Finite Group Databasebeta

← #34443422

Subgroups — #34443422

Order 20224.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23774039C211yesmaximal, characteristic
2#23765608C211yesmaximal, characteristic, complemented
3#23765591C211yesmaximal, characteristic
4#23765552C211yesmaximal, characteristic, complemented
5#23765542C211yesmaximal, characteristic, complemented
6#23765462C211yesmaximal, characteristic, complemented
7#23765462C211yesmaximal, characteristic, complemented
8#23765334C211yesmaximal, characteristic, complemented
9#23765317C211yesmaximal, characteristic
10#23765269C211yesmaximal, characteristic, complemented
11#23765262C211yesmaximal, characteristic, complemented
12C4×#14579107C211yesmaximal, characteristic, complemented
13C4×#14579104C211yesmaximal, characteristic, complemented
14#23765207C211yesmaximal, characteristic, complemented
15C79×#2950C211yesmaximal, characteristic, complemented
16#19099184—21no—
17C2×#14579107C2211yescharacteristic
18C2×#14579107C2211yescharacteristic
19C2×#14579104C2211yescharacteristic
20C2×#14579104C2211yescharacteristic
21#19098968C2211yescharacteristic
22#19098947C2211yescharacteristic
23#19098923—21no—
24#19098809—21no—
25#19098804C2211yescharacteristic
26#19098799C2211yescharacteristic
27#19098665—21no—
28C4×Dic316C2211yescharacteristic
29C4×D632C2211yescharacteristic
30#19098390C2211yescharacteristic
31#19098390C2211yescharacteristic
32#19098388C2211yescharacteristic
33#19098388C2211yescharacteristic
34C4⋊(C79⋊C16)C2211yescharacteristic
35C4⋊(C79⋊C16)C2211yescharacteristic
36#19098367C2211yescharacteristic
37#19098367C2211yescharacteristic
38#19098367C2211yescharacteristic
39#19098367C2211yescharacteristic
40#19098366C2211yescharacteristic
41#19098366C2211yescharacteristic
42#19098363C2211yescharacteristic
43#19098363C2211yescharacteristic
44C22⋊(C79⋊C16)C2211yescharacteristic
45C22⋊(C79⋊C16)C2211yescharacteristic
46#19098339C2211yescharacteristic
47C4×C79⋊C16C2211yescharacteristic
48C22×Q16×C79C2211yescharacteristic
49#519×C79—21no—
50#441×C79—21no—
51#441×C79—21no—
52C4×Q16×C79C2211yescharacteristic
53C4×Q16×C79C2211yescharacteristic
54C4×Q16×C79C2211yescharacteristic
55C4×Q16×C79C2211yescharacteristic
56#427×C79C2211yescharacteristic
57#419×C79—21no—
58#405×C79C2211yescharacteristic
59C2×Dic316C2311yescharacteristic
60C2×#11929613—21no—
61C2×D632C2311yescharacteristic
62#14579161—21no—
63#14579156—41no—
64#14579149—21no—
65#14579147—41no—
66#14579143—41no—
67#14579140—21no—
68#14579139—41no—
69#14579135—21no—
70C4×Dic158—21no—
71C4×D316—21no—
72#14579107—22no—
73#14579107—22no—
74#14579104—22no—
75#14579104—22no—
76C2×C79⋊C16C2311yescharacteristic
77C2×C79⋊C16C2311yescharacteristic
78C2×C79⋊C16C2311yescharacteristic
79C2×C79⋊C16C2311yescharacteristic
80#14579095—21no—
81#14579095C2311yescharacteristic
82#14579095C2311yescharacteristic
83#14579086—21no—
84#14579086—21no—
85#14579083—21no—
86#14579083—21no—
87C22×Q8×C79—21no—
88C2×Q16×C79—22no—
89C2×Q16×C79—22no—
90C2×Q16×C79—21no—
91C2×Q16×C79C2311yescharacteristic
92C2×Q16×C79C2311yescharacteristic
93C2×M16×C79D411yescharacteristic
94C22×C8×C79C2311yescharacteristic
95C4×Q8×C79—21no—
96C4×Q8×C79—21no—
97C4×Q8×C79—21no—
98C4×Q8×C79—21no—
99C4×Q8×C79—41no—
100C4×Q8×C79—41no—
101#117×C79—21no—
102#117×C79—41no—
103#117×C79—41no—
104#117×C79D411yescharacteristic
105#107×C79C2311yescharacteristic
106#107×C79C2311yescharacteristic
107#106×C79—21no—
108#103×C79—21no—
109#103×C79—21no—
110#103×C79—21no—
111#103×C79—21no—
112#97×C79D411yescharacteristic
113#97×C79D411yescharacteristic
114C4×C8×C79C2311yescharacteristic
115C4×C8×C79C2311yescharacteristic
116C2×Dic158—21no—
117C2×Dic158—41no—
118C2×D316—21no—
119C2×C22⋊D79—41no—
120C2×C4×D79—41no—
121Dic316—21no—
122Dic316—21no—
123#11929613—42no—
124D632—21no—
125D632—21no—
126C4⋊Dic79—21no—
127C4⋊Dic79—21no—
128C4⋊Dic79—41no—
129Dic79⋊C4—41no—
130Dic79⋊C4—41no—
131C22⋊Dic79—41no—
132(C2×D79)⋊C4—41no—
133(C2×D79)⋊C4—41no—
134(C2×D79)⋊C4—41no—
135(C2×D79)⋊C4—41no—
136C4×Dic79—41no—
137C79⋊C16—21no—
138C79⋊C16—21no—
139C79⋊C16—21no—
140C79⋊C16—21no—
141C2×Q8×C79—24no—
142C2×Q8×C79—21no—
143C2×Q8×C79—21no—
144C2×Q8×C79—42no—
145C2×Q8×C79—41no—
146C22×C4×C79—41no—
147C22×C4×C79C2×D411yescharacteristic
148Q16×C79—24no—
149Q16×C79—21no—
150Q16×C79—21no—
151Q16×C79#4112yes—
152Q16×C79#4112yes—
153M16×C79—41no—
154C2×C8×C79—21no—
155C2×C8×C79—21no—
156C2×C8×C79C2×D411yescharacteristic
157C2×C8×C79C2×D411yescharacteristic
158C2×C8×C79C2×D411yescharacteristic
159C2×C8×C79C2411yescharacteristic
160C4⋊C4×C79—21no—
161C4⋊C4×C79—21no—
162C4⋊C4×C79—41no—
163C4⋊C4×C79—41no—
164C4⋊C4×C79—41no—
165C4⋊C4×C79—41no—
166C4⋊C4×C79D811yescharacteristic
167C4⋊C4×C79D811yescharacteristic
168C22⋊C4×C79—41no—
169C22⋊C4×C79D811yescharacteristic
170C22⋊C4×C79D811yescharacteristic
171C42×C79—41no—
172C42×C79—41no—
173C42×C79—41no—
174C42×C79—41no—
175C42×C79—41no—
176C42×C79C2×D411yescharacteristic
177C42×C79C2×D411yescharacteristic
178C23×C79C2×D811yescharacteristic
179C22×D79—41no—
180Q8×C79—22no—
181Q8×C79—22no—
182Q8×C79—44no—
183Q8×C79—41no—
184Q8×C79—41no—
185C2×C4×C79—21no—
186C2×C4×C79—21no—
187C2×C4×C79—44no—
188C2×C4×C79—41no—
189C2×C4×C79—41no—
190C2×C4×C79—41no—
191C2×C4×C79—41no—
192C2×C4×C79C2×D811yescharacteristic
193C2×C4×C79C2×D811yescharacteristic
194C2×C4×C79C2×D811yescharacteristic
195C2×C4×C79C2×D811yescharacteristic
196C2×C4×C79C2×D811yescharacteristic
197C2×C4×C79C22×D411yescharacteristic
198C22⋊D79—161no—
199C2×Dic79—41no—
200C2×Dic79—41no—
201C2×Dic79—41no—
202D316—41no—
203D316—41no—
204C4×D79—161no—
205Dic158—41no—
206Dic158—41no—
207Dic158—161no—
208C8×C79—21no—
209C8×C79—21no—
210C8×C79—21no—
211C8×C79C2×#4111yescharacteristic
212C8×C79C2×#4111yescharacteristic
213C22×C79—21no—
214C22×C79—21no—
215C22×C79—21no—
216C22×C79C22×D811yescharacteristic
217C2×D79—81no—
218C2×D79—81no—
219C2×D79—81no—
220C4×C79—21no—
221C4×C79—21no—
222C4×C79—21no—
223C4×C79—21no—
224C4×C79—21no—
225C4×C79—42no—
226C4×C79—42no—
227C4×C79—81no—
228C4×C79—81no—
229C4×C79#52511yescharacteristic
230C4×C79#57511yescharacteristic
231Dic79—81no—
232Dic79—81no—
233Dic79—81no—
234#33681—791nomaximal, Sylow
235C2×C79—41no—
236C2×C79#310011yescharacteristic
237C2×C79#341611yescharacteristic
238C2×C79#341711yescharacteristic
239D79—161no—
240#3175—791no—
241#2950D7911yescharacteristic, complemented
242#2237—791no—
243#2234—791no—
244#2227—791no—
245#2225—791no—
246#2211—791no—
247#2211—791no—
248#2188—791no—
249#2185—791no—
250#2176—791no—
251#2175—791no—
252C4×Q32—791no—
253C4×SD32—791no—
254#2164—791no—
255C79#3368111yescharacteristic, complemented, Sylow
256C22×Q16C2×D7911yescharacteristic
257#542—1581no—
258#519—21no—
259C2×Q32—791no—
260C2×Q32—791no—
261C2×SD32—791no—
262C2×SD32—791no—
263#500—791no—
264#495—791no—
265#489—1581no—
266#468—1581no—
267#467—791no—
268#466—791no—
269#441—21no—
270#441—21no—
271#440—1581no—
272C4×Q16—791no—
273C4×Q16C2×D7911yescharacteristic
274C4×Q16C2×D7911yescharacteristic
275C4×Q16C2×D7911yescharacteristic
276C4×Q16C2×D7911yescharacteristic
277C4×D8—791no—
278#427C2×D7911yescharacteristic
279#419—21no—
280#405C2×D7911yescharacteristic
281#367—791no—
282#367—791no—
283#366—791no—
284#366—791no—
285C4⋊C16—791no—
286C4⋊C16—791no—
287#358—791no—
288#358—791no—
289#358—791no—
290#358—791no—
291#358—791no—
292#358—791no—
293#357—791no—
294#357—791no—
295C22⋊C16—791no—
296C22⋊C16—791no—
297#346—791no—
298C4×C16—791no—
299C22×Q8—21no—
300C2×Q16—22no—
301C2×Q16—22no—
302C2×Q16—21no—
303C2×Q16—791no—
304C2×Q16C22×D7911yescharacteristic
305C2×Q16C22×D7911yescharacteristic
306C2×SD16—1581no—
307C2×D8—791no—
308C2×M16C22⋊D7911yescharacteristic
309C22×C8C22×D7911yescharacteristic
310C4⋊Q8—1581no—
311#126—3161no—
312#124—3161no—
313#124—1581no—
314#123—3161no—
315C22⋊Q8—3161no—
316C22⋊Q8—1581no—
317#121—1581no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—41no—
323C4×Q8—41no—
324C4×Q8—1581no—
325C4×D4—1581no—
326#117—21no—
327#117—41no—
328#117—41no—
329#117C22⋊D7911yescharacteristic
330Q32—1582no—
331Q32—1582no—
332SD32—1582no—
333SD32—1582no—
334C2×C16—791no—
335C2×C16—791no—
336C2×C16—791no—
337C2×C16—791no—
338#107—791no—
339#107—791no—
340#107—1581no—
341#107C22×D7911yescharacteristic
342#107C22×D7911yescharacteristic
343#106—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#103—21no—
348#103—1581no—
349#103—1581no—
350#102—1581no—
351#102—1581no—
352#97C22⋊D7911yescharacteristic
353#97C22⋊D7911yescharacteristic
354C4×C8C22×D7911yescharacteristic
355C4×C8C22×D7911yescharacteristic
356C2×Q8—24no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—41no—
361C2×Q8—3161no—
362C2×Q8—1581no—
363C2×D4—3161no—
364C2×D4—1581no—
365C22×C4—41no—
366C22×C4—3161no—
367C22×C4C2×C22⋊D7911yescharacteristic
368Q16—24no—
369Q16—21no—
370Q16—21no—
371Q16—1581no—
372Q16—1581no—
373Q16#1192962412yes—
374Q16#1192962412yes—
375SD16—3162no—
376D8—1581no—
377D8—1581no—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D7911yescharacteristic
382C2×C8C2×C22⋊D7911yescharacteristic
383C2×C8C2×C22⋊D7911yescharacteristic
384C2×C8C23×D7911yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—3161no—
392C4⋊C4—3161no—
393C4⋊C4—3161no—
394C4⋊C4—1581no—
395C4⋊C4—1581no—
396C4⋊C4#1192960911yescharacteristic
397C4⋊C4#1192960911yescharacteristic
398C22⋊C4—41no—
399C22⋊C4—3161no—
400C22⋊C4—3161no—
401C22⋊C4—3161no—
402C22⋊C4—3161no—
403C22⋊C4—3161no—
404C22⋊C4#1192960911yescharacteristic
405C22⋊C4#1192960911yescharacteristic
406C42—41no—
407C42—41no—
408C42—41no—
409C42—41no—
410C42—41no—
411C42—3161no—
412C42C2×C22⋊D7911yescharacteristic
413C42C2×C22⋊D7911yescharacteristic
414C16—1581no—
415C16—1581no—
416C16—1581no—
417C16—1581no—
418C23—3161no—
419C23C2×#1192960911yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—44no—
423Q8—41no—
424Q8—41no—
425Q8—3161no—
426Q8—3161no—
427Q8—12641no—
428D4—3161no—
429D4—3161no—
430D4—12641no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—3161no—
439C2×C4—3161no—
440C2×C4—3161no—
441C2×C4—12641no—
442C2×C4C2×#1192960911yescharacteristic
443C2×C4C2×#1192960911yescharacteristic
444C2×C4C2×#1192960911yescharacteristic
445C2×C4C2×#1192960911yescharacteristic
446C2×C4C2×#1192960911yescharacteristic
447C2×C4C22×C22⋊D7911yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×#1192962411yescharacteristic
452C8C2×#1192962411yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—6321no—
457C22—6321no—
458C22—6321no—
459C22C22×#1192960911yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—6321no—
470C4—6321no—
471C4—6321no—
472C4#1909907411yescharacteristic
473C4#1909936111yescharacteristic
474C2—41no—
475C2—12641no—
476C2#2377340011yescharacteristic
477C2#2377654411yescharacteristic
478C2#2377655111yescharacteristic
subgroupG/H
centerC22C22×#11929609
commutator, cosocleC2×C8×C79C24
FrattiniC2×C8C23×D79
FittingC79×#2950C2
socleC22×C79C22×D8
prime radical#19098799C22
hypercenter#2950D79
hypocenterC79#33681
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2950

Complements

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

NH ≅ G/Ntype
2. #23765608C2semidirect
4. #23765552C2semidirect
5. #23765542C2semidirect
6. #23765462C2semidirect
7. #23765462C2semidirect
8. #23765334C2semidirect
10. #23765269C2semidirect
11. #23765262C2semidirect
12. C4×#14579107C2semidirect
13. C4×#14579104C2semidirect
14. #23765207C2semidirect
15. C79×#2950C2semidirect
241. #2950D79semidirect
255. C79#33681semidirect

Maximal subgroups

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

subgroupindex
#237740392
#237656082
#237655912
#237655522
#237655422
#237654622
#237653342
#237653172
#237652692
#237652622
C4×#145791072
C4×#145791042
#237652072
C79×#29502
#3368179