Finite Group Databasebeta

← #34294857

Subgroups — #34294857

Order 20224.

1066 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098797C211yesmaximal, characteristic
2C2×#19098673C211yesmaximal, characteristic, complemented
3C2×#19098519C211yesmaximal, characteristic, complemented
4#23766093C211yesmaximal, characteristic, complemented
5#23764275C211yesmaximal, characteristic, complemented
6#23764135C211yesmaximal, characteristic, complemented
7#23764086C211yesmaximal, characteristic, complemented
8#23764082C211yesmaximal, characteristic, complemented
9#23763839C211yesmaximal, characteristic, complemented
10#23763836C211yesmaximal, characteristic, complemented
11#23763423C211yesmaximal, characteristic, complemented
12#23763298C211yesmaximal, characteristic, complemented
13C4×#14579081C211yesmaximal, characteristic, complemented
14C4×#14579082C211yesmaximal, characteristic, complemented
15C79×#2324C211yesmaximal, characteristic, complemented
16C22×#11929609C2211yescharacteristic
17C22×#11929608C2211yescharacteristic
18C23×C79⋊C8C2211yescharacteristic
19C2×#14579135C2211yescharacteristic
20C2×C4×D316C2211yescharacteristic
21#19098797C418yescomplemented
22#19098673—24no—
23C2×#14579094C2211yescharacteristic
24C2×#14579092C2211yescharacteristic
25C2×#14579092C2211yescharacteristic
26C2×#14579082C2211yescharacteristic
27C2×#14579082C2211yescharacteristic
28C2×#14579082C2211yescharacteristic
29C2×#14579081C2211yescharacteristic
30C2×#14579081C2211yescharacteristic
31C2×#14579081C2211yescharacteristic
32#19098519—24no—
33C2×#14579072C2211yescharacteristic
34C2×#14579072C2211yescharacteristic
35C2×C4×C79⋊C8C2211yescharacteristic
36C2×C4×C79⋊C8C2211yescharacteristic
37#19098465C2211yescharacteristic
38#19098463—21no—
39#19098461C2211yescharacteristic
40#19098453—21no—
41#19098439—21no—
42#19098434—21no—
43#19098423C2211yescharacteristic
44C4×C4⋊Dic79C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51C2×#121×C79C2211yescharacteristic
52C2×C4×D4×C79C2211yescharacteristic
53C2×#117×C79C2211yescharacteristic
54#390×C79—21no—
55#390×C79C2211yescharacteristic
56#389×C79C2211yescharacteristic
57#388×C79—21no—
58#386×C79—21no—
59#385×C79—21no—
60#380×C79C2211yescharacteristic
61C4×C4⋊C4×C79C2211yescharacteristic
62C22×D316C2311yescharacteristic
63C22×C22⋊D79—21no—
64C22×C4×D79—21no—
65C2×#11929609—22no—
66C2×#11929609—22no—
67C2×#11929609C2×C414yes—
68C2×#11929608—22no—
69C2×#11929608—22no—
70C2×#11929608—22no—
71C22×C79⋊C8—22no—
72C22×C79⋊C8—22no—
73C22×C79⋊C8C2×C414yescomplemented
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77C22×C79⋊C8C2311yescharacteristic
78#14579135—22no—
79#14579135C2×C414yescomplemented
80C4×D316—22no—
81C4×D316—22no—
82C2×C4⋊Dic79C2311yescharacteristic
83C2×C4⋊Dic79C2311yescharacteristic
84C2×C4⋊Dic79C2311yescharacteristic
85C2×Dic79⋊C4—21no—
86C2×C22⋊Dic79—21no—
87C2×(C2×D79)⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89C2×(C2×D79)⋊C4—21no—
90C2×(C2×D79)⋊C4—21no—
91C2×C4×Dic79—21no—
92#14579094C2×C414yescomplemented
93#14579092—22no—
94#14579092—22no—
95#14579082—22no—
96#14579082—22no—
97#14579082C2×C414yescomplemented
98#14579081—22no—
99#14579081—22no—
100#14579081C2×C414yescomplemented
101#14579072—22no—
102#14579072D414yescomplemented
103C4×C79⋊C8—22no—
104C4×C79⋊C8—22no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C22×D4×C79—21no—
109C22×D4×C79C2311yescharacteristic
110C23×C4×C79—21no—
111C23×C4×C79C2311yescharacteristic
112#121×C79—22no—
113#121×C79C2×C414yescomplemented
114C4×D4×C79—22no—
115C4×D4×C79—22no—
116#117×C79—22no—
117#117×C79—22no—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79D411yescharacteristic
120C2×C4⋊C4×C79D411yescharacteristic
121C2×C4⋊C4×C79C2311yescharacteristic
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C4⋊C4×C79C2311yescharacteristic
124C2×C22⋊C4×C79—21no—
125C2×C22⋊C4×C79—21no—
126C2×C22⋊C4×C79—21no—
127C2×C22⋊C4×C79—21no—
128C2×C22⋊C4×C79—21no—
129C2×C22⋊C4×C79D411yescharacteristic
130C2×C22⋊C4×C79D411yescharacteristic
131C2×C42×C79—21no—
132C2×C42×C79C2311yescharacteristic
133C2×C42×C79C2311yescharacteristic
134#95×C79—21no—
135#95×C79—21no—
136#95×C79—21no—
137C23×D79—21no—
138C2×D316—21no—
139C2×D316—21no—
140C2×D316—21no—
141C2×D316—21no—
142C2×D316—21no—
143C2×D316C22×C412yes—
144C2×C22⋊D79—24no—
145C2×C22⋊D79—81no—
146C2×C22⋊D79—81no—
147C22×Dic79—21no—
148C22×Dic79—21no—
149C22×Dic79—21no—
150C2×C4×D79—42no—
151C2×C4×D79—81no—
152C2×C4×D79—81no—
153#11929609—28no—
154#11929608—28no—
155C2×C79⋊C8—28no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8C22×C412yes—
163C2×C79⋊C8C22×C412yes—
164C2×C79⋊C8C2×D412yes—
165C2×C79⋊C8C2×D412yes—
166C2×C79⋊C8#4112yes—
167C2×C79⋊C8#4112yes—
168C4⋊Dic79—21no—
169C4⋊Dic79—21no—
170C4⋊Dic79—21no—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79C22×C412yes—
174Dic79⋊C4—81no—
175C22⋊Dic79—81no—
176(C2×D79)⋊C4—24no—
177(C2×D79)⋊C4—42no—
178(C2×D79)⋊C4—81no—
179(C2×D79)⋊C4—81no—
180C4×Dic79—81no—
181C24×C79—21no—
182C24×C79C2×D411yescharacteristic
183C2×D4×C79—24no—
184C2×D4×C79—21no—
185C2×D4×C79—21no—
186C2×D4×C79—21no—
187C2×D4×C79—21no—
188C2×D4×C79—21no—
189C2×D4×C79—81no—
190C2×D4×C79—81no—
191C2×D4×C79C22×C412yes—
192C22×C4×C79—21no—
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79—21no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—42no—
200C22×C4×C79—81no—
201C22×C4×C79—81no—
202C22×C4×C79C22×C412yes—
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2×D411yescharacteristic
208C22×C4×C79#4112yes—
209C22×C4×C79C2411yescharacteristic
210C4⋊C4×C79—22no—
211C4⋊C4×C79—22no—
212C4⋊C4×C79—21no—
213C4⋊C4×C79—21no—
214C4⋊C4×C79—21no—
215C4⋊C4×C79—21no—
216C4⋊C4×C79—21no—
217C4⋊C4×C79—81no—
218C4⋊C4×C79C22×C412yes—
219C22⋊C4×C79—24no—
220C22⋊C4×C79—22no—
221C22⋊C4×C79—22no—
222C22⋊C4×C79—42no—
223C22⋊C4×C79—81no—
224C22⋊C4×C79—81no—
225C22⋊C4×C79—81no—
226C42×C79—21no—
227C42×C79—21no—
228C42×C79—81no—
229C42×C79C2×D412yes—
230C42×C79#4112yes—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79—21no—
234C23×C79—21no—
235C23×C79—21no—
236C23×C79—21no—
237C23×C79—22no—
238C23×C79—41no—
239C23×C79—41no—
240C23×C79—41no—
241C23×C79—41no—
242C23×C79—41no—
243C23×C79—41no—
244C23×C79C4×D412yes—
245C23×C79C22×D411yescharacteristic
246C22×D79—22no—
247C22×D79—41no—
248C22×D79—41no—
249C22×D79—41no—
250C22×D79—41no—
251C22×D79—41no—
252C22×D79—41no—
253D4×C79—22no—
254D4×C79—22no—
255D4×C79—41no—
256D4×C79—41no—
257D4×C79—84no—
258C2×C4×C79—21no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—21no—
262C2×C4×C79—21no—
263C2×C4×C79—21no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—22no—
269C2×C4×C79—21no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—41no—
276C2×C4×C79—41no—
277C2×C4×C79—41no—
278C2×C4×C79—41no—
279C2×C4×C79—41no—
280C2×C4×C79—41no—
281C2×C4×C79—41no—
282C2×C4×C79—41no—
283C2×C4×C79—84no—
284C2×C4×C79C4×D412yes—
285C2×C4×C79#12112yes—
286C2×C4×C79#12112yes—
287C2×C4×C79C23×C411yescharacteristic
288C2×C4×C79C22×D411yescharacteristic
289C2×C4×C79C2×#4111yescharacteristic
290C2×C4×C79C2×#4111yescharacteristic
291C2×C4×C79C2×#4111yescharacteristic
292C2×C4×C79C2×#4111yescharacteristic
293C22⋊D79—84no—
294C2×Dic79—22no—
295C2×Dic79—41no—
296C2×Dic79—41no—
297C2×Dic79—41no—
298C2×Dic79—41no—
299C2×Dic79—41no—
300C2×Dic79—41no—
301C2×Dic79—41no—
302C2×Dic79—41no—
303D316—22no—
304D316—22no—
305D316—41no—
306D316—41no—
307C4×D79—84no—
308C79⋊C8—22no—
309C79⋊C8—22no—
310C79⋊C8—22no—
311C79⋊C8C4×D414yes—
312C22×C79—22no—
313C22×C79—22no—
314C22×C79—22no—
315C22×C79—41no—
316C22×C79—41no—
317C22×C79—41no—
318C22×C79—41no—
319C22×C79—42no—
320C22×C79—42no—
321C22×C79—42no—
322C22×C79—81no—
323C22×C79—81no—
324C22×C79—81no—
325C22×C79—81no—
326C22×C79C2×C4×D411yescharacteristic
327C22×C79C2×#12111yescharacteristic
328C22×C79#53211yescharacteristic
329C22×C79#57611yescharacteristic
330C22×C79#57611yescharacteristic
331C22×C79#57711yescharacteristic
332C22×C79#57711yescharacteristic
333C2×D79—42no—
334C2×D79—42no—
335C2×D79—42no—
336C2×D79—81no—
337C2×D79—81no—
338C2×D79—81no—
339C2×D79—81no—
340C4×C79—22no—
341C4×C79—22no—
342C4×C79—22no—
343C4×C79—42no—
344C4×C79—41no—
345C4×C79—41no—
346C4×C79—81no—
347C4×C79—81no—
348C4×C79C2×C4×D411yescharacteristic
349C4×C79C4×#4111yescharacteristic
350C4×C79#52511yescharacteristic
351C4×C79#52911yescharacteristic
352Dic79—42no—
353Dic79—81no—
354Dic79—81no—
355#21529—791nomaximal, Sylow
356C2×C79—42no—
357C2×C79—82no—
358C2×C79C4×#12111yescharacteristic
359C2×C79#294811yescharacteristic
360C2×C79#295211yescharacteristic
361C2×C79#306211yescharacteristic
362C2×C79#306211yescharacteristic
363C2×C79#317911yescharacteristic
364C2×C79#317911yescharacteristic
365D79—82no—
366C2×#466—791no—
367C2×#442—791no—
368C2×#405—791no—
369#2324—791no—
370#2324D7911yescharacteristic, complemented
371#1972—791no—
372#1943—791no—
373#1934—791no—
374#1934—791no—
375#1895—791no—
376#1895—791no—
377#1807—791no—
378#1776—791no—
379C4×#102—791no—
380C4×#102—791no—
381C79#2152911yescharacteristic, complemented, Sylow
382C22×D8—791no—
383C22×M16—791no—
384C23×C8—791no—
385C2×#121—791no—
386C2×#121C2×D7911yescharacteristic
387C2×C4×D4—791no—
388C2×C4×D4C2×D7911yescharacteristic
389C2×#117C2×D7911yescharacteristic
390#466—798no—
391#442—1584no—
392C2×#107—791no—
393C2×#106—791no—
394C2×#106—791no—
395C2×#102—791no—
396C2×#102—791no—
397C2×#102—791no—
398C2×#102—791no—
399C2×#102—791no—
400C2×#102—791no—
401#405—1584no—
402C2×#97—791no—
403C2×#97—791no—
404C2×C4×C8—791no—
405C2×C4×C8—791no—
406#390—21no—
407#390—791no—
408#390—1581no—
409#390C2×D7911yescharacteristic
410#389—791no—
411#389C2×D7911yescharacteristic
412#388—21no—
413#388—1581no—
414#386—21no—
415#386—1581no—
416#385—21no—
417#385—1581no—
418#380—791no—
419#380C2×D7911yescharacteristic
420C4×C4⋊C4—791no—
421C4×C4⋊C4C2×D7911yescharacteristic
422#340—791no—
423#340—791no—
424#340—791no—
425#340—791no—
426#340—791no—
427#340—791no—
428C22×D4—21no—
429C22×D4—791no—
430C22×D4—1581no—
431C22×D4C22×D7911yescharacteristic
432C23×C4—21no—
433C23×C4—1581no—
434C23×C4C22×D7911yescharacteristic
435C2×D8—794no—
436C2×D8—1582no—
437C2×D8—1582no—
438C2×M16—1582no—
439C2×M16—1582no—
440C2×M16—1582no—
441C22×C8—791no—
442C22×C8—794no—
443C22×C8—791no—
444C22×C8—791no—
445C22×C8—791no—
446C22×C8—1582no—
447C22×C8—1582no—
448#121—22no—
449#121—794no—
450#121—1582no—
451#121C4×D7914yescomplemented
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—1582no—
455C4×D4—1582no—
456#117—22no—
457#117—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—791no—
460C2×C4⋊C4—791no—
461C2×C4⋊C4—791no—
462C2×C4⋊C4—1581no—
463C2×C4⋊C4C22⋊D7911yescharacteristic
464C2×C4⋊C4C22⋊D7911yescharacteristic
465C2×C4⋊C4C22×D7911yescharacteristic
466C2×C4⋊C4C22×D7911yescharacteristic
467C2×C4⋊C4C22×D7911yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—1581no—
474C2×C22⋊C4—1581no—
475C2×C22⋊C4—1581no—
476C2×C22⋊C4—1581no—
477C2×C22⋊C4—1581no—
478C2×C22⋊C4C22⋊D7911yescharacteristic
479C2×C22⋊C4C22⋊D7911yescharacteristic
480C2×C42—21no—
481C2×C42—1581no—
482C2×C42C22×D7911yescharacteristic
483C2×C42C22×D7911yescharacteristic
484#107—794no—
485#106—1582no—
486#106—1582no—
487#102—794no—
488#102—794no—
489#102—1582no—
490#102—1582no—
491#102—1582no—
492#102—1582no—
493#97—794no—
494#97—1582no—
495C4×C8—1582no—
496C4×C8—1582no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—1581no—
501#95—1581no—
502#95—1581no—
503C24—21no—
504C24—1581no—
505C24C2×C22⋊D7911yescharacteristic
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—792no—
515C2×D4—6321no—
516C2×D4—6321no—
517C2×D4—1584no—
518C2×D4—1581no—
519C2×D4—1581no—
520C2×D4—1581no—
521C2×D4—1581no—
522C2×D4—1581no—
523C2×D4C2×C4×D7912yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—3162no—
535C22×C4—6321no—
536C22×C4—6321no—
537C22×C4—1581no—
538C22×C4—1581no—
539C22×C4—1581no—
540C22×C4C2×C4×D7912yes—
541C22×C4C2×C22⋊D7911yescharacteristic
542C22×C4C2×C22⋊D7911yescharacteristic
543C22×C4C2×C22⋊D7911yescharacteristic
544C22×C4C2×C22⋊D7911yescharacteristic
545C22×C4C2×C22⋊D7911yescharacteristic
546C22×C4#1192962412yes—
547C22×C4C23×D7911yescharacteristic
548D8—1588no—
549M16—1588no—
550C2×C8—792no—
551C2×C8—792no—
552C2×C8—792no—
553C2×C8—792no—
554C2×C8—792no—
555C2×C8—792no—
556C2×C8—1588no—
557C2×C8—1581no—
558C2×C8—1581no—
559C2×C8—1581no—
560C2×C8—1581no—
561C2×C8—1581no—
562C2×C8—1581no—
563C4⋊C4—21no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—81no—
571C4⋊C4—792no—
572C4⋊C4—6321no—
573C4⋊C4—1581no—
574C4⋊C4—1581no—
575C4⋊C4—1581no—
576C4⋊C4—1581no—
577C4⋊C4—1581no—
578C4⋊C4C2×C4×D7912yes—
579C22⋊C4—24no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—3162no—
587C22⋊C4—6321no—
588C22⋊C4—6321no—
589C22⋊C4—6321no—
590C22⋊C4—1584no—
591C42—21no—
592C42—21no—
593C42—81no—
594C42—6321no—
595C42D4×D7912yes—
596C42#1192962312yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—3161no—
611C23—3161no—
612C23—3161no—
613C23—3161no—
614C23—3161no—
615C23—3161no—
616C23—1582no—
617C23C4×C22⋊D7912yes—
618C23C22×C22⋊D7911yescharacteristic
619D4—22no—
620D4—22no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—3161no—
625D4—3161no—
626D4—6324no—
627D4—1582no—
628D4—1582no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—3161no—
656C2×C4—3161no—
657C2×C4—3161no—
658C2×C4—3161no—
659C2×C4—3161no—
660C2×C4—3161no—
661C2×C4—3161no—
662C2×C4—3161no—
663C2×C4—6324no—
664C2×C4—1582no—
665C2×C4C4×C22⋊D7912yes—
666C2×C4#1457913312yes—
667C2×C4#1457913312yes—
668C2×C4C22×C4×D7911yescharacteristic
669C2×C4C2×D4×D7911yescharacteristic
670C2×C4#41×D7911yescharacteristic
671C2×C4#41×D7911yescharacteristic
672C2×C4C2×#1192962311yescharacteristic
673C2×C4C2×#1192962411yescharacteristic
674C8—794no—
675C8—1582no—
676C8—1582no—
677C8—1582no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—3162no—
693C22—3162no—
694C22—3162no—
695C22—6321no—
696C22—6321no—
697C22—6321no—
698C22—6321no—
699C22C2×C4×C22⋊D7911yescharacteristic
700C22C2×#1457913311yescharacteristic
701C22#1909910911yescharacteristic
702C22#1909936611yescharacteristic
703C22#1909936611yescharacteristic
704C22#1909937111yescharacteristic
705C22#1909937411yescharacteristic
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—3162no—
715C4—6321no—
716C4—6321no—
717C4C4×D4×D7911yescharacteristic
718C4C4×#1192962311yescharacteristic
719C4#1909907211yescharacteristic
720C4#1909909311yescharacteristic
721C2—42no—
722C2—82no—
723C2—6322no—
724C2C4×#1457913311yescharacteristic
725C2#2377225011yescharacteristic
726C2#2377228111yescharacteristic
727C2#2377307611yescharacteristic
728C2#2377308211yescharacteristic
729C2#2377407711yescharacteristic
730C2#2377408511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2324C2
socleC23×C79C22×D4
prime radicalC2×#19098797C2
cosocleC22×C4×C79C24
hypercenter#2324D79
hypocenterC79#21529
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×#19098673C2semidirect
3. C2×#19098519C2semidirect
4. #23766093C2semidirect
5. #23764275C2semidirect
6. #23764135C2semidirect
7. #23764086C2semidirect
8. #23764082C2semidirect
9. #23763839C2semidirect
10. #23763836C2semidirect
11. #23763423C2semidirect
12. #23763298C2semidirect
13. C4×#14579081C2semidirect
14. C4×#14579082C2semidirect
15. C79×#2324C2semidirect
21. #19098797C4semidirect
73. C22×C79⋊C8C2×C4semidirect
79. #14579135C2×C4semidirect
92. #14579094C2×C4semidirect
97. #14579082C2×C4semidirect
100. #14579081C2×C4semidirect
102. #14579072D4semidirect
113. #121×C79C2×C4semidirect
370. #2324D79semidirect
381. C79#21529semidirect
451. #121C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190987972
C2×#190986732
C2×#190985192
#237660932
#237642752
#237641352
#237640862
#237640822
#237638392
#237638362
#237634232
#237632982
C4×#145790812
C4×#145790822
C79×#23242
#2152979