Finite Group Databasebeta

← C29×#13092 #20307992

Subgroups — C29×#13092 #20307992

Order 7424.

702 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#101C211yesmaximal, characteristic, complemented
2C29×#2436C211yesmaximal, characteristic
3C2×C29×#355C212yesmaximal, complemented
4C29×#1784C211yesmaximal, characteristic, complemented
5C29×#1394C212yesmaximal, complemented
6C23×Q8×C29C2211yescharacteristic
7C22×M16×C29—21no—
8C2×C29×#124C411yescharacteristic
9C2×C29×#124C2211yescharacteristic
10C2×C29×#121C411yescharacteristic
11C2×C29×#101—24no—
12C2×C29×#101—21no—
13C2×C29×#101—21no—
14C2×C29×#101C2212yes—
15C2×C29×#101C2212yes—
16C29×#407—21no—
17C29×#393—21no—
18C29×#393—21no—
19C29×#391C411yescharacteristic
20C29×#391C2211yescharacteristic
21C29×#386—21no—
22C29×#386—21no—
23C4×C22⋊C4×C29C411yescharacteristic
24C29×#355—24no—
25C22×Q8×C29—22no—
26C22×Q8×C29—22no—
27C22×Q8×C29—41no—
28C22×Q8×C29—41no—
29C22×Q8×C29—42no—
30C22×Q8×C29C2×C411yescharacteristic
31C22×Q8×C29D411yescharacteristic
32C22×Q8×C29D411yescharacteristic
33C22×Q8×C29C2311yescharacteristic
34C22×D4×C29—21no—
35C22×D4×C29C2×C411yescharacteristic
36C23×C4×C29C2×C411yescharacteristic
37C23×C4×C29D411yescharacteristic
38C23×C4×C29D411yescharacteristic
39C2×M16×C29—24no—
40C2×M16×C29—22no—
41C2×M16×C29—22no—
42C2×M16×C29—41no—
43C2×M16×C29—42no—
44C22×C8×C29—41no—
45C29×#124—22no—
46C29×#124—22no—
47C29×#124—42no—
48C29×#121—41no—
49C29×#121—41no—
50C2×C4⋊C4×C29C2×C411yescharacteristic
51C2×C22⋊C4×C29—21no—
52C2×C22⋊C4×C29—21no—
53C2×C22⋊C4×C29—21no—
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29—21no—
56C2×C22⋊C4×C29—21no—
57C2×C42×C29C2×C411yescharacteristic
58C2×C42×C29C2×C411yescharacteristic
59C29×#101—24no—
60C29×#101—22no—
61C29×#101—22no—
62C29×#101—22no—
63C29×#101—42no—
64C29×#101D414yescomplemented
65C29×C22⋊C8—41no—
66C29×C22⋊C8—41no—
67C29×#95—21no—
68C29×#95—21no—
69C29×#95—21no—
70C29×#95—21no—
71C29×#95—21no—
72C24×C29—21no—
73C24×C29C22⋊C411yescharacteristic
74C2×Q8×C29—22no—
75C2×Q8×C29—22no—
76C2×Q8×C29—22no—
77C2×Q8×C29—21no—
78C2×Q8×C29—22no—
79C2×Q8×C29—21no—
80C2×Q8×C29—41no—
81C2×Q8×C29—41no—
82C2×Q8×C29—41no—
83C2×Q8×C29—41no—
84C2×Q8×C29—41no—
85C2×Q8×C29—41no—
86C2×Q8×C29—44no—
87C2×Q8×C29—44no—
88C2×Q8×C29—44no—
89C2×Q8×C29—44no—
90C2×Q8×C29C2×D412yes—
91C2×Q8×C29#4112yes—
92C2×D4×C29—22no—
93C2×D4×C29—41no—
94C2×D4×C29—41no—
95C2×D4×C29—44no—
96C2×D4×C29—41no—
97C2×D4×C29—41no—
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—22no—
101C22×C4×C29—21no—
102C22×C4×C29—21no—
103C22×C4×C29—21no—
104C22×C4×C29—21no—
105C22×C4×C29—21no—
106C22×C4×C29—21no—
107C22×C4×C29—22no—
108C22×C4×C29—22no—
109C22×C4×C29—21no—
110C22×C4×C29—21no—
111C22×C4×C29—21no—
112C22×C4×C29—41no—
113C22×C4×C29—41no—
114C22×C4×C29C22⋊C411yescharacteristic
115C22×C4×C29C22⋊C411yescharacteristic
116C22×C4×C29C22⋊C411yescharacteristic
117C22×C4×C29C22×C411yescharacteristic
118C22×C4×C29C2×D411yescharacteristic
119C22×C4×C29C2×D411yescharacteristic
120M16×C29—24no—
121M16×C29—44no—
122M16×C29—42no—
123M16×C29—42no—
124M16×C29—42no—
125C2×C8×C29—44no—
126C2×C8×C29—42no—
127C2×C8×C29—42no—
128C4⋊C4×C29—41no—
129C22⋊C4×C29—42no—
130C22⋊C4×C29—42no—
131C22⋊C4×C29—42no—
132C22⋊C4×C29—42no—
133C22⋊C4×C29—41no—
134C22⋊C4×C29—42no—
135C22⋊C4×C29—41no—
136C42×C29—22no—
137C42×C29—41no—
138#13092C2911yesmaximal, characteristic, direct product factor, Sylow
139C23×C29—22no—
140C23×C29—21no—
141C23×C29—21no—
142C23×C29—41no—
143C23×C29—42no—
144C23×C29—42no—
145C23×C29—41no—
146C23×C29—41no—
147C23×C29—41no—
148C23×C29#9911yescharacteristic
149C23×C29#9911yescharacteristic
150C23×C29C2×C22⋊C411yescharacteristic
151Q8×C29—42no—
152Q8×C29—42no—
153Q8×C29—44no—
154Q8×C29—44no—
155Q8×C29—42no—
156Q8×C29—42no—
157D4×C29—82no—
158D4×C29—82no—
159D4×C29—82no—
160C2×C4×C29—22no—
161C2×C4×C29—22no—
162C2×C4×C29—22no—
163C2×C4×C29—22no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—21no—
167C2×C4×C29—21no—
168C2×C4×C29—21no—
169C2×C4×C29—21no—
170C2×C4×C29—21no—
171C2×C4×C29—21no—
172C2×C4×C29—21no—
173C2×C4×C29—21no—
174C2×C4×C29—21no—
175C2×C4×C29—21no—
176C2×C4×C29—21no—
177C2×C4×C29—21no—
178C2×C4×C29—42no—
179C2×C4×C29—42no—
180C2×C4×C29—42no—
181C2×C4×C29—42no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—41no—
186C2×C4×C29—42no—
187C2×C4×C29—41no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29#9912yes—
191C2×C4×C29C4×D412yes—
192C2×C4×C29#12011yescharacteristic
193C2×C4×C29#12112yes—
194C2×C4×C29#12311yescharacteristic
195C8×C29—44no—
196C8×C29—82no—
197C22×#101C2×C2911yescharacteristic, complemented
198#2436C2×C2911yescharacteristic
199C2×#355C2×C2912yescomplemented
200#1784C2×C2911yescharacteristic, complemented
201#1394C2×C2912yescomplemented
202C22×C29—21no—
203C22×C29—21no—
204C22×C29—21no—
205C22×C29—21no—
206C22×C29—21no—
207C22×C29—21no—
208C22×C29—21no—
209C22×C29—42no—
210C22×C29—42no—
211C22×C29—82no—
212C22×C29—82no—
213C22×C29—81no—
214C22×C29—81no—
215C22×C29—81no—
216C22×C29#35512yescomplemented
217C22×C29#38611yescharacteristic
218C22×C29C2×#9911yescharacteristic
219C22×C29C2×#9911yescharacteristic
220C4×C29—21no—
221C4×C29—22no—
222C4×C29—22no—
223C4×C29—21no—
224C4×C29—22no—
225C4×C29—41no—
226C4×C29—41no—
227C4×C29—81no—
228C4×C29—81no—
229C4×C29—81no—
230C23×Q8C22×C2911yescharacteristic
231C22×M16—21no—
232C2×#124C4×C2911yescharacteristic
233C2×#124C22×C2911yescharacteristic
234C2×#121C4×C2911yescharacteristic
235C2×#101—21no—
236C2×#101—24no—
237C2×#101—21no—
238C2×#101C22×C2912yes—
239C2×#101C22×C2912yes—
240#407—21no—
241#393—21no—
242#393—21no—
243#391C4×C2911yescharacteristic
244#391C22×C2911yescharacteristic
245#386—21no—
246#386—21no—
247C4×C22⋊C4C4×C2911yescharacteristic
248#355—24no—
249C2×C29—21no—
250C2×C29—21no—
251C2×C29—22no—
252C2×C29—41no—
253C2×C29—161no—
254C2×C29#189811yescharacteristic
255C2×C29C2×#35511yescharacteristic
256C2×C29#213311yescharacteristic
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—41no—
260C22×Q8—41no—
261C22×Q8—42no—
262C22×Q8C2×C4×C2911yescharacteristic
263C22×Q8D4×C2911yescharacteristic
264C22×Q8D4×C2911yescharacteristic
265C22×Q8C23×C2911yescharacteristic
266C22×D4—21no—
267C22×D4C2×C4×C2911yescharacteristic
268C23×C4C2×C4×C2911yescharacteristic
269C23×C4D4×C2911yescharacteristic
270C23×C4D4×C2911yescharacteristic
271C2×M16—24no—
272C2×M16—22no—
273C2×M16—22no—
274C2×M16—41no—
275C2×M16—42no—
276C22×C8—41no—
277#124—22no—
278#124—22no—
279#124—42no—
280#121—41no—
281#121—41no—
282C2×C4⋊C4C2×C4×C2911yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C42C2×C4×C2911yescharacteristic
290C2×C42C2×C4×C2911yescharacteristic
291#101—24no—
292#101—22no—
293#101—22no—
294#101—22no—
295#101—42no—
296#101D4×C2914yescomplemented
297C22⋊C8—41no—
298C22⋊C8—41no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304C29#1309211yescharacteristic, direct product factor, Sylow
305C24—21no—
306C24C22⋊C4×C2911yescharacteristic
307C2×Q8—22no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×Q8—21no—
311C2×Q8—22no—
312C2×Q8—22no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—41no—
319C2×Q8—44no—
320C2×Q8—44no—
321C2×Q8—44no—
322C2×Q8—44no—
323C2×Q8C2×D4×C2912yes—
324C2×Q8#41×C2912yes—
325C2×D4—22no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—44no—
329C2×D4—41no—
330C2×D4—41no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4C22⋊C4×C2911yescharacteristic
348C22×C4C22⋊C4×C2911yescharacteristic
349C22×C4C22⋊C4×C2911yescharacteristic
350C22×C4C22×C4×C2911yescharacteristic
351C22×C4C2×D4×C2911yescharacteristic
352C22×C4C2×D4×C2911yescharacteristic
353M16—24no—
354M16—44no—
355M16—42no—
356M16—42no—
357M16—42no—
358C2×C8—44no—
359C2×C8—42no—
360C2×C8—42no—
361C4⋊C4—41no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C22⋊C4—41no—
366C22⋊C4—42no—
367C22⋊C4—41no—
368C22⋊C4—42no—
369C42—22no—
370C42—41no—
371C23—22no—
372C23—21no—
373C23—21no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23C29×#9911yescharacteristic
381C23C29×#9911yescharacteristic
382C23C2×C22⋊C4×C2911yescharacteristic
383Q8—42no—
384Q8—42no—
385Q8—44no—
386Q8—44no—
387Q8—42no—
388Q8—42no—
389D4—82no—
390D4—82no—
391D4—82no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4C29×#9912yes—
423C2×C4C4×D4×C2912yes—
424C2×C4C29×#12011yescharacteristic
425C2×C4C29×#12112yes—
426C2×C4C29×#12311yescharacteristic
427C8—44no—
428C8—82no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—82no—
439C22—82no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C29×#35512yescomplemented
444C22C29×#38611yescharacteristic
445C22C2×C29×#9911yescharacteristic
446C22C2×C29×#9911yescharacteristic
447C4—21no—
448C4—22no—
449C4—21no—
450C4—22no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—81no—
455C4—81no—
456C4—81no—
457C2—21no—
458C2—21no—
459C2—22no—
460C2—41no—
461C2—161no—
462C2C29×#189811yescharacteristic
463C2C2×C29×#35511yescharacteristic
464C2C29×#213311yescharacteristic
subgroupG/H
center, socleC22×C29C2×#99
commutatorC22×C4C22×C4×C29
Frattini, cosocleC22×Q8C23×C29
prime radicalC2×C29×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C24×C29 ◁ C23×Q8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C29×#101C2semidirect
3. C2×C29×#355C2semidirect
4. C29×#1784C2semidirect
5. C29×#1394C2semidirect
64. C29×#101D4semidirect
138. #13092C29direct (N × H)
197. C22×#101C2×C29semidirect
199. C2×#355C2×C29semidirect
200. #1784C2×C29semidirect
201. #1394C2×C29semidirect
216. C22×C29#355semidirect
296. #101D4×C29semidirect
304. C29#13092direct (N × H)
443. C22C29×#355semidirect

Maximal subgroups

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

subgroupindex
C22×C29×#1012
C29×#24362
C2×C29×#3552
C29×#17842
C29×#13942
#1309229