Finite Group Databasebeta

← C29×#9173 #20304073

Subgroups — C29×#9173 #20304073

Order 7424.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3038C211yesmaximal, characteristic
2C29×#2906C211yesmaximal, characteristic, complemented
3C29×#1545C211yesmaximal, characteristic, complemented
4C2×C29×#331C211yesmaximal, characteristic, complemented
5C29×#1477C211yesmaximal, characteristic, complemented
6C29×#1301C211yesmaximal, characteristic, complemented
7C29×#1292C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—21no—
9C2×C29×#131—21no—
10C2×C29×#127C2211yescharacteristic
11C4×#41×C29C2211yescharacteristic
12C29×#460—21no—
13C29×#460C412yes—
14C29×#459—21no—
15C29×#459C412yes—
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×#418—21no—
26C29×#331—21no—
27C29×#331—21no—
28C29×#331—22no—
29C29×Q8⋊C8—21no—
30C29×D4⋊C8—21no—
31C2×#41×C29D411yescharacteristic
32C22×D4×C29—21no—
33C22×D4×C29—21no—
34C22×D4×C29—21no—
35C29×AGL(1,ℤ/8)—42no—
36C29×AGL(1,ℤ/8)—42no—
37C2×SD16×C29—22no—
38C2×D8×C29—22no—
39C29×#131—42no—
40C29×#131—42no—
41C2×M16×C29—22no—
42C2×M16×C29—21no—
43C2×M16×C29—21no—
44C22×C8×C29—22no—
45C22×C8×C29—21no—
46C22×C8×C29—21no—
47C29×#127—21no—
48C29×#127—21no—
49C29×#127—21no—
50C29×#127C2×C412yes—
51C4×Q8×C29C2×C411yescharacteristic
52C4×Q8×C29D411yescharacteristic
53C4×D4×C29—21no—
54C4×D4×C29—21no—
55C4×D4×C29C2×C411yescharacteristic
56C4×D4×C29D411yescharacteristic
57C29×#117—21no—
58C29×#117D411yescharacteristic
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×#102—22no—
74C29×#102—22no—
75C29×C22⋊C8—21no—
76C4×C8×C29—21no—
77C24×C29—41no—
78#41×C29—21no—
79#41×C29—21no—
80#41×C29D812yes—
81#41×C29SD1612yes—
82C2×Q8×C29C22⋊C411yescharacteristic
83C2×D4×C29—21no—
84C2×D4×C29—22no—
85C2×D4×C29—22no—
86C2×D4×C29—22no—
87C2×D4×C29—41no—
88C2×D4×C29—41no—
89C2×D4×C29—41no—
90C2×D4×C29—41no—
91C2×D4×C29—41no—
92C2×D4×C29—41no—
93C2×D4×C29—41no—
94C2×D4×C29—81no—
95C2×D4×C29—81no—
96C2×D4×C29—82no—
97C2×D4×C29C22⋊C411yescharacteristic
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29#4111yescharacteristic
103C22×C4×C29#4111yescharacteristic
104SD16×C29—44no—
105D8×C29—44no—
106M16×C29—44no—
107M16×C29—41no—
108M16×C29—41no—
109M16×C29—41no—
110M16×C29—41no—
111C2×C8×C29—22no—
112C2×C8×C29—21no—
113C2×C8×C29—22no—
114C2×C8×C29—21no—
115C2×C8×C29—44no—
116C2×C8×C29—41no—
117C2×C8×C29—41no—
118C2×C8×C29—41no—
119C2×C8×C29—41no—
120C2×C8×C29—81no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29C22⋊C411yescharacteristic
124C4⋊C4×C29C22⋊C411yescharacteristic
125C22⋊C4×C29—21no—
126C22⋊C4×C29—21no—
127C22⋊C4×C29—21no—
128C42×C29—21no—
129C42×C29—21no—
130C42×C29—21no—
131C42×C29C22×C411yescharacteristic
132C42×C29C2×D411yescharacteristic
133C42×C29C2×D411yescharacteristic
134C42×C29C2×D411yescharacteristic
135#9173C2911yesmaximal, characteristic, direct product factor, Sylow
136C23×C29—21no—
137C23×C29—42no—
138C23×C29—82no—
139C23×C29—82no—
140C23×C29—81no—
141C23×C29—81no—
142C23×C29#12311yescharacteristic
143Q8×C29—21no—
144Q8×C29#10212yes—
145D4×C29—22no—
146D4×C29—22no—
147D4×C29—21no—
148D4×C29—42no—
149D4×C29—42no—
150D4×C29—82no—
151D4×C29—82no—
152D4×C29—82no—
153D4×C29—81no—
154D4×C29—81no—
155D4×C29—81no—
156D4×C29—81no—
157D4×C29#10212yes—
158C2×C4×C29—21no—
159C2×C4×C29—22no—
160C2×C4×C29—22no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—81no—
169C2×C4×C29C2×C22⋊C411yescharacteristic
170C2×C4×C29C4×D411yescharacteristic
171C2×C4×C29C4×D411yescharacteristic
172C2×C4×C29#12011yescharacteristic
173C2×C4×C29#12111yescharacteristic
174C2×C4×C29#12111yescharacteristic
175C2×C4×C29C2×D811yescharacteristic
176C2×C4×C29C2×SD1611yescharacteristic
177C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C29#13711yescharacteristic
179C8×C29—42no—
180C8×C29—41no—
181C8×C29—42no—
182C8×C29—41no—
183C8×C29—81no—
184C8×C29—81no—
185#3038C2×C2911yescharacteristic
186#2906C2×C2911yescharacteristic, complemented
187#1545C2×C2911yescharacteristic, complemented
188C2×#331C2×C2911yescharacteristic, complemented
189#1477C2×C2911yescharacteristic, complemented
190#1301C2×C2911yescharacteristic, complemented
191#1292C2×C2911yescharacteristic, complemented
192C22×C29—21no—
193C22×C29—21no—
194C22×C29—22no—
195C22×C29—41no—
196C22×C29—41no—
197C22×C29—82no—
198C22×C29—82no—
199C22×C29—82no—
200C22×C29—162no—
201C22×C29—162no—
202C22×C29#38611yescharacteristic
203C22×C29#48011yescharacteristic
204C22×C29#48111yescharacteristic
205C4×C29—22no—
206C4×C29—21no—
207C4×C29—21no—
208C4×C29—21no—
209C4×C29—41no—
210C4×C29—41no—
211C4×C29C2×#10211yescharacteristic
212C4×C29#41711yescharacteristic
213C4×C29#44711yescharacteristic
214C4×C29#44811yescharacteristic
215C4×C29#47111yescharacteristic
216C4×C29#47211yescharacteristic
217C2×AGL(1,ℤ/8)—21no—
218C2×#131—21no—
219C2×#127C22×C2911yescharacteristic
220C4×#41C22×C2911yescharacteristic
221#460—21no—
222#460C4×C2912yes—
223#459—21no—
224#459C4×C2912yes—
225#431C22×C2911yescharacteristic
226#424—21no—
227#424—22no—
228#423—21no—
229#423C22×C2911yescharacteristic
230#423C22×C2911yescharacteristic
231C2×C4⋊C8—21no—
232C2×C4⋊C8C22×C2911yescharacteristic
233C2×C4⋊C8C22×C2911yescharacteristic
234#418—21no—
235#331—21no—
236#331—21no—
237#331—22no—
238Q8⋊C8—21no—
239D4⋊C8—21no—
240C2×C29—21no—
241C2×C29—21no—
242C2×C29—42no—
243C2×C29—162no—
244C2×C29#187411yescharacteristic
245C2×C29#190311yescharacteristic
246C2×C29#190711yescharacteristic
247C2×#41D4×C2911yescharacteristic
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251AGL(1,ℤ/8)—42no—
252AGL(1,ℤ/8)—42no—
253C2×SD16—22no—
254C2×D8—22no—
255#131—42no—
256#131—42no—
257C2×M16—22no—
258C2×M16—21no—
259C2×M16—21no—
260C22×C8—22no—
261C22×C8—21no—
262C22×C8—21no—
263#127—21no—
264#127—21no—
265#127—21no—
266#127C2×C4×C2912yes—
267C4×Q8C2×C4×C2911yescharacteristic
268C4×Q8D4×C2911yescharacteristic
269C4×D4—21no—
270C4×D4—21no—
271C4×D4C2×C4×C2911yescharacteristic
272C4×D4D4×C2911yescharacteristic
273#117—21no—
274#117D4×C2911yescharacteristic
275C2×C42—21no—
276C2×C42C23×C2911yescharacteristic
277C4⋊C8—22no—
278C4⋊C8—22no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8C2×C4×C2912yes—
286C4⋊C8D4×C2911yescharacteristic
287C4⋊C8D4×C2911yescharacteristic
288C4⋊C8D4×C2912yes—
289#102—22no—
290#102—22no—
291C22⋊C8—21no—
292C4×C8—21no—
293C29#917311yescharacteristic, direct product factor, Sylow
294C24—41no—
295#41—21no—
296#41—21no—
297#41D8×C2912yes—
298#41SD16×C2912yes—
299C2×Q8C22⋊C4×C2911yescharacteristic
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—81no—
312C2×D4—81no—
313C2×D4—82no—
314C2×D4C22⋊C4×C2911yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4C2×D4×C2911yescharacteristic
319C22×C4#41×C2911yescharacteristic
320C22×C4#41×C2911yescharacteristic
321SD16—44no—
322D8—44no—
323M16—44no—
324M16—41no—
325M16—41no—
326M16—41no—
327M16—41no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—44no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—81no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4C22⋊C4×C2911yescharacteristic
341C4⋊C4C22⋊C4×C2911yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42C22×C4×C2911yescharacteristic
349C42C2×D4×C2911yescharacteristic
350C42C2×D4×C2911yescharacteristic
351C42C2×D4×C2911yescharacteristic
352C23—21no—
353C23—42no—
354C23—82no—
355C23—82no—
356C23—81no—
357C23—81no—
358C23C29×#12311yescharacteristic
359Q8—21no—
360Q8C29×#10212yes—
361D4—22no—
362D4—22no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—82no—
367D4—82no—
368D4—82no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4C29×#10212yes—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4C2×C22⋊C4×C2911yescharacteristic
386C2×C4C4×D4×C2911yescharacteristic
387C2×C4C4×D4×C2911yescharacteristic
388C2×C4C29×#12011yescharacteristic
389C2×C4C29×#12111yescharacteristic
390C2×C4C29×#12111yescharacteristic
391C2×C4C2×D8×C2911yescharacteristic
392C2×C4C2×SD16×C2911yescharacteristic
393C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
394C2×C4C29×#13711yescharacteristic
395C8—41no—
396C8—42no—
397C8—41no—
398C8—42no—
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—162no—
410C22—162no—
411C22C29×#38611yescharacteristic
412C22C29×#48011yescharacteristic
413C22C29×#48111yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—22no—
418C4—41no—
419C4—41no—
420C4C2×C29×#10211yescharacteristic
421C4C29×#41711yescharacteristic
422C4C29×#44711yescharacteristic
423C4C29×#44811yescharacteristic
424C4C29×#47111yescharacteristic
425C4C29×#47211yescharacteristic
426C2—21no—
427C2—21no—
428C2—42no—
429C2—162no—
430C2C29×#187411yescharacteristic
431C2C29×#190311yescharacteristic
432C2C29×#190711yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3038C2
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
2. C29×#2906C2semidirect
3. C29×#1545C2semidirect
4. C2×C29×#331C2semidirect
5. C29×#1477C2semidirect
6. C29×#1301C2semidirect
7. C29×#1292C2semidirect
135. #9173C29direct (N × H)
186. #2906C2×C29semidirect
187. #1545C2×C29semidirect
188. C2×#331C2×C29semidirect
189. #1477C2×C29semidirect
190. #1301C2×C29semidirect
191. #1292C2×C29semidirect
293. C29#9173direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30382
C29×#29062
C29×#15452
C2×C29×#3312
C29×#14772
C29×#13012
C29×#12922
#917329