Finite Group Databasebeta

← C29×#8994 #20303894

Subgroups — C29×#8994 #20303894

Order 7424.

430 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3076C211yesmaximal, characteristic
2C29×#2925C211yesmaximal, characteristic
3C29×#1493C211yesmaximal, characteristic, complemented
4C29×#1481C211yesmaximal, characteristic, complemented
5C29×#1476C211yesmaximal, characteristic
6C29×#1301C211yesmaximal, characteristic, complemented
7C29×#1277C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C29×#479—21no—
11C29×#478—21no—
12C29×#477C411yescharacteristic
13C29×#476C411yescharacteristic
14C29×#475C411yescharacteristic
15C29×#474C411yescharacteristic
16C29×#433—22no—
17C29×#432—21no—
18C29×#431—21no—
19C29×#431C2211yescharacteristic
20C29×#427—21no—
21C29×#423C2211yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C29×#416—21no—
25C29×#408—21no—
26C29×#405—21no—
27C2×C4×C8×C29C2211yescharacteristic
28C29×Q8⋊C8—21no—
29C29×Q8⋊C8—21no—
30C29×Q8⋊C8—22no—
31C29×Q8⋊C8—21no—
32C29×D4⋊C8—21no—
33C2×#41×C29D411yescharacteristic
34C2×M16×C29—21no—
35C22×C8×C29—21no—
36C22×C8×C29—21no—
37C22×C8×C29—21no—
38C29×C4⋊Q8C2×C411yescharacteristic
39C29×C4⋊Q8C2×C411yescharacteristic
40C29×#125—21no—
41C29×C22⋊Q8—21no—
42C29×C22⋊Q8—21no—
43C4×Q8×C29—21no—
44C4×Q8×C29—21no—
45C4×Q8×C29C2×C411yescharacteristic
46C4×Q8×C29D411yescharacteristic
47C4×D4×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29C2×C411yescharacteristic
50C4×D4×C29D411yescharacteristic
51C29×#117—21no—
52C29×#117—21no—
53C29×#117D411yescharacteristic
54C2×C42×C29—21no—
55C2×C42×C29C2311yescharacteristic
56C29×#107—21no—
57C29×#107—21no—
58C29×#106—21no—
59C29×#106—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8C2×C411yescharacteristic
65C29×C4⋊C8C2×C411yescharacteristic
66C29×C4⋊C8D411yescharacteristic
67C29×C4⋊C8D411yescharacteristic
68C29×C4⋊C8D412yes—
69C29×#103—21no—
70C29×#103—21no—
71C29×#102—21no—
72C29×#102—21no—
73C29×C22⋊C8—22no—
74C29×C22⋊C8—22no—
75C29×C22⋊C8—21no—
76C29×#97—22no—
77C4×C8×C29—22no—
78C4×C8×C29—21no—
79C4×C8×C29—21no—
80C4×C8×C29—21no—
81#41×C29—21no—
82#41×C29—21no—
83#41×C29—21no—
84#41×C29—21no—
85C2×Q8×C29—21no—
86C2×Q8×C29—21no—
87C2×Q8×C29C22⋊C411yescharacteristic
88C2×D4×C29—21no—
89C2×D4×C29C22⋊C411yescharacteristic
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29C2×D411yescharacteristic
94C22×C4×C29#4111yescharacteristic
95C22×C4×C29#4111yescharacteristic
96M16×C29—41no—
97M16×C29—41no—
98C2×C8×C29—22no—
99C2×C8×C29—21no—
100C2×C8×C29—21no—
101C2×C8×C29—21no—
102C2×C8×C29—21no—
103C2×C8×C29—22no—
104C2×C8×C29—41no—
105C2×C8×C29—41no—
106C2×C8×C29—41no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—41no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29C22⋊C411yescharacteristic
120C4⋊C4×C29C22⋊C411yescharacteristic
121C22⋊C4×C29—21no—
122C22⋊C4×C29—21no—
123C22⋊C4×C29—21no—
124C22⋊C4×C29—41no—
125C42×C29—21no—
126C42×C29—21no—
127C42×C29—21no—
128C42×C29—41no—
129C42×C29C22×C411yescharacteristic
130C42×C29C2×D411yescharacteristic
131C42×C29C2×D411yescharacteristic
132C42×C29C2×D411yescharacteristic
133#8994C2911yesmaximal, characteristic, direct product factor, Sylow
134C23×C29—21no—
135C23×C29#12311yescharacteristic
136Q8×C29—21no—
137Q8×C29—21no—
138Q8×C29—42no—
139Q8×C29—41no—
140Q8×C29—41no—
141D4×C29—21no—
142D4×C29—21no—
143D4×C29—41no—
144D4×C29—41no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—41no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—41no—
155C2×C4×C29—41no—
156C2×C4×C29—41no—
157C2×C4×C29—81no—
158C2×C4×C29C2×C22⋊C411yescharacteristic
159C2×C4×C29C4×D411yescharacteristic
160C2×C4×C29C4×D411yescharacteristic
161C2×C4×C29#12011yescharacteristic
162C2×C4×C29#12111yescharacteristic
163C2×C4×C29#12111yescharacteristic
164C2×C4×C29#13511yescharacteristic
165C2×C4×C29#13511yescharacteristic
166C2×C4×C29#13711yescharacteristic
167C2×C4×C29#13711yescharacteristic
168C8×C29—42no—
169C8×C29—41no—
170C8×C29—41no—
171C8×C29—41no—
172C8×C29—41no—
173C8×C29—42no—
174C8×C29—81no—
175#3076C2×C2911yescharacteristic
176#2925C2×C2911yescharacteristic
177#1493C2×C2911yescharacteristic, complemented
178#1481C2×C2911yescharacteristic, complemented
179#1476C2×C2911yescharacteristic
180#1301C2×C2911yescharacteristic, complemented
181#1277C2×C2911yescharacteristic, complemented
182C22×C29—21no—
183C22×C29—21no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29#38611yescharacteristic
188C22×C29#48511yescharacteristic
189C22×C29#48511yescharacteristic
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—41no—
194C4×C29—41no—
195C4×C29—41no—
196C4×C29—81no—
197C4×C29—81no—
198C4×C29#41611yescharacteristic
199C4×C29#41911yescharacteristic
200C4×C29#44311yescharacteristic
201C4×C29#44411yescharacteristic
202C4×C29#45211yescharacteristic
203C4×C29#45211yescharacteristic
204#533C22×C2911yescharacteristic
205C4×#41C22×C2911yescharacteristic
206#479—21no—
207#478—21no—
208#477C4×C2911yescharacteristic
209#476C4×C2911yescharacteristic
210#475C4×C2911yescharacteristic
211#474C4×C2911yescharacteristic
212#433—22no—
213#432—21no—
214#431—21no—
215#431C22×C2911yescharacteristic
216#427—21no—
217#423C22×C2911yescharacteristic
218C2×C4⋊C8C22×C2911yescharacteristic
219C2×C4⋊C8C22×C2911yescharacteristic
220#416—21no—
221#408—21no—
222#405—21no—
223C2×C4×C8C22×C2911yescharacteristic
224Q8⋊C8—21no—
225Q8⋊C8—21no—
226Q8⋊C8—21no—
227Q8⋊C8—22no—
228D4⋊C8—21no—
229C2×C29—21no—
230C2×C29—21no—
231C2×C29—81no—
232C2×C29#187311yescharacteristic
233C2×C29#187611yescharacteristic
234C2×C29#188111yescharacteristic
235C2×#41D4×C2911yescharacteristic
236C2×M16—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C4⋊Q8C2×C4×C2911yescharacteristic
241C4⋊Q8C2×C4×C2911yescharacteristic
242#125—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8C2×C4×C2911yescharacteristic
248C4×Q8D4×C2911yescharacteristic
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C2×C4×C2911yescharacteristic
252C4×D4D4×C2911yescharacteristic
253#117—21no—
254#117—21no—
255#117D4×C2911yescharacteristic
256C2×C42—21no—
257C2×C42C23×C2911yescharacteristic
258#107—21no—
259#107—21no—
260#106—21no—
261#106—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8C2×C4×C2911yescharacteristic
267C4⋊C8C2×C4×C2911yescharacteristic
268C4⋊C8D4×C2911yescharacteristic
269C4⋊C8D4×C2911yescharacteristic
270C4⋊C8D4×C2912yes—
271#103—21no—
272#103—21no—
273#102—21no—
274#102—21no—
275C22⋊C8—22no—
276C22⋊C8—22no—
277C22⋊C8—21no—
278#97—22no—
279C4×C8—22no—
280C4×C8—21no—
281C4×C8—21no—
282C4×C8—21no—
283C29#899411yescharacteristic, direct product factor, Sylow
284#41—21no—
285#41—21no—
286#41—21no—
287#41—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8C22⋊C4×C2911yescharacteristic
291C2×D4—21no—
292C2×D4C22⋊C4×C2911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4C2×D4×C2911yescharacteristic
297C22×C4#41×C2911yescharacteristic
298C22×C4#41×C2911yescharacteristic
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—21no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊C4×C2911yescharacteristic
323C4⋊C4C22⋊C4×C2911yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—41no—
332C42C22×C4×C2911yescharacteristic
333C42C2×D4×C2911yescharacteristic
334C42C2×D4×C2911yescharacteristic
335C42C2×D4×C2911yescharacteristic
336C23—21no—
337C23C29×#12311yescharacteristic
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—41no—
342Q8—41no—
343D4—21no—
344D4—21no—
345D4—41no—
346D4—41no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4C2×C22⋊C4×C2911yescharacteristic
361C2×C4C4×D4×C2911yescharacteristic
362C2×C4C4×D4×C2911yescharacteristic
363C2×C4C29×#12011yescharacteristic
364C2×C4C29×#12111yescharacteristic
365C2×C4C29×#12111yescharacteristic
366C2×C4C29×#13511yescharacteristic
367C2×C4C29×#13511yescharacteristic
368C2×C4C29×#13711yescharacteristic
369C2×C4C29×#13711yescharacteristic
370C8—42no—
371C8—41no—
372C8—41no—
373C8—42no—
374C8—41no—
375C8—41no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22C29×#38611yescharacteristic
383C22C29×#48511yescharacteristic
384C22C29×#48511yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—81no—
392C4—81no—
393C4C29×#41611yescharacteristic
394C4C29×#41911yescharacteristic
395C4C29×#44311yescharacteristic
396C4C29×#44411yescharacteristic
397C4C29×#45211yescharacteristic
398C4C29×#45211yescharacteristic
399C2—21no—
400C2—21no—
401C2—81no—
402C2C29×#187311yescharacteristic
403C2C29×#187611yescharacteristic
404C2C29×#188111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC2×#41×C29D4
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×#1493C2semidirect
4. C29×#1481C2semidirect
6. C29×#1301C2semidirect
7. C29×#1277C2semidirect
133. #8994C29direct (N × H)
177. #1493C2×C29semidirect
178. #1481C2×C29semidirect
180. #1301C2×C29semidirect
181. #1277C2×C29semidirect
283. C29#8994direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30762
C29×#29252
C29×#14932
C29×#14812
C29×#14762
C29×#13012
C29×#12772
#899429