Finite Group Databasebeta

← #34205170

Subgroups — #34205170

Order 20224.

510 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D79C211yesmaximal, characteristic, complemented
2C2×#19098632C211yesmaximal, characteristic
3C2×#19098345C211yesmaximal, characteristic, complemented
4#23765010C211yesmaximal, characteristic, complemented
5#23761483C211yesmaximal, characteristic, complemented
6#23761483C211yesmaximal, characteristic, complemented
7C2×#349×C79C211yesmaximal, characteristic, complemented
8C22×C8×D79C2211yescharacteristic
9C2×C4×C22⋊D79C411yescharacteristic
10C2×#14579101C2211yescharacteristic
11C2×#14579101C2211yescharacteristic
12C2×#14579100—21no—
13M32×D79—22no—
14M32×D79—22no—
15C2×C16×D79—21no—
16#19098632—21no—
17#19098632—21no—
18#19098632—21no—
19#19098632—21no—
20C2×Dic79⋊C8C411yescharacteristic
21C2×C22⋊(C79⋊C8)C411yescharacteristic
22C2×(C2×D79)⋊C8C411yescharacteristic
23C2×#14579071C2211yescharacteristic
24#19098345—22no—
25(C2×D79)⋊C16—21no—
26(C2×D79)⋊C16—21no—
27C22×M16×C79C2211yescharacteristic
28C2×M32×C79C2211yescharacteristic
29C2×M32×C79C2211yescharacteristic
30#349×C79—22no—
31C22×C22⋊D79C811yescharacteristic
32C22×C4×D79C2×C411yescharacteristic
33C22×C79⋊C8C2×C411yescharacteristic
34C22×C79⋊C8C2×C411yescharacteristic
35C2×C8×D79—21no—
36C2×C8×D79—21no—
37C2×C8×D79—21no—
38C2×C8×D79—21no—
39C2×C8×D79D411yescharacteristic
40C2×C8×D79D411yescharacteristic
41C2×C8×D79D411yescharacteristic
42C2×C8×D79D411yescharacteristic
43C4×C22⋊D79—21no—
44C4×C22⋊D79—21no—
45C4×C22⋊D79—21no—
46C4×C22⋊D79—21no—
47C2×Dic79⋊C4C811yescharacteristic
48C2×C22⋊Dic79C811yescharacteristic
49C2×(C2×D79)⋊C4C811yescharacteristic
50C2×C4×Dic79C2×C411yescharacteristic
51#14579101—21no—
52#14579101—21no—
53#14579101—21no—
54#14579101D412yescomplemented
55#14579100—24no—
56C2×C79⋊C16—21no—
57C2×C79⋊C16—21no—
58C16×D79—24no—
59Dic79⋊C8—21no—
60Dic79⋊C8—21no—
61C22⋊(C79⋊C8)—21no—
62C22⋊(C79⋊C8)—21no—
63(C2×D79)⋊C8—21no—
64(C2×D79)⋊C8—21no—
65#14579071—21no—
66#14579071—21no—
67C23×C4×C79C2×C411yescharacteristic
68C2×M16×C79—21no—
69C2×M16×C79—21no—
70C2×M16×C79—21no—
71C2×M16×C79—21no—
72C2×M16×C79—21no—
73C2×M16×C79—21no—
74C22×C8×C79C2×C411yescharacteristic
75C22×C8×C79C2311yescharacteristic
76M32×C79—21no—
77M32×C79—21no—
78M32×C79—21no—
79M32×C79D412yescomplemented
80C2×C16×C79—21no—
81C2×C16×C79—21no—
82C23×D79C2×C811yescharacteristic
83C2×C22⋊D79—21no—
84C2×C22⋊D79—21no—
85C2×C22⋊D79—42no—
86C22×Dic79C2×C811yescharacteristic
87C22×Dic79C2×C811yescharacteristic
88C22×Dic79C2×C811yescharacteristic
89C2×C4×D79—21no—
90C2×C4×D79—21no—
91C2×C4×D79—21no—
92C2×C4×D79—21no—
93C2×C4×D79C22⋊C411yescharacteristic
94C2×C4×D79C22⋊C411yescharacteristic
95C2×C4×D79M1611yescharacteristic
96C2×C4×D79M1611yescharacteristic
97C2×C79⋊C8—21no—
98C2×C79⋊C8—21no—
99C2×C79⋊C8—21no—
100C2×C79⋊C8—21no—
101C2×C79⋊C8—21no—
102C2×C79⋊C8C22⋊C411yescharacteristic
103C2×C79⋊C8C22⋊C411yescharacteristic
104C8×D79—21no—
105C8×D79—21no—
106C8×D79—21no—
107C8×D79—21no—
108C8×D79—21no—
109C8×D79—21no—
110C8×D79—21no—
111C8×D79—21no—
112Dic79⋊C4—21no—
113Dic79⋊C4—21no—
114C22⋊Dic79—21no—
115C22⋊Dic79—21no—
116(C2×D79)⋊C4—21no—
117(C2×D79)⋊C4—21no—
118C4×Dic79—21no—
119C4×Dic79—21no—
120C79⋊C16—22no—
121C79⋊C16—41no—
122C24×C79C2×C811yescharacteristic
123C22×C4×C79—21no—
124C22×C4×C79—21no—
125C22×C4×C79—21no—
126C22×C4×C79—21no—
127C22×C4×C79—21no—
128C22×C4×C79—21no—
129C22×C4×C79C2×C811yescharacteristic
130C22×C4×C79C22×C411yescharacteristic
131M16×C79—41no—
132M16×C79—41no—
133M16×C79—41no—
134M16×C79—41no—
135C2×C8×C79—21no—
136C2×C8×C79—21no—
137C2×C8×C79—21no—
138C2×C8×C79C2×D411yescharacteristic
139C2×C8×C79C2×D411yescharacteristic
140C2×C8×C79C2×D411yescharacteristic
141C2×C8×C79C2×D411yescharacteristic
142C2×C8×C79#4111yescharacteristic
143C2×C8×C79#4111yescharacteristic
144C16×C79—22no—
145C16×C79—41no—
146C23×C79—21no—
147C23×C79—21no—
148C23×C79—21no—
149C23×C79—41no—
150C23×C79—41no—
151C23×C79C22×C811yescharacteristic
152C22×D79—21no—
153C22×D79—21no—
154C22×D79—22no—
155C22×D79—41no—
156C22×D79C22⋊C811yescharacteristic
157C22×D79C22⋊C811yescharacteristic
158C2×C4×C79—21no—
159C2×C4×C79—21no—
160C2×C4×C79—21no—
161C2×C4×C79—41no—
162C2×C4×C79—41no—
163C2×C4×C79—41no—
164C2×C4×C79—41no—
165C2×C4×C79C2×C22⋊C411yescharacteristic
166C2×C4×C79C4×D411yescharacteristic
167C2×C4×C79C4×D411yescharacteristic
168C2×C4×C79C2×M1611yescharacteristic
169C2×C4×C79#13111yescharacteristic
170C2×C4×C79#13111yescharacteristic
171C22⋊D79—42no—
172C22⋊D79—42no—
173C2×Dic79—21no—
174C2×Dic79—21no—
175C2×Dic79—21no—
176C2×Dic79—21no—
177C2×Dic79—41no—
178C2×Dic79—41no—
179C2×Dic79C22⋊C811yescharacteristic
180C2×Dic79C22⋊C811yescharacteristic
181C4×D79—21no—
182C4×D79—21no—
183C4×D79—21no—
184C4×D79—21no—
185C4×D79—21no—
186C4×D79—21no—
187C4×D79—21no—
188C4×D79—21no—
189C8×C79—41no—
190C8×C79#12011yescharacteristic
191C8×C79#12111yescharacteristic
192C8×C79#12111yescharacteristic
193C8×C79#12311yescharacteristic
194C79⋊C8—21no—
195C79⋊C8—21no—
196C79⋊C8—41no—
197C22×C79—21no—
198C22×C79—21no—
199C22×C79—41no—
200C22×C79—41no—
201C22×C79—41no—
202C22×C79—81no—
203C22×C79—81no—
204C22×C79C2×C22⋊C811yescharacteristic
205C22×C79C8×D411yescharacteristic
206C22×C79C8×D411yescharacteristic
207C2×D79—21no—
208C2×D79—21no—
209C2×D79—21no—
210C2×D79—21no—
211C2×D79—21no—
212C2×D79—42no—
213C2×D79—42no—
214C2×D79#34912yescomplemented
215C4×C79—41no—
216C4×C79#38611yescharacteristic
217C4×C79#40811yescharacteristic
218C4×C79#43511yescharacteristic
219C4×C79#43511yescharacteristic
220Dic79—21no—
221Dic79—21no—
222Dic79—41no—
223Dic79—41no—
224#12985—791nomaximal, Sylow
225C2×C79—21no—
226C2×C79—21no—
227C2×C79—81no—
228C2×C79#186911yescharacteristic
229C2×C79C2×#34911yescharacteristic
230C2×C79#211511yescharacteristic
231D79—22no—
232D79—41no—
233C22×M32—791no—
234C2×#435—791no—
235C2×#349—791no—
236C2×#349D7911yescharacteristic, complemented
237#2112—791no—
238#1377—791no—
239#1377—791no—
240C79#1298511yescharacteristic, complemented, Sylow
241C22×M16C2×D7911yescharacteristic
242C23×C8—791no—
243C2×C4×D4—791no—
244C2×M32—791no—
245C2×M32—791no—
246C2×M32—1581no—
247C2×M32—1582no—
248C2×M32—1582no—
249C2×M32C2×D7911yescharacteristic
250C2×M32C2×D7911yescharacteristic
251C22×C16—1581no—
252#435—1581no—
253#435—1581no—
254#435—1581no—
255#435—1581no—
256C2×C4⋊C8—791no—
257C2×C22⋊C8—791no—
258C2×C22⋊C8—791no—
259C2×#97—791no—
260#349—22no—
261#349—1582no—
262C22⋊C16—1581no—
263C22⋊C16—1581no—
264C22×D4—791no—
265C23×C4—791no—
266C23×C4C4×D7911yescharacteristic
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C22×C8—791no—
274C22×C8—791no—
275C22×C8—791no—
276C22×C8—791no—
277C22×C8—791no—
278C22×C8—791no—
279C22×C8—1581no—
280C22×C8—1581no—
281C22×C8—1581no—
282C22×C8—1581no—
283C22×C8C4×D7911yescharacteristic
284C22×C8C22×D7911yescharacteristic
285C4×D4—1581no—
286C4×D4—1581no—
287C4×D4—1581no—
288C4×D4—1581no—
289C2×C4⋊C4—791no—
290C2×C22⋊C4—791no—
291C2×C22⋊C4—791no—
292C2×C42—791no—
293M32—21no—
294M32—21no—
295M32—21no—
296M32—792no—
297M32—1584no—
298M32—1581no—
299M32—1581no—
300M32—1581no—
301M32C22⋊D7912yescomplemented
302C2×C16—21no—
303C2×C16—21no—
304C2×C16—1584no—
305C2×C16—1581no—
306C2×C16—1581no—
307C4⋊C8—1581no—
308C4⋊C8—1581no—
309C22⋊C8—1581no—
310C22⋊C8—1581no—
311C22⋊C8—1581no—
312C22⋊C8—1581no—
313#97—1581no—
314#97—1581no—
315C24—791no—
316C24C8×D7911yescharacteristic
317C2×D4—3162no—
318C2×D4—1581no—
319C2×D4—1581no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—791no—
327C22×C4—791no—
328C22×C4—791no—
329C22×C4—791no—
330C22×C4—791no—
331C22×C4—791no—
332C22×C4—791no—
333C22×C4—1581no—
334C22×C4—1581no—
335C22×C4—1581no—
336C22×C4—1581no—
337C22×C4C8×D7911yescharacteristic
338C22×C4C2×C4×D7911yescharacteristic
339M16—41no—
340M16—41no—
341M16—41no—
342M16—41no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—791no—
347C2×C8—791no—
348C2×C8—1581no—
349C2×C8—1581no—
350C2×C8—1581no—
351C2×C8—1581no—
352C2×C8—1581no—
353C2×C8—1581no—
354C2×C8—1581no—
355C2×C8—1581no—
356C2×C8—1581no—
357C2×C8—1581no—
358C2×C8—1581no—
359C2×C8—1581no—
360C2×C8—1581no—
361C2×C8D4×D7911yescharacteristic
362C2×C8D4×D7911yescharacteristic
363C2×C8D4×D7911yescharacteristic
364C2×C8C2×C22⋊D7911yescharacteristic
365C2×C8#1192962311yescharacteristic
366C2×C8#1192962411yescharacteristic
367C4⋊C4—1581no—
368C4⋊C4—1581no—
369C22⋊C4—1581no—
370C22⋊C4—1581no—
371C22⋊C4—1581no—
372C22⋊C4—1581no—
373C42—1581no—
374C42—1581no—
375C16—22no—
376C16—41no—
377C16—3161no—
378C16—1582no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—41no—
383C23—41no—
384C23—3161no—
385C23—791no—
386C23—791no—
387C23—1582no—
388C23—1581no—
389C23—1581no—
390C23C2×C8×D7911yescharacteristic
391D4—3162no—
392D4—3162no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—3161no—
401C2×C4—3161no—
402C2×C4—791no—
403C2×C4—791no—
404C2×C4—1581no—
405C2×C4—1581no—
406C2×C4—1581no—
407C2×C4—1581no—
408C2×C4—1581no—
409C2×C4—1581no—
410C2×C4—1581no—
411C2×C4—1581no—
412C2×C4—1581no—
413C2×C4—1581no—
414C2×C4—1581no—
415C2×C4—1581no—
416C2×C4C22⋊C4×D7911yescharacteristic
417C2×C4(C22⋊D79)⋊C411yescharacteristic
418C2×C4C4×C22⋊D7911yescharacteristic
419C2×C4M16×D7911yescharacteristic
420C2×C4#1457916711yescharacteristic
421C2×C4#1457916911yescharacteristic
422C8—41no—
423C8—3161no—
424C8—1581no—
425C8—1581no—
426C8#1457912911yescharacteristic
427C8#1457913211yescharacteristic
428C8#1457913411yescharacteristic
429C8#1457914311yescharacteristic
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22—3162no—
438C22—3162no—
439C22—792no—
440C22—1581no—
441C22—1581no—
442C22—1581no—
443C22—1581no—
444C22—1581no—
445C22C22⋊C8×D7911yescharacteristic
446C22(C22⋊D79)⋊C811yescharacteristic
447C22C8×C22⋊D7911yescharacteristic
448C4—41no—
449C4—3161no—
450C4—3161no—
451C4—1581no—
452C4—1581no—
453C4#1909843911yescharacteristic
454C4#1909852811yescharacteristic
455C4#1909863211yescharacteristic
456C4#1909863711yescharacteristic
457C2—21no—
458C2—21no—
459C2—81no—
460C2—3161no—
461C2—1582no—
462C2#2376368911yescharacteristic
463C2#349×D7911yescharacteristic
464C2#2376501911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D79
commutatorC23×C79C22×C8
FrattiniC22×C8C22×D79
FittingC2×#349×C79C2
socleC22×C79C2×C22⋊C8
prime radicalC22×C22⋊D79C8
cosocleC22×C8×C79C23
hypercenterC2×#349D79
hypocenterC79#12985
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
1. C2×M32×D79C2semidirect
3. C2×#19098345C2semidirect
4. #23765010C2semidirect
5. #23761483C2semidirect
6. #23761483C2semidirect
7. C2×#349×C79C2semidirect
54. #14579101D4semidirect
79. M32×C79D4semidirect
214. C2×D79#349semidirect
236. C2×#349D79semidirect
240. C79#12985semidirect
301. M32C22⋊D79semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D792
C2×#190986322
C2×#190983452
#237650102
#237614832
C2×#349×C792
#1298579