Finite Group Databasebeta

← #34193929

Subgroups — #34193929

Order 20224.

914 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic79C211yesmaximal, characteristic
2C2×#19098326C211yesmaximal, characteristic
3C2×#19098325C211yesmaximal, characteristic
4C2×#19098325C211yesmaximal, characteristic
5C2×#19098317C211yesmaximal, characteristic
6#23761629C211yesmaximal, characteristic
7C2×#340×C79C211yesmaximal, characteristic
8C23×C79⋊C8C2211yescharacteristic
9C22×C4⋊Dic79C2211yescharacteristic
10C22×C4⋊Dic79C2211yescharacteristic
11C22×C4×Dic79—21no—
12C22×C4×Dic79C2211yescharacteristic
13C4⋊C4×Dic79—22no—
14C4⋊C4×Dic79C414yescomplemented
15C2×C79⋊#95—21no—
16C2×C79⋊#95—21no—
17C2×C79⋊#95—21no—
18#19098326C414yescomplemented
19#19098325—22no—
20#19098325C414yescomplemented
21#19098317—22no—
22C23×C8×C79C2211yescharacteristic
23C22×C4⋊C4×C79C2211yescharacteristic
24C22×C4⋊C4×C79C2211yescharacteristic
25#340×C79—22no—
26C23×Dic79—21no—
27C23×Dic79—21no—
28C23×Dic79D411yescharacteristic
29C23×Dic79D411yescharacteristic
30C22×C79⋊C8—21no—
31C22×C79⋊C8—21no—
32C22×C79⋊C8—21no—
33C22×C79⋊C8—21no—
34C22×C79⋊C8—21no—
35C22×C79⋊C8—21no—
36C22×C79⋊C8C2×C412yes—
37C2×C4⋊Dic79—21no—
38C2×C4⋊Dic79—21no—
39C2×C4⋊Dic79—21no—
40C2×C4⋊Dic79—21no—
41C2×C4⋊Dic79—21no—
42C2×C4⋊Dic79—21no—
43C2×C4⋊Dic79—21no—
44C2×C4⋊Dic79—21no—
45C2×C4⋊Dic79C2×C412yes—
46C2×C4⋊Dic79C2×C412yes—
47C2×C4⋊Dic79C2×C412yes—
48C2×C4⋊Dic79C2×C412yes—
49C2×C4×Dic79—21no—
50C2×C4×Dic79—21no—
51C2×C4×Dic79—21no—
52C2×C4×Dic79—21no—
53C2×C4×Dic79—24no—
54C2×C4×Dic79—42no—
55C2×C4×Dic79—42no—
56C2×C4×Dic79C2×C412yes—
57C2×C4×Dic79D412yes—
58C79⋊#95—24no—
59C79⋊#95—42no—
60C79⋊#95—42no—
61C23×C4×C79—21no—
62C23×C4×C79—21no—
63C23×C4×C79C2311yescharacteristic
64C22×C8×C79—21no—
65C22×C8×C79—21no—
66C22×C8×C79—21no—
67C22×C8×C79—21no—
68C22×C8×C79—21no—
69C22×C8×C79—21no—
70C22×C8×C79C2×C412yes—
71C2×C4⋊C4×C79—21no—
72C2×C4⋊C4×C79—21no—
73C2×C4⋊C4×C79—21no—
74C2×C4⋊C4×C79—21no—
75C2×C4⋊C4×C79—21no—
76C2×C4⋊C4×C79—21no—
77C2×C4⋊C4×C79—21no—
78C2×C4⋊C4×C79—21no—
79C2×C4⋊C4×C79C2×C412yes—
80C2×C4⋊C4×C79C2×C412yes—
81C2×C4⋊C4×C79D412yes—
82C2×C4⋊C4×C79Q812yes—
83C22×Dic79—22no—
84C22×Dic79—22no—
85C22×Dic79—22no—
86C22×Dic79—22no—
87C22×Dic79—21no—
88C22×Dic79—21no—
89C22×Dic79—21no—
90C22×Dic79—21no—
91C22×Dic79—21no—
92C22×Dic79—21no—
93C22×Dic79—21no—
94C22×Dic79—21no—
95C22×Dic79—21no—
96C22×Dic79—21no—
97C22×Dic79—41no—
98C22×Dic79—41no—
99C22×Dic79—41no—
100C22×Dic79—41no—
101C22×Dic79—41no—
102C22×Dic79—41no—
103C22×Dic79—41no—
104C22×Dic79—41no—
105C22×Dic79—41no—
106C22×Dic79—41no—
107C22×Dic79C22⋊C412yes—
108C22×Dic79C22⋊C412yes—
109C22×Dic79SD1612yes—
110C22×Dic79Q1612yes—
111C2×C79⋊C8—22no—
112C2×C79⋊C8—22no—
113C2×C79⋊C8—22no—
114C2×C79⋊C8—41no—
115C2×C79⋊C8—41no—
116C2×C79⋊C8—41no—
117C2×C79⋊C8—41no—
118C4⋊Dic79—22no—
119C4⋊Dic79—22no—
120C4⋊Dic79—22no—
121C4⋊Dic79—22no—
122C4⋊Dic79—22no—
123C4⋊Dic79—41no—
124C4⋊Dic79—41no—
125C4⋊Dic79C4214yes—
126C4×Dic79—22no—
127C4×Dic79—22no—
128C4×Dic79—22no—
129C4×Dic79—22no—
130C4×Dic79—48no—
131C24×C79C2×D411yescharacteristic
132C22×C4×C79—22no—
133C22×C4×C79—22no—
134C22×C4×C79—22no—
135C22×C4×C79—22no—
136C22×C4×C79—41no—
137C22×C4×C79—41no—
138C22×C4×C79—41no—
139C22×C4×C79—41no—
140C22×C4×C79—41no—
141C22×C4×C79—41no—
142C22×C4×C79—41no—
143C22×C4×C79—41no—
144C22×C4×C79—41no—
145C22×C4×C79—41no—
146C22×C4×C79C22×C411yescharacteristic
147C22×C4×C79C22×C411yescharacteristic
148C22×C4×C79C22×C411yescharacteristic
149C22×C4×C79C2×D411yescharacteristic
150C22×C4×C79C2×D411yescharacteristic
151C22×C4×C79C2×Q811yescharacteristic
152C22×C4×C79#4111yescharacteristic
153C22×C4×C79#4111yescharacteristic
154C22×C4×C79#4111yescharacteristic
155C22×C4×C79#4111yescharacteristic
156C22×C4×C79#4111yescharacteristic
157C22×C4×C79#4111yescharacteristic
158C22×C4×C79#4111yescharacteristic
159C22×C4×C79#4111yescharacteristic
160C2×C8×C79—22no—
161C2×C8×C79—22no—
162C2×C8×C79—22no—
163C2×C8×C79—41no—
164C2×C8×C79—41no—
165C2×C8×C79—41no—
166C2×C8×C79—41no—
167C4⋊C4×C79—22no—
168C4⋊C4×C79—22no—
169C4⋊C4×C79—22no—
170C4⋊C4×C79—22no—
171C4⋊C4×C79—22no—
172C4⋊C4×C79—41no—
173C4⋊C4×C79—41no—
174C4⋊C4×C79C4⋊C414yes—
175C23×C79C2×C22⋊C411yescharacteristic
176C23×C79C4×D411yescharacteristic
177C23×C79C4×D411yescharacteristic
178C23×C79#12111yescharacteristic
179C23×C79C22⋊Q811yescharacteristic
180C23×C79#12311yescharacteristic
181C23×C79#12311yescharacteristic
182C23×C79C2×SD1611yescharacteristic
183C23×C79C2×Q1611yescharacteristic
184C23×C79#13511yescharacteristic
185C23×C79#13511yescharacteristic
186C23×C79AGL(1,ℤ/8)11yescharacteristic
187C23×C79AGL(1,ℤ/8)11yescharacteristic
188C23×C79AGL(1,ℤ/8)11yescharacteristic
189C23×C79#13711yescharacteristic
190C2×C4×C79—24no—
191C2×C4×C79—42no—
192C2×C4×C79—42no—
193C2×C4×C79—42no—
194C2×C4×C79—42no—
195C2×C4×C79—42no—
196C2×C4×C79—42no—
197C2×C4×C79—42no—
198C2×C4×C79—42no—
199C2×C4×C79—42no—
200C2×C4×C79—81no—
201C2×C4×C79—81no—
202C2×C4×C79—81no—
203C2×C4×C79—81no—
204C2×C4×C79C2×C4211yescharacteristic
205C2×C4×C79C2×C4⋊C411yescharacteristic
206C2×C4×C79#11711yescharacteristic
207C2×C4×C79#11711yescharacteristic
208C2×C4×C79#11711yescharacteristic
209C2×C4×C79#11711yescharacteristic
210C2×C4×C79#11711yescharacteristic
211C2×C4×C79#11711yescharacteristic
212C2×C4×C79#11711yescharacteristic
213C2×C4×C79#11711yescharacteristic
214C2×C4×C79C4×D411yescharacteristic
215C2×C4×C79C4×D411yescharacteristic
216C2×C4×C79C4×D411yescharacteristic
217C2×C4×C79C4×D411yescharacteristic
218C2×C4×C79C4×Q811yescharacteristic
219C2×C4×C79C4×Q811yescharacteristic
220C2×C4×C79#12111yescharacteristic
221C2×C4×C79C22⋊Q811yescharacteristic
222C2×C4×C79#12311yescharacteristic
223C2×C4×C79#12311yescharacteristic
224C2×C4×C79#12411yescharacteristic
225C2×C4×C79#12411yescharacteristic
226C2×C4×C79#12511yescharacteristic
227C2×C4×C79#12511yescharacteristic
228C2×C4×C79#12611yescharacteristic
229C2×C4×C79#12611yescharacteristic
230C2×C4×C79#12611yescharacteristic
231C2×C4×C79#12611yescharacteristic
232C2×Dic79—22no—
233C2×Dic79—22no—
234C2×Dic79—22no—
235C2×Dic79—22no—
236C2×Dic79—22no—
237C2×Dic79—22no—
238C2×Dic79—24no—
239C2×Dic79—22no—
240C2×Dic79—22no—
241C2×Dic79—22no—
242C2×Dic79—42no—
243C2×Dic79—42no—
244C2×Dic79—42no—
245C2×Dic79—42no—
246C2×Dic79—42no—
247C2×Dic79—42no—
248C2×Dic79—41no—
249C2×Dic79—41no—
250C2×Dic79—41no—
251C2×Dic79—41no—
252C2×Dic79—42no—
253C2×Dic79—42no—
254C2×Dic79—42no—
255C2×Dic79—81no—
256C2×Dic79—81no—
257C2×Dic79—81no—
258C2×Dic79—81no—
259C2×Dic79#10314yes—
260C8×C79—42no—
261C79⋊C8—42no—
262C22×C79C4×C22⋊C411yescharacteristic
263C22×C79#38011yescharacteristic
264C22×C79#38111yescharacteristic
265C22×C79#38711yescharacteristic
266C22×C79#38711yescharacteristic
267C22×C79#38811yescharacteristic
268C22×C79#38811yescharacteristic
269C22×C79C2×#10311yescharacteristic
270C22×C79#41611yescharacteristic
271C22×C79#41711yescharacteristic
272C22×C79#41811yescharacteristic
273C22×C79C4×SD1611yescharacteristic
274C22×C79C4×SD1611yescharacteristic
275C22×C79C4×Q1611yescharacteristic
276C22×C79C4×Q1611yescharacteristic
277C22×C79#44011yescharacteristic
278C22×C79#44011yescharacteristic
279C22×C79#44211yescharacteristic
280C22×C79#44211yescharacteristic
281C22×C79#46011yescharacteristic
282C22×C79#46211yescharacteristic
283C22×C79#46311yescharacteristic
284C22×C79#46311yescharacteristic
285C22×C79#47511yescharacteristic
286C22×C79#47711yescharacteristic
287C22×C79#47811yescharacteristic
288C22×C79#47811yescharacteristic
289C22×C79#48111yescharacteristic
290C22×C79#48111yescharacteristic
291C22×C79#48211yescharacteristic
292C22×C79#48211yescharacteristic
293C22×C79#48411yescharacteristic
294C22×C79#48411yescharacteristic
295C22×C79#48511yescharacteristic
296C22×C79#48511yescharacteristic
297C4×C79—44no—
298C4×C79—82no—
299C4×C79#37611yescharacteristic
300C4×C79C4×C4⋊C411yescharacteristic
301C4×C79#38211yescharacteristic
302C4×C79#38311yescharacteristic
303C4×C79#38711yescharacteristic
304C4×C79#38711yescharacteristic
305C4×C79#38811yescharacteristic
306C4×C79#38811yescharacteristic
307Dic79—24no—
308Dic79—42no—
309Dic79—44no—
310Dic79—82no—
311#10807—791nomaximal, Sylow
312C2×C79#143411yescharacteristic
313C2×C79C4×#10311yescharacteristic
314C2×C79#176211yescharacteristic
315C2×C79#180311yescharacteristic
316C2×C79#180411yescharacteristic
317C2×C79#182411yescharacteristic
318C2×C79#182511yescharacteristic
319C2×C79#191911yescharacteristic
320C2×C79#191911yescharacteristic
321C2×C79#192111yescharacteristic
322C2×C79#192111yescharacteristic
323C2×C79#192611yescharacteristic
324C2×C79#192611yescharacteristic
325C2×C79#192811yescharacteristic
326C2×C79#192811yescharacteristic
327C2×C4×C4⋊C4—791no—
328C2×#340—791no—
329C2×#340—791no—
330C2×#340—791no—
331C2×#340D7911yescharacteristic
332C2×#336—791no—
333C4⋊#95—791no—
334C79#1080711yescharacteristic, complemented, Sylow
335C23×C8—791no—
336C23×C8C2×D7911yescharacteristic
337C22×C4⋊C4—791no—
338C22×C4⋊C4—791no—
339C22×C4⋊C4C2×D7911yescharacteristic
340C22×C4⋊C4C2×D7911yescharacteristic
341C22×C42—791no—
342C22×C42—1581no—
343C4×C4⋊C4—794no—
344C4×C4⋊C4—1582no—
345C2×#95—1581no—
346C2×#95—1581no—
347C2×#95—1581no—
348#340—22no—
349#340—794no—
350#340—794no—
351#340—1582no—
352#336—1582no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—791no—
356C23×C4—791no—
357C23×C4—1581no—
358C23×C4—1581no—
359C23×C4C22×D7911yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—792no—
367C22×C8—1581no—
368C22×C8—1581no—
369C22×C8—1581no—
370C22×C8—1581no—
371C22×C8—1581no—
372C22×C8—1581no—
373C22×C8C4×D7912yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—792no—
383C2×C4⋊C4—792no—
384C2×C4⋊C4—792no—
385C2×C4⋊C4—792no—
386C2×C4⋊C4—1581no—
387C2×C4⋊C4—1581no—
388C2×C4⋊C4—1581no—
389C2×C4⋊C4—1581no—
390C2×C4⋊C4—1581no—
391C2×C4⋊C4—1581no—
392C2×C4⋊C4—1581no—
393C2×C4⋊C4—1581no—
394C2×C4⋊C4Dic15812yes—
395C2×C4⋊C4C4×D7912yes—
396C2×C4⋊C4C4×D7912yes—
397C2×C4⋊C4C22⋊D7912yes—
398C2×C42—3162no—
399C2×C42—3162no—
400C2×C42—792no—
401C2×C42—792no—
402C2×C42—1584no—
403C2×C42—1581no—
404C2×C42—1581no—
405C2×C42—1581no—
406C2×C42—1581no—
407#95—3162no—
408#95—3162no—
409#95—1584no—
410C24D4×D7911yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—3161no—
426C22×C4—3161no—
427C22×C4—3161no—
428C22×C4—3161no—
429C22×C4—3161no—
430C22×C4—3161no—
431C22×C4—3161no—
432C22×C4—3161no—
433C22×C4—3161no—
434C22×C4—3161no—
435C22×C4—792no—
436C22×C4—792no—
437C22×C4—792no—
438C22×C4—792no—
439C22×C4—1582no—
440C22×C4—1582no—
441C22×C4—1582no—
442C22×C4—1582no—
443C22×C4—1581no—
444C22×C4—1581no—
445C22×C4—1581no—
446C22×C4—1581no—
447C22×C4—1581no—
448C22×C4—1581no—
449C22×C4—1581no—
450C22×C4—1581no—
451C22×C4—1581no—
452C22×C4—1581no—
453C22×C4C2×C4×D7911yescharacteristic
454C22×C4C2×C4×D7911yescharacteristic
455C22×C4C2×C4×D7911yescharacteristic
456C22×C4D4×D7911yescharacteristic
457C22×C4C2×C22⋊D7911yescharacteristic
458C22×C4C2×Dic15811yescharacteristic
459C22×C4#1192962311yescharacteristic
460C22×C4#1192962311yescharacteristic
461C22×C4#1192962311yescharacteristic
462C22×C4#1192962311yescharacteristic
463C22×C4#1192962411yescharacteristic
464C22×C4#1192962411yescharacteristic
465C22×C4#1192962511yescharacteristic
466C22×C4#1192962511yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—3161no—
475C2×C8—3161no—
476C2×C8—3161no—
477C2×C8—3161no—
478C2×C8—1582no—
479C2×C8—1582no—
480C2×C8—1582no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—3161no—
489C4⋊C4—3161no—
490C4⋊C4—794no—
491C4⋊C4—1582no—
492C4⋊C4—1582no—
493C4⋊C4—1582no—
494C4⋊C4—1582no—
495C4⋊C4—1582no—
496C4⋊C4Dic79⋊C414yes—
497C42—3168no—
498C42—1582no—
499C42—1582no—
500C42—1582no—
501C42—1582no—
502C23C22⋊C4×D7911yescharacteristic
503C23(C22⋊D79)⋊C411yescharacteristic
504C23#1457912311yescharacteristic
505C23#1457913311yescharacteristic
506C23#1457913811yescharacteristic
507C23#1457914311yescharacteristic
508C23#1457914611yescharacteristic
509C23SD16×D7911yescharacteristic
510C23Q16×D7911yescharacteristic
511C23#1457918011yescharacteristic
512C23#1457918211yescharacteristic
513C23#1457918511yescharacteristic
514C23#1457918811yescharacteristic
515C23#1457918811yescharacteristic
516C23#1457919311yescharacteristic
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—3161no—
532C2×C4—3161no—
533C2×C4—3161no—
534C2×C4—3161no—
535C2×C4—3162no—
536C2×C4—3162no—
537C2×C4—3162no—
538C2×C4—3162no—
539C2×C4—3162no—
540C2×C4—3162no—
541C2×C4—3162no—
542C2×C4—3162no—
543C2×C4—3162no—
544C2×C4—794no—
545C2×C4—6321no—
546C2×C4—6321no—
547C2×C4—6321no—
548C2×C4—6321no—
549C2×C4—1584no—
550C2×C4—1582no—
551C2×C4—1582no—
552C2×C4—1582no—
553C2×C4—1582no—
554C2×C4—1582no—
555C2×C4—1582no—
556C2×C4—1582no—
557C2×C4—1582no—
558C2×C4—1582no—
559C2×C4C42×D7911yescharacteristic
560C2×C4C2×Dic79⋊C411yescharacteristic
561C2×C4#1457911711yescharacteristic
562C2×C4#1457911711yescharacteristic
563C2×C4#1457911711yescharacteristic
564C2×C4#1457911811yescharacteristic
565C2×C4#1457911911yescharacteristic
566C2×C4#1457911911yescharacteristic
567C2×C4#1457911911yescharacteristic
568C2×C4#1457911911yescharacteristic
569C2×C4(C22⋊D79)⋊C411yescharacteristic
570C2×C4C4×C22⋊D7911yescharacteristic
571C2×C4C4×C22⋊D7911yescharacteristic
572C2×C4#1457912311yescharacteristic
573C2×C4C4×Dic15811yescharacteristic
574C2×C4C4×Dic15811yescharacteristic
575C2×C4#1457913311yescharacteristic
576C2×C4#1457913811yescharacteristic
577C2×C4#1457914311yescharacteristic
578C2×C4#1457914611yescharacteristic
579C2×C4#1457914811yescharacteristic
580C2×C4#1457915011yescharacteristic
581C2×C4#1457915211yescharacteristic
582C2×C4#1457915211yescharacteristic
583C2×C4#1457915411yescharacteristic
584C2×C4#1457915411yescharacteristic
585C2×C4#1457915611yescharacteristic
586C2×C4#1457915611yescharacteristic
587C8—42no—
588C8—3162no—
589C22#1909841011yescharacteristic
590C22#1909842111yescharacteristic
591C22#1909842511yescharacteristic
592C22#1909844611yescharacteristic
593C22#1909845011yescharacteristic
594C22#1909845311yescharacteristic
595C22#1909845711yescharacteristic
596C22#103×D7911yescharacteristic
597C22#1909855611yescharacteristic
598C22#1909856311yescharacteristic
599C22#1909856611yescharacteristic
600C22#1909865011yescharacteristic
601C22#1909865411yescharacteristic
602C22#1909865511yescharacteristic
603C22#1909865711yescharacteristic
604C22#1909866211yescharacteristic
605C22#1909866611yescharacteristic
606C22#1909867211yescharacteristic
607C22#1909867411yescharacteristic
608C22#1909876111yescharacteristic
609C22#1909877111yescharacteristic
610C22#1909877611yescharacteristic
611C22#1909878011yescharacteristic
612C22#1909884611yescharacteristic
613C22#1909885611yescharacteristic
614C22#1909886111yescharacteristic
615C22#1909886511yescharacteristic
616C22#1909888011yescharacteristic
617C22#1909888311yescharacteristic
618C22#1909888511yescharacteristic
619C22#1909888911yescharacteristic
620C22#1909889711yescharacteristic
621C22#1909890011yescharacteristic
622C22#1909890211yescharacteristic
623C22#1909890611yescharacteristic
624C4—44no—
625C4—82no—
626C4—3164no—
627C4—3162no—
628C4—6322no—
629C4—1584no—
630C4#1909840811yescharacteristic
631C4C4×Dic79⋊C411yescharacteristic
632C4#1909842811yescharacteristic
633C4#1909843011yescharacteristic
634C4#1909844611yescharacteristic
635C4#1909845011yescharacteristic
636C4#1909845311yescharacteristic
637C4#1909845711yescharacteristic
638C2#2376162611yescharacteristic
639C2#2376321911yescharacteristic
640C2#2376322411yescharacteristic
641C2#2376340311yescharacteristic
642C2#2376340811yescharacteristic
643C2#2376348911yescharacteristic
644C2#2376349311yescharacteristic
645C2#2376397711yescharacteristic
646C2#2376398111yescharacteristic
647C2#2376399111yescharacteristic
648C2#2376399511yescharacteristic
649C2#2376402611yescharacteristic
650C2#2376403011yescharacteristic
651C2#2376404011yescharacteristic
652C2#2376404411yescharacteristic
subgroupG/H
centerC24D4×D79
commutatorC2×C4×C79C2×C42
FrattiniC23×C4C22×D79
FittingC2×#340×C79C2
socle, prime radicalC24×C79C2×D4
cosocleC23×C4×C79C23
hypercenterC2×#340D79
hypocenterC79#10807
LCSG ▷ C2×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
14. C4⋊C4×Dic79C4semidirect
18. #19098326C4semidirect
20. #19098325C4semidirect
334. C79#10807semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic792
C2×#190983262
C2×#190983252
C2×#190983172
#237616292
C2×#340×C792
#1080779