Finite Group Databasebeta

← #1347×D79 #34198486

Subgroups — #1347×D79 #34198486

Order 20224.

558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#466×D79C211yesmaximal, characteristic
2C22⋊C16×D79C211yesmaximal, characteristic, complemented
3#340×D79C211yesmaximal, characteristic, complemented
4#23761410C211yesmaximal, characteristic, complemented
5#23761409C211yesmaximal, characteristic, complemented
6#23761408C211yesmaximal, characteristic, complemented
7C79×#1347C211yesmaximal, characteristic, complemented
8C2×D8×D79C411yescharacteristic, complemented
9C22×C8×D79C2211yescharacteristic
10#121×D79—21no—
11C2×C4⋊C4×D79—21no—
12C2×C16×D79—21no—
13#19098800C411yescharacteristic, complemented
14#19098799C2211yescharacteristic
15#19098798—21no—
16#19098797—21no—
17#19098796C411yescharacteristic, complemented
18#107×D79C411yescharacteristic, complemented
19#102×D79—21no—
20C22⋊(C79⋊C16)C2211yescharacteristic, complemented
21(C2×D79)⋊C16—21no—
22#19098326C2211yescharacteristic, complemented
23#19098325—21no—
24#466×C79C2211yescharacteristic
25C22⋊C16×C79C2211yescharacteristic, complemented
26#340×C79C2211yescharacteristic, complemented
27C2×D4×D79—21no—
28C2×D4×D79—41no—
29C22×C4×D79—41no—
30C22×C4×D79D411yescharacteristic
31C2×D632C2×C411yescharacteristic, complemented
32C2×#11929609—21no—
33D8×D79—42no—
34C22×C79⋊C8D411yescharacteristic
35C2×C8×D79—42no—
36C2×C8×D79C2×C411yescharacteristic
37C2×C8×D79C2×C411yescharacteristic
38C2×C8×D79D411yescharacteristic
39C2×C8×D79D411yescharacteristic
40#14579136—21no—
41#14579135—21no—
42#14579134—41no—
43#14579133—41no—
44#14579132—21no—
45C2×C4⋊Dic79—21no—
46C2×Dic79⋊C4—41no—
47C4⋊C4×D79—24no—
48C4⋊C4×D79—21no—
49C4⋊C4×D79—42no—
50C22⋊C4×D79—41no—
51C2×C79⋊C16—21no—
52C16×D79—42no—
53#14579095C2×C411yescharacteristic, complemented
54#14579094—21no—
55#14579083—21no—
56#14579082—21no—
57#14579081—21no—
58C2×D8×C79C2×C411yescharacteristic, complemented
59C22×C8×C79C2311yescharacteristic
60#121×C79—21no—
61C2×C4⋊C4×C79—21no—
62C2×C16×C79—21no—
63#107×C79C2×C411yescharacteristic, complemented
64#102×C79—21no—
65C23×D79—41no—
66C23×D79D811yescharacteristic
67C2×D316—21no—
68C2×D316—41no—
69C2×C22⋊D79—41no—
70C2×C22⋊D79—41no—
71C2×C22⋊D79—41no—
72D4×D79—42no—
73D4×D79—42no—
74D4×D79—82no—
75D4×D79—82no—
76C22×Dic79—41no—
77C22×Dic79D811yescharacteristic
78C2×C4×D79—22no—
79C2×C4×D79—22no—
80C2×C4×D79—44no—
81C2×C4×D79—41no—
82C2×C4×D79—82no—
83C2×C4×D79—82no—
84C2×C4×D79C22⋊C411yescharacteristic
85C2×C4×D79C22⋊C411yescharacteristic
86C2×C4×D79SD1611yescharacteristic
87C2×C4×D79SD1611yescharacteristic
88D632—41no—
89#11929609—42no—
90C2×C79⋊C8—41no—
91C2×C79⋊C8C22⋊C411yescharacteristic
92C2×C79⋊C8C22⋊C411yescharacteristic
93C8×D79—22no—
94C8×D79—22no—
95C8×D79—41no—
96C8×D79—41no—
97C4⋊Dic79—22no—
98C4⋊Dic79—21no—
99C4⋊Dic79—41no—
100Dic79⋊C4—44no—
101Dic79⋊C4—41no—
102C22⋊Dic79—41no—
103(C2×D79)⋊C4—41no—
104(C2×D79)⋊C4—41no—
105C79⋊C16—41no—
106C2×D4×C79—21no—
107C2×D4×C79—41no—
108C22×C4×C79—41no—
109C22×C4×C79C2×D411yescharacteristic
110D8×C79—41no—
111C2×C8×C79—41no—
112C2×C8×C79C22×C411yescharacteristic
113C2×C8×C79C2×D411yescharacteristic
114C4⋊C4×C79—22no—
115C4⋊C4×C79—21no—
116C4⋊C4×C79—41no—
117C22⋊C4×C79—41no—
118C16×C79—41no—
119C23×C79—41no—
120C23×C79C2×D811yescharacteristic
121C22×D79—22no—
122C22×D79—22no—
123C22×D79—41no—
124C22×D79—82no—
125C22×D79—82no—
126C22×D79—82no—
127C22×D79#10211yescharacteristic
128C22×D79#10211yescharacteristic
129C22×D79D1612yes—
130C22×D79SD3212yes—
131D4×C79—41no—
132D4×C79—41no—
133D4×C79—81no—
134D4×C79—81no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—42no—
138C2×C4×C79—41no—
139C2×C4×C79—81no—
140C2×C4×C79—81no—
141C2×C4×C79C2×C22⋊C411yescharacteristic
142C2×C4×C79C2×SD1611yescharacteristic
143C22⋊D79—81no—
144C22⋊D79—81no—
145C22⋊D79—82no—
146C22⋊D79—82no—
147C2×Dic79—22no—
148C2×Dic79—42no—
149C2×Dic79—41no—
150C2×Dic79—81no—
151C2×Dic79—81no—
152C2×Dic79#10211yescharacteristic
153C2×Dic79#10211yescharacteristic
154D316—41no—
155D316—41no—
156D316—82no—
157C4×D79—22no—
158C4×D79—21no—
159C4×D79—21no—
160C4×D79—22no—
161C4×D79—88no—
162C4×D79—82no—
163C4×D79#9912yes—
164C4×D79#10412yes—
165C8×C79—21no—
166C8×C79—21no—
167C79⋊C8—21no—
168C79⋊C8—21no—
169C22×C79—21no—
170C22×C79—21no—
171C22×C79—81no—
172C22×C79—81no—
173C22×C79—81no—
174C22×C79C2×#10211yescharacteristic
175C22×C79C2×D1611yescharacteristic
176C22×C79C2×SD3211yescharacteristic
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—24no—
180C2×D79—24no—
181C2×D79—81no—
182C2×D79—81no—
183C2×D79—81no—
184C2×D79—164no—
185C2×D79#32712yes—
186C2×D79#35712yes—
187C2×D79#35712yes—
188C2×D79#36012yes—
189C4×C79—21no—
190C4×C79—82no—
191C4×C79—81no—
192C4×C79C2×#9911yescharacteristic
193C4×C79C2×#10411yescharacteristic
194Dic79—21no—
195Dic79—82no—
196Dic79—81no—
197Dic79#32712yes—
198C2×#1347—791nomaximal, Sylow
199C2×C79—21no—
200C2×C79—21no—
201C2×C79—161no—
202C2×C79C2×#32711yescharacteristic
203C2×C79C2×#35711yescharacteristic
204C2×C79C2×#36011yescharacteristic
205D79—22no—
206D79—161no—
207D79#134714yesdirect product factor
208C2×#466—791no—
209C2×C22⋊C16—791no—
210C2×#340—791no—
211#1347—791no—
212#1347—791no—
213#1347—791no—
214#1347D7911yescharacteristic, direct product factor
215C79C2×#134711yescharacteristic, complemented, Sylow
216C22×D8—791no—
217C23×C8—791no—
218C2×#121—1581no—
219C22×C4⋊C4—1581no—
220C22×C16—1581no—
221#466—791no—
222#466—791no—
223#466—791no—
224#466—1581no—
225#466—1581no—
226#466C2×D7911yescharacteristic
227C2×#107—791no—
228C2×#102—1581no—
229C22⋊C16—791no—
230C22⋊C16—1581no—
231C22⋊C16C2×D7911yescharacteristic, complemented
232#340—791no—
233#340—1581no—
234#340C2×D7911yescharacteristic, complemented
235C22×D4—3161no—
236C22×D4—1581no—
237C23×C4—3161no—
238C23×C4—791no—
239C2×D8—3162no—
240C2×D8—791no—
241C2×D8—1581no—
242C2×D8C4×D7911yescharacteristic, complemented
243C22×C8—3162no—
244C22×C8—791no—
245C22×C8—791no—
246C22×C8—791no—
247C22×C8—791no—
248C22×C8—791no—
249C22×C8C22×D7911yescharacteristic
250#121—21no—
251#121—3161no—
252#121—3161no—
253#121—1581no—
254#121—1581no—
255#121—1581no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—3162no—
258C2×C4⋊C4—3161no—
259C2×C4⋊C4—1581no—
260C2×C4⋊C4—1584no—
261C2×C4⋊C4—1581no—
262C2×C22⋊C4—3161no—
263C2×C16—21no—
264C2×C16—3162no—
265C2×C16—1581no—
266#107—791no—
267#107—1581no—
268#107C4×D7911yescharacteristic, complemented
269#102—21no—
270#102—1581no—
271#102—1581no—
272#102—1581no—
273C24—3161no—
274C24—791no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—3161no—
278C2×D4—3161no—
279C2×D4—3161no—
280C2×D4—3162no—
281C2×D4—3162no—
282C2×D4—3161no—
283C2×D4—6322no—
284C2×D4—6322no—
285C2×D4—1581no—
286C22×C4—41no—
287C22×C4—3161no—
288C22×C4—3164no—
289C22×C4—3161no—
290C22×C4—791no—
291C22×C4—791no—
292C22×C4—791no—
293C22×C4—791no—
294C22×C4—791no—
295C22×C4—6322no—
296C22×C4—6322no—
297C22×C4—1582no—
298C22×C4—1582no—
299C22×C4D4×D7911yescharacteristic
300D8—41no—
301D8—3161no—
302D8—3162no—
303C2×C8—41no—
304C2×C8—3161no—
305C2×C8—3161no—
306C2×C8—3161no—
307C2×C8—791no—
308C2×C8—791no—
309C2×C8—1582no—
310C2×C8—1582no—
311C2×C8C2×C4×D7911yescharacteristic
312C2×C8D4×D7911yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—3161no—
317C4⋊C4—3161no—
318C4⋊C4—3164no—
319C4⋊C4—1582no—
320C4⋊C4—1581no—
321C22⋊C4—41no—
322C22⋊C4—3161no—
323C22⋊C4—3161no—
324C22⋊C4—3161no—
325C16—41no—
326C16—3161no—
327C23—41no—
328C23—3161no—
329C23—791no—
330C23—792no—
331C23—792no—
332C23—791no—
333C23—6322no—
334C23—6322no—
335C23—6322no—
336C23—1582no—
337C23—1582no—
338C23D8×D7911yescharacteristic
339D4—41no—
340D4—41no—
341D4—81no—
342D4—81no—
343D4—3161no—
344D4—3161no—
345D4—6322no—
346D4—6322no—
347D4—6322no—
348D4—6321no—
349D4—6321no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—3162no—
357C2×C4—3161no—
358C2×C4—791no—
359C2×C4—792no—
360C2×C4—792no—
361C2×C4—791no—
362C2×C4—6322no—
363C2×C4—6328no—
364C2×C4—6321no—
365C2×C4—6321no—
366C2×C4—1582no—
367C2×C4—1582no—
368C2×C4—1582no—
369C2×C4—1581no—
370C2×C4—1581no—
371C2×C4C22⋊C4×D7911yescharacteristic
372C2×C4SD16×D7911yescharacteristic
373C8—21no—
374C8—21no—
375C8—1581no—
376C8—1581no—
377C22—21no—
378C22—21no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—792no—
383C22—792no—
384C22—792no—
385C22—792no—
386C22—6321no—
387C22—6321no—
388C22—6321no—
389C22—1584no—
390C22—1584no—
391C22—1581no—
392C22—1581no—
393C22—12644no—
394C22#102×D7911yescharacteristic
395C22D16×D7911yescharacteristic
396C22SD32×D7911yescharacteristic
397C4—21no—
398C4—82no—
399C4—81no—
400C4—792no—
401C4—6322no—
402C4—6321no—
403C4—1581no—
404C4#99×D7911yescharacteristic
405C4#104×D7911yescharacteristic
406C2—21no—
407C2—21no—
408C2—161no—
409C2—794no—
410C2—1582no—
411C2—12641no—
412C2#327×D7911yescharacteristic
413C2#357×D7911yescharacteristic
414C2#360×D7911yescharacteristic
subgroupG/H
centerC22#102×D79
commutatorC2×C8×C79C22×C4
FrattiniC22×C8C22×D79
FittingC79×#1347C2
socleC22×C79C2×#102
prime radical#466×D79C2
cosocleC22×C8×C79C23
hypercenter#1347D79
hypocenterC79C2×#1347
LCSG ▷ C2×C8×C79 ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. C22⋊C16×D79C2semidirect
3. #340×D79C2semidirect
4. #23761410C2semidirect
5. #23761409C2semidirect
6. #23761408C2semidirect
7. C79×#1347C2semidirect
8. C2×D8×D79C4semidirect
13. #19098800C4semidirect
17. #19098796C4semidirect
18. #107×D79C4semidirect
20. C22⋊(C79⋊C16)C22semidirect
22. #19098326C22semidirect
25. C22⋊C16×C79C22semidirect
26. #340×C79C22semidirect
31. C2×D632C2×C4semidirect
53. #14579095C2×C4semidirect
58. C2×D8×C79C2×C4semidirect
63. #107×C79C2×C4semidirect
207. D79#1347direct (N × H)
214. #1347D79direct (N × H)
215. C79C2×#1347semidirect
231. C22⋊C16C2×D79semidirect
234. #340C2×D79semidirect
242. C2×D8C4×D79semidirect
268. #107C4×D79semidirect

Maximal subgroups

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

subgroupindex
#466×D792
C22⋊C16×D792
#340×D792
#237614102
#237614092
#237614082
C79×#13472
C2×#134779