Finite Group Databasebeta

← C29×#8998 #20303898

Subgroups — C29×#8998 #20303898

Order 7424.

414 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
1C29×#3172C211yesmaximal, characteristic
2C29×#2995C211yesmaximal, characteristic
3C29×#1995C211yesmaximal, characteristic, complemented
4C29×#1500C211yesmaximal, characteristic
5C29×#1497C211yesmaximal, characteristic, complemented
6C29×#1300C211yesmaximal, characteristic, complemented
7C29×#1299C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C29×#529C2211yescharacteristic
10C29×#501C411yescharacteristic, complemented
11C29×#497C411yescharacteristic, complemented
12C29×#491C411yescharacteristic, complemented
13C29×#489C411yescharacteristic, complemented
14C29×#470—21no—
15C29×#468—21no—
16C29×#446—21no—
17C4×Q16×C29—21no—
18C4×SD16×C29—21no—
19C29×#436—21no—
20C29×#435—21no—
21C29×#435—21no—
22C29×#433—21no—
23C29×#432C2211yescharacteristic
24C29×#431C2211yescharacteristic
25C29×#424—21no—
26C29×#423C2211yescharacteristic
27C4×M16×C29C2211yescharacteristic
28C29×#376C2211yescharacteristic
29C29×#339—21no—
30C29×#339—21no—
31C29×#328—21no—
32C29×#327—21no—
33C29×Q8⋊C8—21no—
34C29×Q8⋊C8—21no—
35C2×Q16×C29—21no—
36C2×SD16×C29—21no—
37C2×M16×C29—21no—
38C2×M16×C29—21no—
39C2×M16×C29D411yescharacteristic
40C2×M16×C29D411yescharacteristic
41C22×C8×C29—21no—
42C29×C4⋊Q8C2×C411yescharacteristic
43C29×C4⋊Q8C2×C411yescharacteristic
44C29×#126—21no—
45C29×#125—21no—
46C29×#125C2×C411yescharacteristic
47C29×#124C2×C411yescharacteristic
48C29×#123—21no—
49C29×C22⋊Q8—21no—
50C29×C22⋊Q8—21no—
51C29×C22⋊Q8D411yescharacteristic
52C29×#121D411yescharacteristic
53C4×Q8×C29—21no—
54C4×Q8×C29—21no—
55C4×Q8×C29D411yescharacteristic
56C4×D4×C29—21no—
57C4×D4×C29D411yescharacteristic
58C29×#117—21no—
59C29×#117—21no—
60C2×C42×C29—21no—
61C2×C42×C29C2311yescharacteristic
62C29×#107—21no—
63C29×#106—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×C4⋊C8—21no—
69C29×C4⋊C8D411yescharacteristic
70C29×C4⋊C8D411yescharacteristic
71C29×#103—21no—
72C29×#103—21no—
73C29×#103—21no—
74C29×#102—21no—
75C29×C22⋊C8—21no—
76C29×C22⋊C8—21no—
77C29×C22⋊C8—21no—
78C29×C22⋊C8—21no—
79C29×#97—21no—
80C29×#97—21no—
81C29×#97C2×C411yescharacteristic
82C29×#97C2×C411yescharacteristic
83C4×C8×C29—21no—
84C4×C8×C29—21no—
85C4×C8×C29—21no—
86C29×#95—21no—
87C29×#95—21no—
88C2×Q8×C29—21no—
89C2×Q8×C29—21no—
90C2×Q8×C29C22⋊C411yescharacteristic
91C2×D4×C29—21no—
92C2×D4×C29C22⋊C411yescharacteristic
93C22×C4×C29—21no—
94C22×C4×C29—41no—
95C22×C4×C29C2×D411yescharacteristic
96C22×C4×C29C2×D411yescharacteristic
97C22×C4×C29#4111yescharacteristic
98Q16×C29—42no—
99SD16×C29—42no—
100M16×C29—42no—
101M16×C29—41no—
102M16×C29—41no—
103M16×C29—81no—
104C2×C8×C29—21no—
105C2×C8×C29—21no—
106C2×C8×C29—21no—
107C2×C8×C29—21no—
108C2×C8×C29—21no—
109C2×C8×C29—21no—
110C2×C8×C29—41no—
111C2×C8×C29—81no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—41no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29C22⋊C411yescharacteristic
123C4⋊C4×C29C22⋊C411yescharacteristic
124C22⋊C4×C29—21no—
125C22⋊C4×C29—21no—
126C22⋊C4×C29—21no—
127C22⋊C4×C29—21no—
128C22⋊C4×C29—21no—
129C22⋊C4×C29—41no—
130C42×C29—21no—
131C42×C29—22no—
132C42×C29—41no—
133C42×C29—41no—
134C42×C29C22×C411yescharacteristic
135C42×C29C2×D411yescharacteristic
136C42×C29C2×D411yescharacteristic
137C42×C29#4111yescharacteristic
138#8998C2911yesmaximal, characteristic, direct product factor, Sylow
139C23×C29—21no—
140C23×C29#12111yescharacteristic
141Q8×C29—41no—
142Q8×C29—41no—
143Q8×C29—41no—
144Q8×C29—42no—
145D4×C29—41no—
146D4×C29—81no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—41no—
155C2×C4×C29—41no—
156C2×C4×C29—42no—
157C2×C4×C29—41no—
158C2×C4×C29—41no—
159C2×C4×C29—81no—
160C2×C4×C29—81no—
161C2×C4×C29C2×C22⋊C411yescharacteristic
162C2×C4×C29C4×D411yescharacteristic
163C2×C4×C29C4×D411yescharacteristic
164C2×C4×C29#12011yescharacteristic
165C2×C4×C29#12111yescharacteristic
166C2×C4×C29#12311yescharacteristic
167C8×C29—22no—
168C8×C29—41no—
169C8×C29—41no—
170C8×C29—41no—
171C8×C29—41no—
172C8×C29—41no—
173C8×C29—81no—
174#3172C2×C2911yescharacteristic
175#2995C2×C2911yescharacteristic
176#1995C2×C2911yescharacteristic, complemented
177#1500C2×C2911yescharacteristic
178#1497C2×C2911yescharacteristic, complemented
179#1300C2×C2911yescharacteristic, complemented
180#1299C2×C2911yescharacteristic, complemented
181C22×C29—21no—
182C22×C29—21no—
183C22×C29—21no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29#38611yescharacteristic
188C4×C29—21no—
189C4×C29—21no—
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—41no—
194C4×C29—41no—
195C4×C29—41no—
196C4×C29—82no—
197C4×C29—81no—
198C4×C29—81no—
199C4×C29#45511yescharacteristic
200C4×C29#45611yescharacteristic
201#533C22×C2911yescharacteristic
202#529C22×C2911yescharacteristic
203#501C4×C2911yescharacteristic, complemented
204#497C4×C2911yescharacteristic, complemented
205#491C4×C2911yescharacteristic, complemented
206#489C4×C2911yescharacteristic, complemented
207#470—21no—
208#468—21no—
209#446—21no—
210C4×Q16—21no—
211C4×SD16—21no—
212#436—21no—
213#435—21no—
214#435—21no—
215#433—21no—
216#432C22×C2911yescharacteristic
217#431C22×C2911yescharacteristic
218#424—21no—
219#423C22×C2911yescharacteristic
220C4×M16C22×C2911yescharacteristic
221#376C22×C2911yescharacteristic
222#339—21no—
223#339—21no—
224#328—21no—
225#327—21no—
226Q8⋊C8—21no—
227Q8⋊C8—21no—
228C2×C29—41no—
229C2×C29—81no—
230C2×C29#188111yescharacteristic
231C2×C29#188211yescharacteristic
232C2×C29#188411yescharacteristic
233C2×Q16—21no—
234C2×SD16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16D4×C2911yescharacteristic
238C2×M16D4×C2911yescharacteristic
239C22×C8—21no—
240C4⋊Q8C2×C4×C2911yescharacteristic
241C4⋊Q8C2×C4×C2911yescharacteristic
242#126—21no—
243#125—21no—
244#125C2×C4×C2911yescharacteristic
245#124C2×C4×C2911yescharacteristic
246#123—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8D4×C2911yescharacteristic
250#121D4×C2911yescharacteristic
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8D4×C2911yescharacteristic
254C4×D4—21no—
255C4×D4D4×C2911yescharacteristic
256#117—21no—
257#117—21no—
258C2×C42—21no—
259C2×C42C23×C2911yescharacteristic
260#107—21no—
261#106—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8D4×C2911yescharacteristic
268C4⋊C8D4×C2911yescharacteristic
269#103—21no—
270#103—21no—
271#103—21no—
272#102—21no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277#97—21no—
278#97—21no—
279#97C2×C4×C2911yescharacteristic
280#97C2×C4×C2911yescharacteristic
281C4×C8—21no—
282C4×C8—21no—
283C4×C8—21no—
284#95—21no—
285#95—21no—
286C29#899811yescharacteristic, direct product factor, Sylow
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8C22⋊C4×C2911yescharacteristic
290C2×D4—21no—
291C2×D4C22⋊C4×C2911yescharacteristic
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C2911yescharacteristic
295C22×C4C2×D4×C2911yescharacteristic
296C22×C4#41×C2911yescharacteristic
297Q16—42no—
298SD16—42no—
299M16—42no—
300M16—41no—
301M16—41no—
302M16—81no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—41no—
310C2×C8—81no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4C22⋊C4×C2911yescharacteristic
322C4⋊C4C22⋊C4×C2911yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C42—21no—
330C42—22no—
331C42—41no—
332C42—41no—
333C42C22×C4×C2911yescharacteristic
334C42C2×D4×C2911yescharacteristic
335C42C2×D4×C2911yescharacteristic
336C42#41×C2911yescharacteristic
337C23—21no—
338C23C29×#12111yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—41no—
342Q8—42no—
343D4—41no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
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
365C8—22no—
366C8—41no—
367C8—41no—
368C8—41no—
369C8—41no—
370C8—41no—
371C8—81no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22C29×#38611yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4C29×#45511yescharacteristic
391C4C29×#45611yescharacteristic
392C2—41no—
393C2—81no—
394C2C29×#188111yescharacteristic
395C2C29×#188211yescharacteristic
396C2C29×#188411yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC29×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1995C2semidirect
5. C29×#1497C2semidirect
6. C29×#1300C2semidirect
7. C29×#1299C2semidirect
10. C29×#501C4semidirect
11. C29×#497C4semidirect
12. C29×#491C4semidirect
13. C29×#489C4semidirect
138. #8998C29direct (N × H)
176. #1995C2×C29semidirect
178. #1497C2×C29semidirect
179. #1300C2×C29semidirect
180. #1299C2×C29semidirect
203. #501C4×C29semidirect
204. #497C4×C29semidirect
205. #491C4×C29semidirect
206. #489C4×C29semidirect
286. C29#8998direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31722
C29×#29952
C29×#19952
C29×#15002
C29×#14972
C29×#13002
C29×#12992
#899829