Finite Group Databasebeta

← C29×#10376 #20305276

Subgroups — C29×#10376 #20305276

Order 7424.

464 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2569C211yesmaximal, characteristic, complemented
2C29×#1964C211yesmaximal, characteristic
3C29×#1519C211yesmaximal, characteristic
4C2×C29×#327C211yesmaximal, characteristic
5C29×#1294C211yesmaximal, characteristic, complemented
6C29×#1289C211yesmaximal, characteristic, complemented
7C29×#1282C211yesmaximal, characteristic, complemented
8C2×C29×#121C2211yescharacteristic
9C2×C29×#99—21no—
10C2×C29×#99—21no—
11C2×C29×C22⋊C8C2211yescharacteristic
12C2×C29×C22⋊C8C2211yescharacteristic
13C29×#400—21no—
14C29×#398—21no—
15C29×#387—21no—
16C29×#387—21no—
17C29×#385—21no—
18C29×#380—21no—
19C29×#380C2211yescharacteristic
20C29×#380C2211yescharacteristic
21C4×C22⋊C4×C29C2211yescharacteristic
22C2×C29×#95C2211yescharacteristic
23C29×#327—21no—
24C29×#327—21no—
25C29×#327—21no—
26C29×#327—21no—
27C22×D4×C29—21no—
28C22×D4×C29Q811yescharacteristic
29C23×C4×C29—21no—
30C23×C4×C29C2311yescharacteristic
31C22×C8×C29—21no—
32C22×C8×C29—21no—
33C29×#121—21no—
34C29×#121—21no—
35C29×#121—21no—
36C29×#121—21no—
37C2×C4⋊C4×C29—21no—
38C2×C4⋊C4×C29—21no—
39C2×C4⋊C4×C29—21no—
40C2×C4⋊C4×C29—21no—
41C2×C4⋊C4×C29—21no—
42C2×C4⋊C4×C29—21no—
43C2×C4⋊C4×C29Q811yescharacteristic
44C2×C22⋊C4×C29—21no—
45C2×C22⋊C4×C29—21no—
46C2×C22⋊C4×C29—21no—
47C2×C22⋊C4×C29D411yescharacteristic
48C2×C22⋊C4×C29D411yescharacteristic
49C2×C42×C29—21no—
50C29×#99—42no—
51C29×#99—42no—
52C29×C22⋊C8—21no—
53C29×C22⋊C8—21no—
54C29×C22⋊C8—21no—
55C29×C22⋊C8—21no—
56C29×#95—21no—
57C29×#95—21no—
58C29×#95—21no—
59C29×#95—21no—
60C29×#95—21no—
61C29×#95—21no—
62C29×#95—21no—
63C29×#95D411yescharacteristic
64C29×#95D411yescharacteristic
65C29×#95D411yescharacteristic
66C29×#95D411yescharacteristic
67C24×C29—21no—
68C24×C29C2×D411yescharacteristic
69C2×D4×C29—21no—
70C2×D4×C29—21no—
71C2×D4×C29—41no—
72C2×D4×C29—41no—
73C2×D4×C29—41no—
74C2×D4×C29—41no—
75C2×D4×C29—41no—
76C2×D4×C29—41no—
77C2×D4×C29—81no—
78C22×C4×C29—21no—
79C22×C4×C29—21no—
80C22×C4×C29—21no—
81C22×C4×C29—21no—
82C22×C4×C29—21no—
83C22×C4×C29—21no—
84C22×C4×C29—21no—
85C22×C4×C29—42no—
86C22×C4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29—81no—
90C22×C4×C29—81no—
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29C2×D411yescharacteristic
93C22×C4×C29C2×Q811yescharacteristic
94C22×C4×C29#4111yescharacteristic
95C22×C4×C29#4111yescharacteristic
96C22×C4×C29#4111yescharacteristic
97C2×C8×C29—41no—
98C2×C8×C29—41no—
99C2×C8×C29—81no—
100C2×C8×C29—81no—
101C4⋊C4×C29—21no—
102C4⋊C4×C29—21no—
103C4⋊C4×C29—42no—
104C4⋊C4×C29—42no—
105C4⋊C4×C29—81no—
106C4⋊C4×C29—81no—
107C4⋊C4×C29—81no—
108C4⋊C4×C29—81no—
109C22⋊C4×C29—21no—
110C22⋊C4×C29—21no—
111C22⋊C4×C29—21no—
112C22⋊C4×C29—21no—
113C22⋊C4×C29—41no—
114C22⋊C4×C29—41no—
115C22⋊C4×C29—41no—
116C22⋊C4×C29—41no—
117C22⋊C4×C29—41no—
118C22⋊C4×C29—41no—
119C42×C29—81no—
120#10376C2911yesmaximal, characteristic, direct product factor, Sylow
121C23×C29—41no—
122C23×C29—41no—
123C23×C29—41no—
124C23×C29—41no—
125C23×C29—41no—
126C23×C29—81no—
127C23×C29—81no—
128C23×C29#12011yescharacteristic
129C23×C29C22⋊Q811yescharacteristic
130C23×C29#12411yescharacteristic
131C23×C29#13511yescharacteristic
132C23×C29#13511yescharacteristic
133C23×C29AGL(1,ℤ/8)11yescharacteristic
134C23×C29AGL(1,ℤ/8)11yescharacteristic
135D4×C29—81no—
136D4×C29—81no—
137D4×C29—81no—
138D4×C29—81no—
139D4×C29—81no—
140D4×C29—81no—
141C2×C4×C29—22no—
142C2×C4×C29—41no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—41no—
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—41no—
158C2×C4×C29—41no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—82no—
169C2×C4×C29—82no—
170C2×C4×C29—81no—
171C2×C4×C29—81no—
172C2×C4×C29—81no—
173C2×C4×C29C22⋊Q811yescharacteristic
174C2×C4×C29C22⋊Q811yescharacteristic
175C2×C4×C29#12411yescharacteristic
176C2×C4×C29#12411yescharacteristic
177C8×C29—81no—
178C8×C29—81no—
179#2569C2×C2911yescharacteristic, complemented
180#1964C2×C2911yescharacteristic
181#1519C2×C2911yescharacteristic
182C2×#327C2×C2911yescharacteristic
183#1294C2×C2911yescharacteristic, complemented
184#1289C2×C2911yescharacteristic, complemented
185#1282C2×C2911yescharacteristic, complemented
186C22×C29—21no—
187C22×C29—21no—
188C22×C29—21no—
189C22×C29—21no—
190C22×C29—21no—
191C22×C29—21no—
192C22×C29—41no—
193C22×C29—41no—
194C22×C29—41no—
195C22×C29—41no—
196C22×C29—81no—
197C22×C29—81no—
198C22×C29—81no—
199C22×C29—161no—
200C22×C29—161no—
201C22×C29#39311yescharacteristic
202C22×C29#44911yescharacteristic
203C22×C29#44911yescharacteristic
204C22×C29#47811yescharacteristic
205C22×C29#47811yescharacteristic
206C22×C29#48811yescharacteristic
207C22×C29#49011yescharacteristic
208C4×C29—21no—
209C4×C29—21no—
210C4×C29—21no—
211C4×C29—21no—
212C4×C29—42no—
213C4×C29—81no—
214C4×C29—81no—
215C4×C29—81no—
216C4×C29—81no—
217C4×C29—81no—
218C4×C29—81no—
219C4×C29—161no—
220C2×#121C22×C2911yescharacteristic
221C2×#99—21no—
222C2×#99—21no—
223C2×C22⋊C8C22×C2911yescharacteristic
224C2×C22⋊C8C22×C2911yescharacteristic
225#400—21no—
226#398—21no—
227#387—21no—
228#387—21no—
229#385—21no—
230#380—21no—
231#380C22×C2911yescharacteristic
232#380C22×C2911yescharacteristic
233C4×C22⋊C4C22×C2911yescharacteristic
234C2×#95C22×C2911yescharacteristic
235#327—21no—
236#327—21no—
237#327—21no—
238#327—21no—
239C2×C29—21no—
240C2×C29—21no—
241C2×C29—21no—
242C2×C29—21no—
243C2×C29—21no—
244C2×C29—21no—
245C2×C29—161no—
246C2×C29#202511yescharacteristic
247C2×C29#203111yescharacteristic
248C2×C29#203211yescharacteristic
249C22×D4—21no—
250C22×D4Q8×C2911yescharacteristic
251C23×C4—21no—
252C23×C4C23×C2911yescharacteristic
253C22×C8—21no—
254C22×C8—21no—
255#121—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4Q8×C2911yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4D4×C2911yescharacteristic
270C2×C22⋊C4D4×C2911yescharacteristic
271C2×C42—21no—
272#99—42no—
273#99—42no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95D4×C2911yescharacteristic
286#95D4×C2911yescharacteristic
287#95D4×C2911yescharacteristic
288#95D4×C2911yescharacteristic
289C29#1037611yescharacteristic, direct product factor, Sylow
290C24—21no—
291C24C2×D4×C2911yescharacteristic
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—81no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—81no—
313C22×C4—81no—
314C22×C4C2×D4×C2911yescharacteristic
315C22×C4C2×D4×C2911yescharacteristic
316C22×C4C2×Q8×C2911yescharacteristic
317C22×C4#41×C2911yescharacteristic
318C22×C4#41×C2911yescharacteristic
319C22×C4#41×C2911yescharacteristic
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—81no—
323C2×C8—81no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—81no—
329C4⋊C4—81no—
330C4⋊C4—81no—
331C4⋊C4—81no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—81no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—81no—
349C23—81no—
350C23C29×#12011yescharacteristic
351C23C29×C22⋊Q811yescharacteristic
352C23C29×#12411yescharacteristic
353C23C29×#13511yescharacteristic
354C23C29×#13511yescharacteristic
355C23C29×AGL(1,ℤ/8)11yescharacteristic
356C23C29×AGL(1,ℤ/8)11yescharacteristic
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C29×C22⋊Q811yescharacteristic
396C2×C4C29×C22⋊Q811yescharacteristic
397C2×C4C29×#12411yescharacteristic
398C2×C4C29×#12411yescharacteristic
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—161no—
415C22—161no—
416C22C29×#39311yescharacteristic
417C22C29×#44911yescharacteristic
418C22C29×#44911yescharacteristic
419C22C29×#47811yescharacteristic
420C22C29×#47811yescharacteristic
421C22C29×#48811yescharacteristic
422C22C29×#49011yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—42no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—161no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—161no—
442C2C29×#202511yescharacteristic
443C2C29×#203111yescharacteristic
444C2C29×#203211yescharacteristic
subgroupG/H
center, socleC22×C29#393
commutator, Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2569C2semidirect
5. C29×#1294C2semidirect
6. C29×#1289C2semidirect
7. C29×#1282C2semidirect
120. #10376C29direct (N × H)
179. #2569C2×C29semidirect
183. #1294C2×C29semidirect
184. #1289C2×C29semidirect
185. #1282C2×C29semidirect
289. C29#10376direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#25692
C29×#19642
C29×#15192
C2×C29×#3272
C29×#12942
C29×#12892
C29×#12822
#1037629