Finite Group Databasebeta

← #34255875

Subgroups — #34255875

Order 20224.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777135C211yesmaximal, characteristic
2#23772058C211yesmaximal, characteristic, complemented
3#23761975C211yesmaximal, characteristic, complemented
4#23761959C211yesmaximal, characteristic, complemented
5#23761954C211yesmaximal, characteristic, complemented
6#23761946C211yesmaximal, characteristic, complemented
7#23761936C211yesmaximal, characteristic, complemented
8#23761928C211yesmaximal, characteristic, complemented
9#23761923C211yesmaximal, characteristic, complemented
10#23761907C211yesmaximal, characteristic, complemented
11#23761902C211yesmaximal, characteristic, complemented
12#23761894C211yesmaximal, characteristic, complemented
13#23761884C211yesmaximal, characteristic, complemented
14C2×#19098296C211yesmaximal, characteristic, complemented
15C79×#2343C211yesmaximal, characteristic, complemented
16#19099276—21no—
17#19099261—21no—
18#19099257—21no—
19#19099237—21no—
20#19099237—21no—
21#19099214—21no—
22#19099203—21no—
23#19099203—21no—
24#19099191C411yescharacteristic, complemented
25#19099184C411yescharacteristic, complemented
26#19099184C411yescharacteristic, complemented
27#19099168C411yescharacteristic, complemented
28#19099168C411yescharacteristic, complemented
29#19099132C411yescharacteristic, complemented
30#19099113C2211yescharacteristic
31#19099113C2211yescharacteristic
32#19099097C2211yescharacteristic
33#19099097C2211yescharacteristic
34#19099074C2211yescharacteristic
35C2×#14579135C2211yescharacteristic
36#19099043C411yescharacteristic, complemented
37#19099037C411yescharacteristic, complemented
38#19098624—21no—
39#19098624—21no—
40#19098620C2211yescharacteristic, complemented
41#19098620C2211yescharacteristic, complemented
42#19098616C2211yescharacteristic, complemented
43#19098616C2211yescharacteristic, complemented
44#19098590—21no—
45#19098527C2211yescharacteristic
46C2×C22⋊(C79⋊C8)C2211yescharacteristic
47#19098519—21no—
48#19098299C2211yescharacteristic, complemented
49#19098299C2211yescharacteristic, complemented
50#19098299C2211yescharacteristic, complemented
51#19098299C2211yescharacteristic, complemented
52#19098296C2211yescharacteristic
53#19098296C2211yescharacteristic
54#19098296C2211yescharacteristic
55#19098296C2211yescharacteristic
56#19098296C2211yescharacteristic
57#19098296C2211yescharacteristic
58#19098296C2211yescharacteristic
59#19098296C2211yescharacteristic
60#19098296C2211yescharacteristic, complemented
61#19098296C2211yescharacteristic, complemented
62#19098296C2211yescharacteristic, complemented
63#19098296C2211yescharacteristic, complemented
64C2×#117×C79C2211yescharacteristic
65#387×C79—21no—
66#387×C79—21no—
67#385×C79—21no—
68#383×C79C2211yescharacteristic, complemented
69#382×C79C2211yescharacteristic, complemented
70#381×C79C2211yescharacteristic
71C4×C4⋊C4×C79C2211yescharacteristic, complemented
72C4×C22⋊C4×C79—21no—
73#376×C79C2211yescharacteristic, complemented
74C2×#95×C79C2211yescharacteristic
75C2×#11929624—21no—
76C2×#11929624—21no—
77C2×#11929624C2×C411yescharacteristic
78C22×D316C2×C411yescharacteristic
79C22×C22⋊D79—21no—
80C2×#11929608—21no—
81C22×C79⋊C8—21no—
82#14579161C2×C411yescharacteristic, complemented
83#14579161C2×C411yescharacteristic, complemented
84#14579160—21no—
85#14579158C2×C411yescharacteristic, complemented
86#14579158C2×C411yescharacteristic, complemented
87#14579156—21no—
88#14579156—21no—
89#14579155—21no—
90#14579155—21no—
91#14579153C2×C411yescharacteristic, complemented
92#14579153C2×C411yescharacteristic, complemented
93#14579152—21no—
94#14579149—21no—
95#14579149—21no—
96#14579149C2×C411yescharacteristic, complemented
97#14579149C2×C411yescharacteristic, complemented
98#14579147—21no—
99#14579147—21no—
100#14579146—21no—
101#14579146—21no—
102#14579146—21no—
103#14579146—21no—
104#14579144—21no—
105#14579144—21no—
106#14579144—21no—
107#14579143—21no—
108#14579143—21no—
109#14579140C2×C411yescharacteristic
110#14579140C2311yescharacteristic
111#14579139—21no—
112#14579139—21no—
113#14579138—21no—
114#14579138—21no—
115#14579136—21no—
116#14579136—21no—
117#14579135—21no—
118#14579135—21no—
119#14579135—21no—
120#14579135—21no—
121#14579135C2×C411yescharacteristic
122#14579135C2×C411yescharacteristic
123#14579135C2×C411yescharacteristic
124#14579135C2311yescharacteristic
125#14579135C2311yescharacteristic
126#14579135C2311yescharacteristic
127#14579134—21no—
128#14579134—21no—
129#14579134—21no—
130#14579134—21no—
131#14579131—21no—
132#14579131—21no—
133#14579130—21no—
134C4×Dic158C2×C411yescharacteristic, complemented
135C4×Dic158C2×C411yescharacteristic, complemented
136C4×D316—21no—
137C4×D316—21no—
138C4×D316C2×C411yescharacteristic, complemented
139C4×D316C2×C411yescharacteristic, complemented
140C4×D316C2×C411yescharacteristic, complemented
141C4×D316C2×C411yescharacteristic, complemented
142C4×D316C2×C411yescharacteristic, complemented
143C4×D316C2×C411yescharacteristic, complemented
144#14579123—21no—
145#14579123—21no—
146C4×C22⋊D79—21no—
147C4×C22⋊D79—21no—
148C4×C22⋊D79—21no—
149C4×C22⋊D79—21no—
150(C22⋊D79)⋊C4—21no—
151(C22⋊D79)⋊C4—21no—
152#14579120C2×C411yescharacteristic
153#14579119—21no—
154#14579118—21no—
155#14579118—21no—
156C2×C4⋊Dic79C2×C411yescharacteristic
157C4⋊C4×D79—21no—
158C2×(C2×D79)⋊C4—21no—
159C22⋊C4×D79—21no—
160C22⋊C4×D79—21no—
161C4⋊(C79⋊C8)—21no—
162C4⋊(C79⋊C8)—21no—
163C4⋊(C79⋊C8)—21no—
164C4⋊(C79⋊C8)—21no—
165C22⋊(C79⋊C8)—21no—
166C22⋊(C79⋊C8)—21no—
167C22⋊(C79⋊C8)C2311yescharacteristic
168C22⋊(C79⋊C8)C2311yescharacteristic
169C22⋊(C79⋊C8)C2311yescharacteristic
170C22⋊(C79⋊C8)C2311yescharacteristic
171#14579072—21no—
172#14579072—21no—
173C4×C79⋊C8—21no—
174C4×C79⋊C8—21no—
175C23×C4×C79—21no—
176C23×C4×C79C2311yescharacteristic
177#117×C79C2×C411yescharacteristic
178#117×C79C2×C411yescharacteristic
179#117×C79C2×C411yescharacteristic
180#117×C79C2×C411yescharacteristic
181#117×C79D411yescharacteristic
182#117×C79D411yescharacteristic
183#117×C79D411yescharacteristic
184#117×C79D411yescharacteristic
185C2×C4⋊C4×C79—21no—
186C2×C4⋊C4×C79—21no—
187C2×C4⋊C4×C79D411yescharacteristic
188C2×C4⋊C4×C79D411yescharacteristic
189C2×C22⋊C4×C79—21no—
190C2×C22⋊C4×C79D411yescharacteristic
191C2×C22⋊C4×C79D411yescharacteristic
192C2×C42×C79—21no—
193C2×C42×C79—21no—
194C2×C42×C79C2311yescharacteristic
195C2×C42×C79C2311yescharacteristic
196#95×C79—21no—
197#95×C79—21no—
198#95×C79—21no—
199#95×C79—21no—
200#95×C79—21no—
201#95×C79—21no—
202#95×C79C2311yescharacteristic
203#95×C79C2311yescharacteristic
204#95×C79C2311yescharacteristic
205#95×C79C2311yescharacteristic
206C23×D79—21no—
207#11929624—42no—
208#11929624—81no—
209#11929624—81no—
210#11929624—81no—
211#11929624—81no—
212C2×Dic158—21no—
213C2×Dic158—21no—
214C2×Dic158C22×C411yescharacteristic
215C2×D316—21no—
216C2×D316—21no—
217C2×D316—21no—
218C2×D316—21no—
219C2×D316—21no—
220C2×D316—42no—
221C2×D316C22×C411yescharacteristic
222C2×D316C22×C411yescharacteristic
223C2×D316C22×C411yescharacteristic
224C2×C22⋊D79—21no—
225C2×C22⋊D79—21no—
226C2×C22⋊D79—21no—
227C2×C22⋊D79—21no—
228C2×C22⋊D79—21no—
229C2×C22⋊D79—21no—
230C2×C22⋊D79—21no—
231C2×C22⋊D79—81no—
232C2×C22⋊D79—81no—
233C22×Dic79—21no—
234C2×C4×D79—21no—
235C2×C4×D79—21no—
236C2×C4×D79—21no—
237C2×C4×D79—21no—
238C2×C4×D79—21no—
239C2×C4×D79—21no—
240C2×C4×D79—21no—
241#11929608—42no—
242C2×C79⋊C8—21no—
243C2×C79⋊C8—21no—
244C2×C79⋊C8—21no—
245C2×C79⋊C8—21no—
246C2×C79⋊C8—42no—
247C4⋊Dic79—21no—
248C4⋊Dic79—21no—
249C4⋊Dic79—21no—
250C4⋊Dic79C22×C411yescharacteristic
251C4⋊Dic79C22×C411yescharacteristic
252C4⋊Dic79C22×C411yescharacteristic
253C4⋊Dic79C22×C411yescharacteristic
254Dic79⋊C4—21no—
255Dic79⋊C4—21no—
256Dic79⋊C4—21no—
257Dic79⋊C4—21no—
258Dic79⋊C4—21no—
259Dic79⋊C4—21no—
260Dic79⋊C4—21no—
261Dic79⋊C4—21no—
262C22⋊Dic79—21no—
263C22⋊Dic79—21no—
264C22⋊Dic79—21no—
265(C2×D79)⋊C4—21no—
266(C2×D79)⋊C4—21no—
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—
275(C2×D79)⋊C4—21no—
276(C2×D79)⋊C4—21no—
277(C2×D79)⋊C4—21no—
278(C2×D79)⋊C4—21no—
279(C2×D79)⋊C4—21no—
280(C2×D79)⋊C4—21no—
281C4×Dic79—21no—
282C4×Dic79—21no—
283C4×Dic79—21no—
284C24×C79C2×D411yescharacteristic
285C22×C4×C79—21no—
286C22×C4×C79—21no—
287C22×C4×C79—21no—
288C22×C4×C79—21no—
289C22×C4×C79—42no—
290C22×C4×C79—42no—
291C22×C4×C79—42no—
292C22×C4×C79—81no—
293C22×C4×C79C22×C411yescharacteristic
294C22×C4×C79C22×C411yescharacteristic
295C22×C4×C79C2×D411yescharacteristic
296C22×C4×C79C2×D411yescharacteristic
297C22×C4×C79C2×D411yescharacteristic
298C22×C4×C79C2×D411yescharacteristic
299C22×C4×C79C2×D411yescharacteristic
300C22×C4×C79C2×D411yescharacteristic
301C22×C4×C79C2×D411yescharacteristic
302C22×C4×C79C2411yescharacteristic
303C4⋊C4×C79—42no—
304C4⋊C4×C79—81no—
305C4⋊C4×C79C22⋊C411yescharacteristic
306C4⋊C4×C79C22⋊C411yescharacteristic
307C4⋊C4×C79C22⋊C411yescharacteristic
308C4⋊C4×C79C22⋊C411yescharacteristic
309C4⋊C4×C79C22⋊C411yescharacteristic
310C4⋊C4×C79C22⋊C411yescharacteristic
311C4⋊C4×C79C22⋊C411yescharacteristic
312C4⋊C4×C79C22⋊C411yescharacteristic
313C22⋊C4×C79—42no—
314C22⋊C4×C79C22⋊C411yescharacteristic
315C22⋊C4×C79C22⋊C411yescharacteristic
316C22⋊C4×C79C22⋊C411yescharacteristic
317C22⋊C4×C79C22⋊C411yescharacteristic
318C22⋊C4×C79C22⋊C411yescharacteristic
319C22⋊C4×C79C22⋊C411yescharacteristic
320C22⋊C4×C79C22⋊C411yescharacteristic
321C22⋊C4×C79C22⋊C411yescharacteristic
322C42×C79—42no—
323C42×C79—81no—
324C42×C79C22×C411yescharacteristic
325C42×C79C22×C411yescharacteristic
326C42×C79C22×C411yescharacteristic
327C42×C79C22×C411yescharacteristic
328C42×C79C2×D411yescharacteristic
329C42×C79C2×D411yescharacteristic
330C42×C79C2×D411yescharacteristic
331C42×C79C2×D411yescharacteristic
332C23×C79—21no—
333C23×C79—21no—
334C23×C79—22no—
335C23×C79—41no—
336C23×C79C2×C22⋊C411yescharacteristic
337C23×C79C2×C22⋊C411yescharacteristic
338C23×C79C22×D411yescharacteristic
339C22×D79—21no—
340C22×D79—21no—
341C22×D79—21no—
342C22×D79—42no—
343C22×D79—81no—
344C22×D79—81no—
345C2×C4×C79—21no—
346C2×C4×C79—21no—
347C2×C4×C79—21no—
348C2×C4×C79—21no—
349C2×C4×C79—22no—
350C2×C4×C79—22no—
351C2×C4×C79—22no—
352C2×C4×C79—41no—
353C2×C4×C79—41no—
354C2×C4×C79—41no—
355C2×C4×C79—41no—
356C2×C4×C79—41no—
357C2×C4×C79—41no—
358C2×C4×C79—41no—
359C2×C4×C79—41no—
360C2×C4×C79—41no—
361C2×C4×C79—41no—
362C2×C4×C79—41no—
363C2×C4×C79—41no—
364C2×C4×C79—41no—
365C2×C4×C79—41no—
366C2×C4×C79—41no—
367C2×C4×C79—41no—
368C2×C4×C79—41no—
369C2×C4×C79—84no—
370C2×C4×C79C2×C22⋊C411yescharacteristic
371C2×C4×C79C2×C22⋊C411yescharacteristic
372C2×C4×C79C2×C22⋊C411yescharacteristic
373C2×C4×C79C2×C22⋊C411yescharacteristic
374C2×C4×C79C2×C22⋊C411yescharacteristic
375C2×C4×C79C2×C22⋊C411yescharacteristic
376C2×C4×C79C2×C22⋊C411yescharacteristic
377C2×C4×C79C2×C22⋊C411yescharacteristic
378C2×C4×C79C2×C22⋊C411yescharacteristic
379C2×C4×C79C2×C22⋊C411yescharacteristic
380C2×C4×C79C23×C411yescharacteristic
381C2×C4×C79C22×D411yescharacteristic
382C22⋊D79—41no—
383C22⋊D79—41no—
384C22⋊D79—41no—
385C22⋊D79—41no—
386C22⋊D79—41no—
387C22⋊D79—41no—
388C22⋊D79—42no—
389C22⋊D79—81no—
390C22⋊D79—81no—
391C22⋊D79—81no—
392C2×Dic79—21no—
393C2×Dic79—21no—
394C2×Dic79—21no—
395C2×Dic79—21no—
396C2×Dic79—21no—
397C2×Dic79—81no—
398D316—41no—
399D316—41no—
400D316—41no—
401D316—42no—
402D316—81no—
403D316—81no—
404D316—81no—
405D316—81no—
406C4×D79—42no—
407C4×D79—81no—
408C4×D79—81no—
409C4×D79—81no—
410C4×D79—81no—
411C4×D79—81no—
412C4×D79—81no—
413Dic158—41no—
414Dic158—81no—
415Dic158—81no—
416C79⋊C8—41no—
417C79⋊C8—41no—
418C79⋊C8—41no—
419C79⋊C8—41no—
420C22×C79—21no—
421C22×C79—21no—
422C22×C79—21no—
423C22×C79—21no—
424C22×C79—21no—
425C22×C79—21no—
426C22×C79—21no—
427C22×C79—42no—
428C22×C79—42no—
429C22×C79#41012yes—
430C22×C79C22×C22⋊C411yescharacteristic
431C22×C79#57611yescharacteristic
432C22×C79#57711yescharacteristic
433C2×D79—41no—
434C2×D79—41no—
435C2×D79—41no—
436C2×D79—41no—
437C2×D79—41no—
438C2×D79—41no—
439C2×D79—41no—
440C2×D79—41no—
441C2×D79—41no—
442C2×D79—162no—
443C4×C79—21no—
444C4×C79—21no—
445C4×C79—21no—
446C4×C79—21no—
447C4×C79—21no—
448C4×C79—21no—
449C4×C79—21no—
450C4×C79—21no—
451C4×C79—21no—
452C4×C79—21no—
453C4×C79—21no—
454C4×C79—21no—
455C4×C79—42no—
456C4×C79—81no—
457C4×C79—81no—
458C4×C79—81no—
459Dic79—41no—
460Dic79—41no—
461Dic79—41no—
462Dic79—41no—
463Dic79—41no—
464#17604—791nomaximal, Sylow
465C2×C79—21no—
466C2×C79—21no—
467C2×C79—22no—
468C2×C79—41no—
469C2×C79C2×#41011yescharacteristic
470C2×C79#289711yescharacteristic
471C2×C79#290111yescharacteristic
472D79—81no—
473D79—81no—
474D79—81no—
475#3494—791no—
476#2924—791no—
477#2343D7911yescharacteristic, complemented
478#1521—791no—
479#1517—791no—
480#1516—791no—
481#1514—791no—
482#1512—791no—
483#1510—791no—
484#1509—791no—
485#1505—791no—
486#1504—791no—
487#1502—791no—
488#1500—791no—
489C2×#327—791no—
490C79#1760411yescharacteristic, complemented, Sylow
491#555—1581no—
492#553—1581no—
493#553—1581no—
494#551—1581no—
495#551—1581no—
496#547—1581no—
497#546—1581no—
498#546—1581no—
499#544—791no—
500#542—791no—
501#542—791no—
502#540—791no—
503#540—791no—
504#535—791no—
505#532—791no—
506#532—791no—
507#529—791no—
508#529—791no—
509#525—791no—
510C2×#121—791no—
511#520—791no—
512#518—791no—
513C2×#117C2×D7911yescharacteristic
514#433—1581no—
515#433—1581no—
516#432—791no—
517#432—791no—
518#431—791no—
519#431—791no—
520#424—1581no—
521#407—791no—
522C2×C22⋊C8—791no—
523#405—1581no—
524#387—21no—
525#387—21no—
526#385—21no—
527#383C2×D7911yescharacteristic, complemented
528#382C2×D7911yescharacteristic, complemented
529#381C2×D7911yescharacteristic
530C4×C4⋊C4C2×D7911yescharacteristic, complemented
531C4×C22⋊C4—21no—
532#376C2×D7911yescharacteristic, complemented
533C2×#95C2×D7911yescharacteristic
534#328—791no—
535#328—791no—
536#328—791no—
537#328—791no—
538#327—791no—
539#327—791no—
540#327—791no—
541#327—791no—
542#327—791no—
543#327—791no—
544#327—791no—
545#327—791no—
546#327—791no—
547#327—791no—
548#327—791no—
549#327—791no—
550C2×#41—791no—
551C2×#41—1581no—
552C2×#41—1581no—
553C22×D4—791no—
554C22×D4—1581no—
555C23×C4—21no—
556C23×C4C22×D7911yescharacteristic
557C2×M16—1581no—
558C22×C8—1581no—
559C4⋊Q8—791no—
560C4⋊Q8—791no—
561C4⋊Q8—1581no—
562#127—791no—
563#127—791no—
564#126—1581no—
565#126—1581no—
566#126—1581no—
567#126—1581no—
568#125—791no—
569#125—791no—
570#125—1581no—
571#124—791no—
572#124—791no—
573#124—1581no—
574#124—1581no—
575#124—1581no—
576#124—1581no—
577#123—1581no—
578#123—1581no—
579#123—1581no—
580#123—1581no—
581#123—1581no—
582#123—1581no—
583#123—1581no—
584#123—1581no—
585#123—1581no—
586C22⋊Q8—791no—
587C22⋊Q8—791no—
588C22⋊Q8—1581no—
589C22⋊Q8—1581no—
590C22⋊Q8—1581no—
591C22⋊Q8—1581no—
592#121—791no—
593#121—791no—
594#121—791no—
595#121—791no—
596#121—791no—
597#121—791no—
598#121—1581no—
599#121—1581no—
600#121—1581no—
601#121—1581no—
602#121—1581no—
603#121—1581no—
604#121—1581no—
605#121—1581no—
606#121—1581no—
607#121—1581no—
608#120—1581no—
609#120—1581no—
610#120—1581no—
611C4×Q8—791no—
612C4×Q8—791no—
613C4×D4—791no—
614C4×D4—791no—
615C4×D4—791no—
616C4×D4—791no—
617C4×D4—791no—
618C4×D4—791no—
619C4×D4—1581no—
620C4×D4—1581no—
621C4×D4—1581no—
622C4×D4—1581no—
623C4×D4—1581no—
624C4×D4—1581no—
625C4×D4—1581no—
626C4×D4—1581no—
627C4×D4—1581no—
628C4×D4—1581no—
629#117—791no—
630#117—1581no—
631#117—1581no—
632#117—1581no—
633#117C4×D7911yescharacteristic
634#117C4×D7911yescharacteristic
635#117C4×D7911yescharacteristic
636#117C4×D7911yescharacteristic
637#117D31611yescharacteristic
638#117D31611yescharacteristic
639#117D31611yescharacteristic
640#117D31611yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—791no—
644C2×C4⋊C4—1581no—
645C2×C4⋊C4C22⋊D7911yescharacteristic
646C2×C4⋊C4C22⋊D7911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—1581no—
649C2×C22⋊C4—1581no—
650C2×C22⋊C4—1581no—
651C2×C22⋊C4C22⋊D7911yescharacteristic
652C2×C22⋊C4C22⋊D7911yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42C22×D7911yescharacteristic
656C2×C42C22×D7911yescharacteristic
657C4⋊C8—1581no—
658C4⋊C8—1581no—
659C4⋊C8—1581no—
660C4⋊C8—1581no—
661C22⋊C8—791no—
662C22⋊C8—791no—
663C22⋊C8—791no—
664C22⋊C8—791no—
665C22⋊C8—1581no—
666C22⋊C8—1581no—
667#97—1581no—
668#97—1581no—
669C4×C8—1581no—
670C4×C8—1581no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95C22×D7911yescharacteristic
678#95C22×D7911yescharacteristic
679#95C22×D7911yescharacteristic
680#95C22×D7911yescharacteristic
681C24—1581no—
682C24C2×C22⋊D7911yescharacteristic
683#41—3162no—
684#41—6321no—
685#41—6321no—
686#41—6321no—
687#41—6321no—
688C2×Q8—791no—
689C2×Q8—1581no—
690C2×Q8—1581no—
691C2×D4—3162no—
692C2×D4—791no—
693C2×D4—791no—
694C2×D4—791no—
695C2×D4—6321no—
696C2×D4—6321no—
697C2×D4—1581no—
698C2×D4—1581no—
699C2×D4—1581no—
700C2×D4—1581no—
701C2×D4—1581no—
702C2×D4—1581no—
703C2×D4—1581no—
704C2×D4—1581no—
705C2×D4—1581no—
706C2×D4—1581no—
707C2×D4—1581no—
708C2×D4—1581no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—81no—
717C22×C4—1581no—
718C22×C4—1581no—
719C22×C4—1581no—
720C22×C4—1581no—
721C22×C4—1581no—
722C22×C4—1581no—
723C22×C4—1581no—
724C22×C4—1581no—
725C22×C4C2×C4×D7911yescharacteristic
726C22×C4C2×C4×D7911yescharacteristic
727C22×C4C2×C22⋊D7911yescharacteristic
728C22×C4C2×C22⋊D7911yescharacteristic
729C22×C4C2×C22⋊D7911yescharacteristic
730C22×C4C2×C22⋊D7911yescharacteristic
731C22×C4C2×C22⋊D7911yescharacteristic
732C22×C4C2×D31611yescharacteristic
733C22×C4C2×D31611yescharacteristic
734C22×C4C23×D7911yescharacteristic
735M16—3162no—
736C2×C8—3162no—
737C2×C8—1581no—
738C2×C8—1581no—
739C2×C8—1581no—
740C2×C8—1581no—
741C4⋊C4—42no—
742C4⋊C4—81no—
743C4⋊C4—791no—
744C4⋊C4—791no—
745C4⋊C4—791no—
746C4⋊C4—791no—
747C4⋊C4—1581no—
748C4⋊C4—1581no—
749C4⋊C4—1581no—
750C4⋊C4—1581no—
751C4⋊C4—1581no—
752C4⋊C4—1581no—
753C4⋊C4—1581no—
754C4⋊C4—1581no—
755C4⋊C4—1581no—
756C4⋊C4—1581no—
757C4⋊C4—1581no—
758C4⋊C4(C2×D79)⋊C411yescharacteristic
759C4⋊C4(C2×D79)⋊C411yescharacteristic
760C4⋊C4(C2×D79)⋊C411yescharacteristic
761C4⋊C4(C2×D79)⋊C411yescharacteristic
762C4⋊C4(C2×D79)⋊C411yescharacteristic
763C4⋊C4(C2×D79)⋊C411yescharacteristic
764C4⋊C4(C2×D79)⋊C411yescharacteristic
765C4⋊C4(C2×D79)⋊C411yescharacteristic
766C22⋊C4—42no—
767C22⋊C4—1581no—
768C22⋊C4—1581no—
769C22⋊C4—1581no—
770C22⋊C4—1581no—
771C22⋊C4—1581no—
772C22⋊C4—1581no—
773C22⋊C4—1581no—
774C22⋊C4—1581no—
775C22⋊C4—1581no—
776C22⋊C4—1581no—
777C22⋊C4—1581no—
778C22⋊C4—1581no—
779C22⋊C4—1581no—
780C22⋊C4—1581no—
781C22⋊C4—1581no—
782C22⋊C4—1581no—
783C22⋊C4—1581no—
784C22⋊C4—1581no—
785C22⋊C4—1581no—
786C22⋊C4(C2×D79)⋊C411yescharacteristic
787C22⋊C4(C2×D79)⋊C411yescharacteristic
788C22⋊C4(C2×D79)⋊C411yescharacteristic
789C22⋊C4(C2×D79)⋊C411yescharacteristic
790C22⋊C4(C2×D79)⋊C411yescharacteristic
791C22⋊C4(C2×D79)⋊C411yescharacteristic
792C22⋊C4(C2×D79)⋊C411yescharacteristic
793C22⋊C4(C2×D79)⋊C411yescharacteristic
794C42—42no—
795C42—81no—
796C42—1581no—
797C42—1581no—
798C42—1581no—
799C42C2×C4×D7911yescharacteristic
800C42C2×C4×D7911yescharacteristic
801C42C2×C4×D7911yescharacteristic
802C42C2×C4×D7911yescharacteristic
803C42C2×D31611yescharacteristic
804C42C2×D31611yescharacteristic
805C42C2×D31611yescharacteristic
806C42C2×D31611yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—3162no—
812C23—6321no—
813C23—6321no—
814C23—1581no—
815C23—1581no—
816C23—1581no—
817C23C2×(C2×D79)⋊C411yescharacteristic
818C23C2×(C2×D79)⋊C411yescharacteristic
819C23C22×C22⋊D7911yescharacteristic
820Q8—3161no—
821Q8—6321no—
822Q8—6321no—
823D4—3161no—
824D4—3161no—
825D4—3161no—
826D4—3162no—
827D4—3162no—
828D4—3161no—
829D4—3161no—
830D4—3161no—
831D4—3161no—
832D4—3161no—
833D4—3161no—
834D4—6321no—
835D4—6321no—
836D4—6321no—
837D4—6321no—
838D4—6321no—
839D4—6321no—
840D4—6321no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—84no—
866C2×C4—3162no—
867C2×C4—6321no—
868C2×C4—6321no—
869C2×C4—6321no—
870C2×C4—6321no—
871C2×C4—6321no—
872C2×C4—6321no—
873C2×C4—6321no—
874C2×C4—1581no—
875C2×C4—1581no—
876C2×C4—1581no—
877C2×C4—1581no—
878C2×C4—1581no—
879C2×C4C2×(C2×D79)⋊C411yescharacteristic
880C2×C4C2×(C2×D79)⋊C411yescharacteristic
881C2×C4C2×(C2×D79)⋊C411yescharacteristic
882C2×C4C2×(C2×D79)⋊C411yescharacteristic
883C2×C4C2×(C2×D79)⋊C411yescharacteristic
884C2×C4C2×(C2×D79)⋊C411yescharacteristic
885C2×C4C2×(C2×D79)⋊C411yescharacteristic
886C2×C4C2×(C2×D79)⋊C411yescharacteristic
887C2×C4C2×(C2×D79)⋊C411yescharacteristic
888C2×C4C2×(C2×D79)⋊C411yescharacteristic
889C2×C4C22×C4×D7911yescharacteristic
890C2×C4C22×D31611yescharacteristic
891C8—3161no—
892C8—3161no—
893C8—3161no—
894C8—3161no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—3161no—
905C22—3161no—
906C22—3161no—
907C22—3161no—
908C22—3161no—
909C22—3161no—
910C22—3161no—
911C22—3161no—
912C22—3161no—
913C22—12642no—
914C22#1909853612yes—
915C22C22×(C2×D79)⋊C411yescharacteristic
916C22#1909936611yescharacteristic
917C22#1909937111yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—3161no—
935C4—3161no—
936C4—3161no—
937C4—3161no—
938C4—3161no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—6321no—
944C2—6321no—
945C2—6321no—
946C2C2×#1909853611yescharacteristic
947C2#2377192311yescharacteristic
948C2#2377194811yescharacteristic
subgroupG/H
centerC22C22×(C2×D79)⋊C4
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2343C2
socleC22×C79C22×C22⋊C4
prime radical#23777135C2
cosocleC22×C4×C79C24
hypercenter#2343D79
hypocenterC79#17604
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. #23772058C2semidirect
3. #23761975C2semidirect
4. #23761959C2semidirect
5. #23761954C2semidirect
6. #23761946C2semidirect
7. #23761936C2semidirect
8. #23761928C2semidirect
9. #23761923C2semidirect
10. #23761907C2semidirect
11. #23761902C2semidirect
12. #23761894C2semidirect
13. #23761884C2semidirect
14. C2×#19098296C2semidirect
15. C79×#2343C2semidirect
24. #19099191C4semidirect
25. #19099184C4semidirect
26. #19099184C4semidirect
27. #19099168C4semidirect
28. #19099168C4semidirect
29. #19099132C4semidirect
36. #19099043C4semidirect
37. #19099037C4semidirect
40. #19098620C22semidirect
41. #19098620C22semidirect
42. #19098616C22semidirect
43. #19098616C22semidirect
48. #19098299C22semidirect
49. #19098299C22semidirect
50. #19098299C22semidirect
51. #19098299C22semidirect
60. #19098296C22semidirect
61. #19098296C22semidirect
62. #19098296C22semidirect
63. #19098296C22semidirect
68. #383×C79C22semidirect
69. #382×C79C22semidirect
71. C4×C4⋊C4×C79C22semidirect
73. #376×C79C22semidirect
82. #14579161C2×C4semidirect
83. #14579161C2×C4semidirect
85. #14579158C2×C4semidirect
86. #14579158C2×C4semidirect
91. #14579153C2×C4semidirect
92. #14579153C2×C4semidirect
96. #14579149C2×C4semidirect
97. #14579149C2×C4semidirect
134. C4×Dic158C2×C4semidirect
135. C4×Dic158C2×C4semidirect
138. C4×D316C2×C4semidirect
139. C4×D316C2×C4semidirect
140. C4×D316C2×C4semidirect
141. C4×D316C2×C4semidirect
142. C4×D316C2×C4semidirect
143. C4×D316C2×C4semidirect
477. #2343D79semidirect
490. C79#17604semidirect
527. #383C2×D79semidirect
528. #382C2×D79semidirect
530. C4×C4⋊C4C2×D79semidirect
532. #376C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237771352
#237720582
#237619752
#237619592
#237619542
#237619462
#237619362
#237619282
#237619232
#237619072
#237619022
#237618942
#237618842
C2×#190982962
C79×#23432
#1760479