Finite Group Databasebeta

← C29×#9171 #20304071

Subgroups — C29×#9171 #20304071

Order 7424.

510 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3039C211yesmaximal, characteristic
2C29×#2906C211yesmaximal, characteristic
3C29×#1546C211yesmaximal, characteristic, complemented
4C2×C29×#332C211yesmaximal, characteristic, complemented
5C29×#1477C211yesmaximal, characteristic
6C29×#1301C211yesmaximal, characteristic, complemented
7C29×#1292C211yesmaximal, characteristic, complemented
8C2×C29×#137—21no—
9C2×C29×#131—21no—
10C2×C29×C4⋊Q8C2211yescharacteristic
11C4×#41×C29C2211yescharacteristic
12C29×#462—21no—
13C29×#462C412yes—
14C29×#461—21no—
15C29×#461C412yes—
16C29×#431C2211yescharacteristic
17C29×#424—22no—
18C29×#424—21no—
19C29×#423—21no—
20C29×#423C2211yescharacteristic
21C29×#423C2211yescharacteristic
22C2×C29×C4⋊C8—21no—
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×C4⋊C8C2211yescharacteristic
25C29×#419—21no—
26C29×#332—21no—
27C29×#332—21no—
28C29×#332—22no—
29C29×Q8⋊C8—21no—
30C29×D4⋊C8—21no—
31C2×#41×C29D411yescharacteristic
32C22×Q8×C29—21no—
33C29×#137—42no—
34C29×#137—42no—
35C2×Q16×C29—22no—
36C2×SD16×C29—22no—
37C29×#131—42no—
38C29×#131—42no—
39C2×M16×C29—22no—
40C2×M16×C29—21no—
41C2×M16×C29—21no—
42C22×C8×C29—22no—
43C22×C8×C29—21no—
44C22×C8×C29—21no—
45C29×C4⋊Q8—21no—
46C29×C4⋊Q8—21no—
47C29×C4⋊Q8—21no—
48C29×C4⋊Q8C2×C412yes—
49C4×Q8×C29C2×C411yescharacteristic
50C4×Q8×C29D411yescharacteristic
51C4×D4×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29C2×C411yescharacteristic
54C4×D4×C29D411yescharacteristic
55C29×#117—21no—
56C29×#117D411yescharacteristic
57C2×C4⋊C4×C29—21no—
58C2×C4⋊C4×C29—21no—
59C2×C42×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×C4⋊C8—22no—
62C29×C4⋊C8—22no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×C4⋊C8—21no—
69C29×C4⋊C8C2×C412yes—
70C29×C4⋊C8D411yescharacteristic
71C29×C4⋊C8D411yescharacteristic
72C29×C4⋊C8D412yes—
73C29×#103—22no—
74C29×#103—22no—
75C29×C22⋊C8—21no—
76C4×C8×C29—21no—
77#41×C29—21no—
78#41×C29—21no—
79#41×C29D812yes—
80#41×C29SD1612yes—
81C2×Q8×C29—22no—
82C2×Q8×C29—41no—
83C2×Q8×C29—41no—
84C2×Q8×C29—41no—
85C2×Q8×C29—41no—
86C2×Q8×C29—41no—
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×C29—41no—
94C22×C4×C29C2×D411yescharacteristic
95C22×C4×C29#4111yescharacteristic
96C22×C4×C29#4111yescharacteristic
97Q16×C29—44no—
98SD16×C29—44no—
99M16×C29—44no—
100M16×C29—41no—
101M16×C29—41no—
102M16×C29—41no—
103M16×C29—41no—
104C2×C8×C29—22no—
105C2×C8×C29—21no—
106C2×C8×C29—22no—
107C2×C8×C29—21no—
108C2×C8×C29—44no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C2×C8×C29—41no—
112C2×C8×C29—41no—
113C2×C8×C29—81no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—22no—
117C4⋊C4×C29—22no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29C22⋊C411yescharacteristic
121C4⋊C4×C29C22⋊C411yescharacteristic
122C22⋊C4×C29—21no—
123C22⋊C4×C29—21no—
124C22⋊C4×C29—21no—
125C42×C29—21no—
126C42×C29—21no—
127C42×C29—21no—
128C42×C29C22×C411yescharacteristic
129C42×C29C2×D411yescharacteristic
130C42×C29C2×D411yescharacteristic
131C42×C29C2×D411yescharacteristic
132#9171C2911yesmaximal, characteristic, direct product factor, Sylow
133C23×C29—21no—
134C23×C29#12311yescharacteristic
135Q8×C29—21no—
136Q8×C29—42no—
137Q8×C29—42no—
138Q8×C29—81no—
139Q8×C29—81no—
140Q8×C29#10212yes—
141D4×C29—22no—
142D4×C29—22no—
143D4×C29—21no—
144D4×C29#10212yes—
145C2×C4×C29—21no—
146C2×C4×C29—22no—
147C2×C4×C29—22no—
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—42no—
156C2×C4×C29—81no—
157C2×C4×C29—81no—
158C2×C4×C29—81no—
159C2×C4×C29C2×C22⋊C411yescharacteristic
160C2×C4×C29C4×D411yescharacteristic
161C2×C4×C29C4×D411yescharacteristic
162C2×C4×C29#12011yescharacteristic
163C2×C4×C29#12111yescharacteristic
164C2×C4×C29#12111yescharacteristic
165C2×C4×C29C2×D811yescharacteristic
166C2×C4×C29C2×SD1611yescharacteristic
167C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C29#13711yescharacteristic
169C8×C29—42no—
170C8×C29—41no—
171C8×C29—42no—
172C8×C29—41no—
173C8×C29—81no—
174C8×C29—81no—
175#3039C2×C2911yescharacteristic
176#2906C2×C2911yescharacteristic
177#1546C2×C2911yescharacteristic, complemented
178C2×#332C2×C2911yescharacteristic, complemented
179#1477C2×C2911yescharacteristic
180#1301C2×C2911yescharacteristic, complemented
181#1292C2×C2911yescharacteristic, complemented
182C22×C29—21no—
183C22×C29—21no—
184C22×C29—22no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29#38611yescharacteristic
188C22×C29#48011yescharacteristic
189C22×C29#48111yescharacteristic
190C4×C29—22no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—21no—
194C4×C29—41no—
195C4×C29—41no—
196C4×C29—82no—
197C4×C29C2×#10211yescharacteristic
198C4×C29#41711yescharacteristic
199C4×C29#44711yescharacteristic
200C4×C29#44811yescharacteristic
201C4×C29#47111yescharacteristic
202C4×C29#47311yescharacteristic
203C2×#137—21no—
204C2×#131—21no—
205C2×C4⋊Q8C22×C2911yescharacteristic
206C4×#41C22×C2911yescharacteristic
207#462—21no—
208#462C4×C2912yes—
209#461—21no—
210#461C4×C2912yes—
211#431C22×C2911yescharacteristic
212#424—21no—
213#424—22no—
214#423—21no—
215#423C22×C2911yescharacteristic
216#423C22×C2911yescharacteristic
217C2×C4⋊C8—21no—
218C2×C4⋊C8C22×C2911yescharacteristic
219C2×C4⋊C8C22×C2911yescharacteristic
220#419—21no—
221#332—21no—
222#332—21no—
223#332—22no—
224Q8⋊C8—21no—
225D4⋊C8—21no—
226C2×C29—21no—
227C2×C29—21no—
228C2×C29—42no—
229C2×C29#187411yescharacteristic
230C2×C29#190211yescharacteristic
231C2×C29#190811yescharacteristic
232C2×#41D4×C2911yescharacteristic
233C22×Q8—21no—
234#137—42no—
235#137—42no—
236C2×Q16—22no—
237C2×SD16—22no—
238#131—42no—
239#131—42no—
240C2×M16—22no—
241C2×M16—21no—
242C2×M16—21no—
243C22×C8—22no—
244C22×C8—21no—
245C22×C8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C2×C4×C2912yes—
250C4×Q8C2×C4×C2911yescharacteristic
251C4×Q8D4×C2911yescharacteristic
252C4×D4—21no—
253C4×D4—21no—
254C4×D4C2×C4×C2911yescharacteristic
255C4×D4D4×C2911yescharacteristic
256#117—21no—
257#117D4×C2911yescharacteristic
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C42—21no—
261C2×C42C23×C2911yescharacteristic
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8C2×C4×C2912yes—
271C4⋊C8D4×C2911yescharacteristic
272C4⋊C8D4×C2911yescharacteristic
273C4⋊C8D4×C2912yes—
274#103—22no—
275#103—22no—
276C22⋊C8—21no—
277C4×C8—21no—
278C29#917111yescharacteristic, direct product factor, Sylow
279#41—21no—
280#41—21no—
281#41D8×C2912yes—
282#41SD16×C2912yes—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8C22⋊C4×C2911yescharacteristic
290C2×D4—21no—
291C2×D4C22⋊C4×C2911yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4C2×D4×C2911yescharacteristic
297C22×C4#41×C2911yescharacteristic
298C22×C4#41×C2911yescharacteristic
299Q16—44no—
300SD16—44no—
301M16—44no—
302M16—41no—
303M16—41no—
304M16—41no—
305M16—41no—
306C2×C8—22no—
307C2×C8—21no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—44no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—81no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊C4×C2911yescharacteristic
323C4⋊C4C22⋊C4×C2911yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C42—21no—
328C42—21no—
329C42—21no—
330C42C22×C4×C2911yescharacteristic
331C42C2×D4×C2911yescharacteristic
332C42C2×D4×C2911yescharacteristic
333C42C2×D4×C2911yescharacteristic
334C23—21no—
335C23C29×#12311yescharacteristic
336Q8—21no—
337Q8—42no—
338Q8—42no—
339Q8—81no—
340Q8—81no—
341Q8C29×#10212yes—
342D4—22no—
343D4—22no—
344D4—21no—
345D4C29×#10212yes—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—81no—
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×C4C2×D8×C2911yescharacteristic
367C2×C4C2×SD16×C2911yescharacteristic
368C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
369C2×C4C29×#13711yescharacteristic
370C8—41no—
371C8—42no—
372C8—41no—
373C8—42no—
374C8—81no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22C29×#38611yescharacteristic
382C22C29×#48011yescharacteristic
383C22C29×#48111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—82no—
391C4C2×C29×#10211yescharacteristic
392C4C29×#41711yescharacteristic
393C4C29×#44711yescharacteristic
394C4C29×#44811yescharacteristic
395C4C29×#47111yescharacteristic
396C4C29×#47311yescharacteristic
397C2—21no—
398C2—21no—
399C2—42no—
400C2C29×#187411yescharacteristic
401C2C29×#190211yescharacteristic
402C2C29×#190811yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC2×#41×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1546C2semidirect
4. C2×C29×#332C2semidirect
6. C29×#1301C2semidirect
7. C29×#1292C2semidirect
132. #9171C29direct (N × H)
177. #1546C2×C29semidirect
178. C2×#332C2×C29semidirect
180. #1301C2×C29semidirect
181. #1292C2×C29semidirect
278. C29#9171direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30392
C29×#29062
C29×#15462
C2×C29×#3322
C29×#14772
C29×#13012
C29×#12922
#917129