Finite Group Databasebeta

← C2×#23773351 #35156089

Subgroups — C2×#23773351 #35156089

Order 20224.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099129C211yesmaximal, characteristic
2C2×#19099044C211yesmaximal, characteristic, complemented
3#23773351C2116yesmaximal, direct product factor
4C2×#19098881C211yesmaximal, characteristic, complemented
5C2×#19098880C211yesmaximal, characteristic, complemented
6C2×#19098890C211yesmaximal, characteristic, complemented
7C2×#19098888C211yesmaximal, characteristic, complemented
8C2×#19098885C211yesmaximal, characteristic, complemented
9C2×#19098884C211yesmaximal, characteristic, complemented
10C2×#19098878C211yesmaximal, characteristic, complemented
11C2×#19098604C211yesmaximal, characteristic, complemented
12C2×#19098600C211yesmaximal, characteristic, complemented
13C2×#19098566C211yesmaximal, characteristic, complemented
14C2×#102×D79C211yesmaximal, characteristic, complemented
15C2×#19098528C211yesmaximal, characteristic, complemented
16C2×#480×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×D4×D79C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21#19099129—24no—
22#19099129C2218yes—
23C2×#14579157—21no—
24C2×#14579147—21no—
25C2×#14579136C2211yescharacteristic
26C2×#14579135C2211yescharacteristic
27C2×#14579132C2211yescharacteristic
28C2×#14579131—21no—
29C2×#14579129—21no—
30#19099044—24no—
31#19099044C2218yescomplemented
32C2×#14579126—21no—
33C2×#14579123—21no—
34C2×C4×C22⋊D79—21no—
35C2×C4×C22⋊D79—21no—
36C2×#14579120C2211yescharacteristic, complemented
37C2×#14579119C2211yescharacteristic
38C2×#14579119C2211yescharacteristic
39C2×#14579119C2211yescharacteristic, complemented
40C2×C4⋊C4×D79C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic, complemented
42#19098890C2218yescomplemented
43#19098888C2218yescomplemented
44#19098885C2218yescomplemented
45#19098884C2218yescomplemented
46#19098881C2218yescomplemented
47#19098880C2218yescomplemented
48#19098878C2218yescomplemented
49#19098604C2218yescomplemented
50#19098600C2218yescomplemented
51C2×#14579095C2211yescharacteristic, complemented
52C2×#14579094C2211yescharacteristic, complemented
53C2×#14579093C2211yescharacteristic, complemented
54C2×#14579092C2211yescharacteristic, complemented
55C2×#14579092C2211yescharacteristic, complemented
56C2×#14579092C2211yescharacteristic, complemented
57#19098566C2218yescomplemented
58C2×#14579083C2211yescharacteristic
59C2×#14579083C2211yescharacteristic
60C2×#14579082C2211yescharacteristic
61C2×#14579082C2211yescharacteristic
62C2×#14579081C2211yescharacteristic
63C2×#14579081C2211yescharacteristic
64#102×D79C2218yescomplemented
65#19098528C2218yescomplemented
66C2×C22⋊(C79⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D79)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D79)⋊C8C2211yescharacteristic, complemented
69C2×#121×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic, complemented
71#480×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic, complemented
73C2×#107×C79C2211yescharacteristic, complemented
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic, complemented
77C24×D79—21no—
78C2×#11929624—24no—
79C2×#11929624—24no—
80C2×#11929624D414yes—
81C2×#11929624C2314yes—
82C22×Dic158D411yescharacteristic
83C22×D316—21no—
84C22×D316D411yescharacteristic
85C22×D316C2311yescharacteristic
86C22×C22⋊D79—21no—
87C22×C22⋊D79—21no—
88C22×C22⋊D79—21no—
89C22×C22⋊D79D411yescharacteristic
90C22×C22⋊D79D411yescharacteristic
91C2×D4×D79—22no—
92C2×D4×D79—24no—
93C2×D4×D79—24no—
94C2×D4×D79C2314yes—
95C22×C4×D79—21no—
96C22×C4×D79—21no—
97C22×C4×D79C2311yescharacteristic
98C22×C4×D79C2311yescharacteristic
99C2×#11929607—24no—
100C2×#11929607C2314yes—
101C22×C79⋊C8C2311yescharacteristic
102C22×C79⋊C8C2311yescharacteristic
103C2×C8×D79—24no—
104C2×C8×D79C2314yes—
105#14579157—28no—
106#14579147—28no—
107#14579136—22no—
108#14579136C2314yes—
109#14579135—22no—
110#14579135C2314yes—
111#14579132—22no—
112#14579132C2314yes—
113#14579131—28no—
114#14579129—28no—
115#14579126—28no—
116#14579123—28no—
117C4×C22⋊D79—28no—
118C4×C22⋊D79—28no—
119#14579120—22no—
120#14579120C2314yescomplemented
121#14579119—22no—
122#14579119—22no—
123#14579119—22no—
124#14579119C2314yes—
125#14579119C2314yes—
126#14579119C2314yescomplemented
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×C4⋊Dic79C2311yescharacteristic
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C4⋊C4×D79—22no—
133C4⋊C4×D79—22no—
134C4⋊C4×D79C2314yes—
135C4⋊C4×D79C2314yescomplemented
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79—21no—
145C2×C4×Dic79—21no—
146C2×C4×Dic79—21no—
147#14579095C2314yescomplemented
148#14579094C2314yescomplemented
149#14579093C2314yescomplemented
150#14579092C2314yescomplemented
151#14579092C2314yescomplemented
152#14579092C2314yescomplemented
153#14579083C2314yes—
154#14579083C2314yes—
155#14579082C2314yes—
156#14579082C2314yes—
157#14579081C2314yes—
158#14579081C2314yes—
159C22⋊(C79⋊C8)C2314yescomplemented
160(C2×D79)⋊C8C2314yescomplemented
161(C2×D79)⋊C8C2314yescomplemented
162C22×D4×C79—21no—
163C22×D4×C79C2311yescharacteristic
164C23×C4×C79—21no—
165C23×C4×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168#121×C79—22no—
169#121×C79C2314yes—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79—22no—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C4⋊C4×C79C2314yescomplemented
176C2×C22⋊C4×C79—21no—
177#107×C79C2314yescomplemented
178#107×C79C2314yescomplemented
179#102×C79C2314yes—
180#102×C79C2314yes—
181C22⋊C8×C79C2314yescomplemented
182C23×D79—21no—
183C23×D79—24no—
184C23×D79—44no—
185C23×D79—82no—
186C23×D79—82no—
187C23×D79C2×D411yescharacteristic
188C23×D79C2×D411yescharacteristic
189#11929624—216no—
190#11929624—28no—
191#11929624—28no—
192C2×Dic158—24no—
193C2×Dic158C2×D414yes—
194C2×D316—24no—
195C2×D316—24no—
196C2×D316—21no—
197C2×D316—22no—
198C2×D316—22no—
199C2×D316—82no—
200C2×D316C2×D414yes—
201C2×D316C2412yes—
202C2×C22⋊D79—24no—
203C2×C22⋊D79—24no—
204C2×C22⋊D79—24no—
205C2×C22⋊D79—24no—
206C2×C22⋊D79—24no—
207C2×C22⋊D79—44no—
208C2×C22⋊D79—82no—
209C2×C22⋊D79—82no—
210C2×C22⋊D79C2×D414yes—
211C2×C22⋊D79C2×D414yes—
212D4×D79—28no—
213D4×D79—28no—
214D4×D79—48no—
215C22×Dic79—21no—
216C22×Dic79—21no—
217C22×Dic79—21no—
218C22×Dic79C2×D411yescharacteristic
219C22×Dic79C2×D411yescharacteristic
220C2×C4×D79—24no—
221C2×C4×D79—24no—
222C2×C4×D79—22no—
223C2×C4×D79—22no—
224C2×C4×D79—82no—
225C2×C4×D79—82no—
226C2×C4×D79C2×D412yes—
227C2×C4×D79C2×D412yes—
228C2×C4×D79#4114yes—
229C2×C4×D79#4114yes—
230C2×C4×D79C2412yes—
231C2×C4×D79C2412yes—
232#11929607—28no—
233C2×C79⋊C8—22no—
234C2×C79⋊C8—22no—
235C2×C79⋊C8C2412yes—
236C2×C79⋊C8C2412yes—
237C8×D79—28no—
238C4⋊Dic79—21no—
239C4⋊Dic79—21no—
240C4⋊Dic79—21no—
241C4⋊Dic79C2412yes—
242C4⋊Dic79C2412yes—
243C4⋊Dic79C2412yes—
244Dic79⋊C4—24no—
245Dic79⋊C4—24no—
246C22⋊Dic79—24no—
247C22⋊Dic79—24no—
248(C2×D79)⋊C4—24no—
249(C2×D79)⋊C4—24no—
250(C2×D79)⋊C4—24no—
251(C2×D79)⋊C4—24no—
252(C2×D79)⋊C4—24no—
253C4×Dic79—24no—
254C4×Dic79—24no—
255C4×Dic79—24no—
256C4×Dic79—24no—
257C24×C79—21no—
258C24×C79C2×D411yescharacteristic
259C2×D4×C79—24no—
260C2×D4×C79—21no—
261C2×D4×C79—22no—
262C2×D4×C79—22no—
263C2×D4×C79—82no—
264C2×D4×C79C2412yes—
265C22×C4×C79—22no—
266C22×C4×C79—22no—
267C22×C4×C79—21no—
268C22×C4×C79—21no—
269C22×C4×C79—21no—
270C22×C4×C79—24no—
271C22×C4×C79—82no—
272C22×C4×C79C2×D411yescharacteristic
273C22×C4×C79C2×D412yes—
274C22×C4×C79C2412yes—
275C22×C4×C79C2411yescharacteristic
276C2×C8×C79—22no—
277C2×C8×C79—22no—
278C2×C8×C79C2412yes—
279C2×C8×C79C2412yes—
280C4⋊C4×C79—21no—
281C4⋊C4×C79—21no—
282C4⋊C4×C79—24no—
283C4⋊C4×C79—21no—
284C4⋊C4×C79C2412yes—
285C4⋊C4×C79C2412yes—
286C4⋊C4×C79C2412yes—
287C22⋊C4×C79—24no—
288C23×C79—22no—
289C23×C79—22no—
290C23×C79—22no—
291C23×C79—22no—
292C23×C79—42no—
293C23×C79—42no—
294C23×C79—42no—
295C23×C79C22×D412yes—
296C23×C79C22×D411yescharacteristic
297C22×D79—22no—
298C22×D79—22no—
299C22×D79—22no—
300C22×D79—22no—
301C22×D79—22no—
302C22×D79—22no—
303C22×D79—42no—
304C22×D79—42no—
305C22×D79—42no—
306C22×D79—48no—
307C22×D79—84no—
308C22×D79—84no—
309C22×D79—816no—
310C22×D79#12314yes—
311C22×D79C22×D412yes—
312C22×D79C22×D412yes—
313D4×C79—22no—
314D4×C79—22no—
315D4×C79—42no—
316D4×C79—84no—
317C2×C4×C79—22no—
318C2×C4×C79—24no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79—42no—
325C2×C4×C79—42no—
326C2×C4×C79—42no—
327C2×C4×C79—84no—
328C2×C4×C79C22×D412yes—
329C2×C4×C79C22×D411yescharacteristic
330C2×C4×C79C2×#4112yes—
331C2×C4×C79C2×#4112yes—
332C2×C4×C79C2511yescharacteristic
333C22⋊D79—28no—
334C22⋊D79—28no—
335C22⋊D79—48no—
336C22⋊D79—84no—
337C22⋊D79—84no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—22no—
342C2×Dic79—42no—
343C2×Dic79—42no—
344C2×Dic79—42no—
345C2×Dic79#12314yes—
346C2×Dic79C22×D412yes—
347C2×Dic79C22×D412yes—
348D316—28no—
349D316—22no—
350D316—22no—
351D316—42no—
352D316—84no—
353C4×D79—24no—
354C4×D79—22no—
355C4×D79—22no—
356C4×D79—84no—
357C4×D79—84no—
358C4×D79#12318yes—
359C4×D79C2×#4114yes—
360C4×D79C2×#4114yes—
361Dic158—28no—
362C8×C79—22no—
363C8×C79—22no—
364C79⋊C8—22no—
365C79⋊C8—22no—
366C22×C79—22no—
367C22×C79—22no—
368C22×C79—22no—
369C22×C79—44no—
370C22×C79—42no—
371C22×C79—42no—
372C22×C79—42no—
373C22×C79—84no—
374C22×C79C2×#12312yes—
375C22×C79#57612yes—
376C22×C79#57712yes—
377C22×C79C23×D411yescharacteristic
378C2×D79—28no—
379C2×D79—22no—
380C2×D79—22no—
381C2×D79—22no—
382C2×D79—22no—
383C2×D79—22no—
384C2×D79—44no—
385C2×D79—42no—
386C2×D79—42no—
387C2×D79—42no—
388C2×D79—816no—
389C2×D79—84no—
390C2×D79C2×#12314yes—
391C4×C79—22no—
392C4×C79—42no—
393C4×C79—42no—
394C4×C79—42no—
395C4×C79C2×#12312yes—
396C4×C79C22×#4111yescharacteristic
397C4×C79C22×#4111yescharacteristic
398Dic79—22no—
399Dic79—42no—
400Dic79—42no—
401Dic79—42no—
402Dic79C2×#12314yes—
403C2×#3096—791nomaximal, Sylow
404C2×C79—42no—
405C2×C79—82no—
406C2×C79#309614yescomplemented
407C2×C79C22×#12311yescharacteristic
408C2×C79C2×#57611yescharacteristic
409C2×C79C2×#57711yescharacteristic
410D79—24no—
411D79—42no—
412D79—82no—
413C2×#535—791no—
414C2×#520—791no—
415#3096—7916no—
416C2×#481—791no—
417C2×#481—791no—
418C2×#482—791no—
419C2×#482—791no—
420C2×#482—791no—
421C2×#482—791no—
422C2×#480—791no—
423C2×#480D7911yescharacteristic, complemented
424C2×#428—791no—
425C2×#427—791no—
426C2×#418—791no—
427C22×#102—791no—
428C2×#408—791no—
429C79C2×#309611yescharacteristic, complemented, Sylow
430C22×#41—791no—
431C23×D4—791no—
432C22×M16—791no—
433C23×C8—791no—
434#535—798no—
435#535—1584no—
436C2×#127—1581no—
437C2×#124—1581no—
438C2×#121—791no—
439C2×#121—791no—
440C2×#121—791no—
441C2×#121C2×D7911yescharacteristic
442C2×#120—1581no—
443C2×#120—1581no—
444#520—798no—
445#520—1584no—
446C2×C4×Q8—1581no—
447C2×C4×D4—1581no—
448C2×C4×D4—1581no—
449C2×C4×D4—1581no—
450C2×#117—791no—
451C2×#117—791no—
452C2×#117—791no—
453C2×#117—791no—
454C22×C4⋊C4—791no—
455C22×C4⋊C4—791no—
456C22×C4⋊C4C2×D7911yescharacteristic, complemented
457#482—798no—
458#482—798no—
459#482—798no—
460#482—798no—
461#481—798no—
462#481—798no—
463#480—798no—
464#480C2×D7918yescomplemented
465#428—798no—
466#427—798no—
467C2×#107—791no—
468C2×#107—791no—
469C2×#107C2×D7911yescharacteristic, complemented
470C2×#107C2×D7911yescharacteristic, complemented
471C2×#106—791no—
472C2×#106—791no—
473C2×#106—791no—
474C2×#106—791no—
475#418—798no—
476C2×#102—791no—
477C2×#102—791no—
478C2×#102—791no—
479C2×#102—791no—
480C2×#102—791no—
481C2×#102—791no—
482C2×#102—798no—
483C2×#102C2×D7911yescharacteristic
484C2×#102C2×D7911yescharacteristic
485#408—798no—
486C2×C22⋊C8—791no—
487C2×C22⋊C8—791no—
488C2×C22⋊C8—791no—
489C2×C22⋊C8C2×D7911yescharacteristic, complemented
490C25—1581no—
491C2×#41—794no—
492C2×#41—794no—
493C2×#41—1584no—
494C2×#41—1584no—
495C22×Q8—791no—
496C22×D4—21no—
497C22×D4—791no—
498C22×D4—791no—
499C22×D4—794no—
500C22×D4—791no—
501C22×D4—791no—
502C22×D4—1581no—
503C22×D4—1582no—
504C22×D4—1584no—
505C22×D4—1584no—
506C22×D4—1581no—
507C22×D4—1581no—
508C22×D4—1581no—
509C22×D4C22×D7911yescharacteristic
510C23×C4—21no—
511C23×C4—791no—
512C23×C4—791no—
513C23×C4—1581no—
514C23×C4—1581no—
515C23×C4C22×D7911yescharacteristic
516C2×M16—794no—
517C2×M16—1584no—
518C22×C8—791no—
519C22×C8—791no—
520C22×C8—794no—
521C22×C8—1584no—
522C22×C8C22×D7911yescharacteristic
523C22×C8C22×D7911yescharacteristic
524#127—1588no—
525#124—1588no—
526#121—22no—
527#121—794no—
528#121—794no—
529#121—794no—
530#121—1582no—
531#121—1582no—
532#121—1582no—
533#121C22×D7914yes—
534#120—1588no—
535#120—1588no—
536C4×Q8—1588no—
537C4×D4—1588no—
538C4×D4—1588no—
539C4×D4—1588no—
540#117—794no—
541#117—794no—
542#117—794no—
543#117—794no—
544#117—1582no—
545#117—1582no—
546#117—1582no—
547#117—1582no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—791no—
551C2×C4⋊C4—791no—
552C2×C4⋊C4—791no—
553C2×C4⋊C4—794no—
554C2×C4⋊C4—794no—
555C2×C4⋊C4—1582no—
556C2×C4⋊C4—1582no—
557C2×C4⋊C4—1581no—
558C2×C4⋊C4—1581no—
559C2×C4⋊C4C22×D7911yescharacteristic
560C2×C4⋊C4C22×D7911yescharacteristic
561C2×C4⋊C4C22×D7911yescharacteristic
562C2×C4⋊C4C22×D7914yescomplemented
563C2×C22⋊C4—21no—
564C2×C22⋊C4—1581no—
565C2×C22⋊C4—1581no—
566C2×C22⋊C4—1581no—
567C2×C22⋊C4—1581no—
568C2×C22⋊C4—1581no—
569C2×C22⋊C4—1581no—
570C2×C22⋊C4—1581no—
571C2×C42—1581no—
572C2×C42—1581no—
573C2×C42—1581no—
574C2×C42—1581no—
575#107—794no—
576#107—794no—
577#107C22×D7914yescomplemented
578#107C22×D7914yescomplemented
579#106—794no—
580#106—794no—
581#106—794no—
582#106—794no—
583#102—794no—
584#102—794no—
585#102—794no—
586#102—794no—
587#102—794no—
588#102—794no—
589#102C22×D7914yes—
590#102C22×D7914yes—
591C22⋊C8—794no—
592C22⋊C8—794no—
593C22⋊C8—794no—
594C22⋊C8C22×D7914yescomplemented
595C24—21no—
596C24—3164no—
597C24—791no—
598C24—791no—
599C24—6322no—
600C24—6322no—
601C24—1584no—
602C24—1581no—
603C24D4×D7911yescharacteristic
604#41—15816no—
605#41—1588no—
606#41—1588no—
607C2×Q8—794no—
608C2×Q8—1584no—
609C2×D4—24no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—82no—
614C2×D4—3168no—
615C2×D4—3164no—
616C2×D4—794no—
617C2×D4—794no—
618C2×D4—792no—
619C2×D4—794no—
620C2×D4—6322no—
621C2×D4—6322no—
622C2×D4—6322no—
623C2×D4—1584no—
624C2×D4—1584no—
625C2×D4—1588no—
626C2×D4—1588no—
627C2×D4—1584no—
628C2×D4—1584no—
629C2×D4—1584no—
630C2×D4—1584no—
631C2×D4—1584no—
632C2×D4—1582no—
633C2×D4—1582no—
634C2×D4—1581no—
635C2×D4C23×D7912yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—82no—
643C22×C4—791no—
644C22×C4—794no—
645C22×C4—794no—
646C22×C4—792no—
647C22×C4—792no—
648C22×C4—791no—
649C22×C4—792no—
650C22×C4—792no—
651C22×C4—6322no—
652C22×C4—6322no—
653C22×C4—1584no—
654C22×C4—1584no—
655C22×C4—1581no—
656C22×C4—1581no—
657C22×C4—1581no—
658C22×C4—1582no—
659C22×C4—1582no—
660C22×C4D4×D7912yes—
661C22×C4D4×D7911yescharacteristic
662C22×C4C23×D7912yes—
663C22×C4C23×D7911yescharacteristic
664M16—1588no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—792no—
668C2×C8—792no—
669C2×C8—1588no—
670C2×C8—1582no—
671C2×C8—1582no—
672C2×C8C23×D7912yes—
673C2×C8C23×D7912yes—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—792no—
679C4⋊C4—792no—
680C4⋊C4—792no—
681C4⋊C4—1584no—
682C4⋊C4—1584no—
683C4⋊C4—1581no—
684C4⋊C4—1581no—
685C4⋊C4—1581no—
686C4⋊C4C23×D7912yes—
687C4⋊C4C23×D7912yes—
688C4⋊C4C23×D7912yes—
689C22⋊C4—24no—
690C22⋊C4—1584no—
691C22⋊C4—1584no—
692C22⋊C4—1584no—
693C22⋊C4—1584no—
694C22⋊C4—1584no—
695C22⋊C4—1584no—
696C22⋊C4—1584no—
697C42—1584no—
698C42—1584no—
699C42—1584no—
700C42—1584no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—3168no—
709C23—3162no—
710C23—3162no—
711C23—3162no—
712C23—794no—
713C23—792no—
714C23—792no—
715C23—6324no—
716C23—6324no—
717C23—63216no—
718C23—1582no—
719C23—1582no—
720C23—1582no—
721C23—1582no—
722C23—1582no—
723C23—1582no—
724C23C2×D4×D7912yes—
725C23C2×D4×D7911yescharacteristic
726Q8—1588no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—3168no—
732D4—3162no—
733D4—6324no—
734D4—6324no—
735D4—6324no—
736D4—1588no—
737D4—1588no—
738D4—1588no—
739D4—1582no—
740D4—1582no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—3162no—
753C2×C4—3162no—
754C2×C4—3162no—
755C2×C4—794no—
756C2×C4—792no—
757C2×C4—798no—
758C2×C4—794no—
759C2×C4—794no—
760C2×C4—792no—
761C2×C4—6324no—
762C2×C4—6324no—
763C2×C4—1582no—
764C2×C4—1582no—
765C2×C4—1582no—
766C2×C4—1582no—
767C2×C4—1584no—
768C2×C4—1582no—
769C2×C4—1582no—
770C2×C4C2×D4×D7912yes—
771C2×C4C2×D4×D7911yescharacteristic
772C2×C4#41×D7912yes—
773C2×C4#41×D7912yes—
774C2×C4C24×D7911yescharacteristic
775C8—22no—
776C8—22no—
777C8—1582no—
778C8—1582no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—3164no—
788C22—3162no—
789C22—3162no—
790C22—3162no—
791C22—794no—
792C22—63216no—
793C22—6324no—
794C22—1582no—
795C22—1582no—
796C22—1582no—
797C22—1582no—
798C22—1582no—
799C22—1588no—
800C22#123×D7912yes—
801C22#1909936412yes—
802C22#1909937212yes—
803C22C22×D4×D7911yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—3162no—
809C4—3162no—
810C4—3162no—
811C4—794no—
812C4—1582no—
813C4#123×D7912yes—
814C4C2×#41×D7911yescharacteristic
815C4C2×#41×D7911yescharacteristic
816C2—42no—
817C2—82no—
818C2—3162no—
819C2—6322no—
820C2—1584no—
821C2#2377335114yesdirect product factor
822C2C2×#123×D7911yescharacteristic
823C2C2×#1909936411yescharacteristic
824C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#480×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099129C2
hypercenterC2×#480D79
hypocenterC79C2×#3096
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#19099044C2semidirect
3. #23773351C2direct (N × H)
4. C2×#19098881C2semidirect
5. C2×#19098880C2semidirect
6. C2×#19098890C2semidirect
7. C2×#19098888C2semidirect
8. C2×#19098885C2semidirect
9. C2×#19098884C2semidirect
10. C2×#19098878C2semidirect
11. C2×#19098604C2semidirect
12. C2×#19098600C2semidirect
13. C2×#19098566C2semidirect
14. C2×#102×D79C2semidirect
15. C2×#19098528C2semidirect
16. C2×#480×C79C2semidirect
31. #19099044C22semidirect
36. C2×#14579120C22semidirect
39. C2×#14579119C22semidirect
41. C2×C4⋊C4×D79C22semidirect
42. #19098890C22semidirect
43. #19098888C22semidirect
44. #19098885C22semidirect
45. #19098884C22semidirect
46. #19098881C22semidirect
47. #19098880C22semidirect
48. #19098878C22semidirect
49. #19098604C22semidirect
50. #19098600C22semidirect
51. C2×#14579095C22semidirect
52. C2×#14579094C22semidirect
53. C2×#14579093C22semidirect
54. C2×#14579092C22semidirect
55. C2×#14579092C22semidirect
56. C2×#14579092C22semidirect
57. #19098566C22semidirect
64. #102×D79C22semidirect
65. #19098528C22semidirect
66. C2×C22⋊(C79⋊C8)C22semidirect
67. C2×(C2×D79)⋊C8C22semidirect
68. C2×(C2×D79)⋊C8C22semidirect
70. C22×C4⋊C4×C79C22semidirect
71. #480×C79C22semidirect
72. C2×#107×C79C22semidirect
73. C2×#107×C79C22semidirect
76. C2×C22⋊C8×C79C22semidirect
120. #14579120C23semidirect
126. #14579119C23semidirect
135. C4⋊C4×D79C23semidirect
147. #14579095C23semidirect
148. #14579094C23semidirect
149. #14579093C23semidirect
150. #14579092C23semidirect
151. #14579092C23semidirect
152. #14579092C23semidirect
159. C22⋊(C79⋊C8)C23semidirect
160. (C2×D79)⋊C8C23semidirect
161. (C2×D79)⋊C8C23semidirect
175. C2×C4⋊C4×C79C23semidirect
177. #107×C79C23semidirect
178. #107×C79C23semidirect
181. C22⋊C8×C79C23semidirect
406. C2×C79#3096semidirect
423. C2×#480D79semidirect
429. C79C2×#3096semidirect
456. C22×C4⋊C4C2×D79semidirect
464. #480C2×D79semidirect
469. C2×#107C2×D79semidirect
470. C2×#107C2×D79semidirect
489. C2×C22⋊C8C2×D79semidirect
562. C2×C4⋊C4C22×D79semidirect
577. #107C22×D79semidirect
578. #107C22×D79semidirect
594. C22⋊C8C22×D79semidirect
821. C2#23773351direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991292
C2×#190990442
#237733512
C2×#190988812
C2×#190988802
C2×#190988902
C2×#190988882
C2×#190988852
C2×#190988842
C2×#190988782
C2×#190986042
C2×#190986002
C2×#190985662
C2×#102×D792
C2×#190985282
C2×#480×C792
C2×#309679