Finite Group Databasebeta

← C29×#13332 #20308232

Subgroups — C29×#13332 #20308232

Order 7424.

566 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#510C211yesmaximal, characteristic, complemented
2C2×C29×#509C211yesmaximal, characteristic
3C2×C29×#495C211yesmaximal, characteristic, complemented
4C2×C29×#362C211yesmaximal, characteristic, complemented
5C2×C29×#361C211yesmaximal, characteristic, complemented
6C29×#1974C211yesmaximal, characteristic, complemented
7C29×#1376C211yesmaximal, characteristic, complemented
8C2×C29×#135C2211yescharacteristic
9C22×Q16×C29C2211yescharacteristic
10C22×SD16×C29—21no—
11C22×D8×C29C2211yescharacteristic
12C2×C29×#124—21no—
13C29×#510—22no—
14C29×#510—22no—
15C29×#509—22no—
16C29×#509—22no—
17C2×C29×Q32—21no—
18C2×C29×SD32—21no—
19C2×C29×SD32—21no—
20C2×C29×D16—21no—
21C2×C29×M32C2211yescharacteristic
22C2×C29×M32C2211yescharacteristic
23C29×#495—22no—
24C29×#495—22no—
25C2×C29×#108C2211yescharacteristic
26C2×C29×#104—21no—
27C29×#408—21no—
28C2×C4×C8×C29C2211yescharacteristic
29C29×#362—22no—
30C29×#361—22no—
31C2×#41×C29—21no—
32C22×Q8×C29—21no—
33C22×D4×C29—21no—
34C29×#135—21no—
35C29×#135—21no—
36C29×#135—21no—
37C29×#135—21no—
38C2×Q16×C29—21no—
39C2×Q16×C29—21no—
40C2×Q16×C29—21no—
41C2×Q16×C29—21no—
42C2×Q16×C29—21no—
43C2×Q16×C29D412yes—
44C2×Q16×C29D411yescharacteristic
45C2×SD16×C29—24no—
46C2×SD16×C29—21no—
47C2×SD16×C29—42no—
48C2×SD16×C29—42no—
49C2×D8×C29—21no—
50C2×D8×C29—21no—
51C2×D8×C29—21no—
52C2×D8×C29—21no—
53C2×D8×C29—21no—
54C2×D8×C29D412yes—
55C2×D8×C29D411yescharacteristic
56C2×M16×C29—21no—
57C22×C8×C29D411yescharacteristic
58C22×C8×C29C2311yescharacteristic
59C29×#124—24no—
60C29×#124—42no—
61C2×C22⋊C4×C29—42no—
62C2×C42×C29D411yescharacteristic
63C29×Q32—24no—
64C29×SD32—24no—
65C29×SD32—24no—
66C29×D16—24no—
67C29×M32—21no—
68C29×M32—21no—
69C29×M32D412yes—
70C29×M32D412yes—
71C2×C16×C29—21no—
72C2×C16×C29—21no—
73C29×#108—21no—
74C29×#108—21no—
75C29×#104—42no—
76C29×C22⋊C8—42no—
77C4×C8×C29—21no—
78C4×C8×C29—21no—
79C24×C29—41no—
80#41×C29—41no—
81#41×C29—41no—
82#41×C29—41no—
83#41×C29—41no—
84C2×Q8×C29—22no—
85C2×Q8×C29—21no—
86C2×Q8×C29—41no—
87C2×Q8×C29—41no—
88C2×Q8×C29—41no—
89C2×Q8×C29—41no—
90C2×Q8×C29—41no—
91C2×D4×C29—22no—
92C2×D4×C29—21no—
93C2×D4×C29—41no—
94C2×D4×C29—41no—
95C2×D4×C29—41no—
96C2×D4×C29—41no—
97C2×D4×C29—41no—
98C2×D4×C29—41no—
99C22×C4×C29—21no—
100C22×C4×C29—41no—
101C22×C4×C29—41no—
102C22×C4×C29C2×D411yescharacteristic
103Q16×C29—22no—
104Q16×C29—21no—
105Q16×C29—21no—
106Q16×C29—22no—
107Q16×C29—41no—
108Q16×C29—41no—
109SD16×C29—48no—
110SD16×C29—41no—
111SD16×C29—41no—
112D8×C29—22no—
113D8×C29—21no—
114D8×C29—21no—
115D8×C29—22no—
116D8×C29—41no—
117D8×C29—41no—
118M16×C29—41no—
119M16×C29—41no—
120C2×C8×C29—21no—
121C2×C8×C29—21no—
122C2×C8×C29—41no—
123C2×C8×C29D812yes—
124C2×C8×C29C2×D411yescharacteristic
125C2×C8×C29C2×D411yescharacteristic
126C2×C8×C29C2×D411yescharacteristic
127C2×C8×C29C2×D411yescharacteristic
128C2×C8×C29C2×D411yescharacteristic
129C2×C8×C29#4111yescharacteristic
130C22⋊C4×C29—48no—
131C42×C29—21no—
132C42×C29D812yes—
133C16×C29—22no—
134C16×C29—22no—
135#13332C2911yesmaximal, characteristic, direct product factor, Sylow
136C23×C29—42no—
137C23×C29—41no—
138C23×C29—84no—
139C23×C29—81no—
140C23×C29—81no—
141C23×C29AGL(1,ℤ/8)11yescharacteristic
142Q8×C29—41no—
143Q8×C29—42no—
144Q8×C29—42no—
145Q8×C29—41no—
146Q8×C29—81no—
147Q8×C29—81no—
148D4×C29—42no—
149D4×C29—41no—
150D4×C29—42no—
151D4×C29—41no—
152D4×C29—81no—
153D4×C29—81no—
154D4×C29—81no—
155D4×C29—81no—
156C2×C4×C29—22no—
157C2×C4×C29—42no—
158C2×C4×C29—42no—
159C2×C4×C29—41no—
160C2×C4×C29—81no—
161C2×C4×C29—81no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29#12011yescharacteristic
165C2×C4×C29#12111yescharacteristic
166C2×C4×C29#12711yescharacteristic
167C2×C4×C29C2×D811yescharacteristic
168C2×C4×C29C2×D811yescharacteristic
169C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
170C8×C29—22no—
171C8×C29—81no—
172C8×C29#12011yescharacteristic
173C8×C29#12011yescharacteristic
174C8×C29#12111yescharacteristic
175C8×C29#12111yescharacteristic
176C2×#510C2×C2911yescharacteristic, complemented
177C2×#509C2×C2911yescharacteristic
178C2×#495C2×C2911yescharacteristic, complemented
179C2×#362C2×C2911yescharacteristic, complemented
180C2×#361C2×C2911yescharacteristic, complemented
181#1974C2×C2911yescharacteristic, complemented
182#1376C2×C2911yescharacteristic, complemented
183C22×C29—22no—
184C22×C29—84no—
185C22×C29—82no—
186C22×C29—81no—
187C22×C29—82no—
188C22×C29—162no—
189C22×C29—162no—
190C22×C29#44711yescharacteristic
191C22×C29#45911yescharacteristic
192C22×C29#49611yescharacteristic
193C4×C29—42no—
194C4×C29—81no—
195C4×C29—82no—
196C4×C29#39211yescharacteristic
197C4×C29#44711yescharacteristic
198C4×C29#45911yescharacteristic
199C4×C29#49311yescharacteristic
200C2×#135C22×C2911yescharacteristic
201C22×Q16C22×C2911yescharacteristic
202C22×SD16—21no—
203C22×D8C22×C2911yescharacteristic
204C2×#124—21no—
205#510—22no—
206#510—22no—
207#509—22no—
208#509—22no—
209C2×Q32—21no—
210C2×SD32—21no—
211C2×SD32—21no—
212C2×D16—21no—
213C2×M32C22×C2911yescharacteristic
214C2×M32C22×C2911yescharacteristic
215#495—22no—
216#495—22no—
217C2×#108C22×C2911yescharacteristic
218C2×#104—21no—
219#408—21no—
220C2×C4×C8C22×C2911yescharacteristic
221#362—22no—
222#361—22no—
223C2×C29—21no—
224C2×C29—21no—
225C2×C29—161no—
226C2×C29—162no—
227C2×C29#201111yescharacteristic
228C2×C29#221212yes—
229C2×#41—21no—
230C22×Q8—21no—
231C22×D4—21no—
232#135—21no—
233#135—21no—
234#135—21no—
235#135—21no—
236C2×Q16—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16D4×C2912yes—
242C2×Q16D4×C2911yescharacteristic
243C2×SD16—24no—
244C2×SD16—21no—
245C2×SD16—42no—
246C2×SD16—42no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8D4×C2912yes—
253C2×D8D4×C2911yescharacteristic
254C2×M16—21no—
255C22×C8D4×C2911yescharacteristic
256C22×C8C23×C2911yescharacteristic
257#124—24no—
258#124—42no—
259C2×C22⋊C4—42no—
260C2×C42D4×C2911yescharacteristic
261Q32—24no—
262SD32—24no—
263SD32—24no—
264D16—24no—
265M32—21no—
266M32—21no—
267M32D4×C2912yes—
268M32D4×C2912yes—
269C2×C16—21no—
270C2×C16—21no—
271#108—21no—
272#108—21no—
273#104—42no—
274C22⋊C8—42no—
275C4×C8—21no—
276C4×C8—21no—
277C29#1333211yescharacteristic, direct product factor, Sylow
278C24—41no—
279#41—41no—
280#41—41no—
281#41—41no—
282#41—41no—
283C2×Q8—22no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×D4×C2911yescharacteristic
302Q16—21no—
303Q16—22no—
304Q16—21no—
305Q16—22no—
306Q16—41no—
307Q16—41no—
308SD16—48no—
309SD16—41no—
310SD16—41no—
311D8—21no—
312D8—22no—
313D8—21no—
314D8—22no—
315D8—41no—
316D8—41no—
317M16—41no—
318M16—41no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8D8×C2912yes—
323C2×C8C2×D4×C2911yescharacteristic
324C2×C8C2×D4×C2911yescharacteristic
325C2×C8C2×D4×C2911yescharacteristic
326C2×C8C2×D4×C2911yescharacteristic
327C2×C8C2×D4×C2911yescharacteristic
328C2×C8#41×C2911yescharacteristic
329C22⋊C4—48no—
330C42—21no—
331C42D8×C2912yes—
332C16—22no—
333C16—22no—
334C23—42no—
335C23—41no—
336C23—84no—
337C23—81no—
338C23—81no—
339C23C29×AGL(1,ℤ/8)11yescharacteristic
340Q8—42no—
341Q8—41no—
342Q8—41no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—42no—
347D4—41no—
348D4—42no—
349D4—41no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C29×#12011yescharacteristic
363C2×C4C29×#12111yescharacteristic
364C2×C4C29×#12711yescharacteristic
365C2×C4C2×D8×C2911yescharacteristic
366C2×C4C2×D8×C2911yescharacteristic
367C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
368C8—22no—
369C8—81no—
370C8C29×#12011yescharacteristic
371C8C29×#12011yescharacteristic
372C8C29×#12111yescharacteristic
373C8C29×#12111yescharacteristic
374C22—22no—
375C22—84no—
376C22—82no—
377C22—81no—
378C22—82no—
379C22—162no—
380C22—162no—
381C22C29×#44711yescharacteristic
382C22C29×#45911yescharacteristic
383C22C29×#49611yescharacteristic
384C4—42no—
385C4—81no—
386C4—82no—
387C4C29×#39211yescharacteristic
388C4C29×#44711yescharacteristic
389C4C29×#45911yescharacteristic
390C4C29×#49311yescharacteristic
391C2—21no—
392C2—21no—
393C2—162no—
394C2—161no—
395C2C29×#201111yescharacteristic
396C2C29×#221212yes—
subgroupG/H
center, socleC22×C29#459
commutator, Frattini, cosocleC22×C8C23×C29
prime radicalC2×C29×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C4×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#510C2semidirect
3. C2×C29×#495C2semidirect
4. C2×C29×#362C2semidirect
5. C2×C29×#361C2semidirect
6. C29×#1974C2semidirect
7. C29×#1376C2semidirect
135. #13332C29direct (N × H)
176. C2×#510C2×C29semidirect
178. C2×#495C2×C29semidirect
179. C2×#362C2×C29semidirect
180. C2×#361C2×C29semidirect
181. #1974C2×C29semidirect
182. #1376C2×C29semidirect
277. C29#13332direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5102
C2×C29×#5092
C2×C29×#4952
C2×C29×#3622
C2×C29×#3612
C29×#19742
C29×#13762
#1333229