Finite Group Databasebeta

← C29×#19081 #20313981

Subgroups — C29×#19081 #20313981

Order 7424.

880 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3550C211yesmaximal, characteristic
2C29×#3165C211yesmaximal, characteristic, complemented
3C29×#3141C211yesmaximal, characteristic
4C29×#3139C211yesmaximal, characteristic, complemented
5C29×#1664C218yesmaximal, complemented
6C29×#1526C211yesmaximal, characteristic, complemented
7C29×#1526C211yesmaximal, characteristic, complemented
8C29×#1525C211yesmaximal, characteristic
9C29×#563C2214yes—
10C29×#559—21no—
11Q82×C29—21no—
12C29×#556—21no—
13C29×#556—21no—
14D4×Q8×C29—21no—
15D4×Q8×C29—21no—
16C29×#542—22no—
17C29×#542—22no—
18C29×#536—22no—
19C29×#533C2211yescharacteristic
20C29×#533C2211yescharacteristic
21C29×#532C2211yescharacteristic
22C2×C29×C4⋊Q8C2211yescharacteristic
23C29×#501C2214yes—
24C29×#500—21no—
25C29×#498—21no—
26C29×#491C2214yes—
27C29×#489C2214yes—
28C29×#487—21no—
29C29×#487—21no—
30C29×#487—21no—
31C29×#486—21no—
32C29×#428—22no—
33C29×#419—22no—
34C29×#417—22no—
35C4×M16×C29C2211yescharacteristic
36C4×M16×C29C2211yescharacteristic
37C4×M16×C29C2211yescharacteristic
38C29×#330C2214yes—
39C29×#330C2214yes—
40C29×#329C2214yes—
41C2×#41×C29D412yes—
42C22×Q8×C29—22no—
43C22×Q8×C29—21no—
44C2×M16×C29—21no—
45C2×M16×C29—21no—
46C2×M16×C29—21no—
47C29×C4⋊Q8—22no—
48C29×C4⋊Q8—22no—
49C29×C4⋊Q8—24no—
50C29×C4⋊Q8—21no—
51C29×C4⋊Q8—21no—
52C29×C4⋊Q8—21no—
53C29×C4⋊Q8D411yescharacteristic
54C29×C4⋊Q8D411yescharacteristic
55C29×C4⋊Q8D411yescharacteristic
56C29×C4⋊Q8D411yescharacteristic
57C29×C4⋊Q8D411yescharacteristic
58C29×C4⋊Q8C2312yes—
59C29×#127D411yescharacteristic
60C29×#126—24no—
61C29×#126—24no—
62C29×#125C2312yes—
63C29×#125C2312yes—
64C29×#124—24no—
65C29×#124—22no—
66C29×#124—22no—
67C29×#124C2312yes—
68C29×#123—24no—
69C29×#123—24no—
70C29×C22⋊Q8—22no—
71C29×C22⋊Q8—22no—
72C29×C22⋊Q8—21no—
73C29×C22⋊Q8—21no—
74C29×C22⋊Q8—21no—
75C29×C22⋊Q8—21no—
76C29×C22⋊Q8—24no—
77C29×C22⋊Q8—24no—
78C29×#121—21no—
79C29×#121—21no—
80C4×Q8×C29—22no—
81C4×Q8×C29—22no—
82C4×Q8×C29—21no—
83C4×Q8×C29—21no—
84C4×Q8×C29—21no—
85C4×Q8×C29—21no—
86C4×D4×C29—22no—
87C4×D4×C29—22no—
88C4×D4×C29—21no—
89C4×D4×C29—21no—
90C29×#117—22no—
91C29×#117D412yes—
92C29×#117D412yes—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29—21no—
95C2×C42×C29C2311yescharacteristic
96C29×#107—24no—
97C29×#106—24no—
98C29×#103—24no—
99C29×#103—24no—
100C29×#103—24no—
101C29×#102—24no—
102C29×#97C2312yes—
103C29×#97C2312yes—
104C29×#97C2312yes—
105C4×C8×C29—21no—
106C4×C8×C29—21no—
107C4×C8×C29—21no—
108#41×C29—44no—
109C2×Q8×C29—24no—
110C2×Q8×C29—21no—
111C2×Q8×C29—21no—
112C2×Q8×C29—21no—
113C2×Q8×C29—21no—
114C2×Q8×C29—22no—
115C2×Q8×C29—44no—
116C2×Q8×C29—41no—
117C2×Q8×C29—84no—
118C2×Q8×C29C2×D412yes—
119C2×D4×C29—22no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29C2×D412yes—
123C22×C4×C29—24no—
124C22×C4×C29—22no—
125C22×C4×C29—41no—
126C22×C4×C29C2×D411yescharacteristic
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29C2×D411yescharacteristic
129M16×C29—24no—
130M16×C29—42no—
131M16×C29—42no—
132C2×C8×C29—22no—
133C2×C8×C29—22no—
134C2×C8×C29—22no—
135C4⋊C4×C29—24no—
136C4⋊C4×C29—24no—
137C4⋊C4×C29—21no—
138C4⋊C4×C29—21no—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—22no—
144C4⋊C4×C29—22no—
145C4⋊C4×C29—22no—
146C4⋊C4×C29—22no—
147C4⋊C4×C29—22no—
148C4⋊C4×C29—22no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29C2×D412yes—
152C4⋊C4×C29C2×D412yes—
153C4⋊C4×C29C2×D412yes—
154C4⋊C4×C29C2×D412yes—
155C22⋊C4×C29—24no—
156C22⋊C4×C29—24no—
157C22⋊C4×C29—24no—
158C22⋊C4×C29—22no—
159C22⋊C4×C29—22no—
160C22⋊C4×C29—22no—
161C22⋊C4×C29—22no—
162C42×C29—24no—
163C42×C29—22no—
164C42×C29—22no—
165C42×C29C2×D411yescharacteristic
166C42×C29C2×D411yescharacteristic
167C42×C29C2×D411yescharacteristic
168C42×C29C2411yescharacteristic
169#19081C2911yesmaximal, characteristic, direct product factor, Sylow
170C23×C29—22no—
171C23×C29#12011yescharacteristic
172Q8×C29—42no—
173Q8×C29—44no—
174Q8×C29—42no—
175Q8×C29—42no—
176Q8×C29—42no—
177Q8×C29—42no—
178Q8×C29—84no—
179Q8×C29—82no—
180D4×C29—42no—
181D4×C29—42no—
182D4×C29—42no—
183D4×C29—82no—
184C2×C4×C29—22no—
185C2×C4×C29—22no—
186C2×C4×C29—22no—
187C2×C4×C29—22no—
188C2×C4×C29—22no—
189C2×C4×C29—22no—
190C2×C4×C29—22no—
191C2×C4×C29—22no—
192C2×C4×C29—44no—
193C2×C4×C29—42no—
194C2×C4×C29—84no—
195C2×C4×C29—82no—
196C2×C4×C29#12011yescharacteristic
197C2×C4×C29#12011yescharacteristic
198C2×C4×C29#12011yescharacteristic
199C2×C4×C29C22×D411yescharacteristic
200C2×C4×C29C22×D411yescharacteristic
201C2×C4×C29C22×D411yescharacteristic
202C8×C29—24no—
203C8×C29—42no—
204C8×C29—42no—
205#3550C2×C2911yescharacteristic
206#3165C2×C2911yescharacteristic, complemented
207#3141C2×C2911yescharacteristic
208#3139C2×C2911yescharacteristic, complemented
209#1664C2×C2918yescomplemented
210#1526C2×C2911yescharacteristic, complemented
211#1526C2×C2911yescharacteristic, complemented
212#1525C2×C2911yescharacteristic
213C22×C29—21no—
214C22×C29—21no—
215C22×C29—21no—
216C22×C29—42no—
217C22×C29—42no—
218C22×C29—42no—
219C22×C29C2×#12011yescharacteristic
220C4×C29—21no—
221C4×C29—21no—
222C4×C29—21no—
223C4×C29—42no—
224C4×C29—42no—
225C4×C29—42no—
226C4×C29—42no—
227C4×C29—42no—
228C4×C29—82no—
229C4×C29#45412yes—
230C4×C29#45512yes—
231C4×C29#45612yes—
232#563C22×C2914yes—
233#559—21no—
234Q82—21no—
235#556—21no—
236#556—21no—
237D4×Q8—21no—
238D4×Q8—21no—
239#542—22no—
240#542—22no—
241#536—22no—
242#533C22×C2911yescharacteristic
243#533C22×C2911yescharacteristic
244#532C22×C2911yescharacteristic
245C2×C4⋊Q8C22×C2911yescharacteristic
246#501C22×C2914yes—
247#500—21no—
248#498—21no—
249#491C22×C2914yes—
250#489C22×C2914yes—
251#487—21no—
252#487—21no—
253#487—21no—
254#486—21no—
255#428—22no—
256#419—22no—
257#417—22no—
258C4×M16C22×C2911yescharacteristic
259C4×M16C22×C2911yescharacteristic
260C4×M16C22×C2911yescharacteristic
261#330C22×C2914yes—
262#330C22×C2914yes—
263#329C22×C2914yes—
264C2×C29—41no—
265C2×C29—82no—
266C2×C29C2×#45511yescharacteristic
267C2×C29C2×#45411yescharacteristic
268C2×C29C2×#45611yescharacteristic
269C2×#41D4×C2912yes—
270C22×Q8—22no—
271C22×Q8—21no—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—21no—
275C4⋊Q8—22no—
276C4⋊Q8—22no—
277C4⋊Q8—24no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8D4×C2911yescharacteristic
282C4⋊Q8D4×C2911yescharacteristic
283C4⋊Q8D4×C2911yescharacteristic
284C4⋊Q8D4×C2911yescharacteristic
285C4⋊Q8D4×C2911yescharacteristic
286C4⋊Q8C23×C2912yes—
287#127D4×C2911yescharacteristic
288#126—24no—
289#126—24no—
290#125C23×C2912yes—
291#125C23×C2912yes—
292#124—24no—
293#124—22no—
294#124—22no—
295#124C23×C2912yes—
296#123—24no—
297#123—24no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—24no—
305C22⋊Q8—24no—
306#121—21no—
307#121—21no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—21no—
317C4×D4—21no—
318#117—22no—
319#117D4×C2912yes—
320#117D4×C2912yes—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C42C23×C2911yescharacteristic
324#107—24no—
325#106—24no—
326#103—24no—
327#103—24no—
328#103—24no—
329#102—24no—
330#97C23×C2912yes—
331#97C23×C2912yes—
332#97C23×C2912yes—
333C4×C8—21no—
334C4×C8—21no—
335C4×C8—21no—
336C29#1908111yescharacteristic, direct product factor, Sylow
337#41—44no—
338C2×Q8—24no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—44no—
345C2×Q8—41no—
346C2×Q8—84no—
347C2×Q8C2×D4×C2912yes—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4C2×D4×C2912yes—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—41no—
355C22×C4C2×D4×C2911yescharacteristic
356C22×C4C2×D4×C2911yescharacteristic
357C22×C4C2×D4×C2911yescharacteristic
358M16—24no—
359M16—42no—
360M16—42no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—22no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4C2×D4×C2912yes—
381C4⋊C4C2×D4×C2912yes—
382C4⋊C4C2×D4×C2912yes—
383C4⋊C4C2×D4×C2912yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C42—24no—
392C42—22no—
393C42—22no—
394C42C2×D4×C2911yescharacteristic
395C42C2×D4×C2911yescharacteristic
396C42C2×D4×C2911yescharacteristic
397C42C24×C2911yescharacteristic
398C23—22no—
399C23C29×#12011yescharacteristic
400Q8—42no—
401Q8—44no—
402Q8—42no—
403Q8—42no—
404Q8—42no—
405Q8—42no—
406Q8—84no—
407Q8—82no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—82no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4C29×#12011yescharacteristic
425C2×C4C29×#12011yescharacteristic
426C2×C4C29×#12011yescharacteristic
427C2×C4C22×D4×C2911yescharacteristic
428C2×C4C22×D4×C2911yescharacteristic
429C2×C4C22×D4×C2911yescharacteristic
430C8—24no—
431C8—42no—
432C8—42no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×C29×#12011yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—82no—
449C4C29×#45412yes—
450C4C29×#45512yes—
451C4C29×#45612yes—
452C2—41no—
453C2—82no—
454C2C2×C29×#45511yescharacteristic
455C2C2×C29×#45411yescharacteristic
456C2C2×C29×#45611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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×#3165C2semidirect
4. C29×#3139C2semidirect
5. C29×#1664C2semidirect
6. C29×#1526C2semidirect
7. C29×#1526C2semidirect
169. #19081C29direct (N × H)
206. #3165C2×C29semidirect
208. #3139C2×C29semidirect
209. #1664C2×C29semidirect
210. #1526C2×C29semidirect
211. #1526C2×C29semidirect
336. C29#19081direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35502
C29×#31652
C29×#31412
C29×#31392
C29×#16642
C29×#15262
C29×#15252
#1908129