Finite Group Databasebeta

← C29×#10198 #20305098

Subgroups — C29×#10198 #20305098

Order 7424.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3246C211yesmaximal, characteristic
2C29×#3209C211yesmaximal, characteristic, complemented
3C29×#3141C211yesmaximal, characteristic
4C29×#1987C211yesmaximal, characteristic, complemented
5C29×#1986C211yesmaximal, characteristic, complemented
6C29×#1502C211yesmaximal, characteristic
7C29×#1283C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C29×#532C2211yescharacteristic
10C2×C29×C4⋊Q8C2211yescharacteristic
11C29×#494—21no—
12C29×#489—22no—
13C29×#487—21no—
14C29×#487—21no—
15C29×#486—21no—
16C29×#476—21no—
17C29×#475—21no—
18C29×#465—22no—
19C29×#462—22no—
20C29×#461—21no—
21C29×#460—21no—
22C29×#451—22no—
23C29×#431C2211yescharacteristic
24C2×C29×C4⋊C8C2211yescharacteristic
25C29×#417—22no—
26C4×M16×C29C2211yescharacteristic
27C4×C4⋊C4×C29C2211yescharacteristic
28C29×#340—22no—
29C29×#339—22no—
30C29×#327—22no—
31C2×#41×C29—21no—
32C22×Q8×C29—21no—
33C2×Q16×C29—24no—
34C2×SD16×C29—22no—
35C2×M16×C29D412yes—
36C22×C8×C29D412yes—
37C29×C4⋊Q8—21no—
38C29×C4⋊Q8—21no—
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8D411yescharacteristic
41C29×C4⋊Q8D412yes—
42C29×C4⋊Q8D411yescharacteristic
43C29×C4⋊Q8D411yescharacteristic
44C29×#127D411yescharacteristic
45C29×#125—21no—
46C29×#124—21no—
47C29×C22⋊Q8—21no—
48C29×C22⋊Q8—21no—
49C29×#121—21no—
50C29×#121—21no—
51C4×Q8×C29—21no—
52C4×Q8×C29—21no—
53C4×D4×C29—21no—
54C4×D4×C29—21no—
55C29×#117—21no—
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29—21no—
58C2×C4⋊C4×C29—21no—
59C2×C42×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×#106—22no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×#103—24no—
66C29×#103—22no—
67C29×#103—24no—
68C29×#102—22no—
69C29×#102—24no—
70C29×C22⋊C8D412yes—
71C29×#97—21no—
72C4×C8×C29—21no—
73C4×C8×C29—21no—
74C29×#95—21no—
75#41×C29—42no—
76#41×C29—42no—
77C2×Q8×C29—21no—
78C2×Q8×C29—21no—
79C2×Q8×C29—21no—
80C2×Q8×C29—22no—
81C2×Q8×C29—41no—
82C2×Q8×C29—82no—
83C2×D4×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29—41no—
90C22×C4×C29C2×D411yescharacteristic
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29C2×D411yescharacteristic
93Q16×C29—84no—
94SD16×C29—82no—
95M16×C29—22no—
96M16×C29—22no—
97C2×C8×C29—22no—
98C2×C8×C29—22no—
99C2×C8×C29—22no—
100C2×C8×C29—42no—
101C4⋊C4×C29—22no—
102C4⋊C4×C29—22no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—21no—
105C4⋊C4×C29—21no—
106C4⋊C4×C29—22no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29—41no—
111C4⋊C4×C29—41no—
112C4⋊C4×C29—41no—
113C4⋊C4×C29—41no—
114C4⋊C4×C29—41no—
115C22⋊C4×C29—41no—
116C22⋊C4×C29—41no—
117C22⋊C4×C29—41no—
118C42×C29—41no—
119C42×C29—42no—
120C42×C29C2×D411yescharacteristic
121C42×C29C2×D411yescharacteristic
122C42×C29C2×D411yescharacteristic
123C42×C29#4111yescharacteristic
124#10198C2911yesmaximal, characteristic, direct product factor, Sylow
125C23×C29—41no—
126C23×C29#12711yescharacteristic
127Q8×C29—42no—
128Q8×C29—44no—
129Q8×C29—42no—
130Q8×C29—41no—
131Q8×C29—41no—
132Q8×C29—82no—
133D4×C29—42no—
134D4×C29—41no—
135D4×C29—41no—
136D4×C29—81no—
137D4×C29—81no—
138D4×C29—81no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—41no—
142C2×C4×C29—42no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—42no—
147C2×C4×C29—81no—
148C2×C4×C29—82no—
149C2×C4×C29—81no—
150C2×C4×C29—82no—
151C2×C4×C29#12011yescharacteristic
152C2×C4×C29#12011yescharacteristic
153C2×C4×C29#12011yescharacteristic
154C2×C4×C29#12111yescharacteristic
155C2×C4×C29#12111yescharacteristic
156C2×C4×C29#12111yescharacteristic
157C2×C4×C29#13512yes—
158C2×C4×C29#13712yes—
159C8×C29—42no—
160C8×C29—42no—
161C8×C29—42no—
162#3246C2×C2911yescharacteristic
163#3209C2×C2911yescharacteristic, complemented
164#3141C2×C2911yescharacteristic
165#1987C2×C2911yescharacteristic, complemented
166#1986C2×C2911yescharacteristic, complemented
167#1502C2×C2911yescharacteristic
168#1283C2×C2911yescharacteristic, complemented
169C22×C29—21no—
170C22×C29—21no—
171C22×C29—81no—
172C22×C29—81no—
173C22×C29—81no—
174C22×C29#39211yescharacteristic
175C22×C29#49511yescharacteristic
176C22×C29#49711yescharacteristic
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—82no—
181C4×C29—81no—
182C4×C29—82no—
183C4×C29—81no—
184C4×C29—81no—
185C4×C29#45212yes—
186C4×C29#45511yescharacteristic
187C4×C29#45611yescharacteristic
188C4×C29#46412yes—
189#533C22×C2911yescharacteristic
190#532C22×C2911yescharacteristic
191C2×C4⋊Q8C22×C2911yescharacteristic
192#494—21no—
193#489—22no—
194#487—21no—
195#487—21no—
196#486—21no—
197#476—21no—
198#475—21no—
199#465—22no—
200#462—22no—
201#461—21no—
202#460—21no—
203#451—22no—
204#431C22×C2911yescharacteristic
205C2×C4⋊C8C22×C2911yescharacteristic
206#417—22no—
207C4×M16C22×C2911yescharacteristic
208C4×C4⋊C4C22×C2911yescharacteristic
209#340—22no—
210#339—22no—
211#327—22no—
212C2×C29—21no—
213C2×C29—21no—
214C2×C29—161no—
215C2×C29#200711yescharacteristic
216C2×C29#200811yescharacteristic
217C2×C29#201511yescharacteristic
218C2×#41—21no—
219C22×Q8—21no—
220C2×Q16—24no—
221C2×SD16—22no—
222C2×M16D4×C2912yes—
223C22×C8D4×C2912yes—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8D4×C2912yes—
228C4⋊Q8D4×C2911yescharacteristic
229C4⋊Q8D4×C2911yescharacteristic
230C4⋊Q8D4×C2911yescharacteristic
231#127D4×C2911yescharacteristic
232#125—21no—
233#124—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236#121—21no—
237#121—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—21no—
241C4×D4—21no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C42—21no—
247C2×C42C23×C2911yescharacteristic
248#106—22no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252#103—24no—
253#103—24no—
254#103—22no—
255#102—24no—
256#102—22no—
257C22⋊C8D4×C2912yes—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261#95—21no—
262C29#1019811yescharacteristic, direct product factor, Sylow
263#41—42no—
264#41—42no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C2911yescharacteristic
279C22×C4C2×D4×C2911yescharacteristic
280C22×C4C2×D4×C2911yescharacteristic
281Q16—84no—
282SD16—82no—
283M16—22no—
284M16—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—42no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—41no—
307C42—42no—
308C42C2×D4×C2911yescharacteristic
309C42C2×D4×C2911yescharacteristic
310C42C2×D4×C2911yescharacteristic
311C42#41×C2911yescharacteristic
312C23—41no—
313C23C29×#12711yescharacteristic
314Q8—42no—
315Q8—44no—
316Q8—42no—
317Q8—41no—
318Q8—41no—
319Q8—82no—
320D4—42no—
321D4—41no—
322D4—41no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4C29×#12011yescharacteristic
339C2×C4C29×#12011yescharacteristic
340C2×C4C29×#12011yescharacteristic
341C2×C4C29×#12111yescharacteristic
342C2×C4C29×#12111yescharacteristic
343C2×C4C29×#12111yescharacteristic
344C2×C4C29×#13512yes—
345C2×C4C29×#13712yes—
346C8—42no—
347C8—42no—
348C8—42no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22C29×#39211yescharacteristic
355C22C29×#49511yescharacteristic
356C22C29×#49711yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4C29×#45212yes—
366C4C29×#45511yescharacteristic
367C4C29×#45611yescharacteristic
368C4C29×#46412yes—
369C2—21no—
370C2—21no—
371C2—161no—
372C2C29×#200711yescharacteristic
373C2C29×#200811yescharacteristic
374C2C29×#201511yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3209C2semidirect
4. C29×#1987C2semidirect
5. C29×#1986C2semidirect
7. C29×#1283C2semidirect
124. #10198C29direct (N × H)
163. #3209C2×C29semidirect
165. #1987C2×C29semidirect
166. #1986C2×C29semidirect
168. #1283C2×C29semidirect
262. C29#10198direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32462
C29×#32092
C29×#31412
C29×#19872
C29×#19862
C29×#15022
C29×#12832
#1019829