Finite Group Databasebeta

← C29×#13023 #20307923

Subgroups — C29×#13023 #20307923

Order 7424.

474 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×#510C211yesmaximal, characteristic
2C29×#2951C211yesmaximal, characteristic
3C2×C29×#359C211yesmaximal, characteristic
4C2×C29×#358C211yesmaximal, characteristic, complemented
5C29×#1979C211yesmaximal, characteristic, complemented
6C29×#1387C211yesmaximal, characteristic, complemented
7C29×#1379C211yesmaximal, characteristic, complemented
8C2×C29×#135C2211yescharacteristic
9C22×Q16×C29C2211yescharacteristic
10C29×#520—21no—
11C29×#510—22no—
12C29×#510C414yescomplemented
13C2×C29×Q32—21no—
14C2×C29×SD32—21no—
15C2×C29×M32C2211yescharacteristic
16C22×C16×C29C2211yescharacteristic
17C29×#440—22no—
18C4×Q16×C29—21no—
19C4×D8×C29—21no—
20C2×C29×#108C2211yescharacteristic
21C2×C29×#107C2211yescharacteristic
22C29×#419—21no—
23C29×#417—21no—
24C2×C29×#101—21no—
25C29×#405C2211yescharacteristic
26C29×#359—22no—
27C29×#358—22no—
28C2×#41×C29—21no—
29C22×Q8×C29—21no—
30C29×#135—21no—
31C29×#135—21no—
32C29×#135C2×C412yes—
33C29×#135D412yes—
34C2×Q16×C29—21no—
35C2×Q16×C29—21no—
36C2×Q16×C29—21no—
37C2×Q16×C29—21no—
38C2×Q16×C29—21no—
39C2×Q16×C29C2×C412yescomplemented
40C2×Q16×C29D411yescharacteristic
41C2×SD16×C29—21no—
42C2×D8×C29D411yescharacteristic
43C2×M16×C29—21no—
44C2×M16×C29D411yescharacteristic
45C22×C8×C29C2311yescharacteristic
46C4×Q8×C29—22no—
47C4×D4×C29—22no—
48C4×D4×C29—42no—
49C29×#117—41no—
50C29×#117D411yescharacteristic
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29—41no—
53C29×Q32—24no—
54C29×SD32—24no—
55C29×M32—21no—
56C29×M32C2×C412yescomplemented
57C2×C16×C29—21no—
58C2×C16×C29—21no—
59C2×C16×C29—21no—
60C2×C16×C29—21no—
61C29×#108—21no—
62C29×#108—21no—
63C29×#107—21no—
64C29×#107D412yes—
65C29×#103—22no—
66C29×#103—41no—
67C29×#103—41no—
68C29×#102—22no—
69C29×#101—42no—
70C29×#97—21no—
71C4×C8×C29—21no—
72#41×C29—22no—
73#41×C29—22no—
74#41×C29—41no—
75#41×C29—41no—
76C2×Q8×C29—22no—
77C2×Q8×C29—21no—
78C2×Q8×C29—41no—
79C2×Q8×C29—41no—
80C2×Q8×C29—41no—
81C2×Q8×C29—41no—
82C2×Q8×C29—41no—
83C2×D4×C29—21no—
84C2×D4×C29—41no—
85C22×C4×C29—42no—
86C22×C4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29C2×D411yescharacteristic
90Q16×C29—22no—
91Q16×C29—22no—
92Q16×C29—21no—
93Q16×C29—41no—
94Q16×C29—41no—
95Q16×C29C22⋊C412yes—
96SD16×C29—22no—
97SD16×C29—22no—
98D8×C29—21no—
99D8×C29C22⋊C412yes—
100M16×C29—21no—
101M16×C29—21no—
102M16×C29—41no—
103M16×C29—41no—
104C2×C8×C29—21no—
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—22no—
113C4⋊C4×C29—42no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29D811yescharacteristic
116C4⋊C4×C29D811yescharacteristic
117C22⋊C4×C29—21no—
118C22⋊C4×C29—42no—
119C42×C29—21no—
120C42×C29—42no—
121C16×C29—22no—
122C16×C29—41no—
123#13023C2911yesmaximal, characteristic, direct product factor, Sylow
124C23×C29—41no—
125C23×C29AGL(1,ℤ/8)11yescharacteristic
126Q8×C29—22no—
127Q8×C29—41no—
128Q8×C29—42no—
129Q8×C29—42no—
130Q8×C29—81no—
131Q8×C29—81no—
132D4×C29—22no—
133D4×C29—42no—
134D4×C29—42no—
135D4×C29—41no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—41no—
139C2×C4×C29—42no—
140C2×C4×C29—42no—
141C2×C4×C29—42no—
142C2×C4×C29—42no—
143C2×C4×C29—81no—
144C2×C4×C29—81no—
145C2×C4×C29—162no—
146C2×C4×C29—161no—
147C2×C4×C29C4×D411yescharacteristic
148C2×C4×C29#12011yescharacteristic
149C2×C4×C29#12111yescharacteristic
150C2×C4×C29C2×D811yescharacteristic
151C2×C4×C29#13511yescharacteristic
152C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
153C8×C29—41no—
154C8×C29—81no—
155C8×C29C2×C22⋊C411yescharacteristic
156C8×C29C4×D411yescharacteristic
157C8×C29#12111yescharacteristic
158C8×C29#12311yescharacteristic
159C2×#510C2×C2911yescharacteristic
160#2951C2×C2911yescharacteristic
161C2×#359C2×C2911yescharacteristic
162C2×#358C2×C2911yescharacteristic, complemented
163#1979C2×C2911yescharacteristic, complemented
164#1387C2×C2911yescharacteristic, complemented
165#1379C2×C2911yescharacteristic, complemented
166C22×C29—21no—
167C22×C29—21no—
168C22×C29—42no—
169C22×C29—81no—
170C22×C29—81no—
171C22×C29#44211yescharacteristic
172C22×C29#44711yescharacteristic
173C22×C29#46311yescharacteristic
174C4×C29—42no—
175C4×C29—41no—
176C4×C29—41no—
177C4×C29—82no—
178C4×C29—82no—
179C4×C29#38611yescharacteristic
180C4×C29C4×D811yescharacteristic
181C4×C29#44911yescharacteristic
182C4×C29#45911yescharacteristic
183C2×#135C22×C2911yescharacteristic
184C22×Q16C22×C2911yescharacteristic
185#520—21no—
186#510—22no—
187#510C4×C2914yescomplemented
188C2×Q32—21no—
189C2×SD32—21no—
190C2×M32C22×C2911yescharacteristic
191C22×C16C22×C2911yescharacteristic
192#440—22no—
193C4×Q16—21no—
194C4×D8—21no—
195C2×#108C22×C2911yescharacteristic
196C2×#107C22×C2911yescharacteristic
197#419—21no—
198#417—21no—
199C2×#101—21no—
200#405C22×C2911yescharacteristic
201#359—22no—
202#358—22no—
203C2×C29—21no—
204C2×C29—21no—
205C2×C29—82no—
206C2×C29#187911yescharacteristic
207C2×C29#219411yescharacteristic
208C2×C29#219511yescharacteristic
209C2×#41—21no—
210C22×Q8—21no—
211#135—21no—
212#135—21no—
213#135C2×C4×C2912yes—
214#135D4×C2912yes—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16C2×C4×C2912yescomplemented
221C2×Q16D4×C2911yescharacteristic
222C2×SD16—21no—
223C2×D8D4×C2911yescharacteristic
224C2×M16—21no—
225C2×M16D4×C2911yescharacteristic
226C22×C8C23×C2911yescharacteristic
227C4×Q8—22no—
228C4×D4—22no—
229C4×D4—42no—
230#117—41no—
231#117D4×C2911yescharacteristic
232C2×C4⋊C4—21no—
233C2×C4⋊C4—41no—
234Q32—24no—
235SD32—24no—
236M32—21no—
237M32C2×C4×C2912yescomplemented
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242#108—21no—
243#108—21no—
244#107—21no—
245#107D4×C2912yes—
246#103—22no—
247#103—41no—
248#103—41no—
249#102—22no—
250#101—42no—
251#97—21no—
252C4×C8—21no—
253C29#1302311yescharacteristic, direct product factor, Sylow
254#41—22no—
255#41—22no—
256#41—41no—
257#41—41no—
258C2×Q8—22no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×D4—21no—
266C2×D4—41no—
267C22×C4—42no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×D4×C2911yescharacteristic
272Q16—22no—
273Q16—22no—
274Q16—21no—
275Q16—41no—
276Q16—41no—
277Q16C22⋊C4×C2912yes—
278SD16—22no—
279SD16—22no—
280D8—21no—
281D8C22⋊C4×C2912yes—
282M16—21no—
283M16—21no—
284M16—41no—
285M16—41no—
286C2×C8—21no—
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—22no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4D8×C2911yescharacteristic
298C4⋊C4D8×C2911yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—42no—
301C42—21no—
302C42—42no—
303C16—22no—
304C16—41no—
305C23—41no—
306C23C29×AGL(1,ℤ/8)11yescharacteristic
307Q8—22no—
308Q8—41no—
309Q8—42no—
310Q8—42no—
311Q8—81no—
312Q8—81no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—162no—
327C2×C4—161no—
328C2×C4C4×D4×C2911yescharacteristic
329C2×C4C29×#12011yescharacteristic
330C2×C4C29×#12111yescharacteristic
331C2×C4C2×D8×C2911yescharacteristic
332C2×C4C29×#13511yescharacteristic
333C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
334C8—41no—
335C8—81no—
336C8C2×C22⋊C4×C2911yescharacteristic
337C8C4×D4×C2911yescharacteristic
338C8C29×#12111yescharacteristic
339C8C29×#12311yescharacteristic
340C22—21no—
341C22—21no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22C29×#44211yescharacteristic
346C22C29×#44711yescharacteristic
347C22C29×#46311yescharacteristic
348C4—41no—
349C4—41no—
350C4—42no—
351C4—82no—
352C4—82no—
353C4C29×#38611yescharacteristic
354C4C4×D8×C2911yescharacteristic
355C4C29×#44911yescharacteristic
356C4C29×#45911yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C29×#187911yescharacteristic
361C2C29×#219411yescharacteristic
362C2C29×#219511yescharacteristic
subgroupG/H
center, socleC22×C29#447
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC2×C29×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C29×#358C2semidirect
5. C29×#1979C2semidirect
6. C29×#1387C2semidirect
7. C29×#1379C2semidirect
12. C29×#510C4semidirect
39. C2×Q16×C29C2×C4semidirect
56. C29×M32C2×C4semidirect
123. #13023C29direct (N × H)
162. C2×#358C2×C29semidirect
163. #1979C2×C29semidirect
164. #1387C2×C29semidirect
165. #1379C2×C29semidirect
187. #510C4×C29semidirect
220. C2×Q16C2×C4×C29semidirect
237. M32C2×C4×C29semidirect
253. C29#13023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5102
C29×#29512
C2×C29×#3592
C2×C29×#3582
C29×#19792
C29×#13872
C29×#13792
#1302329