Finite Group Databasebeta

← #1271×D79 #34176201

Subgroups — #1271×D79 #34176201

Order 20224.

714 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D79C211yesmaximal, characteristic
2#336×D79C211yesmaximal, characteristic
3#336×D79C211yesmaximal, characteristic
4#23761224C211yesmaximal, characteristic, complemented
5#23761223C211yesmaximal, characteristic, complemented
6#23761222C211yesmaximal, characteristic, complemented
7C79×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D79—21no—
9C22×C8×D79—21no—
10C2×C4⋊C4×D79—21no—
11C2×C4⋊C4×D79C411yescharacteristic
12C2×C4⋊C4×D79C411yescharacteristic
13C2×C42×D79C2211yescharacteristic
14#19098462C411yescharacteristic
15#19098461C2211yescharacteristic
16#19098460—21no—
17#19098459C411yescharacteristic
18#19098458—21no—
19#95×D79—21no—
20#19098318C2211yescharacteristic
21#19098318C2211yescharacteristic
22#19098317—21no—
23#19098317—21no—
24#389×C79C2211yescharacteristic
25#336×C79C2211yescharacteristic
26#336×C79C2211yescharacteristic
27C22×C4×D79—21no—
28C22×C4×D79—21no—
29C22×C4×D79C2×C411yescharacteristic
30C22×C4×D79D411yescharacteristic
31C22×C4×D79D411yescharacteristic
32C22×C79⋊C8—21no—
33C22×C79⋊C8—21no—
34C2×C8×D79—24no—
35C2×C8×D79—24no—
36C2×C8×D79—42no—
37C2×C8×D79—42no—
38C2×C8×D79—42no—
39C2×C8×D79—42no—
40C2×C4⋊Dic79—21no—
41C2×C4⋊Dic79C2×C411yescharacteristic
42C2×C4⋊Dic79C2×C411yescharacteristic
43C2×Dic79⋊C4—21no—
44C2×Dic79⋊C4—21no—
45C2×Dic79⋊C4—21no—
46C2×Dic79⋊C4—21no—
47C4⋊C4×D79—22no—
48C4⋊C4×D79—42no—
49C4⋊C4×D79—42no—
50C4⋊C4×D79—42no—
51C4⋊C4×D79C814yescomplemented
52C2×C4×Dic79C2×C411yescharacteristic
53C2×C4×Dic79D411yescharacteristic
54C2×C4×Dic79D411yescharacteristic
55C42×D79—42no—
56C79⋊#95—21no—
57C79⋊#95—21no—
58C79⋊#95—21no—
59C22×C8×C79—21no—
60C22×C8×C79—21no—
61C2×C4⋊C4×C79—21no—
62C2×C4⋊C4×C79C2×C411yescharacteristic
63C2×C4⋊C4×C79C2×C411yescharacteristic
64C2×C42×C79C2311yescharacteristic
65#95×C79—21no—
66C23×D79C22⋊C411yescharacteristic
67C22×Dic79—21no—
68C22×Dic79—21no—
69C22×Dic79C22⋊C411yescharacteristic
70C22×Dic79C22⋊C411yescharacteristic
71C22×Dic79C22⋊C411yescharacteristic
72C2×C4×D79—24no—
73C2×C4×D79—22no—
74C2×C4×D79—22no—
75C2×C4×D79—22no—
76C2×C4×D79—22no—
77C2×C4×D79—22no—
78C2×C4×D79—22no—
79C2×C4×D79—42no—
80C2×C4×D79—42no—
81C2×C4×D79—42no—
82C2×C4×D79—42no—
83C2×C4×D79—42no—
84C2×C4×D79C2×C812yes—
85C2×C4×D79M1612yes—
86C2×C4×D79D812yes—
87C2×C4×D79SD1612yes—
88C2×C4×D79SD1612yes—
89C2×C4×D79Q1612yes—
90C2×C79⋊C8—22no—
91C2×C79⋊C8—22no—
92C2×C79⋊C8—41no—
93C2×C79⋊C8—41no—
94C2×C79⋊C8—41no—
95C2×C79⋊C8—41no—
96C8×D79—48no—
97C8×D79—48no—
98C4⋊Dic79—21no—
99C4⋊Dic79—41no—
100C4⋊Dic79—42no—
101C4⋊Dic79C2×C812yescomplemented
102Dic79⋊C4—24no—
103Dic79⋊C4—42no—
104Dic79⋊C4—42no—
105Dic79⋊C4—41no—
106Dic79⋊C4—41no—
107C4×Dic79—41no—
108C4×Dic79—41no—
109C4×Dic79—41no—
110C22×C4×C79—21no—
111C22×C4×C79—21no—
112C22×C4×C79C22×C411yescharacteristic
113C22×C4×C79C2×D411yescharacteristic
114C22×C4×C79C2×D411yescharacteristic
115C2×C8×C79—22no—
116C2×C8×C79—22no—
117C2×C8×C79—41no—
118C2×C8×C79—41no—
119C2×C8×C79—41no—
120C2×C8×C79—41no—
121C4⋊C4×C79—21no—
122C4⋊C4×C79—41no—
123C4⋊C4×C79—41no—
124C4⋊C4×C79—41no—
125C4⋊C4×C79C2×C812yescomplemented
126C42×C79—41no—
127C23×C79C2×C22⋊C411yescharacteristic
128C22×D79C22⋊C812yes—
129C22×D79#9912yes—
130C22×D79#10112yes—
131C22×D79#10212yes—
132C22×D79#10312yes—
133C22×D79#10412yes—
134C22×D79#10412yes—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—22no—
142C2×C4×C79—41no—
143C2×C4×C79—41no—
144C2×C4×C79—41no—
145C2×C4×C79—41no—
146C2×C4×C79—41no—
147C2×C4×C79C22×C811yescharacteristic
148C2×C4×C79C2×M1611yescharacteristic
149C2×C4×C79C2×D811yescharacteristic
150C2×C4×C79C2×SD1611yescharacteristic
151C2×C4×C79C2×SD1611yescharacteristic
152C2×C4×C79C2×Q1611yescharacteristic
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—21no—
158C2×Dic79—21no—
159C2×Dic79—22no—
160C2×Dic79—41no—
161C2×Dic79—41no—
162C2×Dic79—41no—
163C2×Dic79—41no—
164C2×Dic79—41no—
165C2×Dic79C22⋊C812yes—
166C2×Dic79#10212yes—
167C2×Dic79#10312yes—
168C4×D79—24no—
169C4×D79—24no—
170C4×D79—24no—
171C4×D79—24no—
172C4×D79—24no—
173C4×D79—24no—
174C4×D79—48no—
175C4×D79—84no—
176C8×C79—42no—
177C8×C79—42no—
178C79⋊C8—42no—
179C79⋊C8—42no—
180C22×C79C2×C22⋊C811yescharacteristic
181C22×C79C2×#9911yescharacteristic
182C22×C79C2×#10111yescharacteristic
183C22×C79C2×#10211yescharacteristic
184C22×C79C2×#10311yescharacteristic
185C22×C79C2×#10411yescharacteristic
186C22×C79C2×#10411yescharacteristic
187C2×D79#32414yes—
188C2×D79D4⋊C814yes—
189C2×D79Q8⋊C814yes—
190C2×D79#32714yes—
191C2×D79#32814yes—
192C2×D79#33014yes—
193C2×D79#33214yes—
194C4×C79—21no—
195C4×C79—21no—
196C4×C79—21no—
197C4×C79—21no—
198C4×C79—21no—
199C4×C79—21no—
200C4×C79—42no—
201C4×C79—81no—
202Dic79—22no—
203Dic79—22no—
204Dic79—22no—
205Dic79—42no—
206Dic79—81no—
207C2×#1271—791nomaximal, Sylow
208C2×C79C2×#32411yescharacteristic
209C2×C79C2×D4⋊C811yescharacteristic
210C2×C79C2×Q8⋊C811yescharacteristic
211C2×C79C2×#32711yescharacteristic
212C2×C79C2×#32811yescharacteristic
213C2×C79C2×#33011yescharacteristic
214C2×C79C2×#33211yescharacteristic
215D79#127118yesdirect product factor
216C2×#389—791no—
217C2×#336—791no—
218C2×#336—791no—
219#1271—791no—
220#1271—791no—
221#1271—791no—
222#1271D7911yescharacteristic, direct product factor
223C79C2×#127111yescharacteristic, complemented, Sylow
224C23×C8—1581no—
225C23×C8—1581no—
226C22×C4⋊C4—791no—
227C22×C4⋊C4—791no—
228C22×C4⋊C4—1581no—
229C22×C42—791no—
230#389—791no—
231#389—791no—
232#389—791no—
233#389—1581no—
234#389—1581no—
235#389C2×D7911yescharacteristic
236C2×#95—1581no—
237#336—791no—
238#336—791no—
239#336—1581no—
240#336—1581no—
241#336C2×D7911yescharacteristic
242#336C2×D7911yescharacteristic
243C23×C4—791no—
244C23×C4—791no—
245C23×C4—791no—
246C23×C4—1581no—
247C23×C4—1581no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—3162no—
251C22×C8—3162no—
252C22×C8—3162no—
253C22×C8—3162no—
254C22×C8—1584no—
255C22×C8—1584no—
256C22×C8—1581no—
257C22×C8—1581no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—3162no—
260C2×C4⋊C4—3162no—
261C2×C4⋊C4—3162no—
262C2×C4⋊C4—791no—
263C2×C4⋊C4—791no—
264C2×C4⋊C4—794no—
265C2×C4⋊C4—1582no—
266C2×C4⋊C4—1581no—
267C2×C4⋊C4—1581no—
268C2×C4⋊C4—1581no—
269C2×C4⋊C4—1581no—
270C2×C4⋊C4—1581no—
271C2×C4⋊C4C4×D7911yescharacteristic
272C2×C4⋊C4C4×D7911yescharacteristic
273C2×C42—3162no—
274C2×C42—791no—
275C2×C42—791no—
276C2×C42—791no—
277C2×C42C22×D7911yescharacteristic
278#95—21no—
279#95—1581no—
280#95—1581no—
281#95—1581no—
282C24—791no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—3162no—
286C22×C4—3162no—
287C22×C4—3162no—
288C22×C4—3162no—
289C22×C4—3162no—
290C22×C4—791no—
291C22×C4—791no—
292C22×C4—791no—
293C22×C4—792no—
294C22×C4—792no—
295C22×C4—792no—
296C22×C4—792no—
297C22×C4—792no—
298C22×C4—792no—
299C22×C4—1584no—
300C22×C4—1582no—
301C22×C4—1582no—
302C22×C4—1582no—
303C22×C4—1582no—
304C22×C4—1582no—
305C22×C4—1582no—
306C22×C4—1581no—
307C22×C4—1581no—
308C22×C4C2×C4×D7911yescharacteristic
309C22×C4D4×D7911yescharacteristic
310C22×C4D4×D7911yescharacteristic
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—3168no—
318C2×C8—3168no—
319C2×C8—3161no—
320C2×C8—3161no—
321C2×C8—3161no—
322C2×C8—3161no—
323C2×C8—1582no—
324C2×C8—1582no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—3161no—
330C4⋊C4—3162no—
331C4⋊C4—3162no—
332C4⋊C4—3162no—
333C4⋊C4—3161no—
334C4⋊C4—3161no—
335C4⋊C4—792no—
336C4⋊C4—1584no—
337C4⋊C4—1581no—
338C4⋊C4C8×D7912yescomplemented
339C42—41no—
340C42—3161no—
341C42—3161no—
342C42—3161no—
343C23—792no—
344C23—792no—
345C23—792no—
346C23—792no—
347C23—792no—
348C23—792no—
349C23—792no—
350C23C22⋊C4×D7911yescharacteristic
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—3168no—
364C2×C4—3161no—
365C2×C4—3161no—
366C2×C4—3161no—
367C2×C4—3161no—
368C2×C4—3161no—
369C2×C4—792no—
370C2×C4—792no—
371C2×C4—792no—
372C2×C4—6324no—
373C2×C4—1584no—
374C2×C4—1584no—
375C2×C4—1584no—
376C2×C4—1584no—
377C2×C4—1584no—
378C2×C4—1584no—
379C2×C4—1582no—
380C2×C4—1581no—
381C2×C4—1581no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4—1581no—
386C2×C4C2×C8×D7911yescharacteristic
387C2×C4M16×D7911yescharacteristic
388C2×C4D8×D7911yescharacteristic
389C2×C4SD16×D7911yescharacteristic
390C2×C4SD16×D7911yescharacteristic
391C2×C4Q16×D7911yescharacteristic
392C8—42no—
393C8—42no—
394C8—3162no—
395C8—3162no—
396C22—794no—
397C22—794no—
398C22—794no—
399C22—794no—
400C22—794no—
401C22—794no—
402C22—794no—
403C22C22⋊C8×D7911yescharacteristic
404C22#99×D7911yescharacteristic
405C22#101×D7911yescharacteristic
406C22#102×D7911yescharacteristic
407C22#103×D7911yescharacteristic
408C22#104×D7911yescharacteristic
409C22#104×D7911yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—3162no—
419C4—6321no—
420C4—1582no—
421C4—1582no—
422C4—1582no—
423C2—798no—
424C2#324×D7911yescharacteristic
425C2D4⋊C8×D7911yescharacteristic
426C2Q8⋊C8×D7911yescharacteristic
427C2#327×D7911yescharacteristic
428C2#328×D7911yescharacteristic
429C2#330×D7911yescharacteristic
430C2#332×D7911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D79
commutatorC2×C4×C79C22×C8
FrattiniC2×C42C22×D79
FittingC79×#1271C2
socleC23×C79C2×C22⋊C4
prime radicalC23×D79C22⋊C4
cosocleC2×C42×C79C23
hypercenter#1271D79
hypocenterC79C2×#1271
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #23761224C2semidirect
5. #23761223C2semidirect
6. #23761222C2semidirect
7. C79×#1271C2semidirect
51. C4⋊C4×D79C8semidirect
101. C4⋊Dic79C2×C8semidirect
125. C4⋊C4×C79C2×C8semidirect
215. D79#1271direct (N × H)
222. #1271D79direct (N × H)
223. C79C2×#1271semidirect
338. C4⋊C4C8×D79semidirect

Maximal subgroups

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

subgroupindex
#389×D792
#336×D792
#237612242
#237612232
#237612222
C79×#12712
C2×#127179