Finite Group Databasebeta

← #34191685

Subgroups — #34191685

Order 20224.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23768395C211yesmaximal, characteristic
2#23764360C211yesmaximal, characteristic, complemented
3#23763397C211yesmaximal, characteristic
4C2×#19098308C211yesmaximal, characteristic, complemented
5C2×#19098290C211yesmaximal, characteristic
6#23761241C211yesmaximal, characteristic, complemented
7C79×#1947C211yesmaximal, characteristic, complemented
8C2×#14579161C2211yescharacteristic
9C2×#14579149—21no—
10C2×C4×D316C2211yescharacteristic
11C2×C4⋊(C79⋊C8)C2211yescharacteristic
12C2×#14579081—21no—
13C2×C4×C79⋊C8C2211yescharacteristic
14#19098490—22no—
15#19098469—21no—
16#19098420—21no—
17#19098420—21no—
18#19098325—22no—
19#19098325—21no—
20#19098308—22no—
21#19098290—22no—
22C2×#107×C79—21no—
23C2×C4⋊C8×C79C2211yescharacteristic
24#384×C79C2211yescharacteristic
25C4×C4⋊C4×C79C2211yescharacteristic
26#340×C79—21no—
27C22×Dic158—21no—
28C22×D316D411yescharacteristic
29C22×C4×D79—21no—
30C22×C79⋊C8—21no—
31C22×C79⋊C8—21no—
32#14579161—21no—
33#14579161—21no—
34#14579161—21no—
35#14579161—21no—
36#14579149—42no—
37#14579149—42no—
38C4×D316—21no—
39C4×D316—21no—
40C4×D316—21no—
41C4×D316—21no—
42C2×C4⋊Dic79—21no—
43C2×C4⋊Dic79D411yescharacteristic
44C2×C4⋊Dic79D412yes—
45C2×(C2×D79)⋊C4—22no—
46C2×(C2×D79)⋊C4—22no—
47C2×(C2×D79)⋊C4—21no—
48C4⋊(C79⋊C8)—21no—
49C4⋊(C79⋊C8)—21no—
50#14579081—42no—
51C4×C79⋊C8—21no—
52C4×C79⋊C8—21no—
53C79⋊#95—22no—
54C79⋊#95—22no—
55C22×C8×C79—21no—
56C2×C4⋊C4×C79—21no—
57C2×C4⋊C4×C79—21no—
58C2×C4⋊C4×C79—21no—
59C2×C4⋊C4×C79D411yescharacteristic
60C2×C4⋊C4×C79D411yescharacteristic
61C2×C42×C79—21no—
62C2×C42×C79C2311yescharacteristic
63#107×C79—42no—
64C4⋊C8×C79—21no—
65C4⋊C8×C79D412yes—
66#95×C79—21no—
67C23×D79—21no—
68C2×Dic158—41no—
69C2×Dic158—41no—
70C2×Dic158—41no—
71C2×Dic158—41no—
72C2×Dic158—41no—
73C2×Dic158—41no—
74C2×D316—21no—
75C2×D316—21no—
76C2×D316—21no—
77C2×D316—21no—
78C2×D316—21no—
79C2×D316D812yes—
80C22×Dic79—22no—
81C22×Dic79—21no—
82C2×C4×D79—41no—
83C2×C4×D79—41no—
84C2×C4×D79—41no—
85C2×C4×D79—41no—
86C2×C4×D79—41no—
87C2×C4×D79—41no—
88C2×C79⋊C8—22no—
89C2×C79⋊C8—41no—
90C2×C79⋊C8—41no—
91C2×C79⋊C8—41no—
92C2×C79⋊C8—41no—
93C2×C79⋊C8—41no—
94C4⋊Dic79—21no—
95C4⋊Dic79—22no—
96C4⋊Dic79—21no—
97C4⋊Dic79—22no—
98C4⋊Dic79—41no—
99C4⋊Dic79—41no—
100(C2×D79)⋊C4—44no—
101(C2×D79)⋊C4—44no—
102(C2×D79)⋊C4—41no—
103(C2×D79)⋊C4—41no—
104C22×C4×C79—21no—
105C22×C4×C79—21no—
106C22×C4×C79—41no—
107C22×C4×C79C2×D411yescharacteristic
108C22×C4×C79C2×D411yescharacteristic
109C22×C4×C79C2×D411yescharacteristic
110C2×C8×C79—22no—
111C2×C8×C79—41no—
112C2×C8×C79—41no—
113C4⋊C4×C79—21no—
114C4⋊C4×C79—21no—
115C4⋊C4×C79—21no—
116C4⋊C4×C79—21no—
117C4⋊C4×C79—42no—
118C4⋊C4×C79—41no—
119C4⋊C4×C79—41no—
120C4⋊C4×C79—41no—
121C4⋊C4×C79—41no—
122C42×C79—41no—
123C42×C79—41no—
124C42×C79C2×D411yescharacteristic
125C42×C79#4111yescharacteristic
126C42×C79#4111yescharacteristic
127C42×C79#4111yescharacteristic
128C23×C79#12011yescharacteristic
129C22×D79—22no—
130C22×D79—41no—
131C22×D79—41no—
132C22×D79—41no—
133C22×D79—41no—
134C22×D79—41no—
135C22×D79—41no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—41no—
139C2×C4×C79—41no—
140C2×C4×C79—41no—
141C2×C4×C79—41no—
142C2×C4×C79—41no—
143C2×C4×C79—41no—
144C2×C4×C79—81no—
145C2×C4×C79—81no—
146C2×C4×C79—81no—
147C2×C4×C79#12111yescharacteristic
148C2×C4×C79#12111yescharacteristic
149C2×C4×C79#12111yescharacteristic
150C2×C4×C79#12311yescharacteristic
151C2×C4×C79#12311yescharacteristic
152C2×C4×C79#12411yescharacteristic
153C2×C4×C79C2×D811yescharacteristic
154C2×C4×C79#13511yescharacteristic
155C2×C4×C79#13511yescharacteristic
156C2×C4×C79#13511yescharacteristic
157C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C79#13711yescharacteristic
160C2×C4×C79#13711yescharacteristic
161C2×Dic79—41no—
162C2×Dic79—42no—
163C2×Dic79—42no—
164C2×Dic79—41no—
165C2×Dic79—41no—
166C2×Dic79—42no—
167D316—22no—
168D316—22no—
169D316—41no—
170D316—41no—
171C4×D79—81no—
172C4×D79—81no—
173C4×D79—81no—
174C4×D79—81no—
175Dic158—81no—
176Dic158—81no—
177Dic158—81no—
178Dic158—81no—
179C8×C79—42no—
180C79⋊C8—42no—
181C79⋊C8—81no—
182C22×C79#39411yescharacteristic
183C22×C79#44711yescharacteristic
184C22×C79#44911yescharacteristic
185C22×C79#45211yescharacteristic
186C22×C79#45211yescharacteristic
187C22×C79#45411yescharacteristic
188C22×C79#45611yescharacteristic
189C2×D79—42no—
190C2×D79—42no—
191C2×D79—42no—
192C2×D79—81no—
193C2×D79—81no—
194C2×D79—81no—
195C2×D79—81no—
196C4×C79—21no—
197C4×C79—21no—
198C4×C79—81no—
199C4×C79—81no—
200C4×C79—161no—
201C4×C79#46311yescharacteristic
202C4×C79#46411yescharacteristic
203C4×C79#46611yescharacteristic
204C4×C79#46811yescharacteristic
205C4×C79#48011yescharacteristic
206C4×C79#48211yescharacteristic
207C4×C79#48811yescharacteristic
208C4×C79#48911yescharacteristic
209Dic79—82no—
210Dic79—81no—
211#10416—791nomaximal, Sylow
212C2×C79#162511yescharacteristic
213C2×C79#163811yescharacteristic
214C2×C79#164711yescharacteristic
215C2×C79#165211yescharacteristic
216C2×C79#203311yescharacteristic
217C2×C79#203811yescharacteristic
218C2×C79#204211yescharacteristic
219D79—82no—
220#2547—791no—
221#1990—791no—
222#1947D7911yescharacteristic, complemented
223#1802—791no—
224C2×#332—791no—
225C2×D4⋊C8—791no—
226#1279—791no—
227C79#1041611yescharacteristic, complemented, Sylow
228C2×C4⋊Q8—791no—
229C2×#124—1581no—
230C2×C4×D4—791no—
231C2×#107—21no—
232C2×C4⋊C8—791no—
233C2×C4⋊C8C2×D7911yescharacteristic
234C2×#102—1581no—
235C2×C4×C8—791no—
236#397—1582no—
237#391—1581no—
238#384C2×D7911yescharacteristic
239#380—1581no—
240#380—1581no—
241C4×C4⋊C4C2×D7911yescharacteristic
242#340—21no—
243#340—1581no—
244#340—1582no—
245#332—1582no—
246D4⋊C8—1582no—
247C22×Q8—1581no—
248C22×D4—791no—
249C23×C4—1581no—
250C22×C8—21no—
251C22×C8—1581no—
252C22×C8—1581no—
253C4⋊Q8—1581no—
254C4⋊Q8—1581no—
255C4⋊Q8—1581no—
256C4⋊Q8—1581no—
257#124—3162no—
258#124—3162no—
259C4×D4—1581no—
260C4×D4—1581no—
261C4×D4—1581no—
262C4×D4—1581no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—791no—
267C2×C4⋊C4—792no—
268C2×C4⋊C4—1581no—
269C2×C4⋊C4C22⋊D7911yescharacteristic
270C2×C4⋊C4C22⋊D7911yescharacteristic
271C2×C22⋊C4—1582no—
272C2×C22⋊C4—1582no—
273C2×C22⋊C4—1581no—
274C2×C42—21no—
275C2×C42C22×D7911yescharacteristic
276#107—42no—
277C4⋊C8—21no—
278C4⋊C8—1581no—
279C4⋊C8—1581no—
280C4⋊C8D31612yes—
281#102—3162no—
282C4×C8—1581no—
283C4×C8—1581no—
284#95—21no—
285#95—1582no—
286#95—1582no—
287C24—1581no—
288C2×Q8—3161no—
289C2×Q8—3161no—
290C2×Q8—3161no—
291C2×Q8—3161no—
292C2×Q8—3161no—
293C2×Q8—3161no—
294C2×D4—792no—
295C2×D4—1581no—
296C2×D4—1581no—
297C2×D4—1581no—
298C2×D4—1581no—
299C2×D4—1581no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—3161no—
304C22×C4—3161no—
305C22×C4—3161no—
306C22×C4—3161no—
307C22×C4—3161no—
308C22×C4—3161no—
309C22×C4—1581no—
310C22×C4—1582no—
311C22×C4D4×D7911yescharacteristic
312C22×C4D4×D7911yescharacteristic
313C22×C4C2×C22⋊D7911yescharacteristic
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—3161no—
318C2×C8—3161no—
319C2×C8—3161no—
320C2×C8—3161no—
321C2×C8—3161no—
322C2×C8—1582no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—3161no—
333C4⋊C4—3161no—
334C4⋊C4—1581no—
335C4⋊C4—1582no—
336C4⋊C4—1581no—
337C4⋊C4—1582no—
338C22⋊C4—3164no—
339C22⋊C4—3164no—
340C22⋊C4—3161no—
341C22⋊C4—3161no—
342C42—41no—
343C42—41no—
344C42C2×D31611yescharacteristic
345C42#1192962411yescharacteristic
346C42#1192962511yescharacteristic
347C42#1192962511yescharacteristic
348C23—3161no—
349C23—3161no—
350C23—3161no—
351C23—3161no—
352C23—3161no—
353C23—3161no—
354C23—1582no—
355C23#1457912911yescharacteristic
356Q8—6321no—
357Q8—6321no—
358Q8—6321no—
359Q8—6321no—
360D4—3161no—
361D4—3161no—
362D4—1582no—
363D4—1582no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—3162no—
376C2×C4—3161no—
377C2×C4—3161no—
378C2×C4—3162no—
379C2×C4—3161no—
380C2×C4—3162no—
381C2×C4—6321no—
382C2×C4—6321no—
383C2×C4—6321no—
384C2×C4—6321no—
385C2×C4#1457913511yescharacteristic
386C2×C4#1457913611yescharacteristic
387C2×C4#1457913611yescharacteristic
388C2×C4#1457914611yescharacteristic
389C2×C4#1457914611yescharacteristic
390C2×C4#1457915011yescharacteristic
391C2×C4D8×D7911yescharacteristic
392C2×C4#1457918111yescharacteristic
393C2×C4#1457918111yescharacteristic
394C2×C4#1457918411yescharacteristic
395C2×C4#1457918511yescharacteristic
396C2×C4#1457918711yescharacteristic
397C2×C4#1457919211yescharacteristic
398C2×C4#1457919311yescharacteristic
399C8—42no—
400C8—3162no—
401C8—6321no—
402C22—3162no—
403C22—3162no—
404C22—3162no—
405C22—6321no—
406C22—6321no—
407C22—6321no—
408C22—6321no—
409C22#1909848011yescharacteristic
410C22#1909869511yescharacteristic
411C22#1909870611yescharacteristic
412C22#1909872311yescharacteristic
413C22#1909872411yescharacteristic
414C22#1909873411yescharacteristic
415C22#1909874411yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—161no—
421C4—6322no—
422C4—6321no—
423C4#1909877811yescharacteristic
424C4#1909878511yescharacteristic
425C4#1909880011yescharacteristic
426C4#1909881011yescharacteristic
427C4#1909887811yescharacteristic
428C4#1909889011yescharacteristic
429C4#1909892011yescharacteristic
430C4#1909892511yescharacteristic
431C2—6322no—
432C2#2376248811yescharacteristic
433C2#2376257111yescharacteristic
434C2#2376263411yescharacteristic
435C2#2376266811yescharacteristic
436C2#2376458411yescharacteristic
437C2#2376461911yescharacteristic
438C2#2376464111yescharacteristic
subgroupG/H
centerC23#14579129
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1947C2
socleC23×C79#120
prime radicalC22×D316D4
hypercenter#1947D79
hypocenterC79#10416
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #23764360C2semidirect
4. C2×#19098308C2semidirect
6. #23761241C2semidirect
7. C79×#1947C2semidirect
222. #1947D79semidirect
227. C79#10416semidirect

Maximal subgroups

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

subgroupindex
#237683952
#237643602
#237633972
C2×#190983082
C2×#190982902
#237612412
C79×#19472
#1041679