Finite Group Databasebeta

← #34255938

Subgroups — #34255938

Order 20224.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777152C211yesmaximal, characteristic
2#23766260C211yesmaximal, characteristic, complemented
3#23761978C211yesmaximal, characteristic, complemented
4#23761965C211yesmaximal, characteristic, complemented
5#23761957C211yesmaximal, characteristic
6#23761952C211yesmaximal, characteristic, complemented
7#23761939C211yesmaximal, characteristic, complemented
8#23761934C211yesmaximal, characteristic, complemented
9#23761926C211yesmaximal, characteristic, complemented
10#23761913C211yesmaximal, characteristic, complemented
11#23761905C211yesmaximal, characteristic
12#23761900C211yesmaximal, characteristic, complemented
13#23761887C211yesmaximal, characteristic, complemented
14C2×#19098301C211yesmaximal, characteristic, complemented
15C79×#2924C211yesmaximal, characteristic, complemented
16#19099281—21no—
17#19099268—21no—
18#19099252—21no—
19#19099248—21no—
20#19099246—21no—
21#19099246—21no—
22#19099239—21no—
23#19099239—21no—
24#19099191C411yescharacteristic, complemented
25#19099184C411yescharacteristic, complemented
26#19099184C411yescharacteristic, complemented
27#19099175C411yescharacteristic, complemented
28#19099175C411yescharacteristic, complemented
29#19099139C411yescharacteristic, complemented
30#19099120C2211yescharacteristic
31#19099120C2211yescharacteristic
32#19099097C2211yescharacteristic
33#19099097C2211yescharacteristic
34#19099074C2211yescharacteristic
35C2×#14579140C2211yescharacteristic
36#19099043C411yescharacteristic, complemented
37#19099040C411yescharacteristic, complemented
38#19098449—21no—
39#19098449—21no—
40#19098438—21no—
41#19098431C2211yescharacteristic
42#19098429C2211yescharacteristic
43#19098426C2211yescharacteristic
44C4×C4⋊Dic79C2211yescharacteristic
45C22⋊C4×Dic79—21no—
46#19098409C2211yescharacteristic
47C2×C79⋊#95C2211yescharacteristic
48#19098301C2211yescharacteristic
49#19098301C2211yescharacteristic
50#19098301C2211yescharacteristic
51#19098301C2211yescharacteristic
52#19098301C2211yescharacteristic
53#19098301C2211yescharacteristic
54#19098301C2211yescharacteristic
55#19098301C2211yescharacteristic
56#19098301C2211yescharacteristic
57#19098301C2211yescharacteristic
58#19098301C2211yescharacteristic
59#19098301C2211yescharacteristic
60#19098298C2211yescharacteristic
61#19098298C2211yescharacteristic
62#19098298C2211yescharacteristic
63#19098298C2211yescharacteristic
64C2×#117×C79C2211yescharacteristic
65#433×C79—21no—
66#433×C79—21no—
67#432×C79C2211yescharacteristic
68#432×C79C2211yescharacteristic
69#431×C79C2211yescharacteristic
70#431×C79C2211yescharacteristic
71#424×C79—21no—
72#407×C79C2211yescharacteristic
73C2×C22⋊C8×C79C2211yescharacteristic
74#405×C79—21no—
75C2×#11929624C2×C411yescharacteristic
76C22×Dic158C2×C411yescharacteristic
77C23×Dic79—21no—
78#14579161C2×C411yescharacteristic, complemented
79#14579161C2×C411yescharacteristic, complemented
80#14579161C2×C411yescharacteristic, complemented
81#14579161C2×C411yescharacteristic, complemented
82#14579160—21no—
83#14579156—21no—
84#14579156—21no—
85#14579155—21no—
86#14579155—21no—
87#14579154—21no—
88#14579154—21no—
89#14579154—21no—
90#14579154—21no—
91#14579153—21no—
92#14579153—21no—
93#14579153C2×C411yescharacteristic, complemented
94#14579153C2×C411yescharacteristic, complemented
95#14579152—21no—
96#14579151—21no—
97#14579151—21no—
98#14579151—21no—
99#14579151—21no—
100#14579149C2×C411yescharacteristic, complemented
101#14579149C2×C411yescharacteristic, complemented
102#14579147—21no—
103#14579147—21no—
104#14579145—21no—
105#14579145—21no—
106#14579144—21no—
107#14579144—21no—
108#14579144—21no—
109#14579143—21no—
110#14579143—21no—
111#14579141—21no—
112#14579141—21no—
113#14579140—21no—
114#14579140—21no—
115#14579140—21no—
116#14579140—21no—
117#14579140C2×C411yescharacteristic
118#14579140C2×C411yescharacteristic
119#14579140C2×C411yescharacteristic
120#14579140C2311yescharacteristic
121#14579140C2311yescharacteristic
122#14579140C2311yescharacteristic
123#14579139—21no—
124#14579139—21no—
125#14579138—21no—
126#14579138—21no—
127#14579135C2×C411yescharacteristic
128#14579135C2311yescharacteristic
129#14579130—21no—
130C4×Dic158—21no—
131C4×Dic158—21no—
132C4×Dic158C2×C411yescharacteristic, complemented
133C4×Dic158C2×C411yescharacteristic, complemented
134C4×Dic158C2×C411yescharacteristic, complemented
135C4×Dic158C2×C411yescharacteristic, complemented
136C4×Dic158C2×C411yescharacteristic, complemented
137C4×Dic158C2×C411yescharacteristic, complemented
138#14579126—21no—
139#14579126—21no—
140C4×D316C2×C411yescharacteristic, complemented
141C4×D316C2×C411yescharacteristic, complemented
142C4×C22⋊D79—21no—
143C4×C22⋊D79—21no—
144C4×C22⋊D79—21no—
145C4×C22⋊D79—21no—
146(C22⋊D79)⋊C4—21no—
147(C22⋊D79)⋊C4—21no—
148#14579120—21no—
149#14579120—21no—
150#14579120C2×C411yescharacteristic
151#14579119—21no—
152#14579118—21no—
153#14579118—21no—
154#14579117—21no—
155#14579117—21no—
156C2×C4⋊Dic79—21no—
157C2×C4⋊Dic79—21no—
158C2×C4⋊Dic79C2×C411yescharacteristic
159C2×Dic79⋊C4—21no—
160C4⋊C4×D79—21no—
161C2×C22⋊Dic79—21no—
162C2×C22⋊Dic79—21no—
163C2×C4×Dic79—21no—
164C2×C4×Dic79—21no—
165C79⋊#95—21no—
166C79⋊#95—21no—
167C79⋊#95—21no—
168C79⋊#95—21no—
169C79⋊#95—21no—
170C79⋊#95—21no—
171C79⋊#95C2311yescharacteristic
172C79⋊#95C2311yescharacteristic
173C79⋊#95C2311yescharacteristic
174C79⋊#95C2311yescharacteristic
175C23×C4×C79C2311yescharacteristic
176C2×M16×C79—21no—
177C22×C8×C79—21no—
178#117×C79C2×C411yescharacteristic
179#117×C79C2×C411yescharacteristic
180#117×C79C2×C411yescharacteristic
181#117×C79C2×C411yescharacteristic
182#117×C79D411yescharacteristic
183#117×C79D411yescharacteristic
184#117×C79D411yescharacteristic
185#117×C79D411yescharacteristic
186C2×C4⋊C4×C79D411yescharacteristic
187C2×C4⋊C4×C79D411yescharacteristic
188C2×C22⋊C4×C79D411yescharacteristic
189C2×C22⋊C4×C79D411yescharacteristic
190C2×C42×C79C2311yescharacteristic
191C2×C42×C79C2311yescharacteristic
192C4⋊C8×C79—21no—
193C4⋊C8×C79—21no—
194C4⋊C8×C79—21no—
195C4⋊C8×C79—21no—
196C22⋊C8×C79—21no—
197C22⋊C8×C79—21no—
198C22⋊C8×C79C2311yescharacteristic
199C22⋊C8×C79C2311yescharacteristic
200C22⋊C8×C79C2311yescharacteristic
201C22⋊C8×C79C2311yescharacteristic
202#97×C79—21no—
203#97×C79—21no—
204C4×C8×C79—21no—
205C4×C8×C79—21no—
206#11929624—42no—
207C2×Dic158—21no—
208C2×Dic158—21no—
209C2×Dic158—21no—
210C2×Dic158—42no—
211C2×Dic158C22×C411yescharacteristic
212C2×Dic158C22×C411yescharacteristic
213C2×Dic158C22×C411yescharacteristic
214C2×D316C22×C411yescharacteristic
215C2×C22⋊D79—21no—
216C2×C22⋊D79—21no—
217C2×C22⋊D79—21no—
218C22×Dic79—21no—
219C22×Dic79—21no—
220C22×Dic79—21no—
221C22×Dic79—21no—
222C22×Dic79—21no—
223C22×Dic79—21no—
224C22×Dic79—42no—
225C22×Dic79—42no—
226C22×Dic79—81no—
227C2×C4×D79—21no—
228C2×C4×D79—21no—
229C2×C4×D79—21no—
230C4⋊Dic79—21no—
231C4⋊Dic79—21no—
232C4⋊Dic79—21no—
233C4⋊Dic79—21no—
234C4⋊Dic79—21no—
235C4⋊Dic79—21no—
236C4⋊Dic79—21no—
237C4⋊Dic79—42no—
238C4⋊Dic79—81no—
239C4⋊Dic79C22×C411yescharacteristic
240C4⋊Dic79C22×C411yescharacteristic
241C4⋊Dic79C22×C411yescharacteristic
242C4⋊Dic79C22×C411yescharacteristic
243Dic79⋊C4—21no—
244Dic79⋊C4—21no—
245Dic79⋊C4—21no—
246Dic79⋊C4—21no—
247Dic79⋊C4—21no—
248Dic79⋊C4—21no—
249Dic79⋊C4—21no—
250Dic79⋊C4—21no—
251Dic79⋊C4—21no—
252Dic79⋊C4—21no—
253Dic79⋊C4—21no—
254Dic79⋊C4—21no—
255Dic79⋊C4—21no—
256Dic79⋊C4—21no—
257Dic79⋊C4—21no—
258Dic79⋊C4—21no—
259C22⋊Dic79—21no—
260C22⋊Dic79—21no—
261C22⋊Dic79—21no—
262C22⋊Dic79—21no—
263C22⋊Dic79—21no—
264C22⋊Dic79—21no—
265C22⋊Dic79—21no—
266C22⋊Dic79—42no—
267(C2×D79)⋊C4—21no—
268(C2×D79)⋊C4—21no—
269(C2×D79)⋊C4—21no—
270(C2×D79)⋊C4—21no—
271(C2×D79)⋊C4—21no—
272(C2×D79)⋊C4—21no—
273(C2×D79)⋊C4—21no—
274(C2×D79)⋊C4—21no—
275C4×Dic79—21no—
276C4×Dic79—21no—
277C4×Dic79—21no—
278C4×Dic79—21no—
279C4×Dic79—21no—
280C4×Dic79—21no—
281C4×Dic79—21no—
282C4×Dic79—42no—
283C4×Dic79—81no—
284C24×C79C2×D411yescharacteristic
285C22×C4×C79—42no—
286C22×C4×C79C22×C411yescharacteristic
287C22×C4×C79C22×C411yescharacteristic
288C22×C4×C79C2×D411yescharacteristic
289C22×C4×C79C2×D411yescharacteristic
290C22×C4×C79C2×D411yescharacteristic
291C22×C4×C79C2×D411yescharacteristic
292C22×C4×C79C2×D411yescharacteristic
293C22×C4×C79C2×D411yescharacteristic
294C22×C4×C79C2×D411yescharacteristic
295C22×C4×C79C2411yescharacteristic
296M16×C79—42no—
297C2×C8×C79—21no—
298C2×C8×C79—21no—
299C2×C8×C79—21no—
300C2×C8×C79—21no—
301C2×C8×C79—42no—
302C4⋊C4×C79C22⋊C411yescharacteristic
303C4⋊C4×C79C22⋊C411yescharacteristic
304C4⋊C4×C79C22⋊C411yescharacteristic
305C4⋊C4×C79C22⋊C411yescharacteristic
306C4⋊C4×C79C22⋊C411yescharacteristic
307C4⋊C4×C79C22⋊C411yescharacteristic
308C4⋊C4×C79C22⋊C411yescharacteristic
309C4⋊C4×C79C22⋊C411yescharacteristic
310C22⋊C4×C79C22⋊C411yescharacteristic
311C22⋊C4×C79C22⋊C411yescharacteristic
312C22⋊C4×C79C22⋊C411yescharacteristic
313C22⋊C4×C79C22⋊C411yescharacteristic
314C22⋊C4×C79C22⋊C411yescharacteristic
315C22⋊C4×C79C22⋊C411yescharacteristic
316C22⋊C4×C79C22⋊C411yescharacteristic
317C22⋊C4×C79C22⋊C411yescharacteristic
318C42×C79C22×C411yescharacteristic
319C42×C79C22×C411yescharacteristic
320C42×C79C22×C411yescharacteristic
321C42×C79C22×C411yescharacteristic
322C42×C79C2×D411yescharacteristic
323C42×C79C2×D411yescharacteristic
324C42×C79C2×D411yescharacteristic
325C42×C79C2×D411yescharacteristic
326C23×C79—21no—
327C23×C79—21no—
328C23×C79—22no—
329C23×C79—41no—
330C23×C79C2×C22⋊C411yescharacteristic
331C23×C79C2×C22⋊C411yescharacteristic
332C23×C79C22×D411yescharacteristic
333C22×D79—21no—
334C2×C4×C79—21no—
335C2×C4×C79—21no—
336C2×C4×C79—21no—
337C2×C4×C79—21no—
338C2×C4×C79—22no—
339C2×C4×C79—22no—
340C2×C4×C79—41no—
341C2×C4×C79—41no—
342C2×C4×C79—41no—
343C2×C4×C79—41no—
344C2×C4×C79—41no—
345C2×C4×C79—41no—
346C2×C4×C79C2×C22⋊C411yescharacteristic
347C2×C4×C79C2×C22⋊C411yescharacteristic
348C2×C4×C79C2×C22⋊C411yescharacteristic
349C2×C4×C79C2×C22⋊C411yescharacteristic
350C2×C4×C79C2×C22⋊C411yescharacteristic
351C2×C4×C79C2×C22⋊C411yescharacteristic
352C2×C4×C79C2×C22⋊C411yescharacteristic
353C2×C4×C79C2×C22⋊C411yescharacteristic
354C2×C4×C79C2×C22⋊C411yescharacteristic
355C2×C4×C79C2×C22⋊C411yescharacteristic
356C2×C4×C79C23×C411yescharacteristic
357C2×C4×C79C22×D411yescharacteristic
358C22⋊D79—41no—
359C22⋊D79—41no—
360C22⋊D79—42no—
361C22⋊D79—81no—
362C2×Dic79—22no—
363C2×Dic79—21no—
364C2×Dic79—21no—
365C2×Dic79—21no—
366C2×Dic79—21no—
367C2×Dic79—21no—
368C2×Dic79—21no—
369C2×Dic79—21no—
370C2×Dic79—41no—
371C2×Dic79—41no—
372C2×Dic79—42no—
373C2×Dic79—41no—
374C2×Dic79—41no—
375C2×Dic79—41no—
376C2×Dic79—41no—
377C2×Dic79—41no—
378C2×Dic79—41no—
379C2×Dic79—41no—
380C2×Dic79—41no—
381C2×Dic79—41no—
382C2×Dic79—81no—
383C2×Dic79—84no—
384D316—41no—
385C4×D79—42no—
386C4×D79—81no—
387C4×D79—81no—
388Dic158—42no—
389Dic158—41no—
390Dic158—41no—
391Dic158—41no—
392Dic158—81no—
393Dic158—81no—
394C8×C79—41no—
395C8×C79—41no—
396C8×C79—41no—
397C8×C79—41no—
398C22×C79—21no—
399C22×C79—21no—
400C22×C79—21no—
401C22×C79—21no—
402C22×C79—21no—
403C22×C79—21no—
404C22×C79—21no—
405C22×C79—42no—
406C22×C79—42no—
407C22×C79#41012yes—
408C22×C79C22×C22⋊C411yescharacteristic
409C22×C79#57711yescharacteristic
410C22×C79#57811yescharacteristic
411C2×D79—41no—
412C2×D79—41no—
413C2×D79—41no—
414C4×C79—21no—
415C4×C79—21no—
416C4×C79—21no—
417C4×C79—21no—
418C4×C79—21no—
419C4×C79—21no—
420C4×C79—21no—
421C4×C79—21no—
422C4×C79—21no—
423C4×C79—21no—
424C4×C79—21no—
425C4×C79—21no—
426Dic79—42no—
427Dic79—41no—
428Dic79—41no—
429Dic79—41no—
430Dic79—41no—
431Dic79—41no—
432Dic79—41no—
433Dic79—41no—
434Dic79—81no—
435Dic79—81no—
436Dic79—81no—
437#17609—791nomaximal, Sylow
438C2×C79—21no—
439C2×C79—21no—
440C2×C79—22no—
441C2×C79—41no—
442C2×C79C2×#41011yescharacteristic
443C2×C79#289811yescharacteristic
444C2×C79#290111yescharacteristic
445D79—81no—
446#3495—791no—
447#2924D7911yescharacteristic, complemented
448#2343—791no—
449#1521—791no—
450#1518—791no—
451#1516—791no—
452#1515—791no—
453#1512—791no—
454#1511—791no—
455#1509—791no—
456#1506—791no—
457#1504—791no—
458#1503—791no—
459#1500—791no—
460C2×#328—791no—
461C79#1760911yescharacteristic, complemented, Sylow
462#556—1581no—
463#554—1581no—
464#552—1581no—
465#552—1581no—
466#552—1581no—
467#552—1581no—
468#551—1581no—
469#551—1581no—
470#544—791no—
471#542—791no—
472#542—791no—
473#541—791no—
474#541—791no—
475#536—791no—
476#533—791no—
477#533—791no—
478#529—791no—
479#529—791no—
480#525—791no—
481C2×C22⋊Q8—791no—
482#520—791no—
483#519—791no—
484C2×#117C2×D7911yescharacteristic
485#433—21no—
486#433—21no—
487#432C2×D7911yescharacteristic
488#432C2×D7911yescharacteristic
489#431C2×D7911yescharacteristic
490#431C2×D7911yescharacteristic
491#424—21no—
492#407C2×D7911yescharacteristic
493C2×C22⋊C8C2×D7911yescharacteristic
494#405—21no—
495#387—1581no—
496#387—1581no—
497#385—1581no—
498#383—791no—
499#382—791no—
500#381—791no—
501C4×C4⋊C4—791no—
502C4×C22⋊C4—1581no—
503#376—791no—
504C2×#95—791no—
505#328—791no—
506#328—791no—
507#328—791no—
508#328—791no—
509#328—791no—
510#328—791no—
511#328—791no—
512#328—791no—
513#328—791no—
514#328—791no—
515#328—791no—
516#328—791no—
517#327—791no—
518#327—791no—
519#327—791no—
520#327—791no—
521C2×#41—791no—
522C22×Q8—791no—
523C23×C4—1581no—
524C23×C4C22×D7911yescharacteristic
525C2×M16—21no—
526C22×C8—21no—
527C4⋊Q8—791no—
528C4⋊Q8—791no—
529C4⋊Q8—791no—
530C4⋊Q8—791no—
531C4⋊Q8—1581no—
532#126—1581no—
533#126—1581no—
534#126—1581no—
535#126—1581no—
536#126—1581no—
537#126—1581no—
538#126—1581no—
539#126—1581no—
540#125—791no—
541#125—791no—
542#125—1581no—
543#125—1581no—
544#125—1581no—
545#125—1581no—
546#125—1581no—
547#125—1581no—
548#125—1581no—
549#124—791no—
550#124—791no—
551#124—1581no—
552#124—1581no—
553#123—1581no—
554#123—1581no—
555#123—1581no—
556#123—1581no—
557#123—1581no—
558#123—1581no—
559#123—1581no—
560C22⋊Q8—791no—
561C22⋊Q8—791no—
562C22⋊Q8—791no—
563C22⋊Q8—791no—
564C22⋊Q8—791no—
565C22⋊Q8—791no—
566C22⋊Q8—1581no—
567C22⋊Q8—1581no—
568C22⋊Q8—1581no—
569C22⋊Q8—1581no—
570C22⋊Q8—1581no—
571C22⋊Q8—1581no—
572C22⋊Q8—1581no—
573C22⋊Q8—1581no—
574C22⋊Q8—1581no—
575C22⋊Q8—1581no—
576#121—791no—
577#121—791no—
578#120—1581no—
579C4×Q8—791no—
580C4×Q8—791no—
581C4×Q8—791no—
582C4×Q8—791no—
583C4×Q8—791no—
584C4×Q8—791no—
585C4×Q8—1581no—
586C4×Q8—1581no—
587C4×Q8—1581no—
588C4×Q8—1581no—
589C4×D4—791no—
590C4×D4—791no—
591C4×D4—1581no—
592C4×D4—1581no—
593C4×D4—1581no—
594C4×D4—1581no—
595C4×D4—1581no—
596C4×D4—1581no—
597#117—791no—
598#117—1581no—
599#117—1581no—
600#117—1581no—
601#117—1581no—
602#117—1581no—
603#117—1581no—
604#117—1581no—
605#117C4×D7911yescharacteristic
606#117C4×D7911yescharacteristic
607#117C4×D7911yescharacteristic
608#117C4×D7911yescharacteristic
609#117C22⋊D7911yescharacteristic
610#117C22⋊D7911yescharacteristic
611#117C22⋊D7911yescharacteristic
612#117C22⋊D7911yescharacteristic
613C2×C4⋊C4—791no—
614C2×C4⋊C4—1581no—
615C2×C4⋊C4—1581no—
616C2×C4⋊C4—1581no—
617C2×C4⋊C4—1581no—
618C2×C4⋊C4D31611yescharacteristic
619C2×C4⋊C4D31611yescharacteristic
620C2×C22⋊C4—1581no—
621C2×C22⋊C4—1581no—
622C2×C22⋊C4D31611yescharacteristic
623C2×C22⋊C4D31611yescharacteristic
624C2×C42—1581no—
625C2×C42—1581no—
626C2×C42C22×D7911yescharacteristic
627C2×C42C22×D7911yescharacteristic
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C4⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634C22⋊C8C22×D7911yescharacteristic
635C22⋊C8C22×D7911yescharacteristic
636C22⋊C8C22×D7911yescharacteristic
637C22⋊C8C22×D7911yescharacteristic
638#97—21no—
639#97—21no—
640C4×C8—21no—
641C4×C8—21no—
642#95—791no—
643#95—791no—
644#95—791no—
645#95—791no—
646#95—1581no—
647#95—1581no—
648#95—1581no—
649#95—1581no—
650#95—1581no—
651#95—1581no—
652C24C2×D31611yescharacteristic
653#41—3162no—
654C2×Q8—3162no—
655C2×Q8—791no—
656C2×Q8—791no—
657C2×Q8—791no—
658C2×Q8—1581no—
659C2×Q8—1581no—
660C2×Q8—1581no—
661C2×D4—791no—
662C2×D4—1581no—
663C2×D4—1581no—
664C2×D4—1581no—
665C22×C4—42no—
666C22×C4—3162no—
667C22×C4—3162no—
668C22×C4—6321no—
669C22×C4—1581no—
670C22×C4—1581no—
671C22×C4—1581no—
672C22×C4—1581no—
673C22×C4—1581no—
674C22×C4—1581no—
675C22×C4—1581no—
676C22×C4—1581no—
677C22×C4—1581no—
678C22×C4C2×C4×D7911yescharacteristic
679C22×C4C2×C4×D7911yescharacteristic
680C22×C4C2×C22⋊D7911yescharacteristic
681C22×C4C2×C22⋊D7911yescharacteristic
682C22×C4C2×D31611yescharacteristic
683C22×C4C2×D31611yescharacteristic
684C22×C4C2×D31611yescharacteristic
685C22×C4C2×D31611yescharacteristic
686C22×C4C2×D31611yescharacteristic
687C22×C4C23×D7911yescharacteristic
688M16—42no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C4⋊C4—3162no—
695C4⋊C4—791no—
696C4⋊C4—791no—
697C4⋊C4—791no—
698C4⋊C4—791no—
699C4⋊C4—6321no—
700C4⋊C4—1581no—
701C4⋊C4—1581no—
702C4⋊C4—1581no—
703C4⋊C4—1581no—
704C4⋊C4—1581no—
705C4⋊C4—1581no—
706C4⋊C4—1581no—
707C4⋊C4—1581no—
708C4⋊C4—1581no—
709C4⋊C4—1581no—
710C4⋊C4—1581no—
711C4⋊C4—1581no—
712C4⋊C4—1581no—
713C4⋊C4—1581no—
714C4⋊C4—1581no—
715C4⋊C4—1581no—
716C4⋊C4—1581no—
717C4⋊C4—1581no—
718C4⋊C4—1581no—
719C4⋊C4—1581no—
720C4⋊C4—1581no—
721C4⋊C4—1581no—
722C4⋊C4—1581no—
723C4⋊C4(C2×D79)⋊C411yescharacteristic
724C4⋊C4(C2×D79)⋊C411yescharacteristic
725C4⋊C4(C2×D79)⋊C411yescharacteristic
726C4⋊C4(C2×D79)⋊C411yescharacteristic
727C4⋊C4(C2×D79)⋊C411yescharacteristic
728C4⋊C4(C2×D79)⋊C411yescharacteristic
729C4⋊C4(C2×D79)⋊C411yescharacteristic
730C4⋊C4(C2×D79)⋊C411yescharacteristic
731C22⋊C4—3162no—
732C22⋊C4—1581no—
733C22⋊C4—1581no—
734C22⋊C4—1581no—
735C22⋊C4—1581no—
736C22⋊C4—1581no—
737C22⋊C4—1581no—
738C22⋊C4—1581no—
739C22⋊C4—1581no—
740C22⋊C4—1581no—
741C22⋊C4—1581no—
742C22⋊C4—1581no—
743C22⋊C4—1581no—
744C22⋊C4—1581no—
745C22⋊C4—1581no—
746C22⋊C4—1581no—
747C22⋊C4(C2×D79)⋊C411yescharacteristic
748C22⋊C4(C2×D79)⋊C411yescharacteristic
749C22⋊C4(C2×D79)⋊C411yescharacteristic
750C22⋊C4(C2×D79)⋊C411yescharacteristic
751C22⋊C4(C2×D79)⋊C411yescharacteristic
752C22⋊C4(C2×D79)⋊C411yescharacteristic
753C22⋊C4(C2×D79)⋊C411yescharacteristic
754C22⋊C4(C2×D79)⋊C411yescharacteristic
755C42—3162no—
756C42—6321no—
757C42—1581no—
758C42—1581no—
759C42—1581no—
760C42—1581no—
761C42—1581no—
762C42—1581no—
763C42—1581no—
764C42C2×C4×D7911yescharacteristic
765C42C2×C4×D7911yescharacteristic
766C42C2×C4×D7911yescharacteristic
767C42C2×C4×D7911yescharacteristic
768C42C2×C22⋊D7911yescharacteristic
769C42C2×C22⋊D7911yescharacteristic
770C42C2×C22⋊D7911yescharacteristic
771C42C2×C22⋊D7911yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—1581no—
777C23C2×(C2×D79)⋊C411yescharacteristic
778C23C2×(C2×D79)⋊C411yescharacteristic
779C23C22×D31611yescharacteristic
780Q8—3161no—
781Q8—3161no—
782Q8—3161no—
783Q8—3162no—
784Q8—6321no—
785Q8—6321no—
786D4—3161no—
787D4—3162no—
788D4—3161no—
789D4—3161no—
790D4—6321no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—3162no—
804C2×C4—3161no—
805C2×C4—3162no—
806C2×C4—3161no—
807C2×C4—3161no—
808C2×C4—3161no—
809C2×C4—3161no—
810C2×C4—3161no—
811C2×C4—3161no—
812C2×C4—3161no—
813C2×C4—3161no—
814C2×C4—3161no—
815C2×C4—3161no—
816C2×C4—6321no—
817C2×C4—6321no—
818C2×C4—6321no—
819C2×C4—6324no—
820C2×C4—1582no—
821C2×C4—1581no—
822C2×C4—1581no—
823C2×C4—1581no—
824C2×C4—1581no—
825C2×C4—1581no—
826C2×C4—1581no—
827C2×C4—1581no—
828C2×C4C2×(C2×D79)⋊C411yescharacteristic
829C2×C4C2×(C2×D79)⋊C411yescharacteristic
830C2×C4C2×(C2×D79)⋊C411yescharacteristic
831C2×C4C2×(C2×D79)⋊C411yescharacteristic
832C2×C4C2×(C2×D79)⋊C411yescharacteristic
833C2×C4C2×(C2×D79)⋊C411yescharacteristic
834C2×C4C2×(C2×D79)⋊C411yescharacteristic
835C2×C4C2×(C2×D79)⋊C411yescharacteristic
836C2×C4C2×(C2×D79)⋊C411yescharacteristic
837C2×C4C2×(C2×D79)⋊C411yescharacteristic
838C2×C4C22×C4×D7911yescharacteristic
839C2×C4C22×C22⋊D7911yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—3161no—
854C22—3161no—
855C22—3161no—
856C22#1909853612yes—
857C22C22×(C2×D79)⋊C411yescharacteristic
858C22#1909937511yescharacteristic
859C22#1909938011yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—3162no—
873C4—3161no—
874C4—3161no—
875C4—3161no—
876C4—3161no—
877C4—3161no—
878C4—3161no—
879C4—3161no—
880C4—6321no—
881C4—6321no—
882C4—6321no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—6321no—
888C2C2×#1909853611yescharacteristic
889C2#2377193411yescharacteristic
890C2#2377194511yescharacteristic
subgroupG/H
centerC22C22×(C2×D79)⋊C4
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2924C2
socleC22×C79C22×C22⋊C4
prime radical#19099074C22
cosocleC22×C4×C79C24
hypercenter#2924D79
hypocenterC79#17609
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #23766260C2semidirect
3. #23761978C2semidirect
4. #23761965C2semidirect
6. #23761952C2semidirect
7. #23761939C2semidirect
8. #23761934C2semidirect
9. #23761926C2semidirect
10. #23761913C2semidirect
12. #23761900C2semidirect
13. #23761887C2semidirect
14. C2×#19098301C2semidirect
15. C79×#2924C2semidirect
24. #19099191C4semidirect
25. #19099184C4semidirect
26. #19099184C4semidirect
27. #19099175C4semidirect
28. #19099175C4semidirect
29. #19099139C4semidirect
36. #19099043C4semidirect
37. #19099040C4semidirect
78. #14579161C2×C4semidirect
79. #14579161C2×C4semidirect
80. #14579161C2×C4semidirect
81. #14579161C2×C4semidirect
93. #14579153C2×C4semidirect
94. #14579153C2×C4semidirect
100. #14579149C2×C4semidirect
101. #14579149C2×C4semidirect
132. C4×Dic158C2×C4semidirect
133. C4×Dic158C2×C4semidirect
134. C4×Dic158C2×C4semidirect
135. C4×Dic158C2×C4semidirect
136. C4×Dic158C2×C4semidirect
137. C4×Dic158C2×C4semidirect
140. C4×D316C2×C4semidirect
141. C4×D316C2×C4semidirect
447. #2924D79semidirect
461. C79#17609semidirect

Maximal subgroups

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

subgroupindex
#237771522
#237662602
#237619782
#237619652
#237619572
#237619522
#237619392
#237619342
#237619262
#237619132
#237619052
#237619002
#237618872
C2×#190983012
C79×#29242
#1760979