Finite Group Databasebeta

← C29×#10484 #20305384

Subgroups — C29×#10484 #20305384

Order 7424.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#474C211yesmaximal, characteristic
2C29×#1956C211yesmaximal, characteristic, complemented
3C29×#1954C211yesmaximal, characteristic
4C29×#1802C211yesmaximal, characteristic
5C2×C29×#334C211yesmaximal, characteristic, complemented
6C2×C29×#332C211yesmaximal, characteristic, complemented
7C29×#1296C211yesmaximal, characteristic, complemented
8C2×C29×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C29C2211yescharacteristic
10C29×#474—22no—
11C29×#474—22no—
12C2×C29×#107—21no—
13C2×C29×C4⋊C8C2211yescharacteristic
14C2×C29×C4⋊C8C2211yescharacteristic
15C2×C29×C4⋊C8C2211yescharacteristic
16C2×C29×#103—21no—
17C2×C29×#103—21no—
18C2×C29×#102—21no—
19C2×C29×#102—21no—
20C2×C29×C22⋊C8—21no—
21C2×C29×C22⋊C8—21no—
22C2×C4×C8×C29C2211yescharacteristic
23C29×#384C2211yescharacteristic
24C29×#340—21no—
25C29×#334—22no—
26C29×#332—22no—
27C22×Q8×C29—21no—
28C22×D4×C29D411yescharacteristic
29C23×C4×C29—21no—
30C22×C8×C29—21no—
31C22×C8×C29—21no—
32C22×C8×C29—21no—
33C22×C8×C29D411yescharacteristic
34C22×C8×C29D411yescharacteristic
35C29×C4⋊Q8—21no—
36C29×C4⋊Q8—21no—
37C29×C4⋊Q8—21no—
38C29×C4⋊Q8D412yes—
39C4×D4×C29—21no—
40C4×D4×C29—21no—
41C4×D4×C29—21no—
42C4×D4×C29—21no—
43C2×C4⋊C4×C29—21no—
44C2×C4⋊C4×C29—21no—
45C2×C4⋊C4×C29—21no—
46C2×C4⋊C4×C29—21no—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29D411yescharacteristic
49C2×C22⋊C4×C29—21no—
50C2×C42×C29C2311yescharacteristic
51C29×#107—24no—
52C29×C4⋊C8—21no—
53C29×C4⋊C8—21no—
54C29×C4⋊C8—21no—
55C29×C4⋊C8—21no—
56C29×C4⋊C8—21no—
57C29×C4⋊C8D412yes—
58C29×#103—42no—
59C29×#103—42no—
60C29×#102—24no—
61C29×#102—42no—
62C29×C22⋊C8—42no—
63C29×C22⋊C8—42no—
64C4×C8×C29—21no—
65C4×C8×C29—21no—
66C24×C29—21no—
67C2×Q8×C29—22no—
68C2×Q8×C29—41no—
69C2×Q8×C29—41no—
70C2×Q8×C29—41no—
71C2×Q8×C29—41no—
72C2×Q8×C29—41no—
73C2×D4×C29—21no—
74C2×D4×C29—21no—
75C2×D4×C29—21no—
76C2×D4×C29—21no—
77C2×D4×C29—21no—
78C2×D4×C29SD1612yes—
79C22×C4×C29—21no—
80C22×C4×C29—41no—
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×C29—41no—
88C22×C4×C29C2×D411yescharacteristic
89C22×C4×C29C2×D411yescharacteristic
90C22×C4×C29#4111yescharacteristic
91C2×C8×C29—21no—
92C2×C8×C29—21no—
93C2×C8×C29—22no—
94C2×C8×C29—21no—
95C2×C8×C29—21no—
96C2×C8×C29—21no—
97C2×C8×C29—41no—
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×C29D812yes—
106C4⋊C4×C29—22no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—22no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29—41no—
111C4⋊C4×C29—41no—
112C4⋊C4×C29—41no—
113C4⋊C4×C29—41no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29—41no—
116C4⋊C4×C29—81no—
117C22⋊C4×C29—41no—
118C22⋊C4×C29—41no—
119C42×C29C2×D411yescharacteristic
120C42×C29C2×D411yescharacteristic
121C42×C29#4111yescharacteristic
122C42×C29#4111yescharacteristic
123#10484C2911yesmaximal, characteristic, direct product factor, Sylow
124C23×C29—22no—
125C23×C29—41no—
126C23×C29—41no—
127C23×C29—41no—
128C23×C29—41no—
129C23×C29—41no—
130C23×C29—41no—
131C23×C29#12111yescharacteristic
132Q8×C29—42no—
133Q8×C29—42no—
134Q8×C29—81no—
135Q8×C29—81no—
136D4×C29—22no—
137D4×C29—22no—
138D4×C29—41no—
139D4×C29—41no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—41no—
143C2×C4×C29—42no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—81no—
147C2×C4×C29—81no—
148C2×C4×C29—81no—
149C2×C4×C29—81no—
150C2×C4×C29—81no—
151C2×C4×C29—81no—
152C2×C4×C29—81no—
153C2×C4×C29—81no—
154C2×C4×C29—81no—
155C2×C4×C29#12011yescharacteristic
156C2×C4×C29#12111yescharacteristic
157C2×C4×C29#12111yescharacteristic
158C2×C4×C29#12311yescharacteristic
159C2×C4×C29#12311yescharacteristic
160C2×C4×C29#12411yescharacteristic
161C2×C4×C29C2×D811yescharacteristic
162C2×C4×C29C2×SD1611yescharacteristic
163C2×C4×C29#13511yescharacteristic
164C2×C4×C29#13511yescharacteristic
165C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C29#13711yescharacteristic
168C2×C4×C29#13711yescharacteristic
169C8×C29—22no—
170C8×C29—42no—
171C8×C29—41no—
172C8×C29—81no—
173C8×C29—81no—
174C2×#474C2×C2911yescharacteristic
175#1956C2×C2911yescharacteristic, complemented
176#1954C2×C2911yescharacteristic
177#1802C2×C2911yescharacteristic
178C2×#334C2×C2911yescharacteristic, complemented
179C2×#332C2×C2911yescharacteristic, complemented
180#1296C2×C2911yescharacteristic, complemented
181C22×C29—42no—
182C22×C29—42no—
183C22×C29—42no—
184C22×C29—81no—
185C22×C29—81no—
186C22×C29—81no—
187C22×C29—81no—
188C22×C29#39411yescharacteristic
189C22×C29#45911yescharacteristic
190C22×C29#46311yescharacteristic
191C22×C29#46511yescharacteristic
192C22×C29#47011yescharacteristic
193C22×C29#47111yescharacteristic
194C22×C29#47311yescharacteristic
195C4×C29—21no—
196C4×C29—21no—
197C4×C29—81no—
198C4×C29—82no—
199C4×C29—161no—
200C4×C29#44811yescharacteristic
201C4×C29#45211yescharacteristic
202C4×C29#45911yescharacteristic
203C4×C29#46311yescharacteristic
204C4×C29#46611yescharacteristic
205C4×C29#46911yescharacteristic
206C4×C29#48311yescharacteristic
207C4×C29#48511yescharacteristic
208C2×C4⋊Q8C22×C2911yescharacteristic
209C2×C4×D4C22×C2911yescharacteristic
210#474—22no—
211#474—22no—
212C2×#107—21no—
213C2×C4⋊C8C22×C2911yescharacteristic
214C2×C4⋊C8C22×C2911yescharacteristic
215C2×C4⋊C8C22×C2911yescharacteristic
216C2×#103—21no—
217C2×#103—21no—
218C2×#102—21no—
219C2×#102—21no—
220C2×C22⋊C8—21no—
221C2×C22⋊C8—21no—
222C2×C4×C8C22×C2911yescharacteristic
223#384C22×C2911yescharacteristic
224#340—21no—
225#334—22no—
226#332—22no—
227C2×C29—82no—
228C2×C29#166511yescharacteristic
229C2×C29#167911yescharacteristic
230C2×C29#168911yescharacteristic
231C2×C29#170311yescharacteristic
232C2×C29#203511yescharacteristic
233C2×C29#205211yescharacteristic
234C2×C29#205411yescharacteristic
235C22×Q8—21no—
236C22×D4D4×C2911yescharacteristic
237C23×C4—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8D4×C2911yescharacteristic
242C22×C8D4×C2911yescharacteristic
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8D4×C2912yes—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C2911yescharacteristic
257C2×C22⋊C4—21no—
258C2×C42C23×C2911yescharacteristic
259#107—24no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8D4×C2912yes—
266#103—42no—
267#103—42no—
268#102—24no—
269#102—42no—
270C22⋊C8—42no—
271C22⋊C8—42no—
272C4×C8—21no—
273C4×C8—21no—
274C29#1048411yescharacteristic, direct product factor, Sylow
275C24—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4SD16×C2912yes—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4C2×D4×C2911yescharacteristic
298C22×C4C2×D4×C2911yescharacteristic
299C22×C4#41×C2911yescharacteristic
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—22no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8D8×C2912yes—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—81no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42C2×D4×C2911yescharacteristic
329C42C2×D4×C2911yescharacteristic
330C42#41×C2911yescharacteristic
331C42#41×C2911yescharacteristic
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23C29×#12111yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—22no—
345D4—22no—
346D4—41no—
347D4—41no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4C29×#12011yescharacteristic
364C2×C4C29×#12111yescharacteristic
365C2×C4C29×#12111yescharacteristic
366C2×C4C29×#12311yescharacteristic
367C2×C4C29×#12311yescharacteristic
368C2×C4C29×#12411yescharacteristic
369C2×C4C2×D8×C2911yescharacteristic
370C2×C4C2×SD16×C2911yescharacteristic
371C2×C4C29×#13511yescharacteristic
372C2×C4C29×#13511yescharacteristic
373C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
374C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
375C2×C4C29×#13711yescharacteristic
376C2×C4C29×#13711yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—81no—
381C8—81no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C29×#39411yescharacteristic
390C22C29×#45911yescharacteristic
391C22C29×#46311yescharacteristic
392C22C29×#46511yescharacteristic
393C22C29×#47011yescharacteristic
394C22C29×#47111yescharacteristic
395C22C29×#47311yescharacteristic
396C4—21no—
397C4—21no—
398C4—81no—
399C4—82no—
400C4—161no—
401C4C29×#44811yescharacteristic
402C4C29×#45211yescharacteristic
403C4C29×#45911yescharacteristic
404C4C29×#46311yescharacteristic
405C4C29×#46611yescharacteristic
406C4C29×#46911yescharacteristic
407C4C29×#48311yescharacteristic
408C4C29×#48511yescharacteristic
409C2—82no—
410C2C29×#166511yescharacteristic
411C2C29×#167911yescharacteristic
412C2C29×#168911yescharacteristic
413C2C29×#170311yescharacteristic
414C2C29×#203511yescharacteristic
415C2C29×#205211yescharacteristic
416C2C29×#205411yescharacteristic
subgroupG/H
center, socleC23×C29#121
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1956C2semidirect
5. C2×C29×#334C2semidirect
6. C2×C29×#332C2semidirect
7. C29×#1296C2semidirect
123. #10484C29direct (N × H)
175. #1956C2×C29semidirect
178. C2×#334C2×C29semidirect
179. C2×#332C2×C29semidirect
180. #1296C2×C29semidirect
274. C29#10484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4742
C29×#19562
C29×#19542
C29×#18022
C2×C29×#3342
C2×C29×#3322
C29×#12962
#1048429