Finite Group Databasebeta

← #34183485

Subgroups — #34183485

Order 20224.

488 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772539C211yesmaximal, characteristic, complemented
2#23764199C211yesmaximal, characteristic, complemented
3#23761988C211yesmaximal, characteristic, complemented
4#23761843C211yesmaximal, characteristic, complemented
5#23761300C211yesmaximal, characteristic, complemented
6#23761249C211yesmaximal, characteristic, complemented
7C79×#3105C211yesmaximal, characteristic
8#19098694—21no—
9#19098635—21no—
10#19098635—21no—
11D4×C79⋊C8—21no—
12#19098624—21no—
13#19098620C2211yescharacteristic
14#19098590—21no—
15C2×C4⋊(C79⋊C8)C2211yescharacteristic
16C2×C22⋊(C79⋊C8)—21no—
17C2×C22⋊(C79⋊C8)—21no—
18C4×#11929608C2211yescharacteristic
19C2×#14579072C2211yescharacteristic
20#19098305—21no—
21#19098303—21no—
22D4⋊(C79⋊C8)—21no—
23D4⋊(C79⋊C8)—21no—
24#529×C79C2211yescharacteristic
25C2×C4×D4×C79C2211yescharacteristic
26#484×C79C411yescharacteristic
27#481×C79C411yescharacteristic
28#478×C79—21no—
29#463×C79—21no—
30#450×C79C411yescharacteristic
31#447×C79C411yescharacteristic
32C4×SD16×C79—21no—
33C4×D8×C79—21no—
34#431×C79C2211yescharacteristic
35C2×#11929608—21no—
36C2×#11929608—21no—
37C22×C79⋊C8—21no—
38C22×C79⋊C8—21no—
39C22×C79⋊C8D411yescharacteristic
40C22×C79⋊C8D411yescharacteristic
41C4⋊(C79⋊C8)—21no—
42C4⋊(C79⋊C8)—21no—
43C4⋊(C79⋊C8)—21no—
44C4⋊(C79⋊C8)—21no—
45C4⋊(C79⋊C8)D411yescharacteristic
46C4⋊(C79⋊C8)D411yescharacteristic
47C22⋊(C79⋊C8)—21no—
48C22⋊(C79⋊C8)—21no—
49C22⋊(C79⋊C8)—21no—
50C22⋊(C79⋊C8)—42no—
51C22⋊(C79⋊C8)—42no—
52#14579072—21no—
53#14579072—21no—
54#14579072—21no—
55#14579072—21no—
56#14579072—21no—
57C4×C79⋊C8—21no—
58C4×C79⋊C8—21no—
59C22×D4×C79C2×C411yescharacteristic
60C23×C4×C79—21no—
61C2×SD16×C79—21no—
62C2×D8×C79—21no—
63#126×C79—21no—
64#125×C79D411yescharacteristic
65#124×C79D411yescharacteristic
66#123×C79—21no—
67C22⋊Q8×C79C2×C411yescharacteristic
68#121×C79C2×C411yescharacteristic
69C4×Q8×C79D411yescharacteristic
70C4×D4×C79—21no—
71C4×D4×C79—21no—
72C4×D4×C79—21no—
73C4×D4×C79—21no—
74C4×D4×C79—21no—
75C4×D4×C79D411yescharacteristic
76#117×C79—21no—
77C2×C4⋊C4×C79C2×C411yescharacteristic
78C2×C22⋊C4×C79—21no—
79C2×C42×C79C2311yescharacteristic
80#107×C79—21no—
81#106×C79—21no—
82C4⋊C8×C79—21no—
83#103×C79—21no—
84#102×C79—21no—
85#102×C79—21no—
86#102×C79—21no—
87C22⋊C8×C79C2×C411yescharacteristic
88C22⋊C8×C79C2×C411yescharacteristic
89C4×C8×C79—21no—
90#11929608—22no—
91#11929608—41no—
92#11929608—81no—
93C2×C79⋊C8—22no—
94C2×C79⋊C8—21no—
95C2×C79⋊C8—21no—
96C2×C79⋊C8—21no—
97C2×C79⋊C8—21no—
98C2×C79⋊C8—41no—
99C2×C79⋊C8—41no—
100C2×C79⋊C8—41no—
101C2×C79⋊C8—41no—
102C2×C79⋊C8—41no—
103C2×C79⋊C8—81no—
104C24×C79—21no—
105C2×Q8×C79C22⋊C411yescharacteristic
106C2×D4×C79—21no—
107C2×D4×C79—21no—
108C2×D4×C79—21no—
109C2×D4×C79—42no—
110C2×D4×C79C22⋊C411yescharacteristic
111C22×C4×C79—21no—
112C22×C4×C79—21no—
113C22×C4×C79—41no—
114C22×C4×C79—41no—
115C22×C4×C79—41no—
116C22×C4×C79—41no—
117C22×C4×C79—41no—
118C22×C4×C79—41no—
119C22×C4×C79C22×C411yescharacteristic
120C22×C4×C79C2×D411yescharacteristic
121C22×C4×C79#4111yescharacteristic
122SD16×C79—42no—
123D8×C79—42no—
124C2×C8×C79—21no—
125C2×C8×C79—21no—
126C4⋊C4×C79—21no—
127C4⋊C4×C79—21no—
128C4⋊C4×C79—21no—
129C4⋊C4×C79—21no—
130C4⋊C4×C79—21no—
131C4⋊C4×C79—21no—
132C4⋊C4×C79C22⋊C411yescharacteristic
133C4⋊C4×C79C22⋊C411yescharacteristic
134C22⋊C4×C79—21no—
135C22⋊C4×C79—21no—
136C22⋊C4×C79—21no—
137C22⋊C4×C79—21no—
138C22⋊C4×C79—21no—
139C22⋊C4×C79—41no—
140C22⋊C4×C79—41no—
141C42×C79—21no—
142C42×C79C2×D411yescharacteristic
143C42×C79C2×D411yescharacteristic
144C42×C79C2×D411yescharacteristic
145C42×C79#4111yescharacteristic
146C23×C79—22no—
147C23×C79—21no—
148C23×C79—41no—
149C23×C79—41no—
150C23×C79—41no—
151C23×C79—41no—
152C23×C79—41no—
153C23×C79—41no—
154C23×C79C4×D411yescharacteristic
155Q8×C79—41no—
156D4×C79—22no—
157D4×C79—22no—
158D4×C79—41no—
159D4×C79—41no—
160D4×C79—41no—
161D4×C79—41no—
162D4×C79—41no—
163C2×C4×C79—21no—
164C2×C4×C79—21no—
165C2×C4×C79—21no—
166C2×C4×C79—21no—
167C2×C4×C79—21no—
168C2×C4×C79—21no—
169C2×C4×C79—21no—
170C2×C4×C79—41no—
171C2×C4×C79—41no—
172C2×C4×C79—41no—
173C2×C4×C79—41no—
174C2×C4×C79—41no—
175C2×C4×C79—41no—
176C2×C4×C79—81no—
177C2×C4×C79—81no—
178C2×C4×C79—81no—
179C2×C4×C79—81no—
180C2×C4×C79C2×C22⋊C411yescharacteristic
181C2×C4×C79C4×D411yescharacteristic
182C2×C4×C79#12011yescharacteristic
183C2×C4×C79#12111yescharacteristic
184C2×C4×C79#12111yescharacteristic
185C2×C4×C79#12311yescharacteristic
186C8×C79—41no—
187C8×C79—41no—
188C79⋊C8—42no—
189C79⋊C8—42no—
190C79⋊C8—41no—
191C79⋊C8—41no—
192C79⋊C8—41no—
193C79⋊C8—41no—
194C22×C79—21no—
195C22×C79—21no—
196C22×C79—42no—
197C22×C79—42no—
198C22×C79—41no—
199C22×C79—41no—
200C22×C79—42no—
201C22×C79—41no—
202C22×C79—81no—
203C22×C79—81no—
204C22×C79—81no—
205C22×C79—81no—
206C22×C79#38611yescharacteristic
207C22×C79#44311yescharacteristic
208C22×C79#44411yescharacteristic
209C4×C79—21no—
210C4×C79—21no—
211C4×C79—21no—
212C4×C79—21no—
213C4×C79—21no—
214C4×C79—41no—
215C4×C79—41no—
216C4×C79—41no—
217C4×C79—81no—
218C4×C79#45311yescharacteristic
219C4×C79#45411yescharacteristic
220#9052—791nomaximal, Sylow
221C2×C79—21no—
222C2×C79—21no—
223C2×C79—81no—
224C2×C79—82no—
225C2×C79#187611yescharacteristic
226C2×C79#188311yescharacteristic
227C2×C79#189111yescharacteristic
228#3105D7911yescharacteristic
229#2992—791no—
230#1955—791no—
231#1524—791no—
232#1490—791no—
233#1302—791no—
234#1283—791no—
235C79#905211yescharacteristic, complemented, Sylow
236#529C2×D7911yescharacteristic
237C2×C4×D4C2×D7911yescharacteristic
238#484Dic7911yescharacteristic
239#481Dic7911yescharacteristic
240#478—21no—
241#463—21no—
242#450Dic7911yescharacteristic
243#447Dic7911yescharacteristic
244#446—1581no—
245C4×SD16—21no—
246C4×D8—21no—
247#435—1581no—
248#435—1581no—
249C8×D4—1581no—
250#433—1581no—
251#432—791no—
252#431C2×D7911yescharacteristic
253#424—1581no—
254C2×C4⋊C8—791no—
255C2×C22⋊C8—1581no—
256C2×C22⋊C8—1581no—
257C4×M16—791no—
258C2×#97—791no—
259#330—1581no—
260#329—1581no—
261D4⋊C8—1581no—
262D4⋊C8—1581no—
263C22×D4C2×Dic7911yescharacteristic
264C23×C4—21no—
265C2×SD16—21no—
266C2×D8—21no—
267C2×M16—1581no—
268C2×M16—1581no—
269C22×C8—791no—
270C22×C8—791no—
271C22×C8—1581no—
272C22×C8—1581no—
273#126—21no—
274#125C22⋊D7911yescharacteristic
275#124C22⋊D7911yescharacteristic
276#123—21no—
277C22⋊Q8C2×Dic7911yescharacteristic
278#121C2×Dic7911yescharacteristic
279C4×Q8C22⋊D7911yescharacteristic
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4C22⋊D7911yescharacteristic
286#117—21no—
287C2×C4⋊C4C2×Dic7911yescharacteristic
288C2×C22⋊C4—21no—
289C2×C42C22×D7911yescharacteristic
290#107—21no—
291#106—21no—
292C4⋊C8—21no—
293C4⋊C8—791no—
294C4⋊C8—791no—
295C4⋊C8—1581no—
296C4⋊C8—1581no—
297C4⋊C8—1581no—
298C4⋊C8—1581no—
299#103—21no—
300#102—21no—
301#102—21no—
302#102—21no—
303C22⋊C8—3162no—
304C22⋊C8—3162no—
305C22⋊C8—1581no—
306C22⋊C8—1581no—
307C22⋊C8—1581no—
308C22⋊C8C2×Dic7911yescharacteristic
309C22⋊C8C2×Dic7911yescharacteristic
310#97—1581no—
311#97—1581no—
312#97—1581no—
313#97—1581no—
314#97—1581no—
315C4×C8—21no—
316C4×C8—1581no—
317C4×C8—1581no—
318C24—21no—
319C2×Q8C22⋊Dic7911yescharacteristic
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—42no—
324C2×D4C22⋊Dic7911yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4C22×Dic7911yescharacteristic
334C22×C4D4×D7911yescharacteristic
335C22×C4#1192962311yescharacteristic
336SD16—42no—
337D8—42no—
338M16—3161no—
339M16—6321no—
340M16—1582no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—3161no—
344C2×C8—3161no—
345C2×C8—3161no—
346C2×C8—3161no—
347C2×C8—3161no—
348C2×C8—6321no—
349C2×C8—1582no—
350C2×C8—1581no—
351C2×C8—1581no—
352C2×C8—1581no—
353C2×C8—1581no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4C22⋊Dic7911yescharacteristic
361C4⋊C4C22⋊Dic7911yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C42—21no—
370C42D4×D7911yescharacteristic
371C42C2×C22⋊D7911yescharacteristic
372C42C2×C22⋊D7911yescharacteristic
373C42#1192962311yescharacteristic
374C23—22no—
375C23—21no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23D4×Dic7911yescharacteristic
383Q8—41no—
384D4—22no—
385D4—22no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—41no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4C2×C22⋊Dic7911yescharacteristic
409C2×C4D4×Dic7911yescharacteristic
410C2×C4#1457912911yescharacteristic
411C2×C4#1457913311yescharacteristic
412C2×C4#1457913311yescharacteristic
413C2×C4#1457914211yescharacteristic
414C8—41no—
415C8—41no—
416C8—3162no—
417C8—3162no—
418C8—3161no—
419C8—3161no—
420C8—3161no—
421C8—3161no—
422C22—21no—
423C22—21no—
424C22—42no—
425C22—42no—
426C22—41no—
427C22—41no—
428C22—42no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22#1909844311yescharacteristic
435C22#1909868011yescharacteristic
436C22#1909868511yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—81no—
446C4#1909872911yescharacteristic
447C4#1909873411yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2#2376372911yescharacteristic
453C2#2376377811yescharacteristic
454C2#2376381911yescharacteristic
subgroupG/H
centerC2×C4#14579129
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#3105C2
socleC22×C79#386
prime radical#447×C79C4
cosocleC2×C42×C79C23
hypercenter#3105D79
hypocenterC79#9052
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
1. #23772539C2semidirect
2. #23764199C2semidirect
3. #23761988C2semidirect
4. #23761843C2semidirect
5. #23761300C2semidirect
6. #23761249C2semidirect
235. C79#9052semidirect

Maximal subgroups

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

subgroupindex
#237725392
#237641992
#237619882
#237618432
#237613002
#237612492
C79×#31052
#905279