Finite Group Databasebeta

← #34255790

Subgroups — #34255790

Order 20224.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777432C211yesmaximal, characteristic
2#23772435C211yesmaximal, characteristic, complemented
3#23761975C211yesmaximal, characteristic, complemented
4#23761967C211yesmaximal, characteristic, complemented
5#23761959C211yesmaximal, characteristic, complemented
6#23761954C211yesmaximal, characteristic, complemented
7#23761946C211yesmaximal, characteristic, complemented
8#23761941C211yesmaximal, characteristic, complemented
9#23761936C211yesmaximal, characteristic, complemented
10#23761928C211yesmaximal, characteristic, complemented
11#23761915C211yesmaximal, characteristic, complemented
12#23761902C211yesmaximal, characteristic, complemented
13#23761889C211yesmaximal, characteristic, complemented
14C2×#19098296C211yesmaximal, characteristic, complemented
15C79×#2318C211yesmaximal, characteristic, complemented
16#19099278C411yescharacteristic, complemented
17#19099270C411yescharacteristic, complemented
18#19099261—21no—
19#19099259C411yescharacteristic, complemented
20#19099259C411yescharacteristic, complemented
21#19099234C411yescharacteristic, complemented
22#19099209C411yescharacteristic, complemented
23#19099209C411yescharacteristic, complemented
24#19099203—21no—
25#19099203—21no—
26D4×D316C411yescharacteristic, complemented
27D4×C22⋊D79—21no—
28#19099164—21no—
29#19099146—21no—
30#19099146—21no—
31#19099113C2211yescharacteristic
32#19099097C2211yescharacteristic
33#19099074C2211yescharacteristic
34#19099074C2211yescharacteristic
35C2×#14579135C2211yescharacteristic
36C2×#14579135C2211yescharacteristic
37#19099035—21no—
38#19098641—21no—
39#19098635—21no—
40#19098635—21no—
41D4×C79⋊C8—21no—
42#19098620C2211yescharacteristic, complemented
43#19098616C2211yescharacteristic, complemented
44#19098527C2211yescharacteristic, complemented
45#19098527C2211yescharacteristic, complemented
46C2×C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47C2×C22⋊(C79⋊C8)C2211yescharacteristic, complemented
48#19098299C2211yescharacteristic, complemented
49#19098299C2211yescharacteristic, complemented
50#19098299C2211yescharacteristic, complemented
51#19098299C2211yescharacteristic, complemented
52#19098296C2211yescharacteristic
53#19098296C2211yescharacteristic
54#19098296C2211yescharacteristic
55#19098296C2211yescharacteristic
56#19098296C2211yescharacteristic, complemented
57#19098296C2211yescharacteristic, complemented
58#19098296C2211yescharacteristic, complemented
59#19098296C2211yescharacteristic, complemented
60#19098296C2211yescharacteristic, complemented
61#19098296C2211yescharacteristic, complemented
62#19098296C2211yescharacteristic, complemented
63#19098296C2211yescharacteristic, complemented
64C2×C4×D4×C79C2211yescharacteristic
65#388×C79—21no—
66#387×C79—21no—
67#386×C79—21no—
68#385×C79—21no—
69#383×C79C2211yescharacteristic, complemented
70#382×C79C2211yescharacteristic, complemented
71#381×C79C2211yescharacteristic, complemented
72#380×C79C2211yescharacteristic, complemented
73C4×C22⋊C4×C79C2211yescharacteristic, complemented
74C2×#95×C79C2211yescharacteristic, complemented
75C2×#11929624—21no—
76C2×#11929624C2×C411yescharacteristic
77C2×#11929624C2×C411yescharacteristic, complemented
78C22×D316C2×C411yescharacteristic
79C22×D316C2×C411yescharacteristic, complemented
80C22×C22⋊D79—21no—
81C22×C22⋊D79—21no—
82C2×D4×D79—21no—
83C2×#11929608—21no—
84C2×#11929608—21no—
85C22×C79⋊C8—21no—
86C22×C79⋊C8—21no—
87#14579161C2×C411yescharacteristic, complemented
88#14579158C2×C411yescharacteristic, complemented
89#14579157—21no—
90#14579156—21no—
91#14579156—21no—
92#14579155—21no—
93#14579153C2×C411yescharacteristic, complemented
94#14579152—21no—
95#14579149—21no—
96#14579149C2×C411yescharacteristic, complemented
97#14579147—21no—
98#14579147—21no—
99#14579146—21no—
100#14579146—21no—
101#14579144—21no—
102#14579144—21no—
103#14579144—21no—
104#14579143—21no—
105#14579143—21no—
106#14579140C2×C411yescharacteristic
107#14579140C2×C411yescharacteristic, complemented
108#14579140C2311yescharacteristic
109#14579138—21no—
110#14579138—21no—
111#14579136—21no—
112#14579135—21no—
113#14579135—21no—
114#14579135—21no—
115#14579135—21no—
116#14579135—21no—
117#14579135C2×C411yescharacteristic
118#14579135C2×C411yescharacteristic
119#14579135C2×C411yescharacteristic
120#14579135C2×C411yescharacteristic, complemented
121#14579135C2×C411yescharacteristic, complemented
122#14579135C2×C411yescharacteristic, complemented
123#14579135C2311yescharacteristic
124#14579135C2311yescharacteristic
125#14579135C2311yescharacteristic
126#14579134—21no—
127#14579134—21no—
128#14579134—21no—
129#14579134—21no—
130#14579133—21no—
131#14579133—21no—
132#14579132—21no—
133#14579131—21no—
134#14579131—21no—
135#14579130—21no—
136#14579130—21no—
137#14579129—21no—
138#14579129—21no—
139C4×Dic158C2×C411yescharacteristic, complemented
140C4×D316—21no—
141C4×D316C2×C411yescharacteristic, complemented
142C4×D316C2×C411yescharacteristic, complemented
143C4×D316C2×C411yescharacteristic, complemented
144D4×Dic79—21no—
145#14579123—21no—
146C4×C22⋊D79—21no—
147C4×C22⋊D79—21no—
148C4×C22⋊D79—21no—
149C4×C22⋊D79—21no—
150C4×C22⋊D79—21no—
151(C22⋊D79)⋊C4—21no—
152(C22⋊D79)⋊C4—21no—
153#14579120C2×C411yescharacteristic
154#14579120C2×C411yescharacteristic, complemented
155#14579119—21no—
156#14579118—21no—
157C2×C4⋊Dic79C2×C411yescharacteristic
158C2×C4⋊Dic79C2×C411yescharacteristic, complemented
159C2×(C2×D79)⋊C4—21no—
160C2×(C2×D79)⋊C4—21no—
161C22⋊C4×D79—21no—
162C22⋊C4×D79—21no—
163C4⋊(C79⋊C8)—21no—
164C4⋊(C79⋊C8)—21no—
165C22⋊(C79⋊C8)—21no—
166C22⋊(C79⋊C8)—21no—
167C22⋊(C79⋊C8)—21no—
168C22⋊(C79⋊C8)—21no—
169C22⋊(C79⋊C8)C2311yescharacteristic
170C22⋊(C79⋊C8)C2311yescharacteristic
171C22⋊(C79⋊C8)C2311yescharacteristic
172C22⋊(C79⋊C8)C2311yescharacteristic
173#14579072—21no—
174C4×C79⋊C8—21no—
175C22×D4×C79D411yescharacteristic
176C23×C4×C79—21no—
177C23×C4×C79C2311yescharacteristic
178C23×C4×C79C2311yescharacteristic
179C4×D4×C79C2×C411yescharacteristic
180C4×D4×C79C2×C411yescharacteristic
181C4×D4×C79C2×C411yescharacteristic
182C4×D4×C79C2×C411yescharacteristic
183C4×D4×C79D411yescharacteristic
184C4×D4×C79D411yescharacteristic
185C4×D4×C79D411yescharacteristic
186C4×D4×C79D411yescharacteristic
187C2×C4⋊C4×C79—21no—
188C2×C4⋊C4×C79—21no—
189C2×C4⋊C4×C79D411yescharacteristic
190C2×C22⋊C4×C79—21no—
191C2×C22⋊C4×C79—21no—
192C2×C22⋊C4×C79—21no—
193C2×C22⋊C4×C79D411yescharacteristic
194C2×C22⋊C4×C79D411yescharacteristic
195C2×C42×C79—21no—
196C2×C42×C79C2311yescharacteristic
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—
207C23×D79—21no—
208#11929624—81no—
209#11929624—81no—
210#11929624—81no—
211#11929624—81no—
212C2×Dic158—21no—
213C2×Dic158C22×C411yescharacteristic
214C2×D316—21no—
215C2×D316—21no—
216C2×D316—21no—
217C2×D316—21no—
218C2×D316—81no—
219C2×D316—81no—
220C2×D316C22×C411yescharacteristic
221C2×D316C22×C411yescharacteristic
222C2×D316C22×C411yescharacteristic
223C2×C22⋊D79—21no—
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—21no—
232C2×C22⋊D79—21no—
233C2×C22⋊D79—21no—
234C2×C22⋊D79—81no—
235C2×C22⋊D79—81no—
236C2×C22⋊D79—81no—
237C2×C22⋊D79—81no—
238D4×D79—44no—
239C22×Dic79—21no—
240C22×Dic79—21no—
241C2×C4×D79—21no—
242C2×C4×D79—21no—
243C2×C4×D79—21no—
244C2×C4×D79—21no—
245C2×C4×D79—21no—
246#11929608—81no—
247#11929608—81no—
248C2×C79⋊C8—21no—
249C2×C79⋊C8—21no—
250C2×C79⋊C8—21no—
251C2×C79⋊C8—21no—
252C2×C79⋊C8—81no—
253C2×C79⋊C8—81no—
254C4⋊Dic79—21no—
255C4⋊Dic79—21no—
256C4⋊Dic79—21no—
257C4⋊Dic79C22×C411yescharacteristic
258C4⋊Dic79C22×C411yescharacteristic
259C4⋊Dic79C22×C411yescharacteristic
260C4⋊Dic79C22×C411yescharacteristic
261Dic79⋊C4—21no—
262Dic79⋊C4—21no—
263Dic79⋊C4—21no—
264Dic79⋊C4—21no—
265Dic79⋊C4—21no—
266Dic79⋊C4—21no—
267C22⋊Dic79—21no—
268C22⋊Dic79—21no—
269C22⋊Dic79—21no—
270C22⋊Dic79—21no—
271C22⋊Dic79—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—
281(C2×D79)⋊C4—21no—
282(C2×D79)⋊C4—21no—
283(C2×D79)⋊C4—21no—
284(C2×D79)⋊C4—21no—
285(C2×D79)⋊C4—21no—
286C4×Dic79—21no—
287C4×Dic79—21no—
288C4×Dic79—21no—
289C24×C79C2×D411yescharacteristic
290C24×C79C2×D411yescharacteristic
291C2×D4×C79—42no—
292C2×D4×C79C22⋊C411yescharacteristic
293C2×D4×C79C22⋊C411yescharacteristic
294C2×D4×C79C22⋊C411yescharacteristic
295C2×D4×C79C22⋊C411yescharacteristic
296C22×C4×C79—21no—
297C22×C4×C79—21no—
298C22×C4×C79—21no—
299C22×C4×C79—21no—
300C22×C4×C79—42no—
301C22×C4×C79—81no—
302C22×C4×C79—81no—
303C22×C4×C79—81no—
304C22×C4×C79—81no—
305C22×C4×C79C22×C411yescharacteristic
306C22×C4×C79C22×C411yescharacteristic
307C22×C4×C79C22×C411yescharacteristic
308C22×C4×C79C22×C411yescharacteristic
309C22×C4×C79C2×D411yescharacteristic
310C22×C4×C79C2×D411yescharacteristic
311C22×C4×C79C2×D411yescharacteristic
312C22×C4×C79C2×D411yescharacteristic
313C22×C4×C79C2×D411yescharacteristic
314C22×C4×C79C2×D411yescharacteristic
315C22×C4×C79C2×D411yescharacteristic
316C22×C4×C79C2×D411yescharacteristic
317C22×C4×C79C2411yescharacteristic
318C4⋊C4×C79—81no—
319C4⋊C4×C79—81no—
320C4⋊C4×C79C22⋊C411yescharacteristic
321C4⋊C4×C79C22⋊C411yescharacteristic
322C4⋊C4×C79C22⋊C411yescharacteristic
323C4⋊C4×C79C22⋊C411yescharacteristic
324C22⋊C4×C79—42no—
325C22⋊C4×C79—81no—
326C22⋊C4×C79—81no—
327C22⋊C4×C79C22⋊C411yescharacteristic
328C22⋊C4×C79C22⋊C411yescharacteristic
329C22⋊C4×C79C22⋊C411yescharacteristic
330C22⋊C4×C79C22⋊C411yescharacteristic
331C22⋊C4×C79C22⋊C411yescharacteristic
332C22⋊C4×C79C22⋊C411yescharacteristic
333C22⋊C4×C79C22⋊C411yescharacteristic
334C22⋊C4×C79C22⋊C411yescharacteristic
335C42×C79—81no—
336C42×C79C22×C411yescharacteristic
337C42×C79C22×C411yescharacteristic
338C42×C79C2×D411yescharacteristic
339C42×C79C2×D411yescharacteristic
340C23×C79—21no—
341C23×C79—21no—
342C23×C79—22no—
343C23×C79—21no—
344C23×C79—21no—
345C23×C79—41no—
346C23×C79—41no—
347C23×C79—41no—
348C23×C79C2×C22⋊C411yescharacteristic
349C23×C79C2×C22⋊C411yescharacteristic
350C23×C79C2×C22⋊C411yescharacteristic
351C23×C79C2×C22⋊C411yescharacteristic
352C23×C79C22×D411yescharacteristic
353C22×D79—21no—
354C22×D79—21no—
355C22×D79—21no—
356C22×D79—42no—
357C22×D79—42no—
358C22×D79—81no—
359C22×D79—81no—
360C22×D79—81no—
361C22×D79—81no—
362D4×C79—22no—
363D4×C79—22no—
364D4×C79—41no—
365D4×C79—41no—
366C2×C4×C79—21no—
367C2×C4×C79—21no—
368C2×C4×C79—41no—
369C2×C4×C79—41no—
370C2×C4×C79—41no—
371C2×C4×C79—41no—
372C2×C4×C79—41no—
373C2×C4×C79—41no—
374C2×C4×C79—41no—
375C2×C4×C79—41no—
376C2×C4×C79—41no—
377C2×C4×C79—41no—
378C2×C4×C79—41no—
379C2×C4×C79—41no—
380C2×C4×C79—41no—
381C2×C4×C79—41no—
382C2×C4×C79—41no—
383C2×C4×C79—41no—
384C2×C4×C79—41no—
385C2×C4×C79—41no—
386C2×C4×C79—41no—
387C2×C4×C79—41no—
388C2×C4×C79—41no—
389C2×C4×C79—41no—
390C2×C4×C79—41no—
391C2×C4×C79—41no—
392C2×C4×C79—84no—
393C2×C4×C79C2×C22⋊C411yescharacteristic
394C2×C4×C79C2×C22⋊C411yescharacteristic
395C2×C4×C79C2×C22⋊C411yescharacteristic
396C2×C4×C79C2×C22⋊C411yescharacteristic
397C2×C4×C79C2×C22⋊C411yescharacteristic
398C2×C4×C79C2×C22⋊C411yescharacteristic
399C2×C4×C79C2×C22⋊C411yescharacteristic
400C2×C4×C79C2×C22⋊C411yescharacteristic
401C2×C4×C79C23×C411yescharacteristic
402C2×C4×C79C22×D411yescharacteristic
403C22⋊D79—42no—
404C22⋊D79—41no—
405C22⋊D79—41no—
406C22⋊D79—41no—
407C22⋊D79—41no—
408C22⋊D79—41no—
409C22⋊D79—41no—
410C22⋊D79—42no—
411C22⋊D79—81no—
412C22⋊D79—81no—
413C22⋊D79—81no—
414C22⋊D79—81no—
415C22⋊D79—81no—
416C22⋊D79—81no—
417C2×Dic79—21no—
418C2×Dic79—21no—
419C2×Dic79—21no—
420C2×Dic79—21no—
421C2×Dic79—21no—
422C2×Dic79—81no—
423C2×Dic79—81no—
424D316—41no—
425D316—41no—
426D316—41no—
427D316—42no—
428D316—81no—
429D316—81no—
430D316—81no—
431C4×D79—42no—
432C4×D79—81no—
433C4×D79—81no—
434C4×D79—81no—
435C4×D79—81no—
436Dic158—41no—
437Dic158—81no—
438C79⋊C8—41no—
439C79⋊C8—41no—
440C79⋊C8—41no—
441C79⋊C8—41no—
442C22×C79—21no—
443C22×C79—21no—
444C22×C79—21no—
445C22×C79—21no—
446C22×C79—21no—
447C22×C79—21no—
448C22×C79—21no—
449C22×C79—21no—
450C22×C79—21no—
451C22×C79—21no—
452C22×C79—21no—
453C22×C79—21no—
454C22×C79—21no—
455C22×C79—42no—
456C22×C79—42no—
457C22×C79—81no—
458C22×C79—81no—
459C22×C79#42112yes—
460C22×C79C22×C22⋊C411yescharacteristic
461C22×C79#57611yescharacteristic
462C22×C79#57711yescharacteristic
463C2×D79—41no—
464C2×D79—41no—
465C2×D79—41no—
466C2×D79—41no—
467C2×D79—41no—
468C2×D79—41no—
469C2×D79—41no—
470C2×D79—41no—
471C2×D79—41no—
472C2×D79—162no—
473C2×D79—162no—
474C4×C79—21no—
475C4×C79—21no—
476C4×C79—21no—
477C4×C79—21no—
478C4×C79—21no—
479C4×C79—21no—
480C4×C79—21no—
481C4×C79—21no—
482C4×C79—21no—
483C4×C79—21no—
484C4×C79—81no—
485C4×C79—81no—
486C4×C79—81no—
487C4×C79—81no—
488Dic79—41no—
489Dic79—41no—
490Dic79—41no—
491Dic79—41no—
492Dic79—41no—
493#17597—791nomaximal, Sylow
494C2×C79—21no—
495C2×C79—21no—
496C2×C79—22no—
497C2×C79—41no—
498C2×C79—41no—
499C2×C79—41no—
500C2×C79#288311yescharacteristic
501C2×C79#289711yescharacteristic
502C2×C79C2×#42111yescharacteristic
503D79—81no—
504D79—81no—
505D79—81no—
506#3519—791no—
507#2974—791no—
508#2318D7911yescharacteristic, complemented
509#1521—791no—
510#1519—791no—
511#1517—791no—
512#1516—791no—
513#1514—791no—
514#1513—791no—
515#1512—791no—
516#1510—791no—
517#1507—791no—
518#1504—791no—
519#1501—791no—
520C2×#327—791no—
521C79#1759711yescharacteristic, complemented, Sylow
522#555—791no—
523#554—791no—
524#553—791no—
525#553—791no—
526#553—1581no—
527#550—791no—
528#546—791no—
529#546—791no—
530#546—1581no—
531#546—1581no—
532D42—791no—
533D42—1581no—
534#540—1581no—
535#538—1581no—
536#538—1581no—
537#532—791no—
538#529—791no—
539#525—791no—
540#525—791no—
541C2×#121—791no—
542C2×#121—791no—
543#518—1581no—
544C2×C4×D4C2×D7911yescharacteristic
545#436—1581no—
546#435—1581no—
547#435—1581no—
548C8×D4—1581no—
549#432—791no—
550#431—791no—
551#407—791no—
552#407—791no—
553C2×C22⋊C8—791no—
554C2×C22⋊C8—791no—
555#388—21no—
556#387—21no—
557#386—21no—
558#385—21no—
559#383C2×D7911yescharacteristic, complemented
560#382C2×D7911yescharacteristic, complemented
561#381C2×D7911yescharacteristic, complemented
562#380C2×D7911yescharacteristic, complemented
563C4×C22⋊C4C2×D7911yescharacteristic, complemented
564C2×#95C2×D7911yescharacteristic, complemented
565#328—791no—
566#328—791no—
567#328—791no—
568#328—791no—
569#327—791no—
570#327—791no—
571#327—791no—
572#327—791no—
573#327—791no—
574#327—791no—
575#327—791no—
576#327—791no—
577#327—791no—
578#327—791no—
579#327—791no—
580#327—791no—
581C2×#41—791no—
582C2×#41—791no—
583C2×#41—1581no—
584C22×D4—791no—
585C22×D4—791no—
586C22×D4—1581no—
587C22×D4—1581no—
588C22×D4—1581no—
589C22×D4C22⋊D7911yescharacteristic
590C23×C4—21no—
591C23×C4C22×D7911yescharacteristic
592C23×C4C22×D7911yescharacteristic
593C2×M16—1581no—
594C2×M16—1581no—
595C22×C8—1581no—
596C22×C8—1581no—
597C4⋊Q8—791no—
598#127—791no—
599#127—1581no—
600#126—1581no—
601#126—1581no—
602#126—1581no—
603#125—791no—
604#125—1581no—
605#124—791no—
606#124—1581no—
607#124—1581no—
608#124—1581no—
609#123—1581no—
610#123—1581no—
611#123—1581no—
612#123—1581no—
613#123—1581no—
614#123—1581no—
615#123—1581no—
616C22⋊Q8—791no—
617C22⋊Q8—791no—
618C22⋊Q8—791no—
619C22⋊Q8—1581no—
620C22⋊Q8—1581no—
621#121—791no—
622#121—791no—
623#121—791no—
624#121—791no—
625#121—791no—
626#121—791no—
627#121—791no—
628#121—791no—
629#121—791no—
630#121—1581no—
631#121—1581no—
632#121—1581no—
633#121—1581no—
634#121—1581no—
635#121—1581no—
636#121—1581no—
637#121—1581no—
638#121—1581no—
639#121—1581no—
640#121—1581no—
641#121—1581no—
642#121—1581no—
643#120—1581no—
644#120—1581no—
645#120—1581no—
646#120—1581no—
647#120—1581no—
648#120—1581no—
649C4×Q8—791no—
650C4×D4—791no—
651C4×D4—791no—
652C4×D4—791no—
653C4×D4—1581no—
654C4×D4—1581no—
655C4×D4—1581no—
656C4×D4—1581no—
657C4×D4—1581no—
658C4×D4—1581no—
659C4×D4—1581no—
660C4×D4—1581no—
661C4×D4—1581no—
662C4×D4—1581no—
663C4×D4C4×D7911yescharacteristic
664C4×D4C4×D7911yescharacteristic
665C4×D4C4×D7911yescharacteristic
666C4×D4C4×D7911yescharacteristic
667C4×D4D31611yescharacteristic
668C4×D4D31611yescharacteristic
669C4×D4D31611yescharacteristic
670C4×D4D31611yescharacteristic
671#117—791no—
672#117—791no—
673#117—1581no—
674#117—1581no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—791no—
678C2×C4⋊C4—791no—
679C2×C4⋊C4C22⋊D7911yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—1581no—
684C2×C22⋊C4—1581no—
685C2×C22⋊C4—1581no—
686C2×C22⋊C4—1581no—
687C2×C22⋊C4C22⋊D7911yescharacteristic
688C2×C22⋊C4C22⋊D7911yescharacteristic
689C2×C42—21no—
690C2×C42C22×D7911yescharacteristic
691C4⋊C8—1581no—
692C4⋊C8—1581no—
693C22⋊C8—791no—
694C22⋊C8—791no—
695C22⋊C8—791no—
696C22⋊C8—791no—
697C22⋊C8—1581no—
698C22⋊C8—1581no—
699C22⋊C8—1581no—
700C22⋊C8—1581no—
701#97—1581no—
702C4×C8—1581no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C22×D7911yescharacteristic
709#95C22×D7911yescharacteristic
710#95C22×D7911yescharacteristic
711#95C22×D7911yescharacteristic
712C24—1581no—
713C24—1581no—
714C24C2×C22⋊D7911yescharacteristic
715C24C2×C22⋊D7911yescharacteristic
716#41—6321no—
717#41—6321no—
718#41—6321no—
719#41—6321no—
720C2×Q8—791no—
721C2×Q8—1581no—
722C2×D4—42no—
723C2×D4—3164no—
724C2×D4—791no—
725C2×D4—791no—
726C2×D4—791no—
727C2×D4—6321no—
728C2×D4—6321no—
729C2×D4—6321no—
730C2×D4—6321no—
731C2×D4—6321no—
732C2×D4—6321no—
733C2×D4—1581no—
734C2×D4—1581no—
735C2×D4—1581no—
736C2×D4—1581no—
737C2×D4—1581no—
738C2×D4—1581no—
739C2×D4—1581no—
740C2×D4—1581no—
741C2×D4—1581no—
742C2×D4—1581no—
743C2×D4—1581no—
744C2×D4—1581no—
745C2×D4—1581no—
746C2×D4—1581no—
747C2×D4—1581no—
748C2×D4(C2×D79)⋊C411yescharacteristic
749C2×D4(C2×D79)⋊C411yescharacteristic
750C2×D4(C2×D79)⋊C411yescharacteristic
751C2×D4(C2×D79)⋊C411yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—42no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—1581no—
762C22×C4—1581no—
763C22×C4—1581no—
764C22×C4—1581no—
765C22×C4—1581no—
766C22×C4—1581no—
767C22×C4—1581no—
768C22×C4C2×C4×D7911yescharacteristic
769C22×C4C2×C4×D7911yescharacteristic
770C22×C4C2×C4×D7911yescharacteristic
771C22×C4C2×C4×D7911yescharacteristic
772C22×C4C2×C22⋊D7911yescharacteristic
773C22×C4C2×C22⋊D7911yescharacteristic
774C22×C4C2×C22⋊D7911yescharacteristic
775C22×C4C2×C22⋊D7911yescharacteristic
776C22×C4C2×D31611yescharacteristic
777C22×C4C2×D31611yescharacteristic
778C22×C4C2×D31611yescharacteristic
779C22×C4C2×D31611yescharacteristic
780C22×C4C23×D7911yescharacteristic
781M16—6321no—
782M16—6321no—
783C2×C8—6321no—
784C2×C8—6321no—
785C2×C8—1581no—
786C2×C8—1581no—
787C2×C8—1581no—
788C2×C8—1581no—
789C4⋊C4—81no—
790C4⋊C4—81no—
791C4⋊C4—791no—
792C4⋊C4—791no—
793C4⋊C4—791no—
794C4⋊C4—791no—
795C4⋊C4—1581no—
796C4⋊C4—1581no—
797C4⋊C4—1581no—
798C4⋊C4—1581no—
799C4⋊C4—1581no—
800C4⋊C4—1581no—
801C4⋊C4—1581no—
802C4⋊C4—1581no—
803C4⋊C4—1581no—
804C4⋊C4(C2×D79)⋊C411yescharacteristic
805C4⋊C4(C2×D79)⋊C411yescharacteristic
806C4⋊C4(C2×D79)⋊C411yescharacteristic
807C4⋊C4(C2×D79)⋊C411yescharacteristic
808C22⋊C4—42no—
809C22⋊C4—81no—
810C22⋊C4—81no—
811C22⋊C4—1581no—
812C22⋊C4—1581no—
813C22⋊C4—1581no—
814C22⋊C4—1581no—
815C22⋊C4—1581no—
816C22⋊C4—1581no—
817C22⋊C4—1581no—
818C22⋊C4—1581no—
819C22⋊C4—1581no—
820C22⋊C4—1581no—
821C22⋊C4—1581no—
822C22⋊C4—1581no—
823C22⋊C4—1581no—
824C22⋊C4—1581no—
825C22⋊C4—1581no—
826C22⋊C4—1581no—
827C22⋊C4—1581no—
828C22⋊C4—1581no—
829C22⋊C4—1581no—
830C22⋊C4(C2×D79)⋊C411yescharacteristic
831C22⋊C4(C2×D79)⋊C411yescharacteristic
832C22⋊C4(C2×D79)⋊C411yescharacteristic
833C22⋊C4(C2×D79)⋊C411yescharacteristic
834C22⋊C4(C2×D79)⋊C411yescharacteristic
835C22⋊C4(C2×D79)⋊C411yescharacteristic
836C22⋊C4(C2×D79)⋊C411yescharacteristic
837C22⋊C4(C2×D79)⋊C411yescharacteristic
838C42—81no—
839C42—1581no—
840C42—1581no—
841C42—1581no—
842C42C2×C4×D7911yescharacteristic
843C42C2×C4×D7911yescharacteristic
844C42C2×D31611yescharacteristic
845C42C2×D31611yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—3162no—
855C23—3162no—
856C23—6321no—
857C23—6321no—
858C23—6321no—
859C23—6321no—
860C23—1581no—
861C23—1581no—
862C23—1581no—
863C23C2×(C2×D79)⋊C411yescharacteristic
864C23C2×(C2×D79)⋊C411yescharacteristic
865C23C2×(C2×D79)⋊C411yescharacteristic
866C23C2×(C2×D79)⋊C411yescharacteristic
867C23C22×C22⋊D7911yescharacteristic
868Q8—3161no—
869Q8—6321no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—3161no—
875D4—3161no—
876D4—3161no—
877D4—3162no—
878D4—3162no—
879D4—3162no—
880D4—3161no—
881D4—3161no—
882D4—3161no—
883D4—3161no—
884D4—3161no—
885D4—3161no—
886D4—6321no—
887D4—6321no—
888D4—6321no—
889D4—6321no—
890D4—6321no—
891D4—6321no—
892D4—6321no—
893D4—6321no—
894D4—6321no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—84no—
922C2×C4—3162no—
923C2×C4—6321no—
924C2×C4—6321no—
925C2×C4—6321no—
926C2×C4—6321no—
927C2×C4—6321no—
928C2×C4—6321no—
929C2×C4—1581no—
930C2×C4—1581no—
931C2×C4—1581no—
932C2×C4—1581no—
933C2×C4—1581no—
934C2×C4C2×(C2×D79)⋊C411yescharacteristic
935C2×C4C2×(C2×D79)⋊C411yescharacteristic
936C2×C4C2×(C2×D79)⋊C411yescharacteristic
937C2×C4C2×(C2×D79)⋊C411yescharacteristic
938C2×C4C2×(C2×D79)⋊C411yescharacteristic
939C2×C4C2×(C2×D79)⋊C411yescharacteristic
940C2×C4C2×(C2×D79)⋊C411yescharacteristic
941C2×C4C2×(C2×D79)⋊C411yescharacteristic
942C2×C4C22×C4×D7911yescharacteristic
943C2×C4C22×D31611yescharacteristic
944C8—3161no—
945C8—3161no—
946C8—3161no—
947C8—3161no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—3161no—
966C22—3161no—
967C22—3161no—
968C22—3161no—
969C22—3161no—
970C22—3161no—
971C22—3161no—
972C22—3161no—
973C22—3161no—
974C22—12642no—
975C22—12642no—
976C22#1909858112yes—
977C22C22×(C2×D79)⋊C411yescharacteristic
978C22#1909936611yescharacteristic
979C22#1909937111yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—81no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—3161no—
995C4—3161no—
996C4—3161no—
997C4—3161no—
998C4—3161no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—6321no—
1006C2—6321no—
1007C2—6321no—
1008C2#2377186011yescharacteristic
1009C2#2377192311yescharacteristic
1010C2C2×#1909858111yescharacteristic
subgroupG/H
centerC22C22×(C2×D79)⋊C4
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2318C2
socleC22×C79C22×C22⋊C4
prime radical#23777432C2
cosocleC22×C4×C79C24
hypercenter#2318D79
hypocenterC79#17597
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #23772435C2semidirect
3. #23761975C2semidirect
4. #23761967C2semidirect
5. #23761959C2semidirect
6. #23761954C2semidirect
7. #23761946C2semidirect
8. #23761941C2semidirect
9. #23761936C2semidirect
10. #23761928C2semidirect
11. #23761915C2semidirect
12. #23761902C2semidirect
13. #23761889C2semidirect
14. C2×#19098296C2semidirect
15. C79×#2318C2semidirect
16. #19099278C4semidirect
17. #19099270C4semidirect
19. #19099259C4semidirect
20. #19099259C4semidirect
21. #19099234C4semidirect
22. #19099209C4semidirect
23. #19099209C4semidirect
26. D4×D316C4semidirect
42. #19098620C22semidirect
43. #19098616C22semidirect
44. #19098527C22semidirect
45. #19098527C22semidirect
46. C2×C22⋊(C79⋊C8)C22semidirect
47. C2×C22⋊(C79⋊C8)C22semidirect
48. #19098299C22semidirect
49. #19098299C22semidirect
50. #19098299C22semidirect
51. #19098299C22semidirect
56. #19098296C22semidirect
57. #19098296C22semidirect
58. #19098296C22semidirect
59. #19098296C22semidirect
60. #19098296C22semidirect
61. #19098296C22semidirect
62. #19098296C22semidirect
63. #19098296C22semidirect
69. #383×C79C22semidirect
70. #382×C79C22semidirect
71. #381×C79C22semidirect
72. #380×C79C22semidirect
73. C4×C22⋊C4×C79C22semidirect
74. C2×#95×C79C22semidirect
77. C2×#11929624C2×C4semidirect
79. C22×D316C2×C4semidirect
87. #14579161C2×C4semidirect
88. #14579158C2×C4semidirect
93. #14579153C2×C4semidirect
96. #14579149C2×C4semidirect
107. #14579140C2×C4semidirect
120. #14579135C2×C4semidirect
121. #14579135C2×C4semidirect
122. #14579135C2×C4semidirect
139. C4×Dic158C2×C4semidirect
141. C4×D316C2×C4semidirect
142. C4×D316C2×C4semidirect
143. C4×D316C2×C4semidirect
154. #14579120C2×C4semidirect
158. C2×C4⋊Dic79C2×C4semidirect
508. #2318D79semidirect
521. C79#17597semidirect
559. #383C2×D79semidirect
560. #382C2×D79semidirect
561. #381C2×D79semidirect
562. #380C2×D79semidirect
563. C4×C22⋊C4C2×D79semidirect
564. C2×#95C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237774322
#237724352
#237619752
#237619672
#237619592
#237619542
#237619462
#237619412
#237619362
#237619282
#237619152
#237619022
#237618892
C2×#190982962
C79×#23182
#1759779