Finite Group Databasebeta

← C29×#9213 #20304113

Subgroups — C29×#9213 #20304113

Order 7424.

450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3106C211yesmaximal, characteristic
2C29×#2922C211yesmaximal, characteristic, complemented
3C29×#1525C211yesmaximal, characteristic, complemented
4C29×#1492C211yesmaximal, characteristic, complemented
5C29×#1489C211yesmaximal, characteristic, complemented
6C29×#1299C211yesmaximal, characteristic, complemented
7C29×#1278C211yesmaximal, characteristic, complemented
8C29×#532C2211yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C29×#482—21no—
11C29×#477C411yescharacteristic
12C29×#476C411yescharacteristic
13C29×#460C411yescharacteristic
14C29×#459C411yescharacteristic
15C29×#449—21no—
16C4×SD16×C29—21no—
17C4×D8×C29—21no—
18C29×#433—22no—
19C29×#431—22no—
20C29×#431C2211yescharacteristic
21C29×#424—21no—
22C29×#423C2211yescharacteristic
23C29×#408—21no—
24C4×M16×C29C2211yescharacteristic
25C4×M16×C29C2211yescharacteristic
26C2×C4×C8×C29C2211yescharacteristic
27C29×#329—22no—
28C29×Q8⋊C8—21no—
29C29×D4⋊C8—22no—
30C29×D4⋊C8—21no—
31C2×#41×C29—21no—
32C2×#41×C29D411yescharacteristic
33C2×SD16×C29—21no—
34C2×D8×C29—21no—
35C2×M16×C29—21no—
36C2×M16×C29—21no—
37C2×M16×C29—21no—
38C22×C8×C29—21no—
39C29×C4⋊Q8C2×C411yescharacteristic
40C29×#127C2×C411yescharacteristic
41C29×#124—21no—
42C29×#121—21no—
43C29×#121—21no—
44C4×Q8×C29C2×C411yescharacteristic
45C4×Q8×C29D411yescharacteristic
46C4×D4×C29—21no—
47C4×D4×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29—21no—
50C4×D4×C29C2×C411yescharacteristic
51C4×D4×C29D411yescharacteristic
52C29×#117—21no—
53C29×#117D411yescharacteristic
54C2×C42×C29—21no—
55C2×C42×C29C2311yescharacteristic
56C29×#107—21no—
57C29×#106—21no—
58C29×C4⋊C8—24no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8C2×C411yescharacteristic
62C29×C4⋊C8C2×C411yescharacteristic
63C29×#103—21no—
64C29×#102—21no—
65C29×#102—21no—
66C29×#102—21no—
67C29×C22⋊C8—24no—
68C29×C22⋊C8—21no—
69C29×#97—21no—
70C29×#97D412yes—
71C4×C8×C29—21no—
72C4×C8×C29—21no—
73C4×C8×C29—21no—
74C4×C8×C29—21no—
75C4×C8×C29D412yes—
76#41×C29—41no—
77#41×C29—41no—
78#41×C29—81no—
79#41×C29—81no—
80C2×Q8×C29—21no—
81C2×Q8×C29C22⋊C411yescharacteristic
82C2×D4×C29—21no—
83C2×D4×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—41no—
87C2×D4×C29C22⋊C411yescharacteristic
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—21no—
91C22×C4×C29—41no—
92C22×C4×C29C2×D411yescharacteristic
93C22×C4×C29#4111yescharacteristic
94C22×C4×C29#4111yescharacteristic
95SD16×C29—42no—
96D8×C29—42no—
97M16×C29—22no—
98M16×C29—41no—
99M16×C29—41no—
100M16×C29—41no—
101M16×C29—81no—
102C2×C8×C29—21no—
103C2×C8×C29—21no—
104C2×C8×C29—22no—
105C2×C8×C29—22no—
106C2×C8×C29—41no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29—41no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29C22⋊C411yescharacteristic
115C4⋊C4×C29C22⋊C411yescharacteristic
116C22⋊C4×C29—21no—
117C22⋊C4×C29—21no—
118C22⋊C4×C29—21no—
119C22⋊C4×C29—41no—
120C22⋊C4×C29—41no—
121C42×C29—21no—
122C42×C29—21no—
123C42×C29—21no—
124C42×C29C22×C411yescharacteristic
125C42×C29C2×D411yescharacteristic
126C42×C29C2×D411yescharacteristic
127C42×C29C2×D411yescharacteristic
128#9213C2911yesmaximal, characteristic, direct product factor, Sylow
129C23×C29—21no—
130C23×C29—41no—
131C23×C29#12311yescharacteristic
132Q8×C29—21no—
133Q8×C29—21no—
134Q8×C29—81no—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—42no—
138D4×C29—41no—
139D4×C29—41no—
140D4×C29—41no—
141D4×C29—41no—
142D4×C29—81no—
143D4×C29—82no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—42no—
154C2×C4×C29—41no—
155C2×C4×C29—41no—
156C2×C4×C29—41no—
157C2×C4×C29—41no—
158C2×C4×C29—41no—
159C2×C4×C29—81no—
160C2×C4×C29—81no—
161C2×C4×C29C2×C22⋊C411yescharacteristic
162C2×C4×C29C4×D411yescharacteristic
163C2×C4×C29C4×D411yescharacteristic
164C2×C4×C29#12011yescharacteristic
165C2×C4×C29#12111yescharacteristic
166C2×C4×C29#12111yescharacteristic
167C8×C29—42no—
168C8×C29—42no—
169C8×C29—42no—
170C8×C29—41no—
171C8×C29—41no—
172C8×C29—81no—
173#3106C2×C2911yescharacteristic
174#2922C2×C2911yescharacteristic, complemented
175#1525C2×C2911yescharacteristic, complemented
176#1492C2×C2911yescharacteristic, complemented
177#1489C2×C2911yescharacteristic, complemented
178#1299C2×C2911yescharacteristic, complemented
179#1278C2×C2911yescharacteristic, complemented
180C22×C29—21no—
181C22×C29—21no—
182C22×C29—21no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—81no—
187C22×C29—81no—
188C22×C29—81no—
189C22×C29#38611yescharacteristic
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—41no—
194C4×C29—41no—
195C4×C29—41no—
196C4×C29—81no—
197C4×C29#42111yescharacteristic
198C4×C29#42111yescharacteristic
199C4×C29#44311yescharacteristic
200C4×C29#44411yescharacteristic
201C4×C29#47111yescharacteristic
202C4×C29#47211yescharacteristic
203#532C22×C2911yescharacteristic
204C4×#41C22×C2911yescharacteristic
205#482—21no—
206#477C4×C2911yescharacteristic
207#476C4×C2911yescharacteristic
208#460C4×C2911yescharacteristic
209#459C4×C2911yescharacteristic
210#449—21no—
211C4×SD16—21no—
212C4×D8—21no—
213#433—22no—
214#431—22no—
215#431C22×C2911yescharacteristic
216#424—21no—
217#423C22×C2911yescharacteristic
218#408—21no—
219C4×M16C22×C2911yescharacteristic
220C4×M16C22×C2911yescharacteristic
221C2×C4×C8C22×C2911yescharacteristic
222#329—22no—
223Q8⋊C8—21no—
224D4⋊C8—21no—
225D4⋊C8—22no—
226C2×C29—41no—
227C2×C29—81no—
228C2×C29—161no—
229C2×C29#187611yescharacteristic
230C2×C29#189711yescharacteristic
231C2×C29#190711yescharacteristic
232C2×#41—21no—
233C2×#41D4×C2911yescharacteristic
234C2×SD16—21no—
235C2×D8—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C22×C8—21no—
240C4⋊Q8C2×C4×C2911yescharacteristic
241#127C2×C4×C2911yescharacteristic
242#124—21no—
243#121—21no—
244#121—21no—
245C4×Q8C2×C4×C2911yescharacteristic
246C4×Q8D4×C2911yescharacteristic
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C2×C4×C2911yescharacteristic
252C4×D4D4×C2911yescharacteristic
253#117—21no—
254#117D4×C2911yescharacteristic
255C2×C42—21no—
256C2×C42C23×C2911yescharacteristic
257#107—21no—
258#106—21no—
259C4⋊C8—24no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8C2×C4×C2911yescharacteristic
263C4⋊C8C2×C4×C2911yescharacteristic
264#103—21no—
265#102—21no—
266#102—21no—
267#102—21no—
268C22⋊C8—24no—
269C22⋊C8—21no—
270#97—21no—
271#97D4×C2912yes—
272C4×C8—21no—
273C4×C8—21no—
274C4×C8—21no—
275C4×C8—21no—
276C4×C8D4×C2912yes—
277C29#921311yescharacteristic, direct product factor, Sylow
278#41—41no—
279#41—41no—
280#41—81no—
281#41—81no—
282C2×Q8—21no—
283C2×Q8C22⋊C4×C2911yescharacteristic
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4C22⋊C4×C2911yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C2911yescharacteristic
295C22×C4#41×C2911yescharacteristic
296C22×C4#41×C2911yescharacteristic
297SD16—42no—
298D8—42no—
299M16—22no—
300M16—41no—
301M16—41no—
302M16—41no—
303M16—81no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4C22⋊C4×C2911yescharacteristic
317C4⋊C4C22⋊C4×C2911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C22×C4×C2911yescharacteristic
327C42C2×D4×C2911yescharacteristic
328C42C2×D4×C2911yescharacteristic
329C42C2×D4×C2911yescharacteristic
330C23—21no—
331C23—41no—
332C23C29×#12311yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—81no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—41no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—81no—
344D4—82no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C2×C22⋊C4×C2911yescharacteristic
363C2×C4C4×D4×C2911yescharacteristic
364C2×C4C4×D4×C2911yescharacteristic
365C2×C4C29×#12011yescharacteristic
366C2×C4C29×#12111yescharacteristic
367C2×C4C29×#12111yescharacteristic
368C8—42no—
369C8—42no—
370C8—42no—
371C8—41no—
372C8—41no—
373C8—81no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22C29×#38611yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4C29×#42111yescharacteristic
392C4C29×#42111yescharacteristic
393C4C29×#44311yescharacteristic
394C4C29×#44411yescharacteristic
395C4C29×#47111yescharacteristic
396C4C29×#47211yescharacteristic
397C2—41no—
398C2—81no—
399C2—161no—
400C2C29×#187611yescharacteristic
401C2C29×#189711yescharacteristic
402C2C29×#190711yescharacteristic
subgroupG/H
centerC2×C4×C29#121
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC29×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2922C2semidirect
3. C29×#1525C2semidirect
4. C29×#1492C2semidirect
5. C29×#1489C2semidirect
6. C29×#1299C2semidirect
7. C29×#1278C2semidirect
128. #9213C29direct (N × H)
174. #2922C2×C29semidirect
175. #1525C2×C29semidirect
176. #1492C2×C29semidirect
177. #1489C2×C29semidirect
178. #1299C2×C29semidirect
179. #1278C2×C29semidirect
277. C29#9213direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31062
C29×#29222
C29×#15252
C29×#14922
C29×#14892
C29×#12992
C29×#12782
#921329