Finite Group Databasebeta

← #34184585

Subgroups — #34184585

Order 20224.

452 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772058C211yesmaximal, characteristic
2#23763499C211yesmaximal, characteristic
3#23761920C211yesmaximal, characteristic
4#23761764C211yesmaximal, characteristic
5#23761277C211yesmaximal, characteristic
6#23761247C211yesmaximal, characteristic
7C2×#485×C79C211yesmaximal, characteristic
8#19098624—22no—
9#19098620—21no—
10#19098616—21no—
11#19098590—21no—
12#19098527C2211yescharacteristic
13#19098527C2211yescharacteristic
14C2×C22⋊(C79⋊C8)C2211yescharacteristic
15#19098519—21no—
16C4×C22⋊Dic79C2211yescharacteristic
17#19098322—21no—
18#19098322—21no—
19#19098300—22no—
20#19098289—21no—
21#19098289—21no—
22C2×C22⋊Q8×C79C2211yescharacteristic
23C2×#117×C79C2211yescharacteristic
24#485×C79—21no—
25#485×C79—21no—
26#485×C79—21no—
27#485×C79—21no—
28C2×#107×C79C411yescharacteristic, complemented
29C2×#106×C79C411yescharacteristic, complemented
30C2×#103×C79C411yescharacteristic, complemented
31C2×#103×C79C411yescharacteristic, complemented
32C2×C22⋊C8×C79C2211yescharacteristic
33C2×#11929608—21no—
34C2×#11929608—21no—
35C22×C79⋊C8—21no—
36C2×C22⋊Dic79—21no—
37C2×C4×Dic79—21no—
38C4⋊(C79⋊C8)—22no—
39C4⋊(C79⋊C8)—22no—
40C22⋊(C79⋊C8)—21no—
41C22⋊(C79⋊C8)—21no—
42C22⋊(C79⋊C8)—21no—
43C22⋊(C79⋊C8)—21no—
44C22⋊(C79⋊C8)D412yes—
45C22⋊(C79⋊C8)D411yescharacteristic
46C22⋊(C79⋊C8)D411yescharacteristic
47#14579072—22no—
48C4×C79⋊C8—22no—
49C79⋊#95—21no—
50C22×Q8×C79C2×C411yescharacteristic
51C23×C4×C79C2311yescharacteristic
52C22×C8×C79C2×C411yescharacteristic
53C22×C8×C79C2×C411yescharacteristic
54C22⋊Q8×C79—21no—
55C22⋊Q8×C79—21no—
56C22⋊Q8×C79—21no—
57C22⋊Q8×C79—21no—
58#117×C79—21no—
59#117×C79—21no—
60#117×C79D411yescharacteristic
61#117×C79D411yescharacteristic
62#117×C79D411yescharacteristic
63#117×C79D411yescharacteristic
64C2×C4⋊C4×C79—21no—
65C2×C4⋊C4×C79C2×C411yescharacteristic
66C2×C4⋊C4×C79C2×C411yescharacteristic
67C2×C4⋊C4×C79C2×C411yescharacteristic
68C2×C22⋊C4×C79—21no—
69C2×C22⋊C4×C79—21no—
70C2×C42×C79—21no—
71#107×C79—21no—
72#107×C79—21no—
73#106×C79—21no—
74#106×C79—21no—
75#103×C79—21no—
76#103×C79—21no—
77#103×C79—21no—
78#103×C79—21no—
79C22⋊C8×C79—21no—
80C22⋊C8×C79—21no—
81C22×Dic79—41no—
82#11929608—41no—
83#11929608—41no—
84#11929608—41no—
85#11929608—41no—
86C2×C79⋊C8—21no—
87C2×C79⋊C8—22no—
88C2×C79⋊C8—21no—
89C2×C79⋊C8—41no—
90C2×C79⋊C8—41no—
91C2×C79⋊C8—41no—
92C22⋊Dic79—22no—
93C22⋊Dic79—41no—
94C4×Dic79—41no—
95C4×Dic79—41no—
96C24×C79#4111yescharacteristic
97C2×Q8×C79—21no—
98C2×Q8×C79—21no—
99C2×Q8×C79—41no—
100C2×Q8×C79—41no—
101C22×C4×C79—21no—
102C22×C4×C79—21no—
103C22×C4×C79—21no—
104C22×C4×C79—21no—
105C22×C4×C79—41no—
106C22×C4×C79—41no—
107C22×C4×C79C22×C411yescharacteristic
108C22×C4×C79C2×D411yescharacteristic
109C22×C4×C79C2×D411yescharacteristic
110C22×C4×C79C2×D411yescharacteristic
111C22×C4×C79C2×D411yescharacteristic
112C22×C4×C79#4111yescharacteristic
113C2×C8×C79—21no—
114C2×C8×C79—21no—
115C2×C8×C79—41no—
116C2×C8×C79—41no—
117C4⋊C4×C79—21no—
118C4⋊C4×C79—21no—
119C4⋊C4×C79—21no—
120C4⋊C4×C79—21no—
121C4⋊C4×C79—41no—
122C4⋊C4×C79—41no—
123C4⋊C4×C79C22⋊C411yescharacteristic
124C4⋊C4×C79C22⋊C411yescharacteristic
125C4⋊C4×C79C22⋊C411yescharacteristic
126C4⋊C4×C79C22⋊C411yescharacteristic
127C22⋊C4×C79—21no—
128C22⋊C4×C79—21no—
129C22⋊C4×C79—21no—
130C22⋊C4×C79—21no—
131C22⋊C4×C79—41no—
132C22⋊C4×C79—41no—
133C42×C79—21no—
134C42×C79—21no—
135C42×C79—21no—
136C42×C79—21no—
137C23×C79—21no—
138C23×C79—21no—
139C23×C79—41no—
140C23×C79—41no—
141C23×C79C4×D411yescharacteristic
142C23×C79#12111yescharacteristic
143C23×C79#12311yescharacteristic
144Q8×C79—41no—
145Q8×C79—41no—
146Q8×C79—81no—
147C2×C4×C79—21no—
148C2×C4×C79—21no—
149C2×C4×C79—21no—
150C2×C4×C79—21no—
151C2×C4×C79—21no—
152C2×C4×C79—21no—
153C2×C4×C79—21no—
154C2×C4×C79—21no—
155C2×C4×C79—21no—
156C2×C4×C79—21no—
157C2×C4×C79—41no—
158C2×C4×C79—41no—
159C2×C4×C79—41no—
160C2×C4×C79—41no—
161C2×C4×C79—41no—
162C2×C4×C79—41no—
163C2×C4×C79—41no—
164C2×C4×C79—41no—
165C2×C4×C79—41no—
166C2×C4×C79—81no—
167C2×C4×C79—81no—
168C2×C4×C79C2×C22⋊C411yescharacteristic
169C2×C4×C79C4×D411yescharacteristic
170C2×C4×C79#12011yescharacteristic
171C2×C4×C79#12111yescharacteristic
172C2×Dic79—42no—
173C2×Dic79—81no—
174C2×Dic79—81no—
175C8×C79—41no—
176C8×C79—41no—
177C79⋊C8—41no—
178C79⋊C8—41no—
179C79⋊C8—42no—
180C79⋊C8—81no—
181C22×C79—21no—
182C22×C79—21no—
183C22×C79—21no—
184C22×C79—21no—
185C22×C79—21no—
186C22×C79—21no—
187C22×C79—21no—
188C22×C79—21no—
189C22×C79—81no—
190C22×C79—81no—
191C22×C79#38611yescharacteristic
192C22×C79#44311yescharacteristic
193C22×C79#44411yescharacteristic
194C4×C79—21no—
195C4×C79—21no—
196C4×C79—21no—
197C4×C79—41no—
198C4×C79—41no—
199C4×C79—41no—
200C4×C79—41no—
201C4×C79—81no—
202C4×C79—81no—
203C4×C79#41011yescharacteristic
204C4×C79#41011yescharacteristic
205Dic79—82no—
206#9240—791nomaximal, Sylow
207C2×C79—21no—
208C2×C79—21no—
209C2×C79—41no—
210C2×C79—41no—
211C2×C79#187611yescharacteristic
212C2×C79#189911yescharacteristic
213C2×C79#190211yescharacteristic
214C2×#485D7911yescharacteristic
215#2924—791no—
216#1826—791no—
217#1508—791no—
218#1472—791no—
219#1293—791no—
220#1282—791no—
221C79#924011yescharacteristic, complemented, Sylow
222C2×C22⋊Q8C2×D7911yescharacteristic
223C2×#117C2×D7911yescharacteristic
224#485—21no—
225#485—21no—
226#485—21no—
227#485—21no—
228#433—1582no—
229#432—1581no—
230#431—1581no—
231C2×#107Dic7911yescharacteristic, complemented
232C2×#106Dic7911yescharacteristic, complemented
233#424—1581no—
234C2×#103Dic7911yescharacteristic, complemented
235C2×#103Dic7911yescharacteristic, complemented
236#407—791no—
237#407—791no—
238C2×C22⋊C8—791no—
239C2×C22⋊C8C2×D7911yescharacteristic
240#405—1581no—
241C4×C22⋊C4—791no—
242#339—1581no—
243#339—1581no—
244#328—1582no—
245#324—1581no—
246#324—1581no—
247C22×Q8C2×Dic7911yescharacteristic
248C23×C4C22×D7911yescharacteristic
249C2×M16—1581no—
250C2×M16—1581no—
251C22×C8—1581no—
252C22×C8C2×Dic7911yescharacteristic
253C22×C8C2×Dic7911yescharacteristic
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#117—21no—
259#117—21no—
260#117C22⋊D7911yescharacteristic
261#117C22⋊D7911yescharacteristic
262#117C22⋊D7911yescharacteristic
263#117C22⋊D7911yescharacteristic
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×Dic7911yescharacteristic
266C2×C4⋊C4C2×Dic7911yescharacteristic
267C2×C4⋊C4C2×Dic7911yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—1581no—
271C2×C42—21no—
272C2×C42—1581no—
273#107—21no—
274#107—21no—
275#106—21no—
276#106—21no—
277C4⋊C8—1582no—
278C4⋊C8—1582no—
279#103—21no—
280#103—21no—
281#103—21no—
282#103—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—791no—
286C22⋊C8—791no—
287C22⋊C8—792no—
288C22⋊C8—1581no—
289C22⋊C8—1581no—
290C22⋊C8—1581no—
291C22⋊C8—1581no—
292#97—1582no—
293C4×C8—1582no—
294#95—1581no—
295C24#1192962311yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—3161no—
307C22×C4C22×Dic7911yescharacteristic
308C22×C4D4×D7911yescharacteristic
309C22×C4D4×D7911yescharacteristic
310C22×C4C2×C22⋊D7911yescharacteristic
311C22×C4C2×C22⋊D7911yescharacteristic
312C22×C4#1192962311yescharacteristic
313M16—3161no—
314M16—3161no—
315M16—3161no—
316M16—3161no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—3161no—
322C2×C8—3161no—
323C2×C8—3161no—
324C2×C8—1581no—
325C2×C8—1582no—
326C2×C8—1581no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊Dic7911yescharacteristic
334C4⋊C4C22⋊Dic7911yescharacteristic
335C4⋊C4C22⋊Dic7911yescharacteristic
336C4⋊C4C22⋊Dic7911yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—3161no—
344C22⋊C4—1582no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—3161no—
350C42—3161no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23D4×Dic7911yescharacteristic
356C23#1457913311yescharacteristic
357C23#1457914211yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—3162no—
383C2×C4—6321no—
384C2×C4—6321no—
385C2×C4C2×C22⋊Dic7911yescharacteristic
386C2×C4D4×Dic7911yescharacteristic
387C2×C4#1457912911yescharacteristic
388C2×C4#1457913311yescharacteristic
389C8—41no—
390C8—41no—
391C8—3161no—
392C8—3161no—
393C8—3162no—
394C8—6321no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#1909844311yescharacteristic
406C22#1909868011yescharacteristic
407C22#1909868511yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—81no—
417C4—6322no—
418C4#1909853711yescharacteristic
419C4#1909853711yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#2376372911yescharacteristic
425C2#2376385911yescharacteristic
426C2#2376387511yescharacteristic
subgroupG/H
centerC22#19098443
commutatorC22×C4×C79C22×C4
FrattiniC23×C4C22×D79
FittingC2×#485×C79C2
socleC22×C79#386
prime radicalC24×C79#41
cosocleC23×C4×C79C23
hypercenterC2×#485D79
hypocenterC79#9240
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
28. C2×#107×C79C4semidirect
29. C2×#106×C79C4semidirect
30. C2×#103×C79C4semidirect
31. C2×#103×C79C4semidirect
221. C79#9240semidirect
231. C2×#107Dic79semidirect
232. C2×#106Dic79semidirect
234. C2×#103Dic79semidirect
235. C2×#103Dic79semidirect

Maximal subgroups

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

subgroupindex
#237720582
#237634992
#237619202
#237617642
#237612772
#237612472
C2×#485×C792
#924079