Finite Group Databasebeta

← C29×#8364 #20303264

Subgroups — C29×#8364 #20303264

Order 7424.

1074 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#547C211yesmaximal, characteristic
2C29×#1789C212yesmaximal, complemented
3C4×C29×#99C211yesmaximal, characteristic, complemented
4C29×#1508C212yesmaximal, complemented
5C29×#1465C211yesmaximal, characteristic, complemented
6C22×#41×C29C411yescharacteristic, complemented
7C22×#41×C29C2211yescharacteristic
8C29×#547—24no—
9C29×#547—24no—
10C2×C29×C4⋊Q8C411yescharacteristic, complemented
11C2×C29×#123—21no—
12C2×C29×#123—21no—
13C2×C29×C22⋊Q8C411yescharacteristic, complemented
14C2×C29×C22⋊Q8C2211yescharacteristic
15C2×C29×#121—21no—
16C2×C4×D4×C29C411yescharacteristic, complemented
17C2×C4×D4×C29C2211yescharacteristic
18C22×C4⋊C4×C29—21no—
19C2×C29×#104—24no—
20C2×C29×#99—21no—
21C29×#407C2212yes—
22C4×C22⋊C4×C29C2212yes—
23C29×#342—21no—
24C29×#328—24no—
25C29×#324—21no—
26C29×#323—21no—
27C2×#41×C29—22no—
28C2×#41×C29—22no—
29C2×#41×C29—22no—
30C2×#41×C29—44no—
31C2×#41×C29—44no—
32C2×#41×C29D414yes—
33C22×Q8×C29C2×C411yescharacteristic
34C22×Q8×C29C2×C411yescharacteristic
35C22×D4×C29—21no—
36C22×D4×C29—21no—
37C22×D4×C29C2×C411yescharacteristic
38C22×D4×C29D411yescharacteristic
39C23×C4×C29—21no—
40C23×C4×C29—21no—
41C23×C4×C29—21no—
42C23×C4×C29C2×C411yescharacteristic
43C23×C4×C29C2311yescharacteristic
44C2×M16×C29—22no—
45C29×C4⋊Q8—22no—
46C29×C4⋊Q8—22no—
47C29×#123—28no—
48C29×#123—28no—
49C29×C22⋊Q8—22no—
50C29×C22⋊Q8—22no—
51C29×C22⋊Q8—22no—
52C29×C22⋊Q8D414yes—
53C29×#121—28no—
54C4×D4×C29—22no—
55C4×D4×C29—22no—
56C4×D4×C29—22no—
57C4×D4×C29—22no—
58C2×C4⋊C4×C29—28no—
59C2×C4⋊C4×C29—21no—
60C2×C4⋊C4×C29—21no—
61C2×C4⋊C4×C29—21no—
62C2×C4⋊C4×C29—21no—
63C2×C4⋊C4×C29C2×C411yescharacteristic
64C2×C4⋊C4×C29D411yescharacteristic
65C2×C22⋊C4×C29—21no—
66C2×C22⋊C4×C29—21no—
67C2×C22⋊C4×C29—21no—
68C2×C22⋊C4×C29—22no—
69C2×C22⋊C4×C29D411yescharacteristic
70C2×C22⋊C4×C29D411yescharacteristic
71C2×C42×C29—22no—
72C2×C42×C29C2×C411yescharacteristic
73C29×#104—48no—
74C29×#99—24no—
75C29×C22⋊C8—22no—
76C29×C22⋊C8—22no—
77C29×#95—22no—
78C24×C29—21no—
79C24×C29C22⋊C411yescharacteristic
80C24×C29C2×D411yescharacteristic
81#41×C29—28no—
82#41×C29—44no—
83#41×C29—48no—
84#41×C29—48no—
85#41×C29—44no—
86#41×C29—44no—
87C2×Q8×C29—21no—
88C2×Q8×C29—21no—
89C2×Q8×C29—42no—
90C2×Q8×C29—42no—
91C2×Q8×C29C22⋊C412yes—
92C2×Q8×C29C22⋊C412yes—
93C2×D4×C29—24no—
94C2×D4×C29—24no—
95C2×D4×C29—22no—
96C2×D4×C29—24no—
97C2×D4×C29—22no—
98C2×D4×C29—21no—
99C2×D4×C29—41no—
100C2×D4×C29—44no—
101C2×D4×C29—44no—
102C2×D4×C29C22⋊C412yes—
103C22×C4×C29—24no—
104C22×C4×C29—24no—
105C22×C4×C29—21no—
106C22×C4×C29—21no—
107C22×C4×C29—21no—
108C22×C4×C29—21no—
109C22×C4×C29—21no—
110C22×C4×C29—24no—
111C22×C4×C29—42no—
112C22×C4×C29—42no—
113C22×C4×C29—42no—
114C22×C4×C29—44no—
115C22×C4×C29—44no—
116C22×C4×C29—42no—
117C22×C4×C29—42no—
118C22×C4×C29C22⋊C411yescharacteristic
119C22×C4×C29C22⋊C411yescharacteristic
120C22×C4×C29C22⋊C411yescharacteristic
121C22×C4×C29C22×C411yescharacteristic
122C22×C4×C29C2×D412yes—
123C22×C4×C29C2×D412yes—
124C22×C4×C29C2×D411yescharacteristic
125M16×C29—44no—
126C2×C8×C29—42no—
127C4⋊C4×C29—24no—
128C4⋊C4×C29—24no—
129C4⋊C4×C29—24no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—22no—
132C4⋊C4×C29—24no—
133C4⋊C4×C29C22⋊C412yes—
134C22⋊C4×C29—24no—
135C22⋊C4×C29—24no—
136C22⋊C4×C29—24no—
137C22⋊C4×C29—22no—
138C22⋊C4×C29—22no—
139C22⋊C4×C29—24no—
140C22⋊C4×C29—42no—
141C42×C29—21no—
142C42×C29—21no—
143C42×C29—44no—
144#8364C2911yesmaximal, characteristic, direct product factor, Sylow
145C23×C29—24no—
146C23×C29—22no—
147C23×C29—21no—
148C23×C29—21no—
149C23×C29—21no—
150C23×C29—21no—
151C23×C29—21no—
152C23×C29—41no—
153C23×C29—41no—
154C23×C29—42no—
155C23×C29—41no—
156C23×C29—41no—
157C23×C29—41no—
158C23×C29—41no—
159C23×C29C2×C22⋊C411yescharacteristic
160C23×C29#12012yes—
161Q8×C29—24no—
162Q8×C29—42no—
163Q8×C29—42no—
164Q8×C29—42no—
165D4×C29—24no—
166D4×C29—22no—
167D4×C29—44no—
168D4×C29—48no—
169D4×C29—48no—
170D4×C29#9914yescomplemented
171C2×C4×C29—21no—
172C2×C4×C29—21no—
173C2×C4×C29—24no—
174C2×C4×C29—22no—
175C2×C4×C29—21no—
176C2×C4×C29—22no—
177C2×C4×C29—21no—
178C2×C4×C29—22no—
179C2×C4×C29—22no—
180C2×C4×C29—41no—
181C2×C4×C29—42no—
182C2×C4×C29—48no—
183C2×C4×C29—48no—
184C2×C4×C29—42no—
185C2×C4×C29—42no—
186C2×C4×C29—42no—
187C2×C4×C29—48no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—42no—
191C2×C4×C29—41no—
192C2×C4×C29—41no—
193C2×C4×C29—44no—
194C2×C4×C29—82no—
195C2×C4×C29—82no—
196C2×C4×C29#10412yescomplemented
197C2×C4×C29C2×C22⋊C411yescharacteristic
198C2×C4×C29C2×C22⋊C411yescharacteristic
199C2×C4×C29#12012yes—
200C8×C29—82no—
201C2×#547C2×C2911yescharacteristic
202#1789C2×C2912yescomplemented
203C4×#99C2×C2911yescharacteristic, complemented
204#1508C2×C2912yescomplemented
205#1465C2×C2911yescharacteristic, complemented
206C22×C29—21no—
207C22×C29—21no—
208C22×C29—22no—
209C22×C29—22no—
210C22×C29—24no—
211C22×C29—22no—
212C22×C29—44no—
213C22×C29—44no—
214C22×C29—42no—
215C22×C29—42no—
216C22×C29—41no—
217C22×C29—41no—
218C22×C29—41no—
219C22×C29—81no—
220C22×C29—81no—
221C22×C29—81no—
222C22×C29—81no—
223C22×C29#37911yescharacteristic
224C22×C29C2×#10411yescharacteristic
225C22×C29#42111yescharacteristic
226C4×C29—22no—
227C4×C29—21no—
228C4×C29—22no—
229C4×C29—41no—
230C4×C29—41no—
231C4×C29—42no—
232C4×C29—42no—
233C4×C29—42no—
234C4×C29—84no—
235C4×C29C2×#9912yes—
236C22×#41C4×C2911yescharacteristic, complemented
237C22×#41C22×C2911yescharacteristic
238#547—24no—
239#547—24no—
240C2×C4⋊Q8C4×C2911yescharacteristic, complemented
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8C4×C2911yescharacteristic, complemented
244C2×C22⋊Q8C22×C2911yescharacteristic
245C2×#121—21no—
246C2×C4×D4C4×C2911yescharacteristic, complemented
247C2×C4×D4C22×C2911yescharacteristic
248C22×C4⋊C4—21no—
249C2×#104—24no—
250C2×#99—21no—
251#407C22×C2912yes—
252C4×C22⋊C4C22×C2912yes—
253#342—21no—
254#328—24no—
255#324—21no—
256#323—21no—
257C2×C29—21no—
258C2×C29—21no—
259C2×C29—42no—
260C2×C29—44no—
261C2×C29—81no—
262C2×C29#178111yescharacteristic
263C2×C29#178911yescharacteristic
264C2×C29#179611yescharacteristic
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—44no—
269C2×#41—44no—
270C2×#41D4×C2914yes—
271C22×Q8C2×C4×C2911yescharacteristic
272C22×Q8C2×C4×C2911yescharacteristic
273C22×D4—21no—
274C22×D4—21no—
275C22×D4C2×C4×C2911yescharacteristic
276C22×D4D4×C2911yescharacteristic
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4C2×C4×C2911yescharacteristic
281C23×C4C23×C2911yescharacteristic
282C2×M16—22no—
283C4⋊Q8—22no—
284C4⋊Q8—22no—
285#123—28no—
286#123—28no—
287C22⋊Q8—22no—
288C22⋊Q8—22no—
289C22⋊Q8—22no—
290C22⋊Q8D4×C2914yes—
291#121—28no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—22no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4C2×C4×C2911yescharacteristic
302C2×C4⋊C4D4×C2911yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4D4×C2911yescharacteristic
308C2×C22⋊C4D4×C2911yescharacteristic
309C2×C42—22no—
310C2×C42C2×C4×C2911yescharacteristic
311#104—48no—
312#99—24no—
313C22⋊C8—22no—
314C22⋊C8—22no—
315#95—22no—
316C29#836411yescharacteristic, direct product factor, Sylow
317C24—21no—
318C24C22⋊C4×C2911yescharacteristic
319C24C2×D4×C2911yescharacteristic
320#41—28no—
321#41—44no—
322#41—48no—
323#41—48no—
324#41—44no—
325#41—44no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8C22⋊C4×C2912yes—
331C2×Q8C22⋊C4×C2912yes—
332C2×D4—24no—
333C2×D4—24no—
334C2×D4—22no—
335C2×D4—24no—
336C2×D4—21no—
337C2×D4—22no—
338C2×D4—41no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4C22⋊C4×C2912yes—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—24no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—44no—
354C22×C4—44no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4C22⋊C4×C2911yescharacteristic
358C22×C4C22⋊C4×C2911yescharacteristic
359C22×C4C22⋊C4×C2911yescharacteristic
360C22×C4C22×C4×C2911yescharacteristic
361C22×C4C2×D4×C2912yes—
362C22×C4C2×D4×C2912yes—
363C22×C4C2×D4×C2911yescharacteristic
364M16—44no—
365C2×C8—42no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—24no—
372C4⋊C4C22⋊C4×C2912yes—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—24no—
379C22⋊C4—42no—
380C42—21no—
381C42—21no—
382C42—44no—
383C23—24no—
384C23—22no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23C2×C22⋊C4×C2911yescharacteristic
398C23C29×#12012yes—
399Q8—24no—
400Q8—42no—
401Q8—42no—
402Q8—42no—
403D4—24no—
404D4—22no—
405D4—44no—
406D4—48no—
407D4—48no—
408D4C29×#9914yescomplemented
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—48no—
421C2×C4—42no—
422C2×C4—48no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—48no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—44no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4C29×#10412yescomplemented
435C2×C4C2×C22⋊C4×C2911yescharacteristic
436C2×C4C2×C22⋊C4×C2911yescharacteristic
437C2×C4C29×#12012yes—
438C8—82no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—24no—
443C22—22no—
444C22—22no—
445C22—44no—
446C22—44no—
447C22—42no—
448C22—42no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22C29×#37911yescharacteristic
457C22C2×C29×#10411yescharacteristic
458C22C29×#42111yescharacteristic
459C4—22no—
460C4—21no—
461C4—22no—
462C4—41no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—41no—
467C4—84no—
468C4C2×C29×#9912yes—
469C2—21no—
470C2—21no—
471C2—42no—
472C2—44no—
473C2—81no—
474C2C29×#178111yescharacteristic
475C2C29×#178911yescharacteristic
476C2C29×#179611yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#547C2
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
2. C29×#1789C2semidirect
3. C4×C29×#99C2semidirect
4. C29×#1508C2semidirect
5. C29×#1465C2semidirect
6. C22×#41×C29C4semidirect
10. C2×C29×C4⋊Q8C4semidirect
13. C2×C29×C22⋊Q8C4semidirect
16. C2×C4×D4×C29C4semidirect
144. #8364C29direct (N × H)
170. D4×C29#99semidirect
196. C2×C4×C29#104semidirect
202. #1789C2×C29semidirect
203. C4×#99C2×C29semidirect
204. #1508C2×C29semidirect
205. #1465C2×C29semidirect
236. C22×#41C4×C29semidirect
240. C2×C4⋊Q8C4×C29semidirect
243. C2×C22⋊Q8C4×C29semidirect
246. C2×C4×D4C4×C29semidirect
316. C29#8364direct (N × H)
408. D4C29×#99semidirect
434. C2×C4C29×#104semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#5472
C29×#17892
C4×C29×#992
C29×#15082
C29×#14652
#836429