Finite Group Databasebeta

← C29×#12997 #20307897

Subgroups — C29×#12997 #20307897

Order 7424.

492 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#473C211yesmaximal, characteristic
2C29×#2913C211yesmaximal, characteristic
3C29×#2141C211yesmaximal, characteristic, complemented
4C2×C29×#358C211yesmaximal, characteristic, complemented
5C2×C29×#350C211yesmaximal, characteristic
6C29×#1387C211yesmaximal, characteristic, complemented
7C29×#1382C211yesmaximal, characteristic, complemented
8C2×C29×#137—21no—
9C22×Q16×C29C2211yescharacteristic
10C2×C29×#131C2211yescharacteristic
11C29×#520—21no—
12C2×C29×M32C2211yescharacteristic
13C22×C16×C29C2211yescharacteristic
14C29×#473—22no—
15C29×#473C414yescomplemented
16C2×C29×#108C2211yescharacteristic
17C29×#428—22no—
18C29×#428—21no—
19C29×#427—21no—
20C29×#427C2211yescharacteristic
21C2×C29×#107—21no—
22C2×C29×#107C2211yescharacteristic
23C2×C29×#101—21no—
24C29×#358—22no—
25C29×#358—21no—
26C29×#358—21no—
27C29×#350—22no—
28C2×#41×C29D411yescharacteristic
29C22×Q8×C29—21no—
30C29×#137—24no—
31C29×#137—42no—
32C2×Q16×C29—21no—
33C2×Q16×C29—21no—
34C2×Q16×C29—21no—
35C2×Q16×C29—21no—
36C2×Q16×C29—21no—
37C2×Q16×C29—41no—
38C2×Q16×C29C2×C412yescomplemented
39C2×SD16×C29—41no—
40C29×#131—21no—
41C29×#131—21no—
42C29×#131C2×C412yes—
43C29×#131D412yes—
44C2×M16×C29—21no—
45C2×M16×C29—21no—
46C2×M16×C29D411yescharacteristic
47C22×C8×C29—21no—
48C22×C8×C29C2311yescharacteristic
49C4×Q8×C29—41no—
50C4×D4×C29—42no—
51C4×D4×C29—41no—
52C29×#117—22no—
53C29×#117—21no—
54C2×C4⋊C4×C29—22no—
55C2×C4⋊C4×C29—21no—
56C29×M32—21no—
57C29×M32—21no—
58C2×C16×C29—21no—
59C2×C16×C29—21no—
60C2×C16×C29—21no—
61C2×C16×C29—21no—
62C29×#108—21no—
63C29×#108C2×C412yescomplemented
64C29×#107—22no—
65C29×#107—21no—
66C29×#107D411yescharacteristic
67C29×#107D412yes—
68C29×#107D411yescharacteristic
69C29×#106—22no—
70C29×#106—21no—
71C29×#101—24no—
72#41×C29—21no—
73#41×C29—21no—
74#41×C29C22⋊C412yes—
75#41×C29SD1612yes—
76C2×Q8×C29—22no—
77C2×Q8×C29—41no—
78C2×Q8×C29—41no—
79C2×Q8×C29—41no—
80C2×Q8×C29—41no—
81C2×Q8×C29—41no—
82C2×Q8×C29D811yescharacteristic
83C2×D4×C29—21no—
84C2×D4×C29D811yescharacteristic
85C22×C4×C29—21no—
86C22×C4×C29—41no—
87C22×C4×C29—42no—
88C22×C4×C29—41no—
89C22×C4×C29C2×D411yescharacteristic
90Q16×C29—22no—
91Q16×C29—22no—
92Q16×C29—44no—
93Q16×C29—41no—
94Q16×C29—41no—
95SD16×C29—44no—
96M16×C29—21no—
97M16×C29—22no—
98M16×C29—22no—
99M16×C29—22no—
100M16×C29—41no—
101M16×C29C22⋊C412yes—
102C2×C8×C29—21no—
103C2×C8×C29—22no—
104C2×C8×C29—22no—
105C2×C8×C29—41no—
106C2×C8×C29C22×C411yescharacteristic
107C2×C8×C29C2×D411yescharacteristic
108C2×C8×C29C2×D411yescharacteristic
109C2×C8×C29C2×D411yescharacteristic
110C2×C8×C29#4111yescharacteristic
111C2×C8×C29#4111yescharacteristic
112C4⋊C4×C29—21no—
113C4⋊C4×C29—22no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—42no—
116C4⋊C4×C29—41no—
117C22⋊C4×C29—42no—
118C22⋊C4×C29—41no—
119C42×C29—42no—
120C42×C29—41no—
121C16×C29—41no—
122C16×C29—41no—
123#12997C2911yesmaximal, characteristic, direct product factor, Sylow
124C23×C29—21no—
125C23×C29AGL(1,ℤ/8)11yescharacteristic
126Q8×C29—21no—
127Q8×C29—42no—
128Q8×C29—42no—
129Q8×C29—81no—
130Q8×C29—81no—
131Q8×C29#10212yes—
132D4×C29—22no—
133D4×C29—22no—
134D4×C29—21no—
135D4×C29#10212yes—
136C2×C4×C29—21no—
137C2×C4×C29—22no—
138C2×C4×C29—22no—
139C2×C4×C29—42no—
140C2×C4×C29—41no—
141C2×C4×C29—42no—
142C2×C4×C29—41no—
143C2×C4×C29—81no—
144C2×C4×C29—81no—
145C2×C4×C29—161no—
146C2×C4×C29—162no—
147C2×C4×C29C2×C22⋊C411yescharacteristic
148C2×C4×C29#12011yescharacteristic
149C2×C4×C29#12311yescharacteristic
150C2×C4×C29C2×D811yescharacteristic
151C2×C4×C29C2×SD1611yescharacteristic
152C2×C4×C29#13711yescharacteristic
153C8×C29—22no—
154C8×C29—42no—
155C8×C29C4×D411yescharacteristic
156C8×C29C4×D411yescharacteristic
157C8×C29#12111yescharacteristic
158C8×C29#12111yescharacteristic
159C2×#473C2×C2911yescharacteristic
160#2913C2×C2911yescharacteristic
161#2141C2×C2911yescharacteristic, complemented
162C2×#358C2×C2911yescharacteristic, complemented
163C2×#350C2×C2911yescharacteristic
164#1387C2×C2911yescharacteristic, complemented
165#1382C2×C2911yescharacteristic, complemented
166C22×C29—21no—
167C22×C29—21no—
168C22×C29—22no—
169C22×C29—41no—
170C22×C29—41no—
171C22×C29#41711yescharacteristic
172C22×C29#44711yescharacteristic
173C22×C29#48111yescharacteristic
174C4×C29—22no—
175C4×C29—82no—
176C4×C29—82no—
177C4×C29—81no—
178C4×C29—81no—
179C4×C29#38611yescharacteristic
180C4×C29C2×#10211yescharacteristic
181C4×C29#44811yescharacteristic
182C4×C29#48011yescharacteristic
183C2×#137—21no—
184C22×Q16C22×C2911yescharacteristic
185C2×#131C22×C2911yescharacteristic
186#520—21no—
187C2×M32C22×C2911yescharacteristic
188C22×C16C22×C2911yescharacteristic
189#473—22no—
190#473C4×C2914yescomplemented
191C2×#108C22×C2911yescharacteristic
192#428—21no—
193#428—22no—
194#427—21no—
195#427C22×C2911yescharacteristic
196C2×#107—21no—
197C2×#107C22×C2911yescharacteristic
198C2×#101—21no—
199#358—22no—
200#358—21no—
201#358—21no—
202#350—22no—
203C2×C29—21no—
204C2×C29—21no—
205C2×C29—42no—
206C2×C29#187411yescharacteristic
207C2×C29#219411yescharacteristic
208C2×C29#219511yescharacteristic
209C2×#41D4×C2911yescharacteristic
210C22×Q8—21no—
211#137—24no—
212#137—42no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—41no—
219C2×Q16C2×C4×C2912yescomplemented
220C2×SD16—41no—
221#131—21no—
222#131—21no—
223#131C2×C4×C2912yes—
224#131D4×C2912yes—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16D4×C2911yescharacteristic
228C22×C8—21no—
229C22×C8C23×C2911yescharacteristic
230C4×Q8—41no—
231C4×D4—42no—
232C4×D4—41no—
233#117—22no—
234#117—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—21no—
237M32—21no—
238M32—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243#108—21no—
244#108C2×C4×C2912yescomplemented
245#107—22no—
246#107—21no—
247#107D4×C2911yescharacteristic
248#107D4×C2912yes—
249#107D4×C2911yescharacteristic
250#106—22no—
251#106—21no—
252#101—24no—
253C29#1299711yescharacteristic, direct product factor, Sylow
254#41—21no—
255#41—21no—
256#41C22⋊C4×C2912yes—
257#41SD16×C2912yes—
258C2×Q8—22no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8D8×C2911yescharacteristic
265C2×D4—21no—
266C2×D4D8×C2911yescharacteristic
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4C2×D4×C2911yescharacteristic
272Q16—22no—
273Q16—22no—
274Q16—44no—
275Q16—41no—
276Q16—41no—
277SD16—44no—
278M16—21no—
279M16—22no—
280M16—22no—
281M16—22no—
282M16—41no—
283M16C22⋊C4×C2912yes—
284C2×C8—21no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8C22×C4×C2911yescharacteristic
289C2×C8C2×D4×C2911yescharacteristic
290C2×C8C2×D4×C2911yescharacteristic
291C2×C8C2×D4×C2911yescharacteristic
292C2×C8#41×C2911yescharacteristic
293C2×C8#41×C2911yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C42—42no—
302C42—41no—
303C16—41no—
304C16—41no—
305C23—21no—
306C23C29×AGL(1,ℤ/8)11yescharacteristic
307Q8—21no—
308Q8—42no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312Q8C29×#10212yes—
313D4—22no—
314D4—22no—
315D4—21no—
316D4C29×#10212yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—161no—
327C2×C4—162no—
328C2×C4C2×C22⋊C4×C2911yescharacteristic
329C2×C4C29×#12011yescharacteristic
330C2×C4C29×#12311yescharacteristic
331C2×C4C2×D8×C2911yescharacteristic
332C2×C4C2×SD16×C2911yescharacteristic
333C2×C4C29×#13711yescharacteristic
334C8—22no—
335C8—42no—
336C8C4×D4×C2911yescharacteristic
337C8C4×D4×C2911yescharacteristic
338C8C29×#12111yescharacteristic
339C8C29×#12111yescharacteristic
340C22—21no—
341C22—21no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22C29×#41711yescharacteristic
346C22C29×#44711yescharacteristic
347C22C29×#48111yescharacteristic
348C4—22no—
349C4—82no—
350C4—81no—
351C4—81no—
352C4—82no—
353C4C29×#38611yescharacteristic
354C4C2×C29×#10211yescharacteristic
355C4C29×#44811yescharacteristic
356C4C29×#48011yescharacteristic
357C2—21no—
358C2—21no—
359C2—42no—
360C2C29×#187411yescharacteristic
361C2C29×#219411yescharacteristic
362C2C29×#219511yescharacteristic
subgroupG/H
center, socleC22×C29#447
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC2×#41×C29D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×#131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2141C2semidirect
4. C2×C29×#358C2semidirect
6. C29×#1387C2semidirect
7. C29×#1382C2semidirect
15. C29×#473C4semidirect
38. C2×Q16×C29C2×C4semidirect
63. C29×#108C2×C4semidirect
123. #12997C29direct (N × H)
161. #2141C2×C29semidirect
162. C2×#358C2×C29semidirect
164. #1387C2×C29semidirect
165. #1382C2×C29semidirect
190. #473C4×C29semidirect
219. C2×Q16C2×C4×C29semidirect
244. #108C2×C4×C29semidirect
253. C29#12997direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4732
C29×#29132
C29×#21412
C2×C29×#3582
C2×C29×#3502
C29×#13872
C29×#13822
#1299729