Finite Group Databasebeta

← C29×#9312 #20304212

Subgroups — C29×#9312 #20304212

Order 7424.

492 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3116C211yesmaximal, characteristic
2C29×#2875C211yesmaximal, characteristic
3C29×#1531C211yesmaximal, characteristic, complemented
4C29×#1488C211yesmaximal, characteristic
5C29×#1485C211yesmaximal, characteristic, complemented
6C29×#1302C211yesmaximal, characteristic, complemented
7C29×#1291C211yesmaximal, characteristic, complemented
8C2×C29×#131—21no—
9C29×#533C2211yescharacteristic
10C4×#41×C29C2211yescharacteristic
11C29×#485—21no—
12C29×#477C411yescharacteristic
13C29×#476C411yescharacteristic
14C29×#462C411yescharacteristic
15C29×#461C411yescharacteristic
16C29×#452—21no—
17C29×#441—21no—
18C29×#440—21no—
19C29×#432C2211yescharacteristic
20C29×#432C2211yescharacteristic
21C29×#431C2211yescharacteristic
22C29×#405—22no—
23C29×#405—21no—
24C4×M16×C29—21no—
25C4×M16×C29C2211yescharacteristic
26C2×C29×#97—21no—
27C2×C29×#97C2211yescharacteristic
28C29×#330—21no—
29C29×#330—21no—
30C29×Q8⋊C8—22no—
31C29×Q8⋊C8—21no—
32C29×D4⋊C8—21no—
33C2×#41×C29D411yescharacteristic
34C2×Q16×C29—21no—
35C2×SD16×C29—21no—
36C29×#131—24no—
37C29×#131—24no—
38C2×M16×C29—22no—
39C2×M16×C29—21no—
40C22×C8×C29—22no—
41C22×C8×C29—21no—
42C29×C4⋊Q8C2×C411yescharacteristic
43C29×C4⋊Q8C2×C411yescharacteristic
44C29×#125—21no—
45C29×C22⋊Q8—21no—
46C29×C22⋊Q8—21no—
47C4×Q8×C29—21no—
48C4×Q8×C29—21no—
49C4×Q8×C29C2×C411yescharacteristic
50C4×Q8×C29D411yescharacteristic
51C4×D4×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29C2×C411yescharacteristic
54C4×D4×C29D411yescharacteristic
55C29×#117—21no—
56C29×#117—21no—
57C29×#117D411yescharacteristic
58C2×C42×C29—21no—
59C2×C42×C29C2311yescharacteristic
60C29×#107—21no—
61C29×#106—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8C2×C411yescharacteristic
65C29×C4⋊C8C2×C411yescharacteristic
66C29×#103—21no—
67C29×#103—21no—
68C29×#103—21no—
69C29×#102—21no—
70C29×C22⋊C8—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×#97—22no—
74C29×#97—21no—
75C29×#97—21no—
76C29×#97—21no—
77C29×#97—21no—
78C29×#97D411yescharacteristic
79C29×#97D411yescharacteristic
80C4×C8×C29—22no—
81C4×C8×C29—21no—
82C4×C8×C29D412yes—
83#41×C29—22no—
84#41×C29—22no—
85C2×Q8×C29—21no—
86C2×Q8×C29—21no—
87C2×Q8×C29C22⋊C411yescharacteristic
88C2×D4×C29—21no—
89C2×D4×C29C22⋊C411yescharacteristic
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29C2×D411yescharacteristic
94C22×C4×C29#4111yescharacteristic
95C22×C4×C29#4111yescharacteristic
96Q16×C29—42no—
97SD16×C29—42no—
98M16×C29—28no—
99M16×C29—22no—
100M16×C29—22no—
101C2×C8×C29—28no—
102C2×C8×C29—22no—
103C2×C8×C29—22no—
104C2×C8×C29—21no—
105C2×C8×C29—21no—
106C2×C8×C29—22no—
107C2×C8×C29—21no—
108C2×C8×C29—21no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—41no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29C22⋊C411yescharacteristic
120C4⋊C4×C29C22⋊C411yescharacteristic
121C22⋊C4×C29—21no—
122C22⋊C4×C29—21no—
123C22⋊C4×C29—21no—
124C22⋊C4×C29—41no—
125C42×C29—21no—
126C42×C29—21no—
127C42×C29—21no—
128C42×C29—41no—
129C42×C29C22×C411yescharacteristic
130C42×C29C2×D411yescharacteristic
131C42×C29C2×D411yescharacteristic
132C42×C29C2×D411yescharacteristic
133#9312C2911yesmaximal, characteristic, direct product factor, Sylow
134C23×C29—21no—
135C23×C29#12311yescharacteristic
136Q8×C29—21no—
137Q8×C29—42no—
138Q8×C29—41no—
139Q8×C29—41no—
140Q8×C29#10412yes—
141D4×C29—24no—
142D4×C29—21no—
143D4×C29#10412yes—
144C2×C4×C29—24no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—41no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—81no—
155C2×C4×C29—81no—
156C2×C4×C29C2×C22⋊C411yescharacteristic
157C2×C4×C29C4×D411yescharacteristic
158C2×C4×C29C4×D411yescharacteristic
159C2×C4×C29#12011yescharacteristic
160C2×C4×C29#12111yescharacteristic
161C2×C4×C29#12111yescharacteristic
162C8×C29—22no—
163C8×C29—22no—
164C8×C29—24no—
165C8×C29—41no—
166C8×C29—41no—
167C8×C29—81no—
168C8×C29—81no—
169#3116C2×C2911yescharacteristic
170#2875C2×C2911yescharacteristic
171#1531C2×C2911yescharacteristic, complemented
172#1488C2×C2911yescharacteristic
173#1485C2×C2911yescharacteristic, complemented
174#1302C2×C2911yescharacteristic, complemented
175#1291C2×C2911yescharacteristic, complemented
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—22no—
179C22×C29—21no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29#38611yescharacteristic
183C4×C29—21no—
184C4×C29—21no—
185C4×C29—21no—
186C4×C29—22no—
187C4×C29—21no—
188C4×C29—21no—
189C4×C29—41no—
190C4×C29—41no—
191C4×C29—81no—
192C4×C29—81no—
193C4×C29C2×#10411yescharacteristic
194C4×C29C2×#10411yescharacteristic
195C2×#131—21no—
196#533C22×C2911yescharacteristic
197C4×#41C22×C2911yescharacteristic
198#485—21no—
199#477C4×C2911yescharacteristic
200#476C4×C2911yescharacteristic
201#462C4×C2911yescharacteristic
202#461C4×C2911yescharacteristic
203#452—21no—
204#441—21no—
205#440—21no—
206#432C22×C2911yescharacteristic
207#432C22×C2911yescharacteristic
208#431C22×C2911yescharacteristic
209#405—21no—
210#405—22no—
211C4×M16—21no—
212C4×M16C22×C2911yescharacteristic
213C2×#97—21no—
214C2×#97C22×C2911yescharacteristic
215#330—21no—
216#330—21no—
217Q8⋊C8—21no—
218Q8⋊C8—22no—
219D4⋊C8—21no—
220C2×C29—41no—
221C2×C29—42no—
222C2×C29#188111yescharacteristic
223C2×C29#189611yescharacteristic
224C2×C29#190211yescharacteristic
225C2×#41D4×C2911yescharacteristic
226C2×Q16—21no—
227C2×SD16—21no—
228#131—24no—
229#131—24no—
230C2×M16—22no—
231C2×M16—21no—
232C22×C8—22no—
233C22×C8—21no—
234C4⋊Q8C2×C4×C2911yescharacteristic
235C4⋊Q8C2×C4×C2911yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C2×C4×C2911yescharacteristic
242C4×Q8D4×C2911yescharacteristic
243C4×D4—21no—
244C4×D4—21no—
245C4×D4C2×C4×C2911yescharacteristic
246C4×D4D4×C2911yescharacteristic
247#117—21no—
248#117—21no—
249#117D4×C2911yescharacteristic
250C2×C42—21no—
251C2×C42C23×C2911yescharacteristic
252#107—21no—
253#106—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8C2×C4×C2911yescharacteristic
257C4⋊C8C2×C4×C2911yescharacteristic
258#103—21no—
259#103—21no—
260#103—21no—
261#102—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265#97—22no—
266#97—21no—
267#97—21no—
268#97—21no—
269#97—21no—
270#97D4×C2911yescharacteristic
271#97D4×C2911yescharacteristic
272C4×C8—22no—
273C4×C8—21no—
274C4×C8D4×C2912yes—
275C29#931211yescharacteristic, direct product factor, Sylow
276#41—22no—
277#41—22no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8C22⋊C4×C2911yescharacteristic
281C2×D4—21no—
282C2×D4C22⋊C4×C2911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4C2×D4×C2911yescharacteristic
287C22×C4#41×C2911yescharacteristic
288C22×C4#41×C2911yescharacteristic
289Q16—42no—
290SD16—42no—
291M16—28no—
292M16—22no—
293M16—22no—
294C2×C8—28no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—21no—
298C2×C8—22no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—41no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4C22⋊C4×C2911yescharacteristic
313C4⋊C4C22⋊C4×C2911yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—41no—
318C42—21no—
319C42—21no—
320C42—21no—
321C42—41no—
322C42C22×C4×C2911yescharacteristic
323C42C2×D4×C2911yescharacteristic
324C42C2×D4×C2911yescharacteristic
325C42C2×D4×C2911yescharacteristic
326C23—21no—
327C23C29×#12311yescharacteristic
328Q8—21no—
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8C29×#10412yes—
333D4—24no—
334D4—21no—
335D4C29×#10412yes—
336C2×C4—24no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4C2×C22⋊C4×C2911yescharacteristic
349C2×C4C4×D4×C2911yescharacteristic
350C2×C4C4×D4×C2911yescharacteristic
351C2×C4C29×#12011yescharacteristic
352C2×C4C29×#12111yescharacteristic
353C2×C4C29×#12111yescharacteristic
354C8—22no—
355C8—22no—
356C8—24no—
357C8—41no—
358C8—41no—
359C8—81no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22C29×#38611yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—22no—
374C4—41no—
375C4—41no—
376C4—81no—
377C4—81no—
378C4C2×C29×#10411yescharacteristic
379C4C2×C29×#10411yescharacteristic
380C2—41no—
381C2—42no—
382C2C29×#188111yescharacteristic
383C2C29×#189611yescharacteristic
384C2C29×#190211yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC2×#41×C29D4
LCSG ▷ 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×#1531C2semidirect
5. C29×#1485C2semidirect
6. C29×#1302C2semidirect
7. C29×#1291C2semidirect
133. #9312C29direct (N × H)
171. #1531C2×C29semidirect
173. #1485C2×C29semidirect
174. #1302C2×C29semidirect
175. #1291C2×C29semidirect
275. C29#9312direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31162
C29×#28752
C29×#15312
C29×#14882
C29×#14852
C29×#13022
C29×#12912
#931229