no—
473C22×C8C22×D7911yescharacteristic
474C22×C8C22×D7911yescharacteristic
475C4⋊Q8—794no—
476C4⋊Q8—1582no—
477#126—1588no—
478#124—794no—
479#124—1582no—
480#124—1588no—
481#123—1588no—
482C22⋊Q8—794no—
483C22⋊Q8—1582no—
484C22⋊Q8—1588no—
485#121—794no—
486#121—1582no—
487C4×Q8—22no—
488C4×Q8—794no—
489C4×Q8—794no—
490C4×Q8—794no—
491C4×Q8—794no—
492C4×Q8—1588no—
493C4×Q8—1582no—
494C4×Q8—1582no—
495C4×Q8—1588no—
496C4×Q8—1582no—
497C4×Q8—1582no—
498C4×Q8C22×D7914yes—
499C4×D4—22no—
500C4×D4C22×D7914yes—
501#117—794no—
502#117—794no—
503#117—794no—
504#117—1588no—
505#117—1588no—
506#117—1582no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—791no—
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⋊C4C22×D7911yescharacteristic
519C2×C4⋊C4C22×D7911yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—791no—
522C2×C22⋊C4—791no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—21no—
529C2×C42—791no—
530C2×C42—1581no—
531C2×C42—1581no—
532C2×C42—1581no—
533C2×C42—1581no—
534C2×C42—1581no—
535C2×C42C22×D7911yescharacteristic
536#107—794no—
537#107C22×D7914yes—
538#106—794no—
539#106—794no—
540C4⋊C8—794no—
541C4⋊C8—794no—
542#103—794no—
543#103—794no—
544#103—794no—
545#103—794no—
546#103—794no—
547#103C22×D7914yes—
548#102—794no—
549#102C22×D7914yes—
550C22⋊C8—794no—
551C22⋊C8—794no—
552#97C22×D7914yes—
553C4×C8—794no—
554C24—21no—
555C24—791no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—794no—
559C2×Q8—792no—
560C2×Q8—792no—
561C2×Q8—6322no—
562C2×Q8—1584no—
563C2×Q8—1584no—
564C2×Q8—1588no—
565C2×Q8—1582no—
566C2×Q8—1582no—
567C2×Q8—1588no—
568C2×Q8—15816no—
569C2×Q8—1588no—
570C2×Q8—1582no—
571C2×Q8—1581no—
572C2×Q8—1581no—
573C2×Q8#1192962414yes—
574C2×Q8C23×D7912yes—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—6322no—
579C2×D4—1584no—
580C2×D4C23×D7912yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—791no—
587C22×C4—791no—
588C22×C4—791no—
589C22×C4—792no—
590C22×C4—792no—
591C22×C4—1584no—
592C22×C4—1588no—
593C22×C4—1581no—
594C22×C4—1581no—
595C22×C4—1581no—
596C22×C4—1581no—
597C22×C4—1582no—
598C22×C4—1582no—
599C22×C4D4×D7911yescharacteristic
600C22×C4D4×D7911yescharacteristic
601C22×C4C23×D7911yescharacteristic
602Q16—1588no—
603Q16—1588no—
604SD16—28no—
605SD16—1588no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—792no—
609C2×C8—792no—
610C2×C8—1582no—
611C2×C8—1582no—
612C2×C8C23×D7912yes—
613C2×C8C23×D7912yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—794no—
618C4⋊C4—794no—
619C4⋊C4—792no—
620C4⋊C4—792no—
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—794no—
633C22⋊C4—794no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C42—24no—
640C42—792no—
641C42—792no—
642C42—1584no—
643C42—1584no—
644C42—1584no—
645C42—1584no—
646C42—1584no—
647C42D4×D7912yes—
648C42C23×D7912yes—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—792no—
654C23—1582no—
655C23—1582no—
656C23—1582no—
657C23C2×D4×D7911yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—3162no—
661Q8—794no—
662Q8—6324no—
663Q8—15816no—
664Q8—1582no—
665Q8—1582no—
666Q8—1584no—
667Q8—1582no—
668Q8C2×#1192962414yes—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—6324no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—3162no—
683C2×C4—3162no—
684C2×C4—3162no—
685C2×C4—792no—
686C2×C4—792no—
687C2×C4—792no—
688C2×C4—15816no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1584no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1584no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4C2×D4×D7912yes—
701C2×C4C2×D4×D7912yes—
702C2×C4C2×D4×D7911yescharacteristic
703C2×C4#41×D7912yes—
704C2×C4C2×#1192962412yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1582no—
709C8—1582no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—3164no—
715C22—1582no—
716C22—1582no—
717C22—1582no—
718C22#1909907212yes—
719C22#1909937312yes—
720C22#1909937912yes—
721C22C22×D4×D7911yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—1582no—
731C4—1582no—
732C4—1582no—
733C4—1584no—
734C4#1909907212yes—
735C4C2×#41×D7911yescharacteristic
736C4C22×#1192962411yescharacteristic
737C2—82no—
738C2—3162no—
739C2#2377362714yesdirect product factor
740C2C2×#1909907211yescharacteristic
741C2C2×#1909937311yescharacteristic
742C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#440×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579132C22
hypercenterC2×#440D79
hypocenterC79C2×#3121
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#19099039C2semidirect
3. #23773627C2direct (N × H)
4. C2×#19098906C2semidirect
6. C2×#19098857C2semidirect
7. C2×#19098846C2semidirect
8. C2×#19098784C2semidirect
9. C2×#19098783C2semidirect
10. C2×#19098720C2semidirect
12. C2×#19098671C2semidirect
13. C2×C4×#11929614C2semidirect
14. C2×C4×#11929612C2semidirect
15. C2×#19098625C2semidirect
16. C2×#440×C79C2semidirect
32. #19099039C22semidirect
43. #19098906C22semidirect
45. #19098857C22semidirect
46. #19098846C22semidirect
47. #19098784C22semidirect
48. #19098783C22semidirect
49. #19098720C22semidirect
51. #19098671C22semidirect
52. C4×#11929614C22semidirect
53. C4×#11929612C22semidirect
54. #19098625C22semidirect
72. #440×C79C22semidirect
367. C2×C79#3121semidirect
384. C2×#440D79semidirect
388. C79C2×#3121semidirect
427. #440C2×D79semidirect
739. C2#23773627direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991782
C2×#190990392
#237736272
C2×#190989062
C2×#190988862
C2×#190988572
C2×#190988462
C2×#190987842
C2×#190987832
C2×#190987202
C2×#190987002
C2×#190986712
C2×C4×#119296142
C2×C4×#119296122
C2×#190986252
C2×#440×C792
C2×#312179