Finite Group Databasebeta

← #34192067

Subgroups — #34192067

Order 20224.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098758C211yesmaximal, characteristic
2#23764206C211yesmaximal, characteristic, complemented
3#23763400C211yesmaximal, characteristic, complemented
4C2×#19098314C211yesmaximal, characteristic, complemented
5C2×#19098306C211yesmaximal, characteristic, complemented
6#23761284C211yesmaximal, characteristic, complemented
7C79×#1954C211yesmaximal, characteristic, complemented
8C22×#11929609—21no—
9C2×#14579158C2211yescharacteristic
10#19098758—22no—
11#19098758—22no—
12C2×C4⋊(C79⋊C8)C2211yescharacteristic
13C2×C4⋊(C79⋊C8)C2211yescharacteristic
14C2×#14579083—21no—
15C2×#14579083—21no—
16C2×#14579082—21no—
17C2×#14579081—21no—
18#19098433C2211yescharacteristic
19#19098325—21no—
20#19098314—22no—
21#19098306—22no—
22C2×C4×D4×C79C2211yescharacteristic
23C2×C4⋊C8×C79C2211yescharacteristic
24C2×C22⋊C8×C79—21no—
25C2×C22⋊C8×C79—21no—
26C2×C4×C8×C79C2211yescharacteristic
27C22×D316—21no—
28C22×D316—21no—
29C22×D316—21no—
30C2×#11929609—24no—
31C2×#11929609—42no—
32C2×#11929609—42no—
33C22×C79⋊C8—21no—
34C22×C79⋊C8—21no—
35#14579158—21no—
36#14579158—21no—
37#14579158—21no—
38#14579158D412yes—
39C2×C4⋊Dic79—21no—
40C2×C4⋊Dic79—21no—
41C2×C4⋊Dic79—21no—
42C4⋊(C79⋊C8)—21no—
43C4⋊(C79⋊C8)—21no—
44C4⋊(C79⋊C8)—21no—
45C4⋊(C79⋊C8)D412yes—
46#14579083—42no—
47#14579083—42no—
48#14579082—42no—
49#14579081—24no—
50C22×D4×C79D411yescharacteristic
51C23×C4×C79—21no—
52C22×C8×C79—21no—
53C22×C8×C79D411yescharacteristic
54C22×C8×C79D411yescharacteristic
55C4×D4×C79—21no—
56C4×D4×C79—21no—
57C4×D4×C79—21no—
58C4×D4×C79—21no—
59C2×C4⋊C4×C79D411yescharacteristic
60C2×C22⋊C4×C79—21no—
61C2×C42×C79C2311yescharacteristic
62C4⋊C8×C79—21no—
63C4⋊C8×C79—21no—
64C22⋊C8×C79—42no—
65C22⋊C8×C79—42no—
66C4×C8×C79—21no—
67C4×C8×C79—21no—
68C23×D79—41no—
69C2×D316—22no—
70C2×D316—22no—
71C2×D316—22no—
72C2×D316—41no—
73C2×D316—41no—
74C2×D316—41no—
75C2×D316—41no—
76C2×D316—41no—
77C2×D316—41no—
78C2×D316—41no—
79C2×D316—41no—
80C2×D316—41no—
81C2×D316—41no—
82C2×D316—41no—
83C2×D316—81no—
84C2×D316—81no—
85C22×Dic79—41no—
86#11929609—48no—
87C2×C79⋊C8—22no—
88C2×C79⋊C8—41no—
89C2×C79⋊C8—41no—
90C2×C79⋊C8—41no—
91C2×C79⋊C8—41no—
92C2×C79⋊C8—41no—
93C4⋊Dic79—41no—
94C4⋊Dic79—41no—
95C4⋊Dic79—41no—
96C4⋊Dic79—41no—
97C4⋊Dic79—81no—
98C24×C79—21no—
99C2×D4×C79—21no—
100C2×D4×C79—21no—
101C2×D4×C79—21no—
102C2×D4×C79—21no—
103C2×D4×C79—21no—
104C2×D4×C79SD1612yes—
105C22×C4×C79—21no—
106C22×C4×C79—41no—
107C22×C4×C79—41no—
108C22×C4×C79—41no—
109C22×C4×C79—41no—
110C22×C4×C79—41no—
111C22×C4×C79—41no—
112C22×C4×C79C2×D411yescharacteristic
113C22×C4×C79C2×D411yescharacteristic
114C22×C4×C79#4111yescharacteristic
115C2×C8×C79—21no—
116C2×C8×C79—21no—
117C2×C8×C79—21no—
118C2×C8×C79—21no—
119C2×C8×C79—21no—
120C2×C8×C79—41no—
121C2×C8×C79—41no—
122C2×C8×C79—41no—
123C2×C8×C79D812yescomplemented
124C4⋊C4×C79—21no—
125C4⋊C4×C79—21no—
126C22⋊C4×C79—41no—
127C22⋊C4×C79—41no—
128C42×C79C2×D411yescharacteristic
129C42×C79C2×D411yescharacteristic
130C42×C79#4111yescharacteristic
131C42×C79#4111yescharacteristic
132C23×C79—22no—
133C23×C79—41no—
134C23×C79—41no—
135C23×C79—41no—
136C23×C79—41no—
137C23×C79—41no—
138C23×C79—41no—
139C23×C79#12111yescharacteristic
140C22×D79—42no—
141C22×D79—81no—
142C22×D79—81no—
143C22×D79—81no—
144C22×D79—81no—
145C22×D79—81no—
146C22×D79—81no—
147D4×C79—22no—
148D4×C79—22no—
149D4×C79—41no—
150D4×C79—41no—
151C2×C4×C79—21no—
152C2×C4×C79—21no—
153C2×C4×C79—41no—
154C2×C4×C79—41no—
155C2×C4×C79—41no—
156C2×C4×C79—81no—
157C2×C4×C79—81no—
158C2×C4×C79—81no—
159C2×C4×C79—81no—
160C2×C4×C79#12011yescharacteristic
161C2×C4×C79#12111yescharacteristic
162C2×C4×C79#12111yescharacteristic
163C2×C4×C79#12311yescharacteristic
164C2×C4×C79#12311yescharacteristic
165C2×C4×C79#12411yescharacteristic
166C2×C4×C79C2×D811yescharacteristic
167C2×C4×C79C2×SD1611yescharacteristic
168C2×C4×C79#13511yescharacteristic
169C2×C4×C79#13511yescharacteristic
170C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
174C2×Dic79—81no—
175C2×Dic79—81no—
176C2×Dic79—81no—
177D316—42no—
178D316—42no—
179D316—42no—
180D316—42no—
181D316—82no—
182D316—82no—
183D316—81no—
184D316—81no—
185D316—81no—
186D316—81no—
187C8×C79—22no—
188C8×C79—41no—
189C8×C79—81no—
190C79⋊C8—42no—
191C79⋊C8—81no—
192C22×C79—42no—
193C22×C79—42no—
194C22×C79—42no—
195C22×C79—81no—
196C22×C79—81no—
197C22×C79—81no—
198C22×C79—81no—
199C22×C79#39411yescharacteristic
200C22×C79#45911yescharacteristic
201C22×C79#46311yescharacteristic
202C22×C79#46511yescharacteristic
203C22×C79#46911yescharacteristic
204C22×C79#47111yescharacteristic
205C22×C79#47211yescharacteristic
206C2×D79—82no—
207C2×D79—82no—
208C2×D79—82no—
209C2×D79—161no—
210C2×D79—161no—
211C2×D79—161no—
212C2×D79—161no—
213C4×C79—21no—
214C4×C79—21no—
215C4×C79—81no—
216C4×C79#44911yescharacteristic
217C4×C79#45011yescharacteristic
218C4×C79#45911yescharacteristic
219C4×C79#46311yescharacteristic
220C4×C79#46611yescharacteristic
221C4×C79#46911yescharacteristic
222C4×C79#48111yescharacteristic
223C4×C79#48211yescharacteristic
224Dic79—161no—
225#10473—791nomaximal, Sylow
226C2×C79—82no—
227C2×C79#166511yescharacteristic
228C2×C79#167711yescharacteristic
229C2×C79#168711yescharacteristic
230C2×C79#170111yescharacteristic
231C2×C79#203411yescharacteristic
232C2×C79#205111yescharacteristic
233C2×C79#205411yescharacteristic
234D79—162no—
235C2×#459—791no—
236#1957—791no—
237#1954D7911yescharacteristic, complemented
238#1802—791no—
239C2×#334—791no—
240C2×#331—791no—
241#1296—791no—
242C79#1047311yescharacteristic, complemented, Sylow
243C22×D8—1581no—
244C2×#127—791no—
245C2×C4×D4C2×D7911yescharacteristic
246#459—1582no—
247#459—1582no—
248C2×C4⋊C8—791no—
249C2×C4⋊C8—791no—
250C2×C4⋊C8C2×D7911yescharacteristic
251C2×#102—1581no—
252C2×#102—1581no—
253C2×#102—1581no—
254C2×#102—1581no—
255C2×C22⋊C8—21no—
256C2×C22⋊C8—21no—
257C2×C4×C8C2×D7911yescharacteristic
258#384—791no—
259#340—1581no—
260#334—1582no—
261#331—1582no—
262C22×D4—1581no—
263C22×D4—1581no—
264C22×D4—1581no—
265C22×D4D31611yescharacteristic
266C23×C4—21no—
267C2×D8—3162no—
268C2×D8—3162no—
269C2×D8—1584no—
270C22×C8—21no—
271C22×C8—1581no—
272C22×C8—1581no—
273C22×C8C22⋊D7911yescharacteristic
274C22×C8C22⋊D7911yescharacteristic
275#127—792no—
276#127—1581no—
277#127—1581no—
278#127—1581no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—1581no—
284C2×C4⋊C4—1581no—
285C2×C4⋊C4—1581no—
286C2×C4⋊C4D31611yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C22×D7911yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—792no—
292C4⋊C8—1581no—
293C4⋊C8—1581no—
294C4⋊C8—1581no—
295#102—3162no—
296#102—3162no—
297#102—3162no—
298#102—1584no—
299C22⋊C8—42no—
300C22⋊C8—42no—
301C4×C8—21no—
302C4×C8—21no—
303C24—21no—
304C24—3161no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—3161no—
311C2×D4—3161no—
312C2×D4—3161no—
313C2×D4—3161no—
314C2×D4—3161no—
315C2×D4—3161no—
316C2×D4—3161no—
317C2×D4—3161no—
318C2×D4—3161no—
319C2×D4—3161no—
320C2×D4—3161no—
321C2×D4—6321no—
322C2×D4—6321no—
323C2×D4—1582no—
324C2×D4—1582no—
325C2×D4—1582no—
326C2×D4#1192961312yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—3161no—
335C22×C4C2×C22⋊D7911yescharacteristic
336C22×C4C2×D31611yescharacteristic
337C22×C4#1192962411yescharacteristic
338D8—3168no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—3161no—
348C2×C8—3161no—
349C2×C8—3161no—
350C2×C8—3161no—
351C2×C8—3161no—
352C2×C8—1582no—
353C2×C8#1192960912yescomplemented
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—3161no—
357C4⋊C4—3161no—
358C4⋊C4—3161no—
359C4⋊C4—3161no—
360C4⋊C4—6321no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42D4×D7911yescharacteristic
364C42D4×D7911yescharacteristic
365C42#1192962311yescharacteristic
366C42#1192962311yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—3162no—
375C23—6321no—
376C23—6321no—
377C23—6321no—
378C23—6321no—
379C23—6321no—
380C23—6321no—
381C23#1457913511yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—41no—
386D4—3162no—
387D4—3162no—
388D4—3162no—
389D4—3162no—
390D4—6322no—
391D4—6322no—
392D4—6321no—
393D4—6321no—
394D4—6321no—
395D4—6321no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—6321no—
406C2×C4—6321no—
407C2×C4—6321no—
408C2×C4#1457913111yescharacteristic
409C2×C4#1457913211yescharacteristic
410C2×C4#1457913311yescharacteristic
411C2×C4#1457914311yescharacteristic
412C2×C4#1457914511yescharacteristic
413C2×C4#1457914711yescharacteristic
414C2×C4C2×#1192960911yescharacteristic
415C2×C4C2×#1192961311yescharacteristic
416C2×C4#1457918111yescharacteristic
417C2×C4#1457918311yescharacteristic
418C2×C4#1457918611yescharacteristic
419C2×C4#1457918711yescharacteristic
420C2×C4#1457918911yescharacteristic
421C2×C4#1457918911yescharacteristic
422C8—22no—
423C8—41no—
424C8—81no—
425C8—3162no—
426C8—6321no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—6322no—
435C22—6322no—
436C22—6322no—
437C22—12641no—
438C22—12641no—
439C22—12641no—
440C22—12641no—
441C22#1909847911yescharacteristic
442C22#1909875811yescharacteristic
443C22#1909877811yescharacteristic
444C22#1909879211yescharacteristic
445C22#1909881611yescharacteristic
446C22#1909882611yescharacteristic
447C22#1909883311yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—12641no—
452C4#1909871011yescharacteristic
453C4#1909871611yescharacteristic
454C4#1909875511yescharacteristic
455C4#1909877511yescharacteristic
456C4#1909879711yescharacteristic
457C4#1909881411yescharacteristic
458C4#1909888211yescharacteristic
459C4#1909888811yescharacteristic
460C2—82no—
461C2—12642no—
462C2#2376274111yescharacteristic
463C2#2376280911yescharacteristic
464C2#2376287911yescharacteristic
465C2#2376296111yescharacteristic
466C2#2376459011yescharacteristic
467C2#2376469111yescharacteristic
468C2#2376471011yescharacteristic
subgroupG/H
centerC23#14579135
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1954C2
socleC23×C79#121
prime radicalC2×#19098758C2
hypercenter#1954D79
hypocenterC79#10473
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. #23764206C2semidirect
3. #23763400C2semidirect
4. C2×#19098314C2semidirect
5. C2×#19098306C2semidirect
6. #23761284C2semidirect
7. C79×#1954C2semidirect
123. C2×C8×C79D8semidirect
237. #1954D79semidirect
242. C79#10473semidirect
353. C2×C8#11929609semidirect

Maximal subgroups

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

subgroupindex
C2×#190987582
#237642062
#237634002
C2×#190983142
C2×#190983062
#237612842
C79×#19542
#1047379