Finite Group Databasebeta

← C29×#9215 #20304115

Subgroups — C29×#9215 #20304115

Order 7424.

578 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#476C211yesmaximal, characteristic
2C2×C8×D4×C29C211yesmaximal, characteristic
3C29×#1990C211yesmaximal, characteristic, complemented
4C29×#1802C211yesmaximal, characteristic
5C2×C29×#333C211yesmaximal, characteristic, complemented
6C29×#1296C211yesmaximal, characteristic, complemented
7C29×#1277C211yesmaximal, characteristic, complemented
8C23×C8×C29—21no—
9C2×C29×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C29C2211yescharacteristic
11C29×#476—22no—
12C29×#476C414yescomplemented
13C8×D4×C29—22no—
14C8×D4×C29—22no—
15C2×C29×#106—21no—
16C2×C29×C4⋊C8C2211yescharacteristic
17C2×C29×C4⋊C8C2211yescharacteristic
18C2×C29×C4⋊C8C2211yescharacteristic
19C2×C29×#102—21no—
20C2×C29×#102—21no—
21C2×C29×C22⋊C8—21no—
22C2×C4×C8×C29C2211yescharacteristic
23C29×#384C2211yescharacteristic
24C29×#340—21no—
25C29×#340—21no—
26C29×#340—21no—
27C29×#333—22no—
28C22×Q8×C29—21no—
29C22×D4×C29D411yescharacteristic
30C23×C4×C29—21no—
31C22×C8×C29—24no—
32C22×C8×C29—21no—
33C22×C8×C29—21no—
34C22×C8×C29—21no—
35C22×C8×C29—42no—
36C22×C8×C29—42no—
37C22×C8×C29D411yescharacteristic
38C22×C8×C29D411yescharacteristic
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8C2×C412yes—
43C4×D4×C29—21no—
44C4×D4×C29—21no—
45C4×D4×C29C2×C412yes—
46C4×D4×C29D412yes—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29—21no—
49C2×C4⋊C4×C29—21no—
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29D411yescharacteristic
53C2×C22⋊C4×C29—21no—
54C2×C42×C29C2311yescharacteristic
55C29×#106—24no—
56C29×C4⋊C8—21no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8C2×C412yes—
61C29×C4⋊C8D412yes—
62C29×#102—24no—
63C29×#102—42no—
64C29×C22⋊C8—24no—
65C4×C8×C29—21no—
66C4×C8×C29—21no—
67C24×C29—21no—
68C2×Q8×C29—22no—
69C2×Q8×C29—41no—
70C2×Q8×C29—81no—
71C2×Q8×C29—81no—
72C2×D4×C29—21no—
73C2×D4×C29—21no—
74C2×D4×C29—21no—
75C2×D4×C29C22⋊C412yes—
76C2×D4×C29SD1612yes—
77C2×D4×C29Q1612yes—
78C22×C4×C29—21no—
79C22×C4×C29—22no—
80C22×C4×C29—22no—
81C22×C4×C29—41no—
82C22×C4×C29—41no—
83C22×C4×C29—41no—
84C22×C4×C29—41no—
85C22×C4×C29—41no—
86C22×C4×C29—41no—
87C22×C4×C29C2×D411yescharacteristic
88C22×C4×C29C2×D411yescharacteristic
89C22×C4×C29#4111yescharacteristic
90C2×C8×C29—21no—
91C2×C8×C29—21no—
92C2×C8×C29—22no—
93C2×C8×C29—22no—
94C2×C8×C29—21no—
95C2×C8×C29—21no—
96C2×C8×C29—21no—
97C2×C8×C29—48no—
98C2×C8×C29—41no—
99C2×C8×C29—41no—
100C2×C8×C29—41no—
101C2×C8×C29—41no—
102C2×C8×C29—41no—
103C2×C8×C29—41no—
104C2×C8×C29—41no—
105C2×C8×C29SD1612yes—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—22no—
108C4⋊C4×C29—22no—
109C4⋊C4×C29—41no—
110C4⋊C4×C29—41no—
111C4⋊C4×C29—41no—
112C4⋊C4×C29—41no—
113C4⋊C4×C29—41no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29—81no—
116C4⋊C4×C29C22⋊C412yes—
117C22⋊C4×C29—22no—
118C22⋊C4×C29—22no—
119C42×C29C22×C411yescharacteristic
120C42×C29C2×D411yescharacteristic
121C42×C29C2×D411yescharacteristic
122C42×C29#4111yescharacteristic
123#9215C2911yesmaximal, characteristic, direct product factor, Sylow
124C23×C29—22no—
125C23×C29—22no—
126C23×C29—22no—
127C23×C29—41no—
128C23×C29—41no—
129C23×C29—41no—
130C23×C29—41no—
131C23×C29#12111yescharacteristic
132Q8×C29—82no—
133Q8×C29—82no—
134D4×C29—22no—
135D4×C29—22no—
136D4×C29—22no—
137D4×C29#10314yes—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—22no—
141C2×C4×C29—41no—
142C2×C4×C29—41no—
143C2×C4×C29—42no—
144C2×C4×C29—42no—
145C2×C4×C29—42no—
146C2×C4×C29—42no—
147C2×C4×C29—42no—
148C2×C4×C29—81no—
149C2×C4×C29—81no—
150C2×C4×C29—81no—
151C2×C4×C29—81no—
152C2×C4×C29—81no—
153C2×C4×C29C2×C22⋊C411yescharacteristic
154C2×C4×C29C4×D411yescharacteristic
155C2×C4×C29C4×D411yescharacteristic
156C2×C4×C29#12011yescharacteristic
157C2×C4×C29#12111yescharacteristic
158C2×C4×C29#12311yescharacteristic
159C2×C4×C29C2×SD1611yescharacteristic
160C2×C4×C29C2×SD1611yescharacteristic
161C2×C4×C29C2×Q1611yescharacteristic
162C2×C4×C29#13511yescharacteristic
163C2×C4×C29#13511yescharacteristic
164C2×C4×C29#13511yescharacteristic
165C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C29#13711yescharacteristic
167C8×C29—22no—
168C8×C29—42no—
169C8×C29—42no—
170C8×C29—41no—
171C8×C29—81no—
172C2×#476C2×C2911yescharacteristic
173C2×C8×D4C2×C2911yescharacteristic
174#1990C2×C2911yescharacteristic, complemented
175#1802C2×C2911yescharacteristic
176C2×#333C2×C2911yescharacteristic, complemented
177#1296C2×C2911yescharacteristic, complemented
178#1277C2×C2911yescharacteristic, complemented
179C22×C29—24no—
180C22×C29—42no—
181C22×C29—42no—
182C22×C29—42no—
183C22×C29—42no—
184C22×C29—42no—
185C22×C29—42no—
186C22×C29#38611yescharacteristic
187C22×C29#46111yescharacteristic
188C22×C29#46311yescharacteristic
189C22×C29#46511yescharacteristic
190C22×C29#46711yescharacteristic
191C22×C29#47111yescharacteristic
192C22×C29#47211yescharacteristic
193C4×C29—21no—
194C4×C29—21no—
195C4×C29—42no—
196C4×C29—82no—
197C4×C29—161no—
198C4×C29C2×#10311yescharacteristic
199C4×C29#41611yescharacteristic
200C4×C29C4×SD1611yescharacteristic
201C4×C29#44011yescharacteristic
202C4×C29#45011yescharacteristic
203C4×C29#45211yescharacteristic
204C4×C29#46511yescharacteristic
205C4×C29#46711yescharacteristic
206C23×C8—21no—
207C2×C4⋊Q8C22×C2911yescharacteristic
208C2×C4×D4C22×C2911yescharacteristic
209#476—22no—
210#476C4×C2914yescomplemented
211C8×D4—22no—
212C8×D4—22no—
213C2×#106—21no—
214C2×C4⋊C8C22×C2911yescharacteristic
215C2×C4⋊C8C22×C2911yescharacteristic
216C2×C4⋊C8C22×C2911yescharacteristic
217C2×#102—21no—
218C2×#102—21no—
219C2×C22⋊C8—21no—
220C2×C4×C8C22×C2911yescharacteristic
221#384C22×C2911yescharacteristic
222#340—21no—
223#340—21no—
224#340—21no—
225#333—22no—
226C2×C29—44no—
227C2×C29#167111yescharacteristic
228C2×C29#167511yescharacteristic
229C2×C29#167711yescharacteristic
230C2×C29#168311yescharacteristic
231C2×C29#187711yescharacteristic
232C2×C29#189211yescharacteristic
233C2×C29#190711yescharacteristic
234C22×Q8—21no—
235C22×D4D4×C2911yescharacteristic
236C23×C4—21no—
237C22×C8—24no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—42no—
242C22×C8—42no—
243C22×C8D4×C2911yescharacteristic
244C22×C8D4×C2911yescharacteristic
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8C2×C4×C2912yes—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C2×C4×C2912yes—
252C4×D4D4×C2912yes—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C2911yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C23×C2911yescharacteristic
261#106—24no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8C2×C4×C2912yes—
267C4⋊C8D4×C2912yes—
268#102—24no—
269#102—42no—
270C22⋊C8—24no—
271C4×C8—21no—
272C4×C8—21no—
273C29#921511yescharacteristic, direct product factor, Sylow
274C24—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—81no—
278C2×Q8—81no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4C22⋊C4×C2912yes—
283C2×D4SD16×C2912yes—
284C2×D4Q16×C2912yes—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C2×D4×C2911yescharacteristic
295C22×C4C2×D4×C2911yescharacteristic
296C22×C4#41×C2911yescharacteristic
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—21no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—48no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8SD16×C2912yes—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—81no—
323C4⋊C4C22⋊C4×C2912yes—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C42C22×C4×C2911yescharacteristic
327C42C2×D4×C2911yescharacteristic
328C42C2×D4×C2911yescharacteristic
329C42#41×C2911yescharacteristic
330C23—22no—
331C23—22no—
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23C29×#12111yescharacteristic
338Q8—82no—
339Q8—82no—
340D4—22no—
341D4—22no—
342D4—22no—
343D4C29×#10314yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C22⋊C4×C2911yescharacteristic
360C2×C4C4×D4×C2911yescharacteristic
361C2×C4C4×D4×C2911yescharacteristic
362C2×C4C29×#12011yescharacteristic
363C2×C4C29×#12111yescharacteristic
364C2×C4C29×#12311yescharacteristic
365C2×C4C2×SD16×C2911yescharacteristic
366C2×C4C2×SD16×C2911yescharacteristic
367C2×C4C2×Q16×C2911yescharacteristic
368C2×C4C29×#13511yescharacteristic
369C2×C4C29×#13511yescharacteristic
370C2×C4C29×#13511yescharacteristic
371C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
372C2×C4C29×#13711yescharacteristic
373C8—22no—
374C8—42no—
375C8—41no—
376C8—42no—
377C8—81no—
378C22—24no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22C29×#38611yescharacteristic
386C22C29×#46111yescharacteristic
387C22C29×#46311yescharacteristic
388C22C29×#46511yescharacteristic
389C22C29×#46711yescharacteristic
390C22C29×#47111yescharacteristic
391C22C29×#47211yescharacteristic
392C4—21no—
393C4—21no—
394C4—42no—
395C4—82no—
396C4—161no—
397C4C2×C29×#10311yescharacteristic
398C4C29×#41611yescharacteristic
399C4C4×SD16×C2911yescharacteristic
400C4C29×#44011yescharacteristic
401C4C29×#45011yescharacteristic
402C4C29×#45211yescharacteristic
403C4C29×#46511yescharacteristic
404C4C29×#46711yescharacteristic
405C2—44no—
406C2C29×#167111yescharacteristic
407C2C29×#167511yescharacteristic
408C2C29×#167711yescharacteristic
409C2C29×#168311yescharacteristic
410C2C29×#187711yescharacteristic
411C2C29×#189211yescharacteristic
412C2C29×#190711yescharacteristic
subgroupG/H
center, socleC23×C29#121
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1990C2semidirect
5. C2×C29×#333C2semidirect
6. C29×#1296C2semidirect
7. C29×#1277C2semidirect
12. C29×#476C4semidirect
123. #9215C29direct (N × H)
174. #1990C2×C29semidirect
176. C2×#333C2×C29semidirect
177. #1296C2×C29semidirect
178. #1277C2×C29semidirect
210. #476C4×C29semidirect
273. C29#9215direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4762
C2×C8×D4×C292
C29×#19902
C29×#18022
C2×C29×#3332
C29×#12962
C29×#12772
#921529