Finite Group Databasebeta

← C29×#10201 #20305101

Subgroups — C29×#10201 #20305101

Order 7424.

528 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3246C211yesmaximal, characteristic
2C29×#3227C211yesmaximal, characteristic
3C29×#3165C211yesmaximal, characteristic, complemented
4C29×#1981C211yesmaximal, 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×#498—21no—
15C29×#486—21no—
16C29×#481—22no—
17C29×#476—22no—
18C29×#476—21no—
19C29×#475—21no—
20C29×#465—22no—
21C29×#461—21no—
22C29×#460—21no—
23C29×#431C2211yescharacteristic
24C29×#428—22no—
25C2×C29×C4⋊C8C2211yescharacteristic
26C2×C29×#104—22no—
27C2×C29×#103—22no—
28C4×M16×C29C2211yescharacteristic
29C4×C4⋊C4×C29C2211yescharacteristic
30C29×#328—22no—
31C2×#41×C29—21no—
32C22×Q8×C29—21no—
33C2×SD16×C29—22no—
34C2×M16×C29D412yes—
35C22×C8×C29D412yes—
36C29×C4⋊Q8—21no—
37C29×C4⋊Q8—21no—
38C29×C4⋊Q8—21no—
39C29×C4⋊Q8D411yescharacteristic
40C29×C4⋊Q8D411yescharacteristic
41C29×C4⋊Q8D411yescharacteristic
42C29×C4⋊Q8D412yes—
43C29×#127D411yescharacteristic
44C29×#125—21no—
45C29×#124—21no—
46C29×C22⋊Q8—21no—
47C29×C22⋊Q8—21no—
48C29×#121—21no—
49C29×#121—21no—
50C4×Q8×C29—21no—
51C4×Q8×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29—21no—
54C29×#117—21no—
55C2×C4⋊C4×C29—21no—
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29—21no—
58C2×C42×C29—21no—
59C2×C42×C29C2311yescharacteristic
60C29×#107—24no—
61C29×#106—24no—
62C29×#106—22no—
63C29×#106—24no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×#104—44no—
68C29×#103—22no—
69C29×#103—44no—
70C29×#102—22no—
71C29×#102—24no—
72C29×C22⋊C8D412yes—
73C29×#97—21no—
74C4×C8×C29—21no—
75C4×C8×C29—21no—
76C29×#95—21no—
77#41×C29—42no—
78#41×C29—42no—
79C2×Q8×C29—21no—
80C2×Q8×C29—21no—
81C2×Q8×C29—22no—
82C2×Q8×C29—21no—
83C2×Q8×C29—42no—
84C2×Q8×C29—42no—
85C2×Q8×C29—41no—
86C2×D4×C29—21no—
87C2×D4×C29—21no—
88C2×D4×C29—21no—
89C2×D4×C29—41no—
90C22×C4×C29—41no—
91C22×C4×C29—41no—
92C22×C4×C29—41no—
93C22×C4×C29C2×D411yescharacteristic
94C22×C4×C29C2×D411yescharacteristic
95C22×C4×C29C2×D411yescharacteristic
96SD16×C29—82no—
97M16×C29—22no—
98M16×C29SD1614yescomplemented
99C2×C8×C29—22no—
100C2×C8×C29—22no—
101C2×C8×C29—22no—
102C2×C8×C29—42no—
103C4⋊C4×C29—22no—
104C4⋊C4×C29—22no—
105C4⋊C4×C29—22no—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—41no—
113C4⋊C4×C29—41no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29—41no—
116C4⋊C4×C29—41no—
117C22⋊C4×C29—41no—
118C22⋊C4×C29—41no—
119C22⋊C4×C29—41no—
120C42×C29—41no—
121C42×C29—42no—
122C42×C29C2×D411yescharacteristic
123C42×C29C2×D411yescharacteristic
124C42×C29C2×D411yescharacteristic
125C42×C29#4111yescharacteristic
126#10201C2911yesmaximal, characteristic, direct product factor, Sylow
127C23×C29—41no—
128C23×C29#12711yescharacteristic
129Q8×C29—44no—
130Q8×C29—41no—
131Q8×C29—41no—
132Q8×C29—42no—
133Q8×C29—81no—
134Q8×C29—81no—
135Q8×C29—81no—
136D4×C29—42no—
137D4×C29—41no—
138D4×C29—41no—
139D4×C29—42no—
140D4×C29—81no—
141D4×C29—81no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—41no—
145C2×C4×C29—42no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—42no—
150C2×C4×C29—81no—
151C2×C4×C29—82no—
152C2×C4×C29—81no—
153C2×C4×C29—82no—
154C2×C4×C29#12011yescharacteristic
155C2×C4×C29#12011yescharacteristic
156C2×C4×C29#12011yescharacteristic
157C2×C4×C29#12111yescharacteristic
158C2×C4×C29#12111yescharacteristic
159C2×C4×C29#12111yescharacteristic
160C2×C4×C29C2×SD1612yes—
161C2×C4×C29#13712yes—
162C8×C29—24no—
163C8×C29—42no—
164C8×C29—42no—
165#3246C2×C2911yescharacteristic
166#3227C2×C2911yescharacteristic
167#3165C2×C2911yescharacteristic, complemented
168#1981C2×C2911yescharacteristic, complemented
169#1980C2×C2911yescharacteristic
170#1503C2×C2911yescharacteristic, complemented
171#1283C2×C2911yescharacteristic, complemented
172C22×C29—21no—
173C22×C29—21no—
174C22×C29—81no—
175C22×C29—81no—
176C22×C29—81no—
177C22×C29#39211yescharacteristic
178C22×C29#49211yescharacteristic
179C22×C29#49711yescharacteristic
180C4×C29—21no—
181C4×C29—21no—
182C4×C29—21no—
183C4×C29—82no—
184C4×C29—82no—
185C4×C29—81no—
186C4×C29—81no—
187C4×C29—81no—
188C4×C29#44812yes—
189C4×C29#45311yescharacteristic
190C4×C29#45411yescharacteristic
191C4×C29#46112yes—
192#533C22×C2911yescharacteristic
193#532C22×C2911yescharacteristic
194C2×C4⋊Q8C22×C2911yescharacteristic
195#501—22no—
196#500—21no—
197#498—21no—
198#498—21no—
199#486—21no—
200#481—22no—
201#476—22no—
202#476—21no—
203#475—21no—
204#465—22no—
205#461—21no—
206#460—21no—
207#431C22×C2911yescharacteristic
208#428—22no—
209C2×C4⋊C8C22×C2911yescharacteristic
210C2×#104—22no—
211C2×#103—22no—
212C4×M16C22×C2911yescharacteristic
213C4×C4⋊C4C22×C2911yescharacteristic
214#328—22no—
215C2×C29—21no—
216C2×C29—21no—
217C2×C29—161no—
218C2×C29#200611yescharacteristic
219C2×C29#200911yescharacteristic
220C2×C29#201311yescharacteristic
221C2×#41—21no—
222C22×Q8—21no—
223C2×SD16—22no—
224C2×M16D4×C2912yes—
225C22×C8D4×C2912yes—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C2912yes—
230C4⋊Q8D4×C2911yescharacteristic
231C4⋊Q8D4×C2911yescharacteristic
232C4⋊Q8D4×C2911yescharacteristic
233#127D4×C2911yescharacteristic
234#125—21no—
235#124—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238#121—21no—
239#121—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—21no—
243C4×D4—21no—
244#117—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C42—21no—
249C2×C42C23×C2911yescharacteristic
250#107—24no—
251#106—24no—
252#106—22no—
253#106—24no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257#104—44no—
258#103—22no—
259#103—44no—
260#102—22no—
261#102—24no—
262C22⋊C8D4×C2912yes—
263#97—21no—
264C4×C8—21no—
265C4×C8—21no—
266#95—21no—
267C29#1020111yescharacteristic, direct product factor, Sylow
268#41—42no—
269#41—42no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—41no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×D4×C2911yescharacteristic
285C22×C4C2×D4×C2911yescharacteristic
286C22×C4C2×D4×C2911yescharacteristic
287SD16—82no—
288M16—22no—
289M16SD16×C2914yescomplemented
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—42no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C42—41no—
312C42—42no—
313C42C2×D4×C2911yescharacteristic
314C42C2×D4×C2911yescharacteristic
315C42C2×D4×C2911yescharacteristic
316C42#41×C2911yescharacteristic
317C23—41no—
318C23C29×#12711yescharacteristic
319Q8—44no—
320Q8—41no—
321Q8—41no—
322Q8—42no—
323Q8—81no—
324Q8—81no—
325Q8—81no—
326D4—42no—
327D4—41no—
328D4—41no—
329D4—42no—
330D4—81no—
331D4—81no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4C29×#12011yescharacteristic
345C2×C4C29×#12011yescharacteristic
346C2×C4C29×#12011yescharacteristic
347C2×C4C29×#12111yescharacteristic
348C2×C4C29×#12111yescharacteristic
349C2×C4C29×#12111yescharacteristic
350C2×C4C2×SD16×C2912yes—
351C2×C4C29×#13712yes—
352C8—24no—
353C8—42no—
354C8—42no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22C29×#39211yescharacteristic
361C22C29×#49211yescharacteristic
362C22C29×#49711yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4C29×#44812yes—
372C4C29×#45311yescharacteristic
373C4C29×#45411yescharacteristic
374C4C29×#46112yes—
375C2—21no—
376C2—21no—
377C2—161no—
378C2C29×#200611yescharacteristic
379C2C29×#200911yescharacteristic
380C2C29×#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×#1981C2semidirect
6. C29×#1503C2semidirect
7. C29×#1283C2semidirect
98. M16×C29SD16semidirect
126. #10201C29direct (N × H)
167. #3165C2×C29semidirect
168. #1981C2×C29semidirect
170. #1503C2×C29semidirect
171. #1283C2×C29semidirect
267. C29#10201direct (N × H)
289. 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×#32272
C29×#31652
C29×#19812
C29×#19802
C29×#15032
C29×#12832
#1020129