Finite Group Databasebeta

← C29×#13337 #20308237

Subgroups — C29×#13337 #20308237

Order 7424.

554 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#509C211yesmaximal, characteristic
2C22×C29×SD32C211yesmaximal, characteristic, complemented
3C29×#3156C211yesmaximal, characteristic, complemented
4C2×C29×#362C211yesmaximal, characteristic, complemented
5C2×C29×#359C211yesmaximal, characteristic, complemented
6C29×#1978C211yesmaximal, characteristic, complemented
7C29×#1379C211yesmaximal, characteristic, complemented
8C2×C29×#137—21no—
9C2×C29×#135C2211yescharacteristic
10C22×Q16×C29C2211yescharacteristic
11C22×D8×C29C2211yescharacteristic
12C29×#536—21no—
13C29×#509—22no—
14C29×#509—22no—
15C2×C29×SD32—22no—
16C2×C29×SD32—22no—
17C2×C29×SD32—21no—
18C2×C29×SD32—22no—
19C2×C29×D16—21no—
20C2×C29×M32C2211yescharacteristic
21C22×C16×C29C2211yescharacteristic
22C29×#497—22no—
23C29×#495—21no—
24C29×#494—21no—
25C2×C29×#108C2211yescharacteristic
26C29×#418—21no—
27C2×C29×#100—21no—
28C29×#405C2211yescharacteristic
29C29×#362—22no—
30C29×#359—22no—
31C2×#41×C29—21no—
32C22×Q8×C29—21no—
33C22×D4×C29—21no—
34C29×#137—42no—
35C29×#137—42no—
36C29×#135—21no—
37C29×#135—21no—
38C29×#135—21no—
39C29×#135—21no—
40C2×Q16×C29—22no—
41C2×Q16×C29—21no—
42C2×Q16×C29—21no—
43C2×Q16×C29—21no—
44C2×Q16×C29—21no—
45C2×Q16×C29—21no—
46C2×Q16×C29D411yescharacteristic
47C2×Q16×C29D412yes—
48C2×SD16×C29—22no—
49C2×SD16×C29—21no—
50C2×D8×C29—21no—
51C2×D8×C29—21no—
52C2×D8×C29—21no—
53C2×D8×C29—21no—
54C2×D8×C29—21no—
55C2×D8×C29D411yescharacteristic
56C2×D8×C29D412yes—
57C2×M16×C29—21no—
58C2×M16×C29D411yescharacteristic
59C22×C8×C29C2311yescharacteristic
60C29×C4⋊Q8—22no—
61C29×#124—22no—
62C29×#123—42no—
63C29×C22⋊Q8—42no—
64C29×#117D411yescharacteristic
65C29×SD32—28no—
66C29×SD32—24no—
67C29×D16—24no—
68C29×M32—21no—
69C29×M32D412yes—
70C2×C16×C29—21no—
71C2×C16×C29—21no—
72C2×C16×C29—21no—
73C2×C16×C29D412yes—
74C29×#108—21no—
75C29×#108—21no—
76C29×#102—42no—
77C29×#100—42no—
78C29×#97—21no—
79C4×C8×C29—21no—
80C24×C29—41no—
81#41×C29—41no—
82#41×C29—41no—
83#41×C29—41no—
84#41×C29—41no—
85C2×Q8×C29—22no—
86C2×Q8×C29—21no—
87C2×Q8×C29—41no—
88C2×Q8×C29—41no—
89C2×Q8×C29—41no—
90C2×Q8×C29—41no—
91C2×Q8×C29—41no—
92C2×D4×C29—21no—
93C2×D4×C29—22no—
94C2×D4×C29—41no—
95C2×D4×C29—41no—
96C2×D4×C29—41no—
97C2×D4×C29—41no—
98C2×D4×C29—41no—
99C2×D4×C29—41no—
100C22×C4×C29—41no—
101C22×C4×C29—41no—
102C22×C4×C29C2×D411yescharacteristic
103Q16×C29—22no—
104Q16×C29—21no—
105Q16×C29—22no—
106Q16×C29—21no—
107Q16×C29—44no—
108Q16×C29—41no—
109Q16×C29—41no—
110SD16×C29—44no—
111SD16×C29—41no—
112SD16×C29—41no—
113D8×C29—22no—
114D8×C29—22no—
115D8×C29—21no—
116D8×C29—21no—
117D8×C29—41no—
118D8×C29—41no—
119M16×C29—21no—
120M16×C29—41no—
121M16×C29—41no—
122M16×C29D812yes—
123C2×C8×C29—21no—
124C2×C8×C29—41no—
125C2×C8×C29C2×D411yescharacteristic
126C2×C8×C29C2×D411yescharacteristic
127C2×C8×C29C2×D411yescharacteristic
128C2×C8×C29C2×D411yescharacteristic
129C2×C8×C29C2×D411yescharacteristic
130C2×C8×C29#4111yescharacteristic
131C4⋊C4×C29—44no—
132C4⋊C4×C29D812yes—
133C22⋊C4×C29—21no—
134C22⋊C4×C29—44no—
135C42×C29—21no—
136C16×C29—22no—
137C16×C29—22no—
138#13337C2911yesmaximal, characteristic, direct product factor, Sylow
139C23×C29—41no—
140C23×C29—42no—
141C23×C29—81no—
142C23×C29—81no—
143C23×C29—162no—
144C23×C29AGL(1,ℤ/8)11yescharacteristic
145Q8×C29—41no—
146Q8×C29—42no—
147Q8×C29—42no—
148Q8×C29—41no—
149Q8×C29—81no—
150Q8×C29—81no—
151D4×C29—42no—
152D4×C29—41no—
153D4×C29—41no—
154D4×C29—42no—
155D4×C29—81no—
156D4×C29—81no—
157D4×C29—81no—
158D4×C29—81no—
159C2×C4×C29—22no—
160C2×C4×C29—42no—
161C2×C4×C29—41no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29—81no—
165C2×C4×C29—81no—
166C2×C4×C29#12011yescharacteristic
167C2×C4×C29#12111yescharacteristic
168C2×C4×C29#12711yescharacteristic
169C2×C4×C29C2×D811yescharacteristic
170C2×C4×C29C2×D811yescharacteristic
171C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
172C8×C29—22no—
173C8×C29—81no—
174C8×C29#12011yescharacteristic
175C8×C29#12011yescharacteristic
176C8×C29#12111yescharacteristic
177C8×C29#12111yescharacteristic
178C2×#509C2×C2911yescharacteristic
179C22×SD32C2×C2911yescharacteristic, complemented
180#3156C2×C2911yescharacteristic, complemented
181C2×#362C2×C2911yescharacteristic, complemented
182C2×#359C2×C2911yescharacteristic, complemented
183#1978C2×C2911yescharacteristic, complemented
184#1379C2×C2911yescharacteristic, complemented
185C22×C29—22no—
186C22×C29—82no—
187C22×C29—81no—
188C22×C29—82no—
189C22×C29—162no—
190C22×C29—162no—
191C22×C29—162no—
192C22×C29#44711yescharacteristic
193C22×C29#45911yescharacteristic
194C22×C29#49611yescharacteristic
195C4×C29—42no—
196C4×C29—81no—
197C4×C29—82no—
198C4×C29#39211yescharacteristic
199C4×C29#44711yescharacteristic
200C4×C29#45911yescharacteristic
201C4×C29#49311yescharacteristic
202C2×#137—21no—
203C2×#135C22×C2911yescharacteristic
204C22×Q16C22×C2911yescharacteristic
205C22×D8C22×C2911yescharacteristic
206#536—21no—
207#509—22no—
208#509—22no—
209C2×SD32—22no—
210C2×SD32—21no—
211C2×SD32—22no—
212C2×SD32—22no—
213C2×D16—21no—
214C2×M32C22×C2911yescharacteristic
215C22×C16C22×C2911yescharacteristic
216#497—22no—
217#495—21no—
218#494—21no—
219C2×#108C22×C2911yescharacteristic
220#418—21no—
221C2×#100—21no—
222#405C22×C2911yescharacteristic
223#362—22no—
224#359—22no—
225C2×C29—21no—
226C2×C29—21no—
227C2×C29—161no—
228C2×C29—162no—
229C2×C29#201111yescharacteristic
230C2×C29#219312yes—
231C2×#41—21no—
232C22×Q8—21no—
233C22×D4—21no—
234#137—42no—
235#137—42no—
236#135—21no—
237#135—21no—
238#135—21no—
239#135—21no—
240C2×Q16—22no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16D4×C2912yes—
247C2×Q16D4×C2911yescharacteristic
248C2×SD16—22no—
249C2×SD16—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8D4×C2912yes—
256C2×D8D4×C2911yescharacteristic
257C2×M16—21no—
258C2×M16D4×C2911yescharacteristic
259C22×C8C23×C2911yescharacteristic
260C4⋊Q8—22no—
261#124—22no—
262#123—42no—
263C22⋊Q8—42no—
264#117D4×C2911yescharacteristic
265SD32—28no—
266SD32—24no—
267D16—24no—
268M32—21no—
269M32D4×C2912yes—
270C2×C16—21no—
271C2×C16—21no—
272C2×C16—21no—
273C2×C16D4×C2912yes—
274#108—21no—
275#108—21no—
276#102—42no—
277#100—42no—
278#97—21no—
279C4×C8—21no—
280C29#1333711yescharacteristic, direct product factor, Sylow
281C24—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286C2×Q8—22no—
287C2×Q8—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C2×D4×C2911yescharacteristic
304Q16—22no—
305Q16—21no—
306Q16—22no—
307Q16—21no—
308Q16—44no—
309Q16—41no—
310Q16—41no—
311SD16—44no—
312SD16—41no—
313SD16—41no—
314D8—21no—
315D8—22no—
316D8—22no—
317D8—21no—
318D8—41no—
319D8—41no—
320M16—21no—
321M16—41no—
322M16—41no—
323M16D8×C2912yes—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8C2×D4×C2911yescharacteristic
327C2×C8C2×D4×C2911yescharacteristic
328C2×C8C2×D4×C2911yescharacteristic
329C2×C8C2×D4×C2911yescharacteristic
330C2×C8C2×D4×C2911yescharacteristic
331C2×C8#41×C2911yescharacteristic
332C4⋊C4—44no—
333C4⋊C4D8×C2912yes—
334C22⋊C4—21no—
335C22⋊C4—44no—
336C42—21no—
337C16—22no—
338C16—22no—
339C23—41no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23—162no—
344C23C29×AGL(1,ℤ/8)11yescharacteristic
345Q8—42no—
346Q8—41no—
347Q8—41no—
348Q8—42no—
349Q8—81no—
350Q8—81no—
351D4—41no—
352D4—42no—
353D4—42no—
354D4—41no—
355D4—81no—
356D4—81no—
357D4—81no—
358D4—81no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4C29×#12011yescharacteristic
367C2×C4C29×#12111yescharacteristic
368C2×C4C29×#12711yescharacteristic
369C2×C4C2×D8×C2911yescharacteristic
370C2×C4C2×D8×C2911yescharacteristic
371C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
372C8—22no—
373C8—81no—
374C8C29×#12011yescharacteristic
375C8C29×#12011yescharacteristic
376C8C29×#12111yescharacteristic
377C8C29×#12111yescharacteristic
378C22—22no—
379C22—82no—
380C22—81no—
381C22—82no—
382C22—162no—
383C22—162no—
384C22—162no—
385C22C29×#44711yescharacteristic
386C22C29×#45911yescharacteristic
387C22C29×#49611yescharacteristic
388C4—42no—
389C4—81no—
390C4—82no—
391C4C29×#39211yescharacteristic
392C4C29×#44711yescharacteristic
393C4C29×#45911yescharacteristic
394C4C29×#49311yescharacteristic
395C2—21no—
396C2—21no—
397C2—161no—
398C2—162no—
399C2C29×#201111yescharacteristic
400C2C29×#219312yes—
subgroupG/H
center, socleC22×C29#447
commutator, Frattini, cosocleC22×C8C23×C29
prime radicalC2×C29×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C29×SD32C2semidirect
3. C29×#3156C2semidirect
4. C2×C29×#362C2semidirect
5. C2×C29×#359C2semidirect
6. C29×#1978C2semidirect
7. C29×#1379C2semidirect
138. #13337C29direct (N × H)
179. C22×SD32C2×C29semidirect
180. #3156C2×C29semidirect
181. C2×#362C2×C29semidirect
182. C2×#359C2×C29semidirect
183. #1978C2×C29semidirect
184. #1379C2×C29semidirect
280. C29#13337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5092
C22×C29×SD322
C29×#31562
C2×C29×#3622
C2×C29×#3592
C29×#19782
C29×#13792
#1333729