Finite Group Databasebeta

← C29×#9364 #20304264

Subgroups — C29×#9364 #20304264

Order 7424.

732 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3007C211yesmaximal, characteristic
2C29×#2341C211yesmaximal, characteristic
3C29×#1996C211yesmaximal, characteristic, complemented
4C29×#1789C211yesmaximal, characteristic
5C29×#1508C211yesmaximal, characteristic, complemented
6C29×#1305C211yesmaximal, characteristic, complemented
7C29×#1297C211yesmaximal, characteristic, complemented
8C22×#41×C29C2211yescharacteristic
9C2×C29×#137C412yescomplemented
10C2×C29×C22⋊Q8C2211yescharacteristic
11C2×C4×Q8×C29—21no—
12C29×#452—22no—
13C29×#451—21no—
14C29×#450—21no—
15C2×C29×#104—22no—
16C29×#417C412yescomplemented
17C29×#407C2211yescharacteristic
18C29×#407C2211yescharacteristic
19C29×#390—21no—
20C29×#390—22no—
21C29×#380—21no—
22C29×#380C2211yescharacteristic
23C4×C22⋊C4×C29—21no—
24C4×C22⋊C4×C29C2211yescharacteristic
25C4×C22⋊C4×C29C2211yescharacteristic
26C29×#342—22no—
27C29×#328—21no—
28C29×#328—21no—
29C2×#41×C29—21no—
30C2×#41×C29—21no—
31C2×#41×C29—44no—
32C2×#41×C29C2×C412yes—
33C2×#41×C29D412yes—
34C22×Q8×C29C2×C411yescharacteristic
35C22×Q8×C29D411yescharacteristic
36C22×D4×C29—21no—
37C22×D4×C29D411yescharacteristic
38C23×C4×C29—21no—
39C23×C4×C29C2311yescharacteristic
40C29×#137—44no—
41C2×Q16×C29—22no—
42C2×SD16×C29—22no—
43C2×M16×C29—21no—
44C2×M16×C29C2×C412yes—
45C29×C22⋊Q8—21no—
46C29×C22⋊Q8—21no—
47C29×C22⋊Q8—21no—
48C29×C22⋊Q8—21no—
49C4×Q8×C29—44no—
50C2×C4⋊C4×C29—22no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29C2×C411yescharacteristic
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29—22no—
56C2×C22⋊C4×C29—21no—
57C2×C22⋊C4×C29—21no—
58C2×C22⋊C4×C29—22no—
59C2×C22⋊C4×C29D412yes—
60C2×C42×C29—22no—
61C2×C42×C29—21no—
62C2×C42×C29—21no—
63C29×#104—44no—
64C29×#103—22no—
65C29×#102—22no—
66C29×C22⋊C8—21no—
67C29×C22⋊C8—21no—
68C29×C22⋊C8—21no—
69C29×C22⋊C8—21no—
70C29×#95—21no—
71C29×#95—21no—
72C29×#95D411yescharacteristic
73C29×#95D411yescharacteristic
74C24×C29—21no—
75C24×C29C2×D411yescharacteristic
76#41×C29—24no—
77#41×C29—24no—
78#41×C29—42no—
79#41×C29—42no—
80#41×C29—44no—
81#41×C29—44no—
82C2×Q8×C29—24no—
83C2×Q8×C29—21no—
84C2×Q8×C29—21no—
85C2×Q8×C29—21no—
86C2×Q8×C29—42no—
87C2×Q8×C29C22⋊C412yes—
88C2×D4×C29—22no—
89C2×D4×C29—22no—
90C2×D4×C29—21no—
91C2×D4×C29—42no—
92C2×D4×C29—44no—
93C2×D4×C29C22⋊C412yes—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—22no—
97C22×C4×C29—22no—
98C22×C4×C29—21no—
99C22×C4×C29—22no—
100C22×C4×C29—21no—
101C22×C4×C29—21no—
102C22×C4×C29—42no—
103C22×C4×C29—44no—
104C22×C4×C29—41no—
105C22×C4×C29C22×C411yescharacteristic
106C22×C4×C29C2×D411yescharacteristic
107C22×C4×C29C2×D411yescharacteristic
108C22×C4×C29C2×D411yescharacteristic
109C22×C4×C29#4111yescharacteristic
110C22×C4×C29#4111yescharacteristic
111Q16×C29—44no—
112SD16×C29—44no—
113M16×C29—42no—
114M16×C29—42no—
115C2×C8×C29—22no—
116C2×C8×C29—41no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—44no—
120C4⋊C4×C29—42no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29—41no—
123C22⋊C4×C29—22no—
124C22⋊C4×C29—42no—
125C22⋊C4×C29—44no—
126C22⋊C4×C29—41no—
127C22⋊C4×C29—41no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29—42no—
130C22⋊C4×C29—82no—
131C42×C29—44no—
132C42×C29—42no—
133C42×C29—42no—
134#9364C2911yesmaximal, characteristic, direct product factor, Sylow
135C23×C29—21no—
136C23×C29—21no—
137C23×C29—22no—
138C23×C29—41no—
139C23×C29—41no—
140C23×C29—42no—
141C23×C29—42no—
142C23×C29—41no—
143C23×C29—41no—
144C23×C29C4×D411yescharacteristic
145C23×C29#12011yescharacteristic
146C23×C29#12111yescharacteristic
147Q8×C29—24no—
148Q8×C29—22no—
149Q8×C29—42no—
150Q8×C29—81no—
151Q8×C29#9914yes—
152D4×C29—22no—
153D4×C29—22no—
154D4×C29—44no—
155D4×C29—44no—
156D4×C29—42no—
157C2×C4×C29—24no—
158C2×C4×C29—22no—
159C2×C4×C29—22no—
160C2×C4×C29—22no—
161C2×C4×C29—22no—
162C2×C4×C29—22no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—44no—
167C2×C4×C29—44no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—42no—
172C2×C4×C29—42no—
173C2×C4×C29—41no—
174C2×C4×C29—42no—
175C2×C4×C29—41no—
176C2×C4×C29—41no—
177C2×C4×C29—42no—
178C2×C4×C29—41no—
179C2×C4×C29—81no—
180C2×C4×C29—81no—
181C2×C4×C29—81no—
182C2×C4×C29—81no—
183C2×C4×C29C2×C22⋊C411yescharacteristic
184C2×C4×C29C4×D411yescharacteristic
185C2×C4×C29#12111yescharacteristic
186C2×C4×C29#12311yescharacteristic
187C8×C29—42no—
188C8×C29—81no—
189#3007C2×C2911yescharacteristic
190#2341C2×C2911yescharacteristic
191#1996C2×C2911yescharacteristic, complemented
192#1789C2×C2911yescharacteristic
193#1508C2×C2911yescharacteristic, complemented
194#1305C2×C2911yescharacteristic, complemented
195#1297C2×C2911yescharacteristic, complemented
196C22×C29—21no—
197C22×C29—21no—
198C22×C29—21no—
199C22×C29—21no—
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—21no—
203C22×C29—21no—
204C22×C29—42no—
205C22×C29—42no—
206C22×C29—42no—
207C22×C29—81no—
208C22×C29—81no—
209C22×C29—82no—
210C22×C29—82no—
211C22×C29#38611yescharacteristic
212C22×C29#45511yescharacteristic
213C22×C29#45611yescharacteristic
214C4×C29—21no—
215C4×C29—24no—
216C4×C29—21no—
217C4×C29—21no—
218C4×C29—42no—
219C4×C29—82no—
220C4×C29—81no—
221C4×C29—82no—
222C4×C29—81no—
223C4×C29—81no—
224C4×C29C2×#9912yes—
225C22×#41C22×C2911yescharacteristic
226C2×#137C4×C2912yescomplemented
227C2×C22⋊Q8C22×C2911yescharacteristic
228C2×C4×Q8—21no—
229#452—22no—
230#451—21no—
231#450—21no—
232C2×#104—22no—
233#417C4×C2912yescomplemented
234#407C22×C2911yescharacteristic
235#407C22×C2911yescharacteristic
236#390—21no—
237#390—22no—
238#380—21no—
239#380C22×C2911yescharacteristic
240C4×C22⋊C4—21no—
241C4×C22⋊C4C22×C2911yescharacteristic
242C4×C22⋊C4C22×C2911yescharacteristic
243#342—22no—
244#328—21no—
245#328—21no—
246C2×C29—21no—
247C2×C29—21no—
248C2×C29—41no—
249C2×C29—41no—
250C2×C29—82no—
251C2×C29#188211yescharacteristic
252C2×C29#189811yescharacteristic
253C2×C29#190611yescharacteristic
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—44no—
257C2×#41C2×C4×C2912yes—
258C2×#41D4×C2912yes—
259C22×Q8C2×C4×C2911yescharacteristic
260C22×Q8D4×C2911yescharacteristic
261C22×D4—21no—
262C22×D4D4×C2911yescharacteristic
263C23×C4—21no—
264C23×C4C23×C2911yescharacteristic
265#137—44no—
266C2×Q16—22no—
267C2×SD16—22no—
268C2×M16—21no—
269C2×M16C2×C4×C2912yes—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C4×Q8—44no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4C2×C4×C2911yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4D4×C2912yes—
285C2×C42—22no—
286C2×C42—21no—
287C2×C42—21no—
288#104—44no—
289#103—22no—
290#102—22no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295#95—21no—
296#95—21no—
297#95D4×C2911yescharacteristic
298#95D4×C2911yescharacteristic
299C29#936411yescharacteristic, direct product factor, Sylow
300C24—21no—
301C24C2×D4×C2911yescharacteristic
302#41—24no—
303#41—24no—
304#41—42no—
305#41—42no—
306#41—44no—
307#41—44no—
308C2×Q8—24no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—42no—
313C2×Q8C22⋊C4×C2912yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—42no—
318C2×D4—44no—
319C2×D4C22⋊C4×C2912yes—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—44no—
330C22×C4—41no—
331C22×C4C22×C4×C2911yescharacteristic
332C22×C4C2×D4×C2911yescharacteristic
333C22×C4C2×D4×C2911yescharacteristic
334C22×C4C2×D4×C2911yescharacteristic
335C22×C4#41×C2911yescharacteristic
336C22×C4#41×C2911yescharacteristic
337Q16—44no—
338SD16—44no—
339M16—42no—
340M16—42no—
341C2×C8—22no—
342C2×C8—41no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—44no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C22⋊C4—22no—
350C22⋊C4—42no—
351C22⋊C4—44no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—42no—
356C22⋊C4—82no—
357C42—44no—
358C42—42no—
359C42—42no—
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23C4×D4×C2911yescharacteristic
370C23C29×#12011yescharacteristic
371C23C29×#12111yescharacteristic
372Q8—24no—
373Q8—22no—
374Q8—42no—
375Q8—81no—
376Q8C29×#9914yes—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—44no—
381D4—42no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4C2×C22⋊C4×C2911yescharacteristic
409C2×C4C4×D4×C2911yescharacteristic
410C2×C4C29×#12111yescharacteristic
411C2×C4C29×#12311yescharacteristic
412C8—42no—
413C8—81no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22C29×#38611yescharacteristic
430C22C29×#45511yescharacteristic
431C22C29×#45611yescharacteristic
432C4—21no—
433C4—24no—
434C4—21no—
435C4—21no—
436C4—42no—
437C4—82no—
438C4—81no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4C2×C29×#9912yes—
443C2—21no—
444C2—21no—
445C2—41no—
446C2—41no—
447C2—82no—
448C2C29×#188211yescharacteristic
449C2C29×#189811yescharacteristic
450C2C29×#190611yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC22×#41×C29C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1996C2semidirect
5. C29×#1508C2semidirect
6. C29×#1305C2semidirect
7. C29×#1297C2semidirect
9. C2×C29×#137C4semidirect
16. C29×#417C4semidirect
134. #9364C29direct (N × H)
191. #1996C2×C29semidirect
193. #1508C2×C29semidirect
194. #1305C2×C29semidirect
195. #1297C2×C29semidirect
226. C2×#137C4×C29semidirect
233. #417C4×C29semidirect
299. C29#9364direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30072
C29×#23412
C29×#19962
C29×#17892
C29×#15082
C29×#13052
C29×#12972
#936429