Finite Group Databasebeta

← #34183734

Subgroups — #34183734

Order 20224.

546 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C79⋊C8C211yesmaximal, characteristic, complemented
2C4×#14579186C211yesmaximal, characteristic
3C2×#19098290C211yesmaximal, characteristic, complemented
4#23761720C211yesmaximal, characteristic, complemented
5#23761250C211yesmaximal, characteristic, complemented
6#23761236C211yesmaximal, characteristic, complemented
7C79×#1477C211yesmaximal, characteristic, complemented
8C2×#14579186C411yescharacteristic
9C2×C4×D316C2211yescharacteristic
10Q8×C79⋊C8—21no—
11#19098673—21no—
12#19098661—21no—
13C4×#11929611—21no—
14C4×#11929609—21no—
15D4×C79⋊C8—22no—
16D4×C79⋊C8—21no—
17#19098616—21no—
18#19098616C2211yescharacteristic
19#19098606C411yescharacteristic
20#19098567C411yescharacteristic
21#19098564C411yescharacteristic
22C4×#11929608C2211yescharacteristic
23C2×C4×C79⋊C8—21no—
24C2×C4×C79⋊C8C2211yescharacteristic
25#19098290—21no—
26#19098290—21no—
27#19098286—22no—
28C4×#41×C79C2211yescharacteristic
29#431×C79C2211yescharacteristic
30C2×C4⋊C8×C79C2211yescharacteristic
31Q8⋊C8×C79—21no—
32D4⋊C8×C79—21no—
33C22×D316C2×C411yescharacteristic
34C22×C4×D79—21no—
35#14579186—22no—
36#14579186C814yescomplemented
37C2×#11929611—21no—
38C2×#11929609—21no—
39C2×#11929608C2×C411yescharacteristic
40C2×#11929608C2×C411yescharacteristic
41C22×C79⋊C8—22no—
42C22×C79⋊C8—21no—
43C4×D316—21no—
44C4×D316—21no—
45C4×D316—21no—
46C4×D316—21no—
47C2×C4⋊Dic79C2×C411yescharacteristic
48C2×(C2×D79)⋊C4—21no—
49#14579094—21no—
50#14579092—21no—
51C4⋊(C79⋊C8)—22no—
52C4⋊(C79⋊C8)—21no—
53#14579085—21no—
54#14579082—21no—
55#14579081—21no—
56#14579081—21no—
57C22⋊(C79⋊C8)—22no—
58C22⋊(C79⋊C8)D412yes—
59#14579072—21no—
60C4×C79⋊C8—22no—
61C4×C79⋊C8—21no—
62C4×C79⋊C8—21no—
63C4×C79⋊C8—21no—
64C4×C79⋊C8D411yescharacteristic
65C4×C79⋊C8D411yescharacteristic
66C2×#41×C79C2×C411yescharacteristic
67C22×C8×C79—21no—
68C4×Q8×C79D411yescharacteristic
69C4×Q8×C79D411yescharacteristic
70C4×D4×C79—21no—
71C4×D4×C79—21no—
72C4×D4×C79D411yescharacteristic
73C4×D4×C79D411yescharacteristic
74#117×C79—21no—
75#117×C79C2×C411yescharacteristic
76C2×C42×C79—21no—
77C2×C42×C79C2311yescharacteristic
78C4⋊C8×C79—21no—
79C4⋊C8×C79—21no—
80C4⋊C8×C79—21no—
81C22⋊C8×C79—21no—
82C4×C8×C79—21no—
83C23×D79—21no—
84C2×D316—21no—
85C2×D316—21no—
86C2×D316—21no—
87C2×D316—21no—
88C2×D316—21no—
89C2×D316C2×C812yescomplemented
90C22×Dic79—21no—
91C2×C4×D79—41no—
92C2×C4×D79—41no—
93C2×C4×D79—81no—
94C2×C4×D79—81no—
95#11929611—24no—
96#11929609—24no—
97#11929608—21no—
98#11929608—21no—
99#11929608—21no—
100#11929608C2×C812yescomplemented
101C2×C79⋊C8—21no—
102C2×C79⋊C8—21no—
103C2×C79⋊C8—21no—
104C2×C79⋊C8—22no—
105C2×C79⋊C8—21no—
106C2×C79⋊C8—42no—
107C2×C79⋊C8—44no—
108C4⋊Dic79—21no—
109C4⋊Dic79—21no—
110(C2×D79)⋊C4—41no—
111(C2×D79)⋊C4—41no—
112#41×C79—21no—
113#41×C79—21no—
114#41×C79C2×C812yes—
115#41×C79M1612yes—
116C2×Q8×C79C22⋊C411yescharacteristic
117C2×D4×C79—21no—
118C2×D4×C79C22⋊C411yescharacteristic
119C22×C4×C79—21no—
120C22×C4×C79—21no—
121C22×C4×C79—21no—
122C22×C4×C79C22×C411yescharacteristic
123C22×C4×C79C2×D411yescharacteristic
124C22×C4×C79#4111yescharacteristic
125C2×C8×C79—41no—
126C2×C8×C79—41no—
127C2×C8×C79—81no—
128C4⋊C4×C79—21no—
129C4⋊C4×C79—21no—
130C4⋊C4×C79C22⋊C411yescharacteristic
131C4⋊C4×C79C22⋊C411yescharacteristic
132C22⋊C4×C79—21no—
133C22⋊C4×C79—21no—
134C22⋊C4×C79—21no—
135C42×C79—21no—
136C42×C79—21no—
137C42×C79—21no—
138C42×C79C2×D411yescharacteristic
139C42×C79C2×D411yescharacteristic
140C42×C79C2×D411yescharacteristic
141C42×C79#4111yescharacteristic
142C23×C79—21no—
143C23×C79C4×D411yescharacteristic
144C22×D79—22no—
145C22×D79—41no—
146C22×D79—41no—
147C22×D79—81no—
148C22×D79—81no—
149Q8×C79—21no—
150Q8×C79C22⋊C812yes—
151D4×C79—22no—
152D4×C79—22no—
153D4×C79—21no—
154D4×C79C22⋊C812yes—
155C2×C4×C79—21no—
156C2×C4×C79—22no—
157C2×C4×C79—22no—
158C2×C4×C79—21no—
159C2×C4×C79—21no—
160C2×C4×C79—21no—
161C2×C4×C79—21no—
162C2×C4×C79—41no—
163C2×C4×C79—42no—
164C2×C4×C79—41no—
165C2×C4×C79—41no—
166C2×C4×C79C2×C22⋊C411yescharacteristic
167C2×C4×C79C4×D411yescharacteristic
168C2×C4×C79#12011yescharacteristic
169C2×C4×C79#12111yescharacteristic
170C2×C4×C79#12111yescharacteristic
171C2×C4×C79#12311yescharacteristic
172C2×C4×C79C22×C811yescharacteristic
173C2×C4×C79C2×M1611yescharacteristic
174C2×C4×C79#13111yescharacteristic
175C2×C4×C79#13111yescharacteristic
176C2×Dic79—41no—
177C2×Dic79—81no—
178D316—22no—
179D316—22no—
180D316—41no—
181D316—41no—
182C4×D79—82no—
183C4×D79—81no—
184C4×D79—81no—
185C8×C79—81no—
186C8×C79—81no—
187C79⋊C8—22no—
188C79⋊C8—22no—
189C79⋊C8—42no—
190C79⋊C8—41no—
191C79⋊C8—41no—
192C22×C79—21no—
193C22×C79—21no—
194C22×C79—22no—
195C22×C79—41no—
196C22×C79—41no—
197C22×C79#38611yescharacteristic
198C22×C79C8×D411yescharacteristic
199C22×C79#43511yescharacteristic
200C2×D79—42no—
201C2×D79—82no—
202C2×D79—81no—
203C2×D79—81no—
204C2×D79—82no—
205C4×C79—22no—
206C4×C79—21no—
207C4×C79—21no—
208C4×C79—21no—
209C4×C79—41no—
210C4×C79—41no—
211C4×C79C2×C22⋊C811yescharacteristic
212C4×C79#40811yescharacteristic
213C4×C79C8×D411yescharacteristic
214C4×C79#43511yescharacteristic
215C4×C79#47111yescharacteristic
216C4×C79#47211yescharacteristic
217Dic79—81no—
218#9095—791nomaximal, Sylow
219C2×C79—21no—
220C2×C79—21no—
221C2×C79—42no—
222C2×C79#186911yescharacteristic
223C2×C79#190611yescharacteristic
224C2×C79#190711yescharacteristic
225D79—82no—
226C8×#41—791no—
227C4×AGL(1,ℤ/8)—791no—
228#1477D7911yescharacteristic, complemented
229C2×D4⋊C8—791no—
230#1460—791no—
231#1283—791no—
232#1278—791no—
233C79#909511yescharacteristic, complemented, Sylow
234C2×AGL(1,ℤ/8)—791no—
235C4×#41C2×D7911yescharacteristic
236C2×C4×D4—791no—
237C8×Q8—1581no—
238#442—1581no—
239#440—1581no—
240C4×SD16—1581no—
241C4×D8—1581no—
242C8×D4—1582no—
243C8×D4—1581no—
244#431—791no—
245#431—1581no—
246#431C2×D7911yescharacteristic
247#428—791no—
248C2×C4⋊C8C2×D7911yescharacteristic
249#418—791no—
250#417—791no—
251C4×M16—791no—
252C2×C4×C8—791no—
253C2×C4×C8—1581no—
254Q8⋊C8—21no—
255D4⋊C8—21no—
256D4⋊C8—1581no—
257D4⋊C8—1581no—
258#323—1582no—
259C2×#41C4×D7911yescharacteristic
260C22×D4—791no—
261C23×C4—1581no—
262AGL(1,ℤ/8)—794no—
263AGL(1,ℤ/8)—1582no—
264C2×SD16—1581no—
265C2×D8—1581no—
266C2×M16—791no—
267C2×M16—791no—
268C22×C8—21no—
269C22×C8—1582no—
270C22×C8—1581no—
271C4×Q8D31611yescharacteristic
272C4×Q8C22⋊D7911yescharacteristic
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—1581no—
276C4×D4—1581no—
277C4×D4—1581no—
278C4×D4—1581no—
279C4×D4D31611yescharacteristic
280C4×D4C22⋊D7911yescharacteristic
281#117—21no—
282#117C4×D7911yescharacteristic
283C2×C4⋊C4—791no—
284C2×C22⋊C4—1581no—
285C2×C42—21no—
286C2×C42C22×D7911yescharacteristic
287#107—1581no—
288#106—1581no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—1582no—
293C4⋊C8—1581no—
294#103—1581no—
295#102—1581no—
296#102—1581no—
297#102—1581no—
298C22⋊C8—21no—
299C22⋊C8—792no—
300C22⋊C8—1582no—
301#97—1581no—
302C4×C8—21no—
303C4×C8—791no—
304C4×C8—791no—
305C4×C8—1582no—
306C4×C8—1581no—
307C4×C8—1581no—
308C4×C8—1581no—
309C24—1581no—
310#41—21no—
311#41—21no—
312#41C8×D7912yes—
313#41#1192960712yes—
314C2×Q8(C2×D79)⋊C411yescharacteristic
315C2×D4—21no—
316C2×D4—792no—
317C2×D4—1581no—
318C2×D4—1581no—
319C2×D4—1581no—
320C2×D4—1581no—
321C2×D4—1581no—
322C2×D4(C2×D79)⋊C411yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—3161no—
327C22×C4—3161no—
328C22×C4—6321no—
329C22×C4—6321no—
330C22×C4—1581no—
331C22×C4C2×C4×D7911yescharacteristic
332C22×C4D4×D7911yescharacteristic
333C22×C4#1192962311yescharacteristic
334SD16—1584no—
335D8—1584no—
336M16—792no—
337M16—1581no—
338M16—1581no—
339M16—1581no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—81no—
343C2×C8—3162no—
344C2×C8—3164no—
345C2×C8—1581no—
346C2×C8—1581no—
347C2×C8—1582no—
348C2×C8—1581no—
349C2×C8—1581no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—1581no—
353C4⋊C4—1581no—
354C4⋊C4(C2×D79)⋊C411yescharacteristic
355C4⋊C4(C2×D79)⋊C411yescharacteristic
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—3161no—
360C22⋊C4—3161no—
361C42—21no—
362C42—21no—
363C42—21no—
364C42D4×D7911yescharacteristic
365C42C2×C22⋊D7911yescharacteristic
366C42C2×D31611yescharacteristic
367C42#1192962311yescharacteristic
368C23—21no—
369C23—3161no—
370C23—3161no—
371C23—6321no—
372C23—6321no—
373C23—1582no—
374C23(C22⋊D79)⋊C411yescharacteristic
375Q8—21no—
376Q8(C2×D79)⋊C812yes—
377D4—22no—
378D4—22no—
379D4—21no—
380D4—3161no—
381D4—3161no—
382D4—1582no—
383D4—1582no—
384D4(C2×D79)⋊C812yes—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—3161no—
397C2×C4—6322no—
398C2×C4—6321no—
399C2×C4—6321no—
400C2×C4—6321no—
401C2×C4C2×(C2×D79)⋊C411yescharacteristic
402C2×C4(C22⋊D79)⋊C411yescharacteristic
403C2×C4#1457913111yescharacteristic
404C2×C4#1457913311yescharacteristic
405C2×C4#1457913311yescharacteristic
406C2×C4#1457914511yescharacteristic
407C2×C4C2×C8×D7911yescharacteristic
408C2×C4C2×#1192960711yescharacteristic
409C2×C4#1457916911yescharacteristic
410C2×C4#1457916911yescharacteristic
411C8—81no—
412C8—81no—
413C8—3161no—
414C8—3162no—
415C8—3161no—
416C8—1582no—
417C8—1582no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—3162no—
424C22—6322no—
425C22—6322no—
426C22—6321no—
427C22—6321no—
428C22#1909844011yescharacteristic
429C22(C22⋊D79)⋊C811yescharacteristic
430C22#1909863111yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—22no—
435C4—41no—
436C4—41no—
437C4—6321no—
438C4C2×(C2×D79)⋊C811yescharacteristic
439C4#1909853111yescharacteristic
440C4(C22⋊D79)⋊C811yescharacteristic
441C4#1909863111yescharacteristic
442C4#1909882811yescharacteristic
443C4#1909883111yescharacteristic
444C2—21no—
445C2—21no—
446C2—42no—
447C2—6322no—
448C2#2376369011yescharacteristic
449C2#2376389911yescharacteristic
450C2#2376390611yescharacteristic
subgroupG/H
centerC2×C4#14579133
commutatorC2×C4×C79C22×C8
FrattiniC2×C42C22×D79
FittingC79×#1477C2
socleC22×C79#386
prime radicalC2×#14579186C4
cosocleC2×C42×C79C23
hypercenter#1477D79
hypocenterC79#9095
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
1. #41×C79⋊C8C2semidirect
3. C2×#19098290C2semidirect
4. #23761720C2semidirect
5. #23761250C2semidirect
6. #23761236C2semidirect
7. C79×#1477C2semidirect
36. #14579186C8semidirect
89. C2×D316C2×C8semidirect
100. #11929608C2×C8semidirect
228. #1477D79semidirect
233. C79#9095semidirect

Maximal subgroups

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

subgroupindex
#41×C79⋊C82
C4×#145791862
C2×#190982902
#237617202
#237612502
#237612362
C79×#14772
#909579