Finite Group Databasebeta

← C2×#23774652 #35160457

Subgroups — C2×#23774652 #35160457

Order 20224.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099190C211yesmaximal, characteristic, complemented
2C2×#19099164C211yesmaximal, characteristic
3#23774652C2116yesmaximal, direct product factor
4C2×#19098970C211yesmaximal, characteristic, complemented
5C2×#19098963C211yesmaximal, characteristic, complemented
6C2×#19098926C211yesmaximal, characteristic, complemented
7C2×#19098908C211yesmaximal, characteristic, complemented
8C2×#19098883C211yesmaximal, characteristic, complemented
9C2×#19098889C211yesmaximal, characteristic, complemented
10C2×#19098886C211yesmaximal, characteristic, complemented
11C2×#19098875C211yesmaximal, characteristic, complemented
12C2×#19098864C211yesmaximal, characteristic, complemented
13C2×#19098863C211yesmaximal, characteristic, complemented
14C2×#19098840C211yesmaximal, characteristic, complemented
15C2×#19098623C211yesmaximal, characteristic, complemented
16C2×#476×C79C211yesmaximal, characteristic, complemented
17#19099190—24no—
18#19099190C2218yescomplemented
19#19099164—24no—
20#19099164C2218yes—
21C2×#14579160C2211yescharacteristic
22C2×#14579159—21no—
23C2×#14579157C2211yescharacteristic
24C2×#14579153C2211yescharacteristic
25C2×#14579152C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579151—21no—
28C2×#14579144—21no—
29C2×#14579143—21no—
30C2×#14579139—21no—
31C2×#14579137—21no—
32C2×#14579136C2211yescharacteristic
33C2×#14579135—21no—
34C2×#14579134—21no—
35C2×#14579132C2211yescharacteristic
36C2×C4×D316C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×#14579118C2211yescharacteristic
39C2×C4⋊C4×D79C2211yescharacteristic
40#19098970C2218yescomplemented
41#19098963C2218yescomplemented
42#19098926C2218yescomplemented
43#19098908C2218yescomplemented
44#19098889C2218yescomplemented
45#19098886C2218yescomplemented
46#19098883C2218yescomplemented
47#19098875C2218yescomplemented
48#19098864C2218yescomplemented
49#19098863C2218yescomplemented
50#19098840C2218yescomplemented
51#19098623C2218yescomplemented
52C2×#14579095C2211yescharacteristic
53C2×#14579094C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×C4⋊(C79⋊C8)C2211yescharacteristic
59C2×#14579083C2211yescharacteristic
60C2×#14579083C2211yescharacteristic
61C2×#14579082C2211yescharacteristic
62C2×#14579082C2211yescharacteristic
63C2×#14579081C2211yescharacteristic
64C2×#14579081C2211yescharacteristic
65C2×(C2×D79)⋊C8C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C2×C4⋊Q8×C79C2211yescharacteristic
70C2×C4×D4×C79C2211yescharacteristic
71#476×C79C2218yescomplemented
72C2×#106×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×D316—21no—
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C22×C22⋊D79—21no—
82C22×C22⋊D79—21no—
83C22×C4×D79—21no—
84C22×C4×D79—21no—
85C22×C4×D79C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87C22×C79⋊C8C2311yescharacteristic
88#14579160—22no—
89#14579160C2314yes—
90#14579159—28no—
91#14579157—22no—
92#14579157C2314yes—
93#14579153—22no—
94#14579153C2314yes—
95#14579152—22no—
96#14579152—22no—
97#14579152C2314yes—
98#14579152C2314yes—
99#14579151—28no—
100#14579144—28no—
101#14579143—28no—
102#14579139—28no—
103#14579137—28no—
104#14579136—22no—
105#14579136C2314yes—
106#14579135—28no—
107#14579134—28no—
108#14579132—22no—
109#14579132C2314yes—
110C4×D316—22no—
111C4×D316C2314yes—
112#14579119—22no—
113#14579119C2314yes—
114#14579118D414yes—
115#14579118C2314yes—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79C2311yescharacteristic
119C2×C4⋊Dic79C2311yescharacteristic
120C2×C4⋊Dic79C2311yescharacteristic
121C2×Dic79⋊C4—21no—
122C2×Dic79⋊C4—21no—
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4D411yescharacteristic
128C2×Dic79⋊C4D411yescharacteristic
129C4⋊C4×D79—22no—
130C4⋊C4×D79C2314yes—
131C2×C22⋊Dic79—21no—
132C2×(C2×D79)⋊C4—21no—
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4D411yescharacteristic
136C2×(C2×D79)⋊C4D411yescharacteristic
137C2×C4×Dic79—21no—
138C2×C4×Dic79C2311yescharacteristic
139#14579095C2314yes—
140#14579094C2314yes—
141#14579094C2314yes—
142#14579094C2314yes—
143#14579093C2314yes—
144#14579092C2314yes—
145C4⋊(C79⋊C8)C2314yes—
146#14579083C2314yes—
147#14579083C2314yes—
148#14579082C2314yes—
149#14579082C2314yes—
150#14579081C2314yes—
151#14579081C2314yes—
152(C2×D79)⋊C8C2314yes—
153(C2×D79)⋊C8C2314yes—
154#14579071C2314yes—
155C8×Dic79C2314yes—
156C22×Q8×C79—21no—
157C22×D4×C79C2311yescharacteristic
158C23×C4×C79—21no—
159C22×C8×C79C2311yescharacteristic
160C22×C8×C79C2311yescharacteristic
161C4⋊Q8×C79—22no—
162C4⋊Q8×C79C2314yes—
163C4×D4×C79—22no—
164C4×D4×C79C2314yes—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79C2311yescharacteristic
167C2×C4⋊C4×C79C2311yescharacteristic
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C22⋊C4×C79—21no—
170C2×C42×C79C2311yescharacteristic
171#106×C79C2314yes—
172#106×C79C2314yes—
173C4⋊C8×C79C2314yes—
174#102×C79C2314yes—
175#102×C79C2314yes—
176C23×D79—21no—
177C23×D79C2×D411yescharacteristic
178C2×Dic158—24no—
179C2×Dic158—82no—
180C2×D316—24no—
181C2×D316—21no—
182C2×D316—22no—
183C2×D316—22no—
184C2×D316—82no—
185C2×D316C2412yes—
186C2×C22⋊D79—24no—
187C2×C22⋊D79—24no—
188C2×C22⋊D79—24no—
189C2×C22⋊D79—82no—
190C2×C22⋊D79—82no—
191C2×C22⋊D79—82no—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79C2×D411yescharacteristic
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C2×C4×D79—24no—
199C2×C4×D79—24no—
200C2×C4×D79—22no—
201C2×C4×D79—22no—
202C2×C4×D79—82no—
203C2×C4×D79—82no—
204C2×C4×D79C2×D412yes—
205C2×C4×D79C2412yes—
206C2×C79⋊C8—22no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8C2412yes—
209C2×C79⋊C8C2412yes—
210C4⋊Dic79—24no—
211C4⋊Dic79—24no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79—21no—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4C2×D414yes—
225Dic79⋊C4C2×D414yes—
226C22⋊Dic79—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4C2×D414yes—
231(C2×D79)⋊C4C2×D414yes—
232C4×Dic79—24no—
233C4×Dic79C2×D412yes—
234C4×Dic79C2412yes—
235C24×C79—21no—
236C2×Q8×C79—24no—
237C2×Q8×C79—82no—
238C2×D4×C79—21no—
239C2×D4×C79—22no—
240C2×D4×C79—22no—
241C2×D4×C79C2412yes—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—24no—
246C22×C4×C79—82no—
247C22×C4×C79C2×D411yescharacteristic
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2411yescharacteristic
250C2×C8×C79—22no—
251C2×C8×C79—22no—
252C2×C8×C79C2412yes—
253C2×C8×C79C2412yes—
254C4⋊C4×C79—24no—
255C4⋊C4×C79—21no—
256C4⋊C4×C79—21no—
257C4⋊C4×C79—21no—
258C4⋊C4×C79C2412yes—
259C4⋊C4×C79C2412yes—
260C4⋊C4×C79C2412yes—
261C22⋊C4×C79—24no—
262C42×C79C2×D412yes—
263C42×C79C2412yes—
264C23×C79—22no—
265C23×C79—42no—
266C23×C79—42no—
267C23×C79—42no—
268C23×C79C22×D411yescharacteristic
269C22×D79—22no—
270C22×D79—22no—
271C22×D79—22no—
272C22×D79—22no—
273C22×D79—42no—
274C22×D79—42no—
275C22×D79—42no—
276C22×D79C22×D412yes—
277Q8×C79—84no—
278D4×C79—22no—
279D4×C79—22no—
280D4×C79—42no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—42no—
287C2×C4×C79—42no—
288C2×C4×C79—42no—
289C2×C4×C79—84no—
290C2×C4×C79C22×D412yes—
291C2×C4×C79C22×D412yes—
292C2×C4×C79C22×D411yescharacteristic
293C2×C4×C792−1+412yes—
294C2×C4×C792−1+412yes—
295C2×C4×C79C2511yescharacteristic
296C22⋊D79—84no—
297C22⋊D79—84no—
298C22⋊D79—84no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—42no—
306C2×Dic79—42no—
307C2×Dic79—42no—
308C2×Dic79C22×D412yes—
309C2×Dic79C22×D412yes—
310C2×Dic79C22×D412yes—
311D316—22no—
312D316—22no—
313D316—42no—
314D316—84no—
315C4×D79—24no—
316C4×D79—22no—
317C4×D79—22no—
318C4×D79—84no—
319C4×D79—84no—
320Dic158—84no—
321C8×C79—22no—
322C8×C79—22no—
323C79⋊C8—22no—
324C79⋊C8—22no—
325C22×C79—42no—
326C22×C79—42no—
327C22×C79—42no—
328C22×C79—84no—
329C22×C79#53612yes—
330C22×C79#57612yes—
331C22×C79#57712yes—
332C22×C79C23×D411yescharacteristic
333C2×D79—22no—
334C2×D79—22no—
335C2×D79—22no—
336C2×D79—44no—
337C2×D79—42no—
338C2×D79—42no—
339C2×D79—42no—
340C2×D79—84no—
341C4×C79—22no—
342C4×C79—22no—
343C4×C79—42no—
344C4×C79—42no—
345C4×C79—42no—
346C4×C79#53612yes—
347C4×C79C2×2−1+411yescharacteristic
348C4×C79C2×2−1+411yescharacteristic
349Dic79—22no—
350Dic79—22no—
351Dic79—22no—
352Dic79—42no—
353Dic79—42no—
354Dic79—42no—
355C2×#3241—791nomaximal, Sylow
356C2×C79—82no—
357C2×C79#324114yescomplemented
358C2×C79C2×#53611yescharacteristic
359C2×C79C2×#57611yescharacteristic
360C2×C79C2×#57711yescharacteristic
361D79—42no—
362D79—82no—
363C2×#544—791no—
364C2×#540—791no—
365#3241—7916no—
366C2×#501—791no—
367C2×#499—791no—
368C2×#490—791no—
369C2×#486—791no—
370C2×#481—791no—
371C2×#482—791no—
372C2×#482—791no—
373C2×#480—791no—
374C2×#478—791no—
375C2×#478—791no—
376C2×#476D7911yescharacteristic, complemented
377C2×#474—791no—
378C2×#433—791no—
379C79C2×#324111yescharacteristic, complemented, Sylow
380#544—798no—
381#544—1584no—
382#540—798no—
383#540—1584no—
384C2×C4⋊Q8—791no—
385C2×C4⋊Q8—1581no—
386C2×C4⋊Q8C2×D7911yescharacteristic
387C2×#127—791no—
388C2×#125—791no—
389C2×#125—791no—
390C2×#125—791no—
391C2×#125—1581no—
392C2×#123—1581no—
393C2×#123—1581no—
394C2×C22⋊Q8—1581no—
395C2×C22⋊Q8—1581no—
396C2×#121—791no—
397C2×#121—791no—
398C2×#121—1581no—
399C2×#121—1581no—
400C2×C4×D4—791no—
401C2×C4×D4C2×D7911yescharacteristic
402C2×#117—791no—
403C2×#117—791no—
404C22×C4⋊C4—791no—
405#501—798no—
406#499—798no—
407#490—798no—
408#486—798no—
409#482—798no—
410#482—798no—
411#481—798no—
412#480—798no—
413#478—798no—
414#478—798no—
415#476C2×D7918yescomplemented
416#474—798no—
417#433—798no—
418C2×#107—791no—
419C2×#107—791no—
420C2×#107—791no—
421C2×#107—791no—
422C2×#106—791no—
423C2×#106—791no—
424C2×#106C2×D7911yescharacteristic
425C2×#106C2×D7911yescharacteristic
426C2×C4⋊C8—791no—
427C2×C4⋊C8C2×D7911yescharacteristic
428C2×#102—791no—
429C2×#102—791no—
430C2×#102—791no—
431C2×#102—791no—
432C2×#102—791no—
433C2×#102—791no—
434C2×#102C2×D7911yescharacteristic
435C2×#102C2×D7911yescharacteristic
436C2×C22⋊C8—791no—
437C2×C22⋊C8—791no—
438C2×#97—791no—
439C2×C4×C8—791no—
440C22×Q8—21no—
441C22×Q8—1581no—
442C22×D4—791no—
443C22×D4—1581no—
444C22×D4—1581no—
445C22×D4—1581no—
446C22×D4—1581no—
447C22×D4C22×D7911yescharacteristic
448C23×C4—21no—
449C23×C4—791no—
450C23×C4—1581no—
451C23×C4—1581no—
452C22×C8—791no—
453C22×C8—791no—
454C22×C8C22×D7911yescharacteristic
455C22×C8C22×D7911yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8—794no—
458C4⋊Q8—1582no—
459C4⋊Q8—1588no—
460C4⋊Q8C22×D7914yes—
461#127—794no—
462#127—1582no—
463#125—794no—
464#125—794no—
465#125—794no—
466#125—1582no—
467#125—1582no—
468#125—1588no—
469#125—1582no—
470#123—1588no—
471#123—1588no—
472C22⋊Q8—1588no—
473C22⋊Q8—1588no—
474#121—794no—
475#121—794no—
476#121—1588no—
477#121—1588no—
478#121—1582no—
479#121—1582no—
480C4×D4—22no—
481C4×D4—794no—
482C4×D4—1582no—
483C4×D4C22×D7914yes—
484#117—794no—
485#117—794no—
486#117—794no—
487#117—1582no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—791no—
490C2×C4⋊C4—791no—
491C2×C4⋊C4—791no—
492C2×C4⋊C4—791no—
493C2×C4⋊C4—791no—
494C2×C4⋊C4—794no—
495C2×C4⋊C4—1582no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1581no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4C22×D7911yescharacteristic
505C2×C4⋊C4C22×D7911yescharacteristic
506C2×C4⋊C4C22×D7911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—791no—
509C2×C22⋊C4—791no—
510C2×C22⋊C4—1581no—
511C2×C22⋊C4—1581no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C42—791no—
515C2×C42—1581no—
516C2×C42C22×D7911yescharacteristic
517#107—794no—
518#107—794no—
519#107—794no—
520#107—794no—
521#106—794no—
522#106—794no—
523#106C22×D7914yes—
524#106C22×D7914yes—
525C4⋊C8—794no—
526C4⋊C8C22×D7914yes—
527#102—794no—
528#102—794no—
529#102—794no—
530#102—794no—
531#102—794no—
532#102—794no—
533#102C22×D7914yes—
534#102C22×D7914yes—
535C22⋊C8—794no—
536C22⋊C8—794no—
537#97—794no—
538C4×C8—794no—
539C24—21no—
540C24—791no—
541C24—1581no—
542C2×Q8—24no—
543C2×Q8—82no—
544C2×Q8—6322no—
545C2×Q8—1584no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—792no—
550C2×D4—6322no—
551C2×D4—6322no—
552C2×D4—6322no—
553C2×D4—6322no—
554C2×D4—1584no—
555C2×D4—1584no—
556C2×D4—1584no—
557C2×D4—1584no—
558C2×D4—1582no—
559C2×D4—1582no—
560C2×D4—1581no—
561C2×D4C23×D7912yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—791no—
568C22×C4—791no—
569C22×C4—791no—
570C22×C4—792no—
571C22×C4—792no—
572C22×C4—6322no—
573C22×C4—6322no—
574C22×C4—1584no—
575C22×C4—1581no—
576C22×C4—1581no—
577C22×C4—1581no—
578C22×C4—1584no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4D4×D7911yescharacteristic
582C22×C4D4×D7911yescharacteristic
583C22×C4C23×D7911yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—792no—
587C2×C8—792no—
588C2×C8—1582no—
589C2×C8—1582no—
590C2×C8C23×D7912yes—
591C2×C8C23×D7912yes—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—794no—
597C4⋊C4—794no—
598C4⋊C4—792no—
599C4⋊C4—792no—
600C4⋊C4—792no—
601C4⋊C4—1584no—
602C4⋊C4—1584no—
603C4⋊C4—1584no—
604C4⋊C4—1584no—
605C4⋊C4—1584no—
606C4⋊C4—1584no—
607C4⋊C4—1584no—
608C4⋊C4—1584no—
609C4⋊C4—1581no—
610C4⋊C4—1581no—
611C4⋊C4—1581no—
612C4⋊C4C23×D7912yes—
613C4⋊C4C23×D7912yes—
614C4⋊C4C23×D7912yes—
615C22⋊C4—24no—
616C22⋊C4—794no—
617C22⋊C4—794no—
618C22⋊C4—1584no—
619C22⋊C4—1584no—
620C22⋊C4—1584no—
621C22⋊C4—1584no—
622C42—792no—
623C42—792no—
624C42—1584no—
625C42D4×D7912yes—
626C42C23×D7912yes—
627C23—22no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—3162no—
632C23—3162no—
633C23—3162no—
634C23—792no—
635C23—1582no—
636C23—1582no—
637C23—1582no—
638C23—1582no—
639C23C2×D4×D7911yescharacteristic
640Q8—84no—
641Q8—6324no—
642D4—22no—
643D4—22no—
644D4—42no—
645D4—3162no—
646D4—6324no—
647D4—6324no—
648D4—6324no—
649D4—6324no—
650D4—1582no—
651D4—1582no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—84no—
661C2×C4—3162no—
662C2×C4—3162no—
663C2×C4—3162no—
664C2×C4—792no—
665C2×C4—792no—
666C2×C4—792no—
667C2×C4—6324no—
668C2×C4—6324no—
669C2×C4—1582no—
670C2×C4—1582no—
671C2×C4—1582no—
672C2×C4—1582no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1584no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4C2×D4×D7912yes—
679C2×C4C2×D4×D7912yes—
680C2×C4C2×D4×D7911yescharacteristic
681C2×C4#1457920812yes—
682C2×C4#1457920912yes—
683C2×C4C24×D7911yescharacteristic
684C8—22no—
685C8—22no—
686C8—1582no—
687C8—1582no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—84no—
692C22—3164no—
693C22—3162no—
694C22—3162no—
695C22—3162no—
696C22—6324no—
697C22—1582no—
698C22—1582no—
699C22—1582no—
700C22#1909913612yes—
701C22#1909936712yes—
702C22#1909936912yes—
703C22C22×D4×D7911yescharacteristic
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—3162no—
710C4—3162no—
711C4—3162no—
712C4—1582no—
713C4—1582no—
714C4—1582no—
715C4#1909913612yes—
716C4C2×#1457920811yescharacteristic
717C4C2×#1457920911yescharacteristic
718C2—82no—
719C2—3162no—
720C2—6322no—
721C2#2377465214yesdirect product factor
722C2C2×#1909913611yescharacteristic
723C2C2×#1909936711yescharacteristic
724C2C2×#1909936911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#476×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099164C2
hypercenterC2×#476D79
hypocenterC79C2×#3241
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#19099190C2semidirect
3. #23774652C2direct (N × H)
4. C2×#19098970C2semidirect
5. C2×#19098963C2semidirect
6. C2×#19098926C2semidirect
7. C2×#19098908C2semidirect
8. C2×#19098883C2semidirect
9. C2×#19098889C2semidirect
10. C2×#19098886C2semidirect
11. C2×#19098875C2semidirect
12. C2×#19098864C2semidirect
13. C2×#19098863C2semidirect
14. C2×#19098840C2semidirect
15. C2×#19098623C2semidirect
16. C2×#476×C79C2semidirect
18. #19099190C22semidirect
40. #19098970C22semidirect
41. #19098963C22semidirect
42. #19098926C22semidirect
43. #19098908C22semidirect
44. #19098889C22semidirect
45. #19098886C22semidirect
46. #19098883C22semidirect
47. #19098875C22semidirect
48. #19098864C22semidirect
49. #19098863C22semidirect
50. #19098840C22semidirect
51. #19098623C22semidirect
71. #476×C79C22semidirect
357. C2×C79#3241semidirect
376. C2×#476D79semidirect
379. C79C2×#3241semidirect
415. #476C2×D79semidirect
721. C2#23774652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991902
C2×#190991642
#237746522
C2×#190989702
C2×#190989632
C2×#190989262
C2×#190989082
C2×#190988832
C2×#190988892
C2×#190988862
C2×#190988752
C2×#190988642
C2×#190988632
C2×#190988402
C2×#190986232
C2×#476×C792
C2×#324179