Finite Group Databasebeta

← #34205146

Subgroups — #34205146

Order 20224.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098678C211yesmaximal, characteristic
2C2×#19098348C211yesmaximal, characteristic, complemented
3C2×#19098347C211yesmaximal, characteristic, complemented
4#23765013C211yesmaximal, characteristic, complemented
5#23761481C211yesmaximal, characteristic, complemented
6#23761477C211yesmaximal, characteristic, complemented
7C2×#504×C79C211yesmaximal, characteristic, complemented
8C2×#14579181C411yescharacteristic
9C2×#14579167C2211yescharacteristic
10C2×#14579101C2211yescharacteristic
11C22×C79⋊C16C2211yescharacteristic
12#19098678—22no—
13#19098678—22no—
14C2×#14579096C411yescharacteristic
15C2×#14579088C411yescharacteristic
16C2×#14579087C411yescharacteristic
17C2×C8×Dic79C2211yescharacteristic
18#19098348—22no—
19#19098347—22no—
20(C2×D79)⋊C16—21no—
21(C2×D79)⋊C16—21no—
22C2×#131×C79C2211yescharacteristic
23#504×C79—22no—
24#504×C79—22no—
25C2×M32×C79—21no—
26C2×M32×C79C2211yescharacteristic
27C22×C16×C79—21no—
28C22×C16×C79C2211yescharacteristic
29C2×#11929624C2×C411yescharacteristic
30#14579181—22no—
31#14579181—22no—
32C2×#11929614C811yescharacteristic
33C2×#11929612C811yescharacteristic
34C2×#11929611C811yescharacteristic
35C2×#11929609C811yescharacteristic
36#14579167—21no—
37#14579167—21no—
38#14579167—21no—
39#14579167—21no—
40C2×#11929608C2×C411yescharacteristic
41C2×#11929607—21no—
42C22×C79⋊C8C2×C411yescharacteristic
43C2×C8×D79—21no—
44C2×C4×Dic79C2×C411yescharacteristic
45#14579101—21no—
46#14579101—21no—
47C2×C79⋊C16—21no—
48C2×C79⋊C16—21no—
49C2×C79⋊C16—21no—
50C2×C79⋊C16—21no—
51#14579096—22no—
52#14579088—22no—
53#14579087—22no—
54C8×Dic79—21no—
55C8×Dic79—21no—
56C2×#41×C79C2×C411yescharacteristic
57#131×C79—21no—
58#131×C79—21no—
59#131×C79D412yes—
60#131×C79D412yes—
61C2×M16×C79—21no—
62C2×M16×C79C2×C411yescharacteristic
63C22×C8×C79—21no—
64C22×C8×C79C2311yescharacteristic
65M32×C79—24no—
66M32×C79—21no—
67M32×C79D412yes—
68C2×C16×C79—24no—
69C2×C16×C79—21no—
70C2×C16×C79—21no—
71C2×C16×C79—21no—
72C2×C16×C79D411yescharacteristic
73C2×C16×C79D411yescharacteristic
74#11929624—21no—
75#11929624—21no—
76#11929624—21no—
77#11929624—21no—
78C2×Dic158C2×C811yescharacteristic
79C2×D316C2×C811yescharacteristic
80C2×C22⋊D79—21no—
81C22×Dic79—21no—
82C2×C4×D79—21no—
83#11929614—22no—
84#11929612—22no—
85#11929611—22no—
86#11929609—22no—
87#11929608—21no—
88#11929608—21no—
89#11929607—41no—
90#11929607—41no—
91C2×C79⋊C8—21no—
92C2×C79⋊C8—21no—
93C2×C79⋊C8—21no—
94C2×C79⋊C8C2×C811yescharacteristic
95C2×C79⋊C8C2×C811yescharacteristic
96C8×D79—41no—
97C8×D79—41no—
98C4×Dic79—21no—
99C4×Dic79—21no—
100C79⋊C16—41no—
101C79⋊C16—41no—
102#41×C79—21no—
103#41×C79—21no—
104#41×C79C22⋊C412yes—
105#41×C79M1612yes—
106C2×Q8×C79C2×C811yescharacteristic
107C2×D4×C79—21no—
108C2×D4×C79C2×C811yescharacteristic
109C22×C4×C79—21no—
110C22×C4×C79C22×C411yescharacteristic
111M16×C79—22no—
112M16×C79—22no—
113M16×C79—21no—
114M16×C79C22⋊C412yes—
115C2×C8×C79—22no—
116C2×C8×C79—22no—
117C2×C8×C79—21no—
118C2×C8×C79C2×D411yescharacteristic
119C2×C8×C79C2×D411yescharacteristic
120C2×C8×C79C2×D411yescharacteristic
121C2×C8×C79C2×D411yescharacteristic
122C2×C8×C79#4111yescharacteristic
123C2×C8×C79#4111yescharacteristic
124C16×C79—21no—
125C16×C79—22no—
126C16×C79—21no—
127C23×C79—21no—
128C23×C79#13111yescharacteristic
129C22×D79—21no—
130Q8×C79—21no—
131Q8×C79C22⋊C812yes—
132D4×C79—22no—
133D4×C79—22no—
134D4×C79—21no—
135D4×C79C22⋊C812yes—
136C2×C4×C79—21no—
137C2×C4×C79—22no—
138C2×C4×C79—22no—
139C2×C4×C79C2×C22⋊C411yescharacteristic
140C2×C4×C79C4×D411yescharacteristic
141C2×C4×C79C4×D411yescharacteristic
142C2×C4×C79C22×C811yescharacteristic
143C2×C4×C79C2×M1611yescharacteristic
144C2×C4×C79#13111yescharacteristic
145C22⋊D79—41no—
146C22⋊D79—41no—
147C2×Dic79—22no—
148C2×Dic79—21no—
149C2×Dic79—41no—
150C2×Dic79—41no—
151D316—21no—
152D316—21no—
153C4×D79—41no—
154C4×D79—41no—
155Dic158—21no—
156Dic158—21no—
157C8×C79—22no—
158C8×C79#12011yescharacteristic
159C8×C79#12111yescharacteristic
160C8×C79#12111yescharacteristic
161C8×C79#12311yescharacteristic
162C79⋊C8—21no—
163C79⋊C8—21no—
164C79⋊C8—41no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79—22no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79#40811yescharacteristic
171C22×C79C8×D411yescharacteristic
172C22×C79#43511yescharacteristic
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C4×C79—22no—
177C4×C79#38611yescharacteristic
178C4×C79C2×C22⋊C811yescharacteristic
179C4×C79C8×D411yescharacteristic
180C4×C79#43511yescharacteristic
181Dic79—42no—
182Dic79—41no—
183#12980—791nomaximal, Sylow
184C2×C79—21no—
185C2×C79—21no—
186C2×C79—42no—
187C2×C79#186911yescharacteristic
188C2×C79#217011yescharacteristic
189C2×C79#217111yescharacteristic
190D79—81no—
191C2×#504D7911yescharacteristic, complemented
192C2×#443—791no—
193C2×#350—791no—
194C2×#350—791no—
195#2113—791no—
196#1376—791no—
197#1374—791no—
198C79#1298011yescharacteristic, complemented, Sylow
199C2×#135—791no—
200C2×#131—791no—
201C2×#131C2×D7911yescharacteristic
202#504—22no—
203#504—22no—
204C2×M32—21no—
205C2×M32—791no—
206C2×M32C2×D7911yescharacteristic
207C22×C16—21no—
208C22×C16—791no—
209C22×C16C2×D7911yescharacteristic
210#443—1582no—
211#443—1582no—
212C2×#108—791no—
213C2×#104—791no—
214C2×#104—791no—
215C2×C4×C8—791no—
216#350—1582no—
217#350—1582no—
218C22⋊C16—1581no—
219C22⋊C16—1581no—
220C2×#41—791no—
221C2×#41C4×D7911yescharacteristic
222#135—1582no—
223#135—1582no—
224C2×Q16—791no—
225C2×SD16—791no—
226C2×SD16—791no—
227C2×D8—791no—
228#131—21no—
229#131—21no—
230#131—1581no—
231#131—1581no—
232#131—1581no—
233#131—1581no—
234#131D31612yes—
235#131C22⋊D7912yes—
236C2×M16—21no—
237C2×M16—791no—
238C2×M16—1581no—
239C2×M16C4×D7911yescharacteristic
240C22×C8—21no—
241C22×C8—791no—
242C22×C8—1581no—
243C22×C8C22×D7911yescharacteristic
244C2×C42—791no—
245M32—24no—
246M32—21no—
247M32—1581no—
248M32—1581no—
249M32C22⋊D7912yes—
250C2×C16—24no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—1581no—
255C2×C16—1581no—
256C2×C16—1581no—
257C2×C16—1581no—
258C2×C16C22⋊D7911yescharacteristic
259C2×C16C22⋊D7911yescharacteristic
260#108—1582no—
261#104—1582no—
262#104—1582no—
263C4×C8—1581no—
264C4×C8—1581no—
265#41—21no—
266#41—21no—
267#41—1581no—
268#41—1581no—
269#41—1581no—
270#41—1581no—
271#41(C2×D79)⋊C412yes—
272#41#1192960712yes—
273C2×Q8—791no—
274C2×Q8C8×D7911yescharacteristic
275C2×D4—21no—
276C2×D4—791no—
277C2×D4—1581no—
278C2×D4C8×D7911yescharacteristic
279C22×C4—21no—
280C22×C4—1581no—
281C22×C4—1581no—
282C22×C4C2×C4×D7911yescharacteristic
283Q16—1582no—
284SD16—1582no—
285SD16—1582no—
286D8—1582no—
287M16—21no—
288M16—22no—
289M16—22no—
290M16—3161no—
291M16—3161no—
292M16—1581no—
293M16—1581no—
294M16(C2×D79)⋊C412yes—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—3161no—
299C2×C8—3161no—
300C2×C8—791no—
301C2×C8—791no—
302C2×C8—1581no—
303C2×C8—1581no—
304C2×C8—1581no—
305C2×C8C2×C22⋊D7911yescharacteristic
306C2×C8C2×C22⋊D7911yescharacteristic
307C2×C8C2×C22⋊D7911yescharacteristic
308C2×C8C2×D31611yescharacteristic
309C2×C8#1192962411yescharacteristic
310C2×C8#1192962411yescharacteristic
311C42—1581no—
312C42—1581no—
313C16—21no—
314C16—22no—
315C16—21no—
316C16—3161no—
317C16—3161no—
318C23—21no—
319C23—1581no—
320C23#1457916711yescharacteristic
321Q8—21no—
322Q8—1581no—
323Q8—1581no—
324Q8(C2×D79)⋊C812yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—3161no—
329D4—3161no—
330D4—1581no—
331D4—1581no—
332D4(C2×D79)⋊C812yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—3161no—
337C2×C4—3161no—
338C2×C4—3161no—
339C2×C4—3161no—
340C2×C4—1582no—
341C2×C4—1581no—
342C2×C4C2×(C2×D79)⋊C411yescharacteristic
343C2×C4C4×C22⋊D7911yescharacteristic
344C2×C4C4×C22⋊D7911yescharacteristic
345C2×C4C2×C8×D7911yescharacteristic
346C2×C4C2×#1192960711yescharacteristic
347C2×C4#1457916711yescharacteristic
348C8—22no—
349C8—3161no—
350C8—1581no—
351C8—1581no—
352C8#1457913011yescharacteristic
353C8#1457913511yescharacteristic
354C8#1457913511yescharacteristic
355C8#1457914411yescharacteristic
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22#1909852911yescharacteristic
365C22C8×C22⋊D7911yescharacteristic
366C22#1909863411yescharacteristic
367C4—22no—
368C4—3162no—
369C4—3161no—
370C4#1909844211yescharacteristic
371C4C2×(C2×D79)⋊C811yescharacteristic
372C4C8×C22⋊D7911yescharacteristic
373C4#1909863411yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—6321no—
378C2#2376369211yescharacteristic
379C2#2376523511yescharacteristic
380C2#2376524011yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D79
commutatorC2×C4×C79C22×C8
FrattiniC22×C8C22×D79
FittingC2×#504×C79C2
socleC22×C79C8×D4
prime radicalC2×#14579181C4
cosocleC22×C8×C79C23
hypercenterC2×#504D79
hypocenterC79#12980
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
2. C2×#19098348C2semidirect
3. C2×#19098347C2semidirect
4. #23765013C2semidirect
5. #23761481C2semidirect
6. #23761477C2semidirect
7. C2×#504×C79C2semidirect
191. C2×#504D79semidirect
198. C79#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#190986782
C2×#190983482
C2×#190983472
#237650132
#237614812
#237614772
C2×#504×C792
#1298079