Finite Group Databasebeta

← #34196898

Subgroups — #34196898

Order 20224.

958 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579092C211yesmaximal, characteristic
2C2×#19098462C211yesmaximal, characteristic
3C2×#19098459C211yesmaximal, characteristic
4C2×#19098326C211yesmaximal, characteristic
5C2×#19098325C211yesmaximal, characteristic
6C2×#19098317C211yesmaximal, characteristic
7C2×#340×C79C211yesmaximal, characteristic
8C23×C79⋊C8C2211yescharacteristic
9C22×C4⋊Dic79—21no—
10C22×C4⋊Dic79C2211yescharacteristic
11C22×C4⋊Dic79C2211yescharacteristic
12C22×Dic79⋊C4—21no—
13C22×C4×Dic79C2211yescharacteristic
14C2×#14579092—22no—
15C2×#14579092—22no—
16C2×#14579092—22no—
17#19098462—22no—
18#19098462—22no—
19#19098459—22no—
20#19098459—22no—
21C2×C79⋊#95—21no—
22C2×C79⋊#95—21no—
23#19098326—22no—
24#19098325C414yescomplemented
25#19098317—22no—
26C23×C8×C79C2211yescharacteristic
27C22×C4⋊C4×C79C2211yescharacteristic
28C22×C4⋊C4×C79C2211yescharacteristic
29#340×C79—22no—
30C23×Dic79—21no—
31C23×Dic79—21no—
32C23×Dic79D411yescharacteristic
33C23×Dic79D411yescharacteristic
34C22×C79⋊C8—21no—
35C22×C79⋊C8—21no—
36C22×C79⋊C8—21no—
37C22×C79⋊C8—21no—
38C22×C79⋊C8C2×C412yes—
39C22×C79⋊C8D412yes—
40C22×C79⋊C8Q812yes—
41C2×C4⋊Dic79—21no—
42C2×C4⋊Dic79—21no—
43C2×C4⋊Dic79—21no—
44C2×C4⋊Dic79—21no—
45C2×C4⋊Dic79—21no—
46C2×C4⋊Dic79—21no—
47C2×C4⋊Dic79—21no—
48C2×C4⋊Dic79—24no—
49C2×C4⋊Dic79—21no—
50C2×C4⋊Dic79—42no—
51C2×C4⋊Dic79—42no—
52C2×C4⋊Dic79C2×C412yes—
53C2×C4⋊Dic79D412yes—
54C2×C4⋊Dic79D412yes—
55C2×C4⋊Dic79Q812yes—
56C2×Dic79⋊C4—24no—
57C2×Dic79⋊C4—42no—
58C2×Dic79⋊C4—42no—
59C2×C4×Dic79—21no—
60C2×C4×Dic79—21no—
61C2×C4×Dic79—21no—
62C2×C4×Dic79—21no—
63C2×C4×Dic79—21no—
64C2×C4×Dic79—21no—
65#14579092—28no—
66C79⋊#95—24no—
67C79⋊#95—24no—
68C23×C4×C79—21no—
69C23×C4×C79—21no—
70C23×C4×C79C2311yescharacteristic
71C22×C8×C79—21no—
72C22×C8×C79—21no—
73C22×C8×C79—21no—
74C22×C8×C79—21no—
75C22×C8×C79—21no—
76C22×C8×C79—21no—
77C22×C8×C79Q812yes—
78C2×C4⋊C4×C79—21no—
79C2×C4⋊C4×C79—21no—
80C2×C4⋊C4×C79—21no—
81C2×C4⋊C4×C79—21no—
82C2×C4⋊C4×C79—21no—
83C2×C4⋊C4×C79—21no—
84C2×C4⋊C4×C79—21no—
85C2×C4⋊C4×C79—21no—
86C2×C4⋊C4×C79C2×C412yes—
87C2×C4⋊C4×C79D412yes—
88C2×C4⋊C4×C79D412yes—
89C2×C4⋊C4×C79Q812yes—
90C22×Dic79—22no—
91C22×Dic79—21no—
92C22×Dic79—21no—
93C22×Dic79—22no—
94C22×Dic79—21no—
95C22×Dic79—21no—
96C22×Dic79—22no—
97C22×Dic79—21no—
98C22×Dic79—21no—
99C22×Dic79—22no—
100C22×Dic79—21no—
101C22×Dic79—21no—
102C22×Dic79—21no—
103C22×Dic79—21no—
104C22×Dic79—21no—
105C22×Dic79—21no—
106C22×Dic79—41no—
107C22×Dic79—41no—
108C22×Dic79—41no—
109C22×Dic79—41no—
110C22×Dic79—41no—
111C22×Dic79—41no—
112C22×Dic79—41no—
113C22×Dic79—41no—
114C22×Dic79—41no—
115C22×Dic79—41no—
116C22×Dic79SD1612yes—
117C22×Dic79SD1612yes—
118C2×C79⋊C8—22no—
119C2×C79⋊C8—22no—
120C2×C79⋊C8—22no—
121C2×C79⋊C8—22no—
122C2×C79⋊C8—22no—
123C2×C79⋊C8—22no—
124C2×C79⋊C8C4⋊C414yescomplemented
125C4⋊Dic79—22no—
126C4⋊Dic79—22no—
127C4⋊Dic79—22no—
128C4⋊Dic79—22no—
129C4⋊Dic79—22no—
130C4⋊Dic79—48no—
131C4⋊Dic79—41no—
132C4⋊Dic79—41no—
133C4⋊Dic79C4⋊C414yescomplemented
134Dic79⋊C4—48no—
135C4×Dic79—41no—
136C4×Dic79—41no—
137C4×Dic79—41no—
138C4×Dic79—41no—
139C24×C79C2×D411yescharacteristic
140C22×C4×C79—22no—
141C22×C4×C79—22no—
142C22×C4×C79—22no—
143C22×C4×C79—22no—
144C22×C4×C79—41no—
145C22×C4×C79—41no—
146C22×C4×C79—41no—
147C22×C4×C79—41no—
148C22×C4×C79—41no—
149C22×C4×C79—41no—
150C22×C4×C79—41no—
151C22×C4×C79—41no—
152C22×C4×C79—41no—
153C22×C4×C79—41no—
154C22×C4×C79C22×C411yescharacteristic
155C22×C4×C79C2×D411yescharacteristic
156C22×C4×C79C2×D411yescharacteristic
157C22×C4×C79C2×D411yescharacteristic
158C22×C4×C79C2×D411yescharacteristic
159C22×C4×C79C2×D411yescharacteristic
160C22×C4×C79C2×Q811yescharacteristic
161C22×C4×C79C2×Q811yescharacteristic
162C22×C4×C79C2×Q811yescharacteristic
163C22×C4×C79C2×Q811yescharacteristic
164C22×C4×C79#4111yescharacteristic
165C22×C4×C79#4111yescharacteristic
166C22×C4×C79#4111yescharacteristic
167C22×C4×C79#4111yescharacteristic
168C2×C8×C79—22no—
169C2×C8×C79—22no—
170C2×C8×C79—22no—
171C2×C8×C79—41no—
172C2×C8×C79—41no—
173C2×C8×C79—41no—
174C2×C8×C79—41no—
175C4⋊C4×C79—22no—
176C4⋊C4×C79—22no—
177C4⋊C4×C79—22no—
178C4⋊C4×C79—22no—
179C4⋊C4×C79—22no—
180C4⋊C4×C79—41no—
181C4⋊C4×C79—41no—
182C4⋊C4×C79C4⋊C414yescomplemented
183C23×C79C4×D411yescharacteristic
184C23×C79#12011yescharacteristic
185C23×C79#12011yescharacteristic
186C23×C79#12111yescharacteristic
187C23×C79C22⋊Q811yescharacteristic
188C23×C79C22⋊Q811yescharacteristic
189C23×C79C4⋊Q811yescharacteristic
190C23×C79C2×SD1611yescharacteristic
191C23×C79C2×SD1611yescharacteristic
192C23×C79#13511yescharacteristic
193C23×C79#13511yescharacteristic
194C23×C79AGL(1,ℤ/8)11yescharacteristic
195C23×C79AGL(1,ℤ/8)11yescharacteristic
196C23×C79#13711yescharacteristic
197C23×C79#13711yescharacteristic
198C2×C4×C79—24no—
199C2×C4×C79—42no—
200C2×C4×C79—42no—
201C2×C4×C79—42no—
202C2×C4×C79—42no—
203C2×C4×C79—42no—
204C2×C4×C79—42no—
205C2×C4×C79—42no—
206C2×C4×C79—42no—
207C2×C4×C79—42no—
208C2×C4×C79—81no—
209C2×C4×C79—81no—
210C2×C4×C79—81no—
211C2×C4×C79—81no—
212C2×C4×C79C2×C4⋊C411yescharacteristic
213C2×C4×C79C2×C4⋊C411yescharacteristic
214C2×C4×C79C2×C4⋊C411yescharacteristic
215C2×C4×C79C4×D411yescharacteristic
216C2×C4×C79C4×D411yescharacteristic
217C2×C4×C79C4×Q811yescharacteristic
218C2×C4×C79#12011yescharacteristic
219C2×C4×C79#12111yescharacteristic
220C2×C4×C79#12111yescharacteristic
221C2×C4×C79C22⋊Q811yescharacteristic
222C2×C4×C79C22⋊Q811yescharacteristic
223C2×C4×C79C22⋊Q811yescharacteristic
224C2×C4×C79C22⋊Q811yescharacteristic
225C2×C4×C79C22⋊Q811yescharacteristic
226C2×C4×C79C22⋊Q811yescharacteristic
227C2×C4×C79C22⋊Q811yescharacteristic
228C2×C4×C79#12311yescharacteristic
229C2×C4×C79#12311yescharacteristic
230C2×C4×C79#12311yescharacteristic
231C2×C4×C79#12511yescharacteristic
232C2×C4×C79#12511yescharacteristic
233C2×C4×C79#12511yescharacteristic
234C2×C4×C79#12711yescharacteristic
235C2×C4×C79C4⋊Q811yescharacteristic
236C2×C4×C79C4⋊Q811yescharacteristic
237C2×C4×C79C4⋊Q811yescharacteristic
238C2×C4×C79C4⋊Q811yescharacteristic
239C2×C4×C79C4⋊Q811yescharacteristic
240C2×Dic79—24no—
241C2×Dic79—22no—
242C2×Dic79—22no—
243C2×Dic79—22no—
244C2×Dic79—22no—
245C2×Dic79—22no—
246C2×Dic79—22no—
247C2×Dic79—41no—
248C2×Dic79—41no—
249C2×Dic79—42no—
250C2×Dic79—42no—
251C2×Dic79—41no—
252C2×Dic79—41no—
253C2×Dic79—42no—
254C2×Dic79—42no—
255C2×Dic79—41no—
256C2×Dic79—41no—
257C2×Dic79—41no—
258C2×Dic79—41no—
259C2×Dic79—42no—
260C2×Dic79—42no—
261C2×Dic79—42no—
262C2×Dic79—42no—
263C2×Dic79—42no—
264C2×Dic79—81no—
265C2×Dic79—81no—
266C2×Dic79—81no—
267C2×Dic79—81no—
268C8×C79—42no—
269C79⋊C8—24no—
270C22×C79#38511yescharacteristic
271C22×C79#38511yescharacteristic
272C22×C79#38911yescharacteristic
273C22×C79#39211yescharacteristic
274C22×C79#39511yescharacteristic
275C22×C79#39511yescharacteristic
276C22×C79#39811yescharacteristic
277C22×C79C4×SD1611yescharacteristic
278C22×C79C4×SD1611yescharacteristic
279C22×C79#44111yescharacteristic
280C22×C79#44211yescharacteristic
281C22×C79#44811yescharacteristic
282C22×C79#44811yescharacteristic
283C22×C79#44911yescharacteristic
284C22×C79#44911yescharacteristic
285C22×C79#45011yescharacteristic
286C22×C79#45011yescharacteristic
287C22×C79#45211yescharacteristic
288C22×C79#45211yescharacteristic
289C22×C79#46511yescharacteristic
290C22×C79#46511yescharacteristic
291C22×C79#46811yescharacteristic
292C22×C79#46811yescharacteristic
293C22×C79#47511yescharacteristic
294C22×C79#47511yescharacteristic
295C22×C79#47611yescharacteristic
296C22×C79#47611yescharacteristic
297C22×C79#47811yescharacteristic
298C22×C79#47811yescharacteristic
299C22×C79#47911yescharacteristic
300C22×C79#47911yescharacteristic
301C22×C79#49811yescharacteristic
302C22×C79#49911yescharacteristic
303C22×C79#50111yescharacteristic
304C22×C79#50111yescharacteristic
305C4×C79—44no—
306C4×C79—82no—
307C4×C79#38411yescharacteristic
308C4×C79#38511yescharacteristic
309C4×C79#38911yescharacteristic
310C4×C79#38911yescharacteristic
311C4×C79#39511yescharacteristic
312C4×C79#39811yescharacteristic
313C4×C79#39811yescharacteristic
314C4×C79#39911yescharacteristic
315Dic79—44no—
316Dic79—42no—
317Dic79—42no—
318Dic79—82no—
319#11327—791nomaximal, Sylow
320C2×C79#144411yescharacteristic
321C2×C79#186411yescharacteristic
322C2×C79#186411yescharacteristic
323C2×C79#186511yescharacteristic
324C2×C79#186511yescharacteristic
325C2×C79#194111yescharacteristic
326C2×C79#194311yescharacteristic
327C2×C79#200011yescharacteristic
328C2×C79#200011yescharacteristic
329C2×C79#205811yescharacteristic
330C2×C79#205811yescharacteristic
331C2×C79#205911yescharacteristic
332C2×C79#205911yescharacteristic
333C2×C79#208811yescharacteristic
334C2×C79#208811yescharacteristic
335C22×#106—791no—
336C2×#389—791no—
337C2×#389—791no—
338C2×#340—791no—
339C2×#340—791no—
340C2×#340D7911yescharacteristic
341C2×#336—791no—
342C79#1132711yescharacteristic, complemented, Sylow
343C23×C8—791no—
344C23×C8C2×D7911yescharacteristic
345C22×C4⋊C4—791no—
346C22×C4⋊C4—791no—
347C22×C4⋊C4—1581no—
348C22×C4⋊C4—1581no—
349C22×C4⋊C4C2×D7911yescharacteristic
350C22×C4⋊C4C2×D7911yescharacteristic
351C22×C42—791no—
352C2×#106—1582no—
353C2×#106—1582no—
354C2×#106—1582no—
355#389—1582no—
356#389—1582no—
357#389—1582no—
358#389—1582no—
359C2×#95—1581no—
360C2×#95—1581no—
361#340—22no—
362#340—794no—
363#340—1582no—
364#336—1582no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—791no—
368C23×C4—791no—
369C23×C4—1581no—
370C23×C4—1581no—
371C23×C4C22×D7911yescharacteristic
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—792no—
379C22×C8—792no—
380C22×C8—792no—
381C22×C8—1581no—
382C22×C8—1581no—
383C22×C8—1581no—
384C22×C8—1581no—
385C22×C8Dic15812yes—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—3162no—
395C2×C4⋊C4—3162no—
396C2×C4⋊C4—3162no—
397C2×C4⋊C4—3162no—
398C2×C4⋊C4—792no—
399C2×C4⋊C4—792no—
400C2×C4⋊C4—792no—
401C2×C4⋊C4—792no—
402C2×C4⋊C4—1584no—
403C2×C4⋊C4—1584no—
404C2×C4⋊C4—1581no—
405C2×C4⋊C4—1581no—
406C2×C4⋊C4—1581no—
407C2×C4⋊C4—1581no—
408C2×C4⋊C4—1581no—
409C2×C4⋊C4—1581no—
410C2×C4⋊C4—1581no—
411C2×C4⋊C4—1581no—
412C2×C4⋊C4Dic15812yes—
413C2×C4⋊C4C4×D7912yes—
414C2×C4⋊C4D31612yes—
415C2×C4⋊C4C22⋊D7912yes—
416C2×C42—1581no—
417C2×C42—1581no—
418C2×C42—1581no—
419C2×C42—1581no—
420C2×C42—1581no—
421C2×C42—1581no—
422#106—1588no—
423#95—1584no—
424#95—1584no—
425C24D4×D7911yescharacteristic
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—3161no—
441C22×C4—3161no—
442C22×C4—3161no—
443C22×C4—3161no—
444C22×C4—3161no—
445C22×C4—3161no—
446C22×C4—3161no—
447C22×C4—3161no—
448C22×C4—3161no—
449C22×C4—3161no—
450C22×C4—792no—
451C22×C4—792no—
452C22×C4—1582no—
453C22×C4—1582no—
454C22×C4—1581no—
455C22×C4—1581no—
456C22×C4—1581no—
457C22×C4—1582no—
458C22×C4—1581no—
459C22×C4—1581no—
460C22×C4—1581no—
461C22×C4—1582no—
462C22×C4—1581no—
463C22×C4—1581no—
464C22×C4—1581no—
465C22×C4—1581no—
466C22×C4—1581no—
467C22×C4—1581no—
468C22×C4C2×C4×D7911yescharacteristic
469C22×C4D4×D7911yescharacteristic
470C22×C4D4×D7911yescharacteristic
471C22×C4D4×D7911yescharacteristic
472C22×C4C2×C22⋊D7911yescharacteristic
473C22×C4C2×D31611yescharacteristic
474C22×C4Q8×D7911yescharacteristic
475C22×C4Q8×D7911yescharacteristic
476C22×C4C2×Dic15811yescharacteristic
477C22×C4C2×Dic15811yescharacteristic
478C22×C4#1192962311yescharacteristic
479C22×C4#1192962311yescharacteristic
480C22×C4#1192962411yescharacteristic
481C22×C4#1192962411yescharacteristic
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—794no—
490C2×C8—1582no—
491C2×C8—1582no—
492C2×C8—1582no—
493C2×C8—1582no—
494C2×C8—1582no—
495C2×C8—1582no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—3168no—
504C4⋊C4—3168no—
505C4⋊C4—3161no—
506C4⋊C4—3161no—
507C4⋊C4—794no—
508C4⋊C4—1582no—
509C4⋊C4—1582no—
510C4⋊C4—1582no—
511C4⋊C4—1582no—
512C4⋊C4—1582no—
513C4⋊C4Dic79⋊C414yescomplemented
514C42—3161no—
515C42—3161no—
516C42—3161no—
517C42—3161no—
518C23(C22⋊D79)⋊C411yescharacteristic
519C23#1457912911yescharacteristic
520C23#1457913111yescharacteristic
521C23#1457913411yescharacteristic
522C23#1457913811yescharacteristic
523C23#1457913911yescharacteristic
524C23#1457916011yescharacteristic
525C23SD16×D7911yescharacteristic
526C23SD16×D7911yescharacteristic
527C23#1457918011yescharacteristic
528C23#1457918411yescharacteristic
529C23#1457918511yescharacteristic
530C23#1457918811yescharacteristic
531C23#1457919011yescharacteristic
532C23#1457919311yescharacteristic
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—3162no—
548C2×C4—3162no—
549C2×C4—3161no—
550C2×C4—3162no—
551C2×C4—3161no—
552C2×C4—3162no—
553C2×C4—3161no—
554C2×C4—3161no—
555C2×C4—3161no—
556C2×C4—3161no—
557C2×C4—3161no—
558C2×C4—3161no—
559C2×C4—3162no—
560C2×C4—3162no—
561C2×C4—3162no—
562C2×C4—3162no—
563C2×C4—3162no—
564C2×C4—6321no—
565C2×C4—6321no—
566C2×C4—6321no—
567C2×C4—6321no—
568C2×C4—1584no—
569C2×C4—1582no—
570C2×C4—1582no—
571C2×C4—1582no—
572C2×C4—1582no—
573C2×C4—1582no—
574C2×C4—1582no—
575C2×C4C4⋊C4×D7911yescharacteristic
576C2×C4C4⋊C4×D7911yescharacteristic
577C2×C4C2×Dic79⋊C411yescharacteristic
578C2×C4(C22⋊D79)⋊C411yescharacteristic
579C2×C4C4×D31611yescharacteristic
580C2×C4C4×Dic15811yescharacteristic
581C2×C4#1457913111yescharacteristic
582C2×C4#1457913411yescharacteristic
583C2×C4#1457913511yescharacteristic
584C2×C4#1457913811yescharacteristic
585C2×C4#1457913811yescharacteristic
586C2×C4#1457913811yescharacteristic
587C2×C4#1457913911yescharacteristic
588C2×C4#1457914011yescharacteristic
589C2×C4#1457914111yescharacteristic
590C2×C4#1457914111yescharacteristic
591C2×C4#1457914211yescharacteristic
592C2×C4#1457914311yescharacteristic
593C2×C4#1457914311yescharacteristic
594C2×C4#1457915111yescharacteristic
595C2×C4#1457915111yescharacteristic
596C2×C4#1457915311yescharacteristic
597C2×C4#1457915711yescharacteristic
598C2×C4#1457915911yescharacteristic
599C2×C4#1457916011yescharacteristic
600C2×C4#1457916011yescharacteristic
601C2×C4#1457916011yescharacteristic
602C2×C4#1457916111yescharacteristic
603C8—42no—
604C8—1584no—
605C22#1909843511yescharacteristic
606C22#1909843711yescharacteristic
607C22#1909846011yescharacteristic
608C22#1909847211yescharacteristic
609C22#1909848311yescharacteristic
610C22#1909848411yescharacteristic
611C22#1909849711yescharacteristic
612C22#1909864811yescharacteristic
613C22#1909865411yescharacteristic
614C22#1909866711yescharacteristic
615C22#1909867211yescharacteristic
616C22#1909870011yescharacteristic
617C22#1909870311yescharacteristic
618C22#1909870511yescharacteristic
619C22#1909871111yescharacteristic
620C22#1909871211yescharacteristic
621C22#1909871511yescharacteristic
622C22#1909872411yescharacteristic
623C22#1909872611yescharacteristic
624C22#1909879111yescharacteristic
625C22#1909879511yescharacteristic
626C22#1909880811yescharacteristic
627C22#1909881211yescharacteristic
628C22#1909884611yescharacteristic
629C22#1909884711yescharacteristic
630C22#1909885111yescharacteristic
631C22#1909885211yescharacteristic
632C22#1909886111yescharacteristic
633C22#1909886611yescharacteristic
634C22#1909886911yescharacteristic
635C22#1909887211yescharacteristic
636C22#1909896011yescharacteristic
637C22#1909896411yescharacteristic
638C22#1909897011yescharacteristic
639C22#1909897111yescharacteristic
640C4—44no—
641C4—82no—
642C4—3162no—
643C4—3162no—
644C4—3164no—
645C4—6322no—
646C4#1909843211yescharacteristic
647C4#1909843711yescharacteristic
648C4#1909846011yescharacteristic
649C4#1909846111yescharacteristic
650C4#1909848411yescharacteristic
651C4#1909849311yescharacteristic
652C4#1909849711yescharacteristic
653C4#1909849911yescharacteristic
654C2#2376166411yescharacteristic
655C2#2376365911yescharacteristic
656C2#2376366211yescharacteristic
657C2#2376366611yescharacteristic
658C2#2376366911yescharacteristic
659C2#2376412711yescharacteristic
660C2#2376413711yescharacteristic
661C2#2376440211yescharacteristic
662C2#2376440411yescharacteristic
663C2#2376473111yescharacteristic
664C2#2376473211yescharacteristic
665C2#2376473611yescharacteristic
666C2#2376474111yescharacteristic
667C2#2376490311yescharacteristic
668C2#2376490411yescharacteristic
subgroupG/H
centerC24D4×D79
commutatorC22×C4×C79C22×C4
FrattiniC23×C4C22×D79
FittingC2×#340×C79C2
socle, prime radicalC24×C79C2×D4
cosocleC23×C4×C79C23
hypercenterC2×#340D79
hypocenterC79#11327
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
24. #19098325C4semidirect
124. C2×C79⋊C8C4⋊C4semidirect
133. C4⋊Dic79C4⋊C4semidirect
182. C4⋊C4×C79C4⋊C4semidirect
342. C79#11327semidirect
513. C4⋊C4Dic79⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#145790922
C2×#190984622
C2×#190984592
C2×#190983262
C2×#190983252
C2×#190983172
C2×#340×C792
#1132779