Finite Group Databasebeta

← C29×#7770 #20302670

Subgroups — C29×#7770 #20302670

Order 7424.

460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2724C211yesmaximal, characteristic
2C29×#2058C211yesmaximal, characteristic, complemented
3C29×#2043C211yesmaximal, characteristic, complemented
4C29×#2023C211yesmaximal, characteristic
5C29×#1271C211yesmaximal, characteristic, complemented
6C29×#1271C211yesmaximal, characteristic, complemented
7C29×#1270C211yesmaximal, characteristic
8C2×C29×C4⋊Q8C2211yescharacteristic
9C2×C29×#123—21no—
10C2×C29×#106—21no—
11C2×C29×#103—21no—
12C2×C29×#103—21no—
13C2×C29×#102—21no—
14C29×#398—21no—
15C29×#397—21no—
16C29×#397—21no—
17C29×#390C2211yescharacteristic
18C29×#389C2211yescharacteristic
19C29×#389C2211yescharacteristic
20C29×#385—21no—
21C29×#385—21no—
22C29×#340—21no—
23C29×#340—21no—
24C29×#336C2211yescharacteristic
25C29×#336C2211yescharacteristic
26C29×#336C2211yescharacteristic
27C22×Q8×C29—21no—
28C22×D4×C29D411yescharacteristic
29C23×C4×C29—21no—
30C22×C8×C29—21no—
31C22×C8×C29—21no—
32C22×C8×C29—21no—
33C29×C4⋊Q8—42no—
34C29×#123—42no—
35C29×#123—42no—
36C2×C4⋊C4×C29—21no—
37C2×C4⋊C4×C29—21no—
38C2×C4⋊C4×C29—21no—
39C2×C4⋊C4×C29—21no—
40C2×C4⋊C4×C29—21no—
41C2×C4⋊C4×C29D411yescharacteristic
42C2×C4⋊C4×C29D411yescharacteristic
43C2×C4⋊C4×C29D411yescharacteristic
44C2×C4⋊C4×C29D411yescharacteristic
45C2×C4⋊C4×C29D411yescharacteristic
46C2×C22⋊C4×C29—21no—
47C2×C22⋊C4×C29—21no—
48C2×C22⋊C4×C29—21no—
49C2×C22⋊C4×C29—21no—
50C2×C22⋊C4×C29—21no—
51C2×C42×C29C2311yescharacteristic
52C29×#106—42no—
53C29×#103—42no—
54C29×#103—42no—
55C29×#102—42no—
56C29×#95—21no—
57C29×#95—21no—
58C29×#95—21no—
59C29×#95—21no—
60C29×#95—21no—
61C24×C29—21no—
62C2×Q8×C29—22no—
63C2×Q8×C29—41no—
64C2×Q8×C29—41no—
65C2×Q8×C29—41no—
66C2×Q8×C29—41no—
67C2×Q8×C29—41no—
68C2×D4×C29—21no—
69C2×D4×C29—41no—
70C2×D4×C29—41no—
71C2×D4×C29SD1612yes—
72C22×C4×C29—21no—
73C22×C4×C29—21no—
74C22×C4×C29—21no—
75C22×C4×C29—21no—
76C22×C4×C29—21no—
77C22×C4×C29—42no—
78C22×C4×C29—41no—
79C22×C4×C29—81no—
80C22×C4×C29—81no—
81C22×C4×C29C2×D411yescharacteristic
82C22×C4×C29C2×D411yescharacteristic
83C22×C4×C29C2×D411yescharacteristic
84C2×C8×C29—22no—
85C2×C8×C29—41no—
86C2×C8×C29—41no—
87C2×C8×C29—41no—
88C2×C8×C29—41no—
89C2×C8×C29—41no—
90C2×C8×C29—41no—
91C2×C8×C29—41no—
92C2×C8×C29—41no—
93C4⋊C4×C29—22no—
94C4⋊C4×C29—22no—
95C4⋊C4×C29—21no—
96C4⋊C4×C29—21no—
97C4⋊C4×C29—21no—
98C4⋊C4×C29—21no—
99C4⋊C4×C29—41no—
100C4⋊C4×C29—41no—
101C4⋊C4×C29—41no—
102C4⋊C4×C29—41no—
103C4⋊C4×C29—41no—
104C4⋊C4×C29—41no—
105C4⋊C4×C29—41no—
106C4⋊C4×C29—41no—
107C4⋊C4×C29—41no—
108C4⋊C4×C29—81no—
109C22⋊C4×C29—42no—
110C22⋊C4×C29—42no—
111C22⋊C4×C29—42no—
112C22⋊C4×C29—41no—
113C22⋊C4×C29—41no—
114C22⋊C4×C29—41no—
115C22⋊C4×C29—41no—
116C42×C29—41no—
117#7770C2911yesmaximal, characteristic, direct product factor, Sylow
118C23×C29—22no—
119C23×C29—41no—
120C23×C29—41no—
121C23×C29—41no—
122C23×C29—41no—
123C23×C29—41no—
124C23×C29—41no—
125C23×C29#12011yescharacteristic
126Q8×C29—42no—
127Q8×C29—42no—
128Q8×C29—81no—
129Q8×C29—81no—
130D4×C29—42no—
131D4×C29—81no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—41no—
139C2×C4×C29—41no—
140C2×C4×C29—41no—
141C2×C4×C29—41no—
142C2×C4×C29—41no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—41no—
150C2×C4×C29—41no—
151C2×C4×C29—42no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—84no—
155C2×C4×C29—81no—
156C2×C4×C29—81no—
157C2×C4×C29C2×SD1611yescharacteristic
158C2×C4×C29#13511yescharacteristic
159C2×C4×C29#13511yescharacteristic
160C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C29#13711yescharacteristic
163C8×C29—42no—
164C8×C29—81no—
165C8×C29—81no—
166#2724C2×C2911yescharacteristic
167#2058C2×C2911yescharacteristic, complemented
168#2043C2×C2911yescharacteristic, complemented
169#2023C2×C2911yescharacteristic
170#1271C2×C2911yescharacteristic, complemented
171#1271C2×C2911yescharacteristic, complemented
172#1270C2×C2911yescharacteristic
173C22×C29—42no—
174C22×C29—42no—
175C22×C29—42no—
176C22×C29—81no—
177C22×C29—81no—
178C22×C29—81no—
179C22×C29—81no—
180C22×C29#44911yescharacteristic
181C22×C29#45011yescharacteristic
182C22×C29#45211yescharacteristic
183C22×C29#45411yescharacteristic
184C22×C29#45511yescharacteristic
185C22×C29#45611yescharacteristic
186C22×C29B(4,𝔽2)11yescharacteristic
187C4×C29—21no—
188C4×C29—21no—
189C4×C29—21no—
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—82no—
194C4×C29—81no—
195C4×C29—81no—
196C4×C29—81no—
197C4×C29—81no—
198C4×C29—81no—
199C2×C4⋊Q8C22×C2911yescharacteristic
200C2×#123—21no—
201C2×#106—21no—
202C2×#103—21no—
203C2×#103—21no—
204C2×#102—21no—
205#398—21no—
206#397—21no—
207#397—21no—
208#390C22×C2911yescharacteristic
209#389C22×C2911yescharacteristic
210#389C22×C2911yescharacteristic
211#385—21no—
212#385—21no—
213#340—21no—
214#340—21no—
215#336C22×C2911yescharacteristic
216#336C22×C2911yescharacteristic
217#336C22×C2911yescharacteristic
218C2×C29—82no—
219C2×C29#159711yescharacteristic
220C2×C29#160111yescharacteristic
221C2×C29#160311yescharacteristic
222C2×C29#163511yescharacteristic
223C2×C29#164011yescharacteristic
224C2×C29#165411yescharacteristic
225C2×C29#166411yescharacteristic
226C22×Q8—21no—
227C22×D4D4×C2911yescharacteristic
228C23×C4—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C4⋊Q8—42no—
233#123—42no—
234#123—42no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4D4×C2911yescharacteristic
241C2×C4⋊C4D4×C2911yescharacteristic
242C2×C4⋊C4D4×C2911yescharacteristic
243C2×C4⋊C4D4×C2911yescharacteristic
244C2×C4⋊C4D4×C2911yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C42C23×C2911yescharacteristic
251#106—42no—
252#103—42no—
253#103—42no—
254#102—42no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260C29#777011yescharacteristic, direct product factor, Sylow
261C24—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4SD16×C2912yes—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4C2×D4×C2911yescharacteristic
282C22×C4C2×D4×C2911yescharacteristic
283C22×C4C2×D4×C2911yescharacteristic
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—81no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—41no—
317C23—22no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23C29×#12011yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—81no—
329D4—42no—
330D4—81no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—84no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4C2×SD16×C2911yescharacteristic
357C2×C4C29×#13511yescharacteristic
358C2×C4C29×#13511yescharacteristic
359C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
360C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
361C2×C4C29×#13711yescharacteristic
362C8—42no—
363C8—81no—
364C8—81no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22C29×#44911yescharacteristic
373C22C29×#45011yescharacteristic
374C22C29×#45211yescharacteristic
375C22C29×#45411yescharacteristic
376C22C29×#45511yescharacteristic
377C22C29×#45611yescharacteristic
378C22C29×B(4,𝔽2)11yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—81no—
386C4—82no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C2—82no—
392C2C29×#159711yescharacteristic
393C2C29×#160111yescharacteristic
394C2C29×#160311yescharacteristic
395C2C29×#163511yescharacteristic
396C2C29×#164011yescharacteristic
397C2C29×#165411yescharacteristic
398C2C29×#166411yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2058C2semidirect
3. C29×#2043C2semidirect
5. C29×#1271C2semidirect
6. C29×#1271C2semidirect
117. #7770C29direct (N × H)
167. #2058C2×C29semidirect
168. #2043C2×C29semidirect
170. #1271C2×C29semidirect
171. #1271C2×C29semidirect
260. C29#7770direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#27242
C29×#20582
C29×#20432
C29×#20232
C29×#12712
C29×#12702
#777029