Finite Group Databasebeta

← C4×#19098354 #34203409

Subgroups — C4×#19098354 #34203409

Order 20224.

576 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14579142C211yesmaximal, characteristic
2C2×#19098354C212yesmaximal
3C4×#14579076C211yesmaximal, characteristic
4#23761519C212yesmaximal
5C4×#100×C79C211yesmaximal, characteristic
6C2×#14579142C2211yescharacteristic
7C22×C4×Dic79C411yescharacteristic, complemented
8C2×#14579076C2212yes—
9#19098451—21no—
10#19098444—21no—
11#19098443C2211yescharacteristic
12#19098435C411yescharacteristic, complemented
13#19098424C411yescharacteristic, complemented
14C4×Dic79⋊C4—21no—
15C4×C22⋊Dic79—21no—
16C4×C22⋊Dic79—21no—
17C4×C22⋊Dic79C411yescharacteristic, complemented
18#19098354C418yesdirect product factor
19#19098330—21no—
20C2×C4×D4×C79C2211yescharacteristic
21C2×#100×C79C2212yes—
22C4×M16×C79—21no—
23#343×C79—21no—
24C23×Dic79C2×C411yescharacteristic
25C23×Dic79C2×C411yescharacteristic
26#14579142—22no—
27#14579142C2×C414yes—
28C2×Dic79⋊C4—21no—
29C2×Dic79⋊C4—21no—
30C2×C22⋊Dic79—21no—
31C2×C22⋊Dic79—22no—
32C2×C22⋊Dic79—21no—
33C2×C22⋊Dic79C2×C411yescharacteristic
34C2×C22⋊Dic79C2×C411yescharacteristic
35C2×C4×Dic79—21no—
36C2×C4×Dic79—21no—
37C2×C4×Dic79—21no—
38C2×C4×Dic79—41no—
39C2×C4×Dic79—41no—
40C2×C4×Dic79—41no—
41#14579076—22no—
42#14579076C2×C414yes—
43C79⋊#95—21no—
44C79⋊#95—21no—
45C79⋊#95—21no—
46C79⋊#95—21no—
47C79⋊#95—21no—
48C79⋊#95—41no—
49C22×D4×C79C2311yescharacteristic
50C23×C4×C79C2×C411yescharacteristic
51C23×C4×C79D411yescharacteristic
52C2×M16×C79—22no—
53C4×D4×C79—41no—
54C4×D4×C79—41no—
55C2×C4⋊C4×C79D411yescharacteristic
56C2×C22⋊C4×C79C2×C411yescharacteristic
57C2×C22⋊C4×C79D411yescharacteristic
58C2×C42×C79D411yescharacteristic
59#100×C79—22no—
60#100×C79C2×C414yes—
61#97×C79—41no—
62C4×C8×C79—41no—
63C22×Dic79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C22×Dic79—41no—
69C22×Dic79—41no—
70C22×Dic79—41no—
71C22×Dic79—42no—
72C22×Dic79—42no—
73C22×Dic79C4212yescomplemented
74Dic79⋊C4—24no—
75Dic79⋊C4—42no—
76C22⋊Dic79—21no—
77C22⋊Dic79—24no—
78C22⋊Dic79—24no—
79C22⋊Dic79—41no—
80C22⋊Dic79—42no—
81C22⋊Dic79—42no—
82C22⋊Dic79C4212yescomplemented
83C4×Dic79—42no—
84C4×Dic79—42no—
85C4×Dic79—41no—
86C4×Dic79—41no—
87C4×Dic79—82no—
88C24×C79C22×C411yescharacteristic
89C24×C79C2×D411yescharacteristic
90C2×D4×C79—41no—
91C2×D4×C79—41no—
92C2×D4×C79C22×C412yes—
93C2×D4×C79#4112yes—
94C22×C4×C79—21no—
95C22×C4×C79—21no—
96C22×C4×C79—21no—
97C22×C4×C79—21no—
98C22×C4×C79—42no—
99C22×C4×C79—42no—
100C22×C4×C79C22⋊C411yescharacteristic
101C22×C4×C79C22⋊C411yescharacteristic
102C22×C4×C79C22⋊C411yescharacteristic
103C22×C4×C79C22⋊C411yescharacteristic
104C22×C4×C79C2×D411yescharacteristic
105M16×C79—24no—
106M16×C79—42no—
107C2×C8×C79—42no—
108C4⋊C4×C79—41no—
109C22⋊C4×C79—41no—
110C22⋊C4×C79—41no—
111C42×C79—21no—
112C42×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C23×C79—41no—
118C23×C79—41no—
119C23×C79—41no—
120C23×C79—41no—
121C23×C79C2×C4211yescharacteristic
122C23×C79C2×C22⋊C411yescharacteristic
123C23×C79#11711yescharacteristic
124C23×C79C4×D412yes—
125D4×C79—42no—
126D4×C79—42no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—22no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—42no—
134C2×C4×C79—42no—
135C2×C4×C79—42no—
136C2×C4×C79—41no—
137C2×C4×C79—41no—
138C2×C4×C79—41no—
139C2×C4×C79—81no—
140C2×C4×C79#9911yescharacteristic
141C2×C4×C79#9911yescharacteristic
142C2×C4×C79C4×D412yes—
143C2×Dic79—22no—
144C2×Dic79—22no—
145C2×Dic79—22no—
146C2×Dic79—41no—
147C2×Dic79—41no—
148C2×Dic79—41no—
149C2×Dic79—42no—
150C2×Dic79—42no—
151C2×Dic79—41no—
152C2×Dic79—41no—
153C2×Dic79—41no—
154C2×Dic79—42no—
155C2×Dic79—42no—
156C2×Dic79—41no—
157C2×Dic79—44no—
158C2×Dic79—41no—
159C2×Dic79—41no—
160C2×Dic79—82no—
161C2×Dic79—82no—
162C8×C79—44no—
163C22×C79—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79—22no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—42no—
171C22×C79—42no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79—81no—
177C22×C79C4×C22⋊C411yescharacteristic
178C22×C79C2×#9911yescharacteristic
179C22×C79#41011yescharacteristic
180C4×C79—21no—
181C4×C79—22no—
182C4×C79—41no—
183C4×C79—41no—
184C4×C79—41no—
185C4×C79#35212yescomplemented
186Dic79—42no—
187Dic79—42no—
188Dic79—42no—
189Dic79—81no—
190Dic79—84no—
191C4×#352—791nomaximal, Sylow
192C2×C79—21no—
193C2×C79—21no—
194C2×C79—42no—
195C2×C79—41no—
196C2×C79—41no—
197C2×C79C4×#9911yescharacteristic
198C2×C79C2×#35211yescharacteristic
199C2×C79#212011yescharacteristic
200C4×#123—791no—
201C2×#352—792no—
202C4×#100D7911yescharacteristic
203C4×#99—791no—
204#1390—792no—
205C79C4×#35211yescharacteristic, complemented, Sylow
206C2×#123—791no—
207C2×C4×D4C2×D7911yescharacteristic
208C22×C42—791no—
209C2×#100C2×D7912yes—
210C2×#99—792no—
211C4×M16—21no—
212#388—1581no—
213#387—1581no—
214#386—791no—
215#385—791no—
216#381—791no—
217C4×C4⋊C4—1581no—
218C4×C22⋊C4—791no—
219C4×C22⋊C4—1581no—
220C4×C22⋊C4—1581no—
221#352—798no—
222#343—21no—
223#342—1581no—
224C22×D4C22×D7911yescharacteristic
225C23×C4—791no—
226C23×C4—791no—
227C23×C4C4×D7911yescharacteristic
228C23×C4D31611yescharacteristic
229C2×M16—22no—
230#123—794no—
231#123—1582no—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—1581no—
235C2×C4⋊C4—1581no—
236C2×C4⋊C4C22⋊D7911yescharacteristic
237C2×C22⋊C4—791no—
238C2×C22⋊C4—791no—
239C2×C22⋊C4—1581no—
240C2×C22⋊C4—1582no—
241C2×C22⋊C4—1581no—
242C2×C22⋊C4C4×D7911yescharacteristic
243C2×C22⋊C4D31611yescharacteristic
244C2×C42—3161no—
245C2×C42—3161no—
246C2×C42—3161no—
247C2×C42—1581no—
248C2×C42—1581no—
249C2×C42—1581no—
250C2×C42C22⋊D7911yescharacteristic
251#100—22no—
252#100C4×D7914yes—
253#99—794no—
254#99—1582no—
255#97—41no—
256C4×C8—41no—
257#95—3161no—
258#95—1581no—
259#95—1581no—
260#95—1581no—
261#95—1581no—
262#95—1581no—
263C24C2×C4×D7911yescharacteristic
264C24C2×D31611yescharacteristic
265C2×D4—41no—
266C2×D4—41no—
267C2×D4C2×C4×D7912yes—
268C2×D4#1192962412yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—3161no—
276C22×C4—3161no—
277C22×C4—3161no—
278C22×C4—3162no—
279C22×C4—3162no—
280C22×C4—792no—
281C22×C4—1581no—
282C22×C4—1581no—
283C22×C4—1581no—
284C22×C4—1581no—
285C22×C4—1581no—
286C22×C4(C2×D79)⋊C411yescharacteristic
287C22×C4(C2×D79)⋊C411yescharacteristic
288C22×C4(C2×D79)⋊C411yescharacteristic
289C22×C4(C2×D79)⋊C411yescharacteristic
290C22×C4C2×C22⋊D7911yescharacteristic
291M16—24no—
292M16—42no—
293C2×C8—42no—
294C4⋊C4—41no—
295C4⋊C4—3162no—
296C4⋊C4—1584no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—3162no—
300C22⋊C4—3162no—
301C22⋊C4—3161no—
302C22⋊C4—792no—
303C22⋊C4—1584no—
304C22⋊C4—1581no—
305C22⋊C4—1584no—
306C42—21no—
307C42—21no—
308C42—3162no—
309C42—3162no—
310C42—3161no—
311C42—3161no—
312C42—6322no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C42×D7911yescharacteristic
322C23C2×(C2×D79)⋊C411yescharacteristic
323C23#1457911811yescharacteristic
324C23C4×D31612yes—
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—3161no—
341C2×C4—3161no—
342C2×C4—3161no—
343C2×C4—3162no—
344C2×C4—3162no—
345C2×C4—3161no—
346C2×C4—3161no—
347C2×C4—3161no—
348C2×C4—3162no—
349C2×C4—3162no—
350C2×C4—3161no—
351C2×C4—3161no—
352C2×C4—3164no—
353C2×C4—3161no—
354C2×C4—6322no—
355C2×C4—6322no—
356C2×C4—1582no—
357C2×C4—1582no—
358C2×C4—1582no—
359C2×C4#1457907511yescharacteristic
360C2×C4#1457907511yescharacteristic
361C2×C4C4×C22⋊D7912yes—
362C8—44no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22C4×(C2×D79)⋊C411yescharacteristic
378C22C2×#1457907511yescharacteristic
379C22#1909853611yescharacteristic
380C4—21no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—3162no—
386C4—3162no—
387C4—3162no—
388C4—6321no—
389C4—6324no—
390C4#1909835412yesdirect product factor
391C2—21no—
392C2—21no—
393C2—42no—
394C2—41no—
395C2—41no—
396C2C4×#1457907511yescharacteristic
397C2C2×#1909835411yescharacteristic
398C2#2376504211yescharacteristic
subgroupG/H
centerC2×C4#14579075
commutatorC23×C79C2×C42
FrattiniC22×D4C22×D79
FittingC4×#100×C79C2
socleC22×C79C2×#99
prime radical, cosocleC22×D4×C79C23
hypercenterC4×#100D79
hypocenterC79C4×#352
LCSG ▷ C23×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
7. C22×C4×Dic79C4semidirect
12. #19098435C4semidirect
13. #19098424C4semidirect
17. C4×C22⋊Dic79C4semidirect
18. #19098354C4direct (N × H)
73. C22×Dic79C42semidirect
82. C22⋊Dic79C42semidirect
185. C4×C79#352semidirect
205. C79C4×#352semidirect
390. C4#19098354direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#145791422
C2×#190983542
C4×#145790762
#237615192
C4×#100×C792
C4×#35279