Finite Group Databasebeta

← #34182236

Subgroups — #34182236

Order 20224.

558 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772422C211yesmaximal, characteristic
2#23763690C211yesmaximal, characteristic
3#23763580C211yesmaximal, characteristic, complemented
4#23763577C211yesmaximal, characteristic, complemented
5C4×#14579075C211yesmaximal, characteristic
6#23761246C211yesmaximal, characteristic, complemented
7C79×#1282C211yesmaximal, characteristic, complemented
8C23×C79⋊C8C2211yescharacteristic
9C2×C4×C22⋊D79C2211yescharacteristic
10C8×C22⋊D79—21no—
11C8×C22⋊D79—21no—
12(C22⋊D79)⋊C8—21no—
13(C22⋊D79)⋊C8—21no—
14#19098613—21no—
15C2×C4⋊(C79⋊C8)—21no—
16C2×Dic79⋊C8—21no—
17C2×#14579075C411yescharacteristic
18C2×#14579075C411yescharacteristic
19C2×C22⋊(C79⋊C8)C2211yescharacteristic
20C2×(C2×D79)⋊C8—21no—
21C22⋊C8×D79—21no—
22C4×C22⋊Dic79C2211yescharacteristic
23#19098329C411yescharacteristic
24#19098329C411yescharacteristic
25#19098318—21no—
26#19098317—21no—
27#19098317—21no—
28C2×C22⋊C8×C79C2211yescharacteristic
29C2×C22⋊C8×C79C2211yescharacteristic
30C4×C22⋊C4×C79C2211yescharacteristic
31C22×C22⋊D79C2×C411yescharacteristic
32C22×C4×D79D411yescharacteristic
33C22×C79⋊C8—21no—
34C22×C79⋊C8—21no—
35C22×C79⋊C8—21no—
36C22×C79⋊C8—42no—
37C22×C79⋊C8D411yescharacteristic
38C22×C79⋊C8D411yescharacteristic
39C2×C8×D79—21no—
40C2×C8×D79—21no—
41C4×C22⋊D79—21no—
42C4×C22⋊D79—21no—
43C4×C22⋊D79—21no—
44C4×C22⋊D79—21no—
45C2×Dic79⋊C4Q811yescharacteristic
46C2×C22⋊Dic79C2×C411yescharacteristic
47C2×C22⋊Dic79C2×C411yescharacteristic
48C2×C22⋊Dic79C2×C411yescharacteristic
49C2×(C2×D79)⋊C4Q811yescharacteristic
50C2×C4×Dic79—21no—
51C2×C4×Dic79D411yescharacteristic
52C4⋊(C79⋊C8)—42no—
53Dic79⋊C8—21no—
54Dic79⋊C8—21no—
55Dic79⋊C8—42no—
56#14579075—22no—
57#14579075C814yescomplemented
58C22⋊(C79⋊C8)—21no—
59C22⋊(C79⋊C8)—21no—
60(C2×D79)⋊C8—21no—
61(C2×D79)⋊C8—21no—
62(C2×D79)⋊C8—42no—
63C8×Dic79—21no—
64C8×Dic79—21no—
65C79⋊#95—21no—
66C23×C4×C79C2311yescharacteristic
67C22×C8×C79—21no—
68C22×C8×C79D411yescharacteristic
69C22×C8×C79D411yescharacteristic
70C2×C22⋊C4×C79C2×C411yescharacteristic
71C2×C22⋊C4×C79C2×C411yescharacteristic
72C2×C42×C79—21no—
73C22⋊C8×C79—21no—
74C22⋊C8×C79—21no—
75C22⋊C8×C79—21no—
76C22⋊C8×C79—21no—
77#95×C79—21no—
78C23×D79C4⋊C411yescharacteristic
79C2×C22⋊D79—21no—
80C2×C22⋊D79—21no—
81C2×C22⋊D79—21no—
82C2×C22⋊D79—21no—
83C2×C22⋊D79C2×C812yes—
84C2×C22⋊D79M1612yes—
85C22×Dic79—21no—
86C22×Dic79—21no—
87C22×Dic79C4⋊C411yescharacteristic
88C22×Dic79C4⋊C411yescharacteristic
89C22×Dic79C4⋊C411yescharacteristic
90C2×C4×D79—21no—
91C2×C4×D79—21no—
92C2×C4×D79—41no—
93C2×C4×D79—41no—
94C2×C79⋊C8—22no—
95C2×C79⋊C8—22no—
96C2×C79⋊C8—22no—
97C2×C79⋊C8—21no—
98C2×C79⋊C8—21no—
99C2×C79⋊C8—41no—
100C2×C79⋊C8—41no—
101C2×C79⋊C8—41no—
102C2×C79⋊C8—41no—
103C2×C79⋊C8—41no—
104C2×C79⋊C8—41no—
105C8×D79—81no—
106C8×D79—81no—
107Dic79⋊C4—21no—
108Dic79⋊C4—21no—
109C22⋊Dic79—21no—
110C22⋊Dic79—21no—
111C22⋊Dic79—21no—
112C22⋊Dic79—21no—
113C22⋊Dic79—21no—
114C22⋊Dic79C2×C812yescomplemented
115(C2×D79)⋊C4—21no—
116(C2×D79)⋊C4—21no—
117C4×Dic79—21no—
118C4×Dic79—21no—
119C4×Dic79—41no—
120C4×Dic79—41no—
121C24×C79C22×C411yescharacteristic
122C22×C4×C79—21no—
123C22×C4×C79—21no—
124C22×C4×C79—41no—
125C22×C4×C79—41no—
126C22×C4×C79C2×D411yescharacteristic
127C22×C4×C79C2×D411yescharacteristic
128C22×C4×C79C2×D411yescharacteristic
129C22×C4×C79C2×Q811yescharacteristic
130C22×C4×C79#4111yescharacteristic
131C22×C4×C79#4111yescharacteristic
132C2×C8×C79—21no—
133C2×C8×C79—21no—
134C2×C8×C79—41no—
135C2×C8×C79—41no—
136C2×C8×C79—41no—
137C2×C8×C79—41no—
138C2×C8×C79—41no—
139C22⋊C4×C79—21no—
140C22⋊C4×C79—21no—
141C22⋊C4×C79—21no—
142C22⋊C4×C79C2×C812yescomplemented
143C42×C79—41no—
144C42×C79—41no—
145C23×C79—41no—
146C23×C79—41no—
147C23×C79C2×C4⋊C411yescharacteristic
148C23×C79C4×D411yescharacteristic
149C23×C79C4×D411yescharacteristic
150C23×C79C22×C811yescharacteristic
151C23×C79C2×M1611yescharacteristic
152C23×C79#13111yescharacteristic
153C23×C79#13111yescharacteristic
154C22×D79—21no—
155C22×D79—21no—
156C22×D79—41no—
157C22×D79—41no—
158C22×D79C4⋊C812yescomplemented
159C2×C4×C79—21no—
160C2×C4×C79—21no—
161C2×C4×C79—21no—
162C2×C4×C79—21no—
163C2×C4×C79—21no—
164C2×C4×C79—21no—
165C2×C4×C79—22no—
166C2×C4×C79—41no—
167C2×C4×C79—41no—
168C2×C4×C79—41no—
169C2×C4×C79—41no—
170C2×C4×C79—41no—
171C2×C4×C79—41no—
172C2×C4×C79—41no—
173C2×C4×C79—41no—
174C2×C4×C79#12011yescharacteristic
175C2×C4×C79C22⋊Q811yescharacteristic
176C2×C4×C79C22⋊Q811yescharacteristic
177C2×C4×C79#12311yescharacteristic
178C22⋊D79—22no—
179C22⋊D79—22no—
180C22⋊D79—22no—
181C22⋊D79—22no—
182C2×Dic79—21no—
183C2×Dic79—21no—
184C2×Dic79—21no—
185C2×Dic79—21no—
186C2×Dic79—22no—
187C2×Dic79—41no—
188C2×Dic79—41no—
189C2×Dic79—41no—
190C2×Dic79—41no—
191C2×Dic79—41no—
192C2×Dic79—41no—
193C2×Dic79—41no—
194C2×Dic79C4⋊C812yescomplemented
195C4×D79—41no—
196C4×D79—41no—
197C4×D79—81no—
198C8×C79—41no—
199C8×C79—41no—
200C8×C79—81no—
201C79⋊C8—41no—
202C79⋊C8—42no—
203C79⋊C8—41no—
204C22×C79—21no—
205C22×C79—21no—
206C22×C79—21no—
207C22×C79—21no—
208C22×C79—21no—
209C22×C79—21no—
210C22×C79—41no—
211C22×C79—41no—
212C22×C79—41no—
213C22×C79—41no—
214C22×C79#38511yescharacteristic
215C22×C79C2×C4⋊C811yescharacteristic
216C22×C79#42411yescharacteristic
217C22×C79C8×D411yescharacteristic
218C22×C79C8×D411yescharacteristic
219C22×C79#43511yescharacteristic
220C22×C79#43511yescharacteristic
221C2×D79—22no—
222C2×D79—41no—
223C2×D79—41no—
224C2×D79—42no—
225C2×D79—81no—
226C4×C79—21no—
227C4×C79—21no—
228C4×C79—21no—
229C4×C79—42no—
230C4×C79—81no—
231C4×C79B(4,𝔽2)11yescharacteristic
232C4×C79#45811yescharacteristic
233Dic79—22no—
234Dic79—42no—
235Dic79—41no—
236Dic79—41no—
237Dic79—81no—
238#8851—791nomaximal, Sylow
239C2×C79—21no—
240C2×C79—21no—
241C2×C79—21no—
242C2×C79—21no—
243C2×C79—21no—
244C2×C79—21no—
245C2×C79#185011yescharacteristic
246C2×C79#186711yescharacteristic
247C2×C79#186811yescharacteristic
248D79—42no—
249#2972—791no—
250#1869—791no—
251#1850—791no—
252#1850—791no—
253C4×#99—791no—
254#1282—791no—
255#1282D7911yescharacteristic, complemented
256C79#885111yescharacteristic, complemented, Sylow
257C23×C8—791no—
258C2×C4×D4—791no—
259C8×D4—1581no—
260C8×D4—1581no—
261C8×D4—1581no—
262C8×D4—1581no—
263#431—1581no—
264C2×C4⋊C8—1581no—
265C2×C4⋊C8—1581no—
266C2×#99—791no—
267C2×#99—791no—
268C2×C22⋊C8—791no—
269C2×C22⋊C8—1581no—
270C2×C22⋊C8—1581no—
271C2×C22⋊C8C2×D7911yescharacteristic
272C2×C22⋊C8C2×D7911yescharacteristic
273C4×C22⋊C4—791no—
274C4×C22⋊C4C2×D7911yescharacteristic
275#342—791no—
276#342—791no—
277#336—1581no—
278#336—1581no—
279#336—1581no—
280C22×D4—791no—
281C23×C4—791no—
282C23×C4C22×D7911yescharacteristic
283C22×C8—21no—
284C22×C8—3162no—
285C22×C8—791no—
286C22×C8—791no—
287C22×C8—1581no—
288C22×C8—1581no—
289C22×C8—1581no—
290C22×C8—1581no—
291C22×C8—1581no—
292C22×C8D31611yescharacteristic
293C22×C8D31611yescharacteristic
294C4×D4—1581no—
295C4×D4—1581no—
296C4×D4—1581no—
297C4×D4—1581no—
298C2×C4⋊C4—791no—
299C2×C22⋊C4—791no—
300C2×C22⋊C4—791no—
301C2×C22⋊C4—791no—
302C2×C22⋊C4—791no—
303C2×C22⋊C4C4×D7911yescharacteristic
304C2×C22⋊C4C4×D7911yescharacteristic
305C2×C42—21no—
306C2×C42—791no—
307C2×C42—1581no—
308C4⋊C8—3162no—
309C4⋊C8—3162no—
310C4⋊C8—1581no—
311C4⋊C8—1581no—
312#99—794no—
313#99—1582no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—3162no—
319C22⋊C8—1581no—
320C22⋊C8—1581no—
321C22⋊C8—1581no—
322C22⋊C8—1581no—
323C4×C8—1581no—
324C4×C8—1581no—
325#95—21no—
326#95—1581no—
327C24—791no—
328C24C2×C4×D7911yescharacteristic
329C2×D4—792no—
330C2×D4—792no—
331C2×D4—1581no—
332C2×D4—1581no—
333C2×D4—1581no—
334C2×D4—1581no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—3161no—
340C22×C4—3161no—
341C22×C4—791no—
342C22×C4—791no—
343C22×C4—791no—
344C22×C4—1581no—
345C22×C4—1581no—
346C22×C4—1581no—
347C22×C4—1581no—
348C22×C4D4×D7911yescharacteristic
349C22×C4D4×D7911yescharacteristic
350C22×C4C2×D31611yescharacteristic
351C22×C4Q8×D7911yescharacteristic
352C22×C4#1192962311yescharacteristic
353C22×C4#1192962411yescharacteristic
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—3161no—
362C2×C8—3161no—
363C2×C8—3161no—
364C2×C8—3161no—
365C2×C8—3161no—
366C2×C8—3161no—
367C2×C8—6321no—
368C2×C8—6321no—
369C2×C8—1582no—
370C2×C8—1582no—
371C2×C8—1582no—
372C2×C8—1581no—
373C2×C8—1581no—
374C4⋊C4—1581no—
375C4⋊C4—1581no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—792no—
380C22⋊C4—1581no—
381C22⋊C4—1581no—
382C22⋊C4—1581no—
383C22⋊C4—1581no—
384C22⋊C4—1581no—
385C22⋊C4—1581no—
386C22⋊C4—1581no—
387C22⋊C4C8×D7912yescomplemented
388C42—41no—
389C42—41no—
390C42—3161no—
391C42—3161no—
392C42—1581no—
393C42—1581no—
394C23—41no—
395C23—41no—
396C23—3161no—
397C23—3161no—
398C23—792no—
399C23—1581no—
400C23—1581no—
401C23C4⋊C4×D7911yescharacteristic
402C23(C22⋊D79)⋊C411yescharacteristic
403C23C4×D31611yescharacteristic
404C23C2×C8×D7911yescharacteristic
405C23M16×D7911yescharacteristic
406C23#1457916711yescharacteristic
407C23#1457916911yescharacteristic
408D4—1582no—
409D4—1582no—
410D4—1582no—
411D4—1582no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—3161no—
428C2×C4—3161no—
429C2×C4—3161no—
430C2×C4—3161no—
431C2×C4—3161no—
432C2×C4—3161no—
433C2×C4—3161no—
434C2×C4—3161no—
435C2×C4—3161no—
436C2×C4—792no—
437C2×C4—6321no—
438C2×C4—1582no—
439C2×C4—1581no—
440C2×C4—1581no—
441C2×C4—1581no—
442C2×C4—1581no—
443C2×C4#1457913111yescharacteristic
444C2×C4#1457913911yescharacteristic
445C2×C4#1457914111yescharacteristic
446C2×C4#1457914311yescharacteristic
447C8—41no—
448C8—41no—
449C8—81no—
450C8—3162no—
451C8—3161no—
452C8—3161no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—3162no—
464C22—3161no—
465C22—3161no—
466C22—6321no—
467C22—1582no—
468C22#1909843711yescharacteristic
469C22C4⋊C8×D7911yescharacteristic
470C22#1909858811yescharacteristic
471C22(C22⋊D79)⋊C811yescharacteristic
472C22C8×D31611yescharacteristic
473C22#1909863611yescharacteristic
474C22#1909863711yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—81no—
480C4—3162no—
481C4—3161no—
482C4—3161no—
483C4—6321no—
484C4—1582no—
485C4#1909875111yescharacteristic
486C4#1909875411yescharacteristic
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—3162no—
494C2#2376357911yescharacteristic
495C2#2376368211yescharacteristic
496C2#2376368711yescharacteristic
subgroupG/H
centerC2×C4#14579131
commutatorC23×C79C22×C8
FrattiniC23×C4C22×D79
FittingC79×#1282C2
socleC22×C79#385
prime radicalC22×C22⋊D79C2×C4
cosocleC23×C4×C79C23
hypercenter#1282D79
hypocenterC79#8851
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
3. #23763580C2semidirect
4. #23763577C2semidirect
6. #23761246C2semidirect
7. C79×#1282C2semidirect
57. #14579075C8semidirect
114. C22⋊Dic79C2×C8semidirect
142. C22⋊C4×C79C2×C8semidirect
158. C22×D79C4⋊C8semidirect
194. C2×Dic79C4⋊C8semidirect
255. #1282D79semidirect
256. C79#8851semidirect
387. C22⋊C4C8×D79semidirect

Maximal subgroups

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

subgroupindex
#237724222
#237636902
#237635802
#237635772
C4×#145790752
#237612462
C79×#12822
#885179