Finite Group Databasebeta

← C29×#10197 #20305097

Subgroups — C29×#10197 #20305097

Order 7424.

524 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3246C211yesmaximal, characteristic
2C29×#3206C211yesmaximal, characteristic
3C29×#3165C211yesmaximal, characteristic, complemented
4C29×#1987C211yesmaximal, characteristic, complemented
5C29×#1980C211yesmaximal, characteristic
6C29×#1503C211yesmaximal, characteristic, complemented
7C29×#1283C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C29×#532C2211yescharacteristic
10C2×C29×C4⋊Q8C2211yescharacteristic
11C29×#501—22no—
12C29×#500—21no—
13C29×#498—21no—
14C29×#492—21no—
15C29×#487—21no—
16C29×#476—21no—
17C29×#475—21no—
18C29×#465—22no—
19C29×#461—22no—
20C29×#461—21no—
21C29×#460—21no—
22C29×#448—22no—
23C29×#431C2211yescharacteristic
24C29×#428—22no—
25C2×C29×C4⋊C8C2211yescharacteristic
26C2×C29×#104—22no—
27C4×M16×C29C2211yescharacteristic
28C4×C4⋊C4×C29C2211yescharacteristic
29C29×#340—22no—
30C29×#328—22no—
31C2×#41×C29—21no—
32C22×Q8×C29—21no—
33C2×SD16×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×#107—24no—
62C29×#106—24no—
63C29×#106—22no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×#104—44no—
68C29×#103—24no—
69C29×#103—22no—
70C29×#102—22no—
71C29×C22⋊C8D412yes—
72C29×#97—21no—
73C4×C8×C29—21no—
74C4×C8×C29—21no—
75C29×#95—21no—
76#41×C29—42no—
77#41×C29—42no—
78C2×Q8×C29—21no—
79C2×Q8×C29—22no—
80C2×Q8×C29—21no—
81C2×Q8×C29—21no—
82C2×Q8×C29—41no—
83C2×Q8×C29—82no—
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—21no—
87C2×D4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29—41no—
90C22×C4×C29—41no—
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29C2×D411yescharacteristic
93C22×C4×C29C2×D411yescharacteristic
94SD16×C29—84no—
95SD16×C29—82no—
96M16×C29—22no—
97M16×C29SD1614yescomplemented
98C2×C8×C29—22no—
99C2×C8×C29—22no—
100C2×C8×C29—22no—
101C2×C8×C29—42no—
102C4⋊C4×C29—22no—
103C4⋊C4×C29—22no—
104C4⋊C4×C29—21no—
105C4⋊C4×C29—21no—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—22no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—41no—
112C4⋊C4×C29—41no—
113C4⋊C4×C29—41no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29—41no—
116C22⋊C4×C29—41no—
117C22⋊C4×C29—41no—
118C22⋊C4×C29—41no—
119C42×C29—41no—
120C42×C29—42no—
121C42×C29C2×D411yescharacteristic
122C42×C29C2×D411yescharacteristic
123C42×C29C2×D411yescharacteristic
124C42×C29#4111yescharacteristic
125#10197C2911yesmaximal, characteristic, direct product factor, Sylow
126C23×C29—41no—
127C23×C29#12711yescharacteristic
128Q8×C29—44no—
129Q8×C29—41no—
130Q8×C29—41no—
131Q8×C29—42no—
132Q8×C29—81no—
133Q8×C29—82no—
134D4×C29—42no—
135D4×C29—41no—
136D4×C29—41no—
137D4×C29—42no—
138D4×C29—81no—
139D4×C29—81no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—41no—
143C2×C4×C29—42no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—42no—
148C2×C4×C29—81no—
149C2×C4×C29—82no—
150C2×C4×C29—81no—
151C2×C4×C29—82no—
152C2×C4×C29#12011yescharacteristic
153C2×C4×C29#12011yescharacteristic
154C2×C4×C29#12011yescharacteristic
155C2×C4×C29#12111yescharacteristic
156C2×C4×C29#12111yescharacteristic
157C2×C4×C29#12111yescharacteristic
158C2×C4×C29C2×SD1612yes—
159C2×C4×C29#13712yes—
160C8×C29—24no—
161C8×C29—42no—
162C8×C29—42no—
163#3246C2×C2911yescharacteristic
164#3206C2×C2911yescharacteristic
165#3165C2×C2911yescharacteristic, complemented
166#1987C2×C2911yescharacteristic, complemented
167#1980C2×C2911yescharacteristic
168#1503C2×C2911yescharacteristic, complemented
169#1283C2×C2911yescharacteristic, complemented
170C22×C29—21no—
171C22×C29—21no—
172C22×C29—81no—
173C22×C29—81no—
174C22×C29—81no—
175C22×C29#39211yescharacteristic
176C22×C29#49211yescharacteristic
177C22×C29#49711yescharacteristic
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—21no—
181C4×C29—82no—
182C4×C29—81no—
183C4×C29—82no—
184C4×C29—81no—
185C4×C29—81no—
186C4×C29#44812yes—
187C4×C29#45511yescharacteristic
188C4×C29#45611yescharacteristic
189C4×C29#46112yes—
190#533C22×C2911yescharacteristic
191#532C22×C2911yescharacteristic
192C2×C4⋊Q8C22×C2911yescharacteristic
193#501—22no—
194#500—21no—
195#498—21no—
196#492—21no—
197#487—21no—
198#476—21no—
199#475—21no—
200#465—22no—
201#461—22no—
202#461—21no—
203#460—21no—
204#448—22no—
205#431C22×C2911yescharacteristic
206#428—22no—
207C2×C4⋊C8C22×C2911yescharacteristic
208C2×#104—22no—
209C4×M16C22×C2911yescharacteristic
210C4×C4⋊C4C22×C2911yescharacteristic
211#340—22no—
212#328—22no—
213C2×C29—21no—
214C2×C29—21no—
215C2×C29—161no—
216C2×C29#200711yescharacteristic
217C2×C29#200811yescharacteristic
218C2×C29#201311yescharacteristic
219C2×#41—21no—
220C22×Q8—21no—
221C2×SD16—24no—
222C2×SD16—22no—
223C2×M16D4×C2912yes—
224C22×C8D4×C2912yes—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C2912yes—
229C4⋊Q8D4×C2911yescharacteristic
230C4⋊Q8D4×C2911yescharacteristic
231C4⋊Q8D4×C2911yescharacteristic
232#127D4×C2911yescharacteristic
233#125—21no—
234#124—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237#121—21no—
238#121—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42C23×C2911yescharacteristic
249#107—24no—
250#106—24no—
251#106—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255#104—44no—
256#103—24no—
257#103—22no—
258#102—22no—
259C22⋊C8D4×C2912yes—
260#97—21no—
261C4×C8—21no—
262C4×C8—21no—
263#95—21no—
264C29#1019711yescharacteristic, direct product factor, Sylow
265#41—42no—
266#41—42no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—41no—
272C2×Q8—82no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4C2×D4×C2911yescharacteristic
281C22×C4C2×D4×C2911yescharacteristic
282C22×C4C2×D4×C2911yescharacteristic
283SD16—84no—
284SD16—82no—
285M16—22no—
286M16SD16×C2914yescomplemented
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—42no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42—42no—
310C42C2×D4×C2911yescharacteristic
311C42C2×D4×C2911yescharacteristic
312C42C2×D4×C2911yescharacteristic
313C42#41×C2911yescharacteristic
314C23—41no—
315C23C29×#12711yescharacteristic
316Q8—44no—
317Q8—41no—
318Q8—41no—
319Q8—42no—
320Q8—81no—
321Q8—82no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4C29×#12011yescharacteristic
341C2×C4C29×#12011yescharacteristic
342C2×C4C29×#12011yescharacteristic
343C2×C4C29×#12111yescharacteristic
344C2×C4C29×#12111yescharacteristic
345C2×C4C29×#12111yescharacteristic
346C2×C4C2×SD16×C2912yes—
347C2×C4C29×#13712yes—
348C8—24no—
349C8—42no—
350C8—42no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C29×#39211yescharacteristic
357C22C29×#49211yescharacteristic
358C22C29×#49711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4C29×#44812yes—
368C4C29×#45511yescharacteristic
369C4C29×#45611yescharacteristic
370C4C29×#46112yes—
371C2—21no—
372C2—21no—
373C2—161no—
374C2C29×#200711yescharacteristic
375C2C29×#200811yescharacteristic
376C2C29×#201311yescharacteristic
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
3. C29×#3165C2semidirect
4. C29×#1987C2semidirect
6. C29×#1503C2semidirect
7. C29×#1283C2semidirect
97. M16×C29SD16semidirect
125. #10197C29direct (N × H)
165. #3165C2×C29semidirect
166. #1987C2×C29semidirect
168. #1503C2×C29semidirect
169. #1283C2×C29semidirect
264. C29#10197direct (N × H)
286. M16SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#32462
C29×#32062
C29×#31652
C29×#19872
C29×#19802
C29×#15032
C29×#12832
#1019729