Finite Group Databasebeta

← C29×#9219 #20304119

Subgroups — C29×#9219 #20304119

Order 7424.

594 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#474C211yesmaximal, characteristic
2C2×C8×D4×C29C211yesmaximal, characteristic
3C29×#1956C211yesmaximal, characteristic, complemented
4C29×#1802C211yesmaximal, characteristic
5C2×C29×#332C211yesmaximal, characteristic, complemented
6C29×#1296C211yesmaximal, characteristic, complemented
7C29×#1277C211yesmaximal, characteristic, complemented
8C23×C8×C29—21no—
9C2×C29×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C29C2211yescharacteristic
11C29×#474—22no—
12C29×#474C414yescomplemented
13C8×D4×C29—22no—
14C8×D4×C29—22no—
15C2×C29×#107—21no—
16C2×C29×C4⋊C8C2211yescharacteristic
17C2×C29×C4⋊C8C2211yescharacteristic
18C2×C29×C4⋊C8C2211yescharacteristic
19C2×C29×#103—21no—
20C2×C29×#103—21no—
21C2×C29×#102—21no—
22C2×C29×#102—21no—
23C2×C29×C22⋊C8—21no—
24C2×C4×C8×C29C2211yescharacteristic
25C29×#384C2211yescharacteristic
26C29×#340—21no—
27C29×#332—22no—
28C22×Q8×C29—21no—
29C22×D4×C29D411yescharacteristic
30C23×C4×C29—21no—
31C22×C8×C29—24no—
32C22×C8×C29—21no—
33C22×C8×C29—21no—
34C22×C8×C29—21no—
35C22×C8×C29—42no—
36C22×C8×C29—42no—
37C22×C8×C29D411yescharacteristic
38C22×C8×C29D411yescharacteristic
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8C2×C412yes—
43C4×D4×C29—21no—
44C4×D4×C29—21no—
45C4×D4×C29C2×C412yes—
46C4×D4×C29D412yes—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29—21no—
49C2×C4⋊C4×C29—21no—
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29D411yescharacteristic
53C2×C22⋊C4×C29—21no—
54C2×C42×C29C2311yescharacteristic
55C29×#107—24no—
56C29×C4⋊C8—21no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8C2×C412yes—
61C29×C4⋊C8D412yes—
62C29×#103—42no—
63C29×#103—42no—
64C29×#102—24no—
65C29×#102—42no—
66C29×C22⋊C8—24no—
67C4×C8×C29—21no—
68C4×C8×C29—21no—
69C24×C29—21no—
70C2×Q8×C29—22no—
71C2×Q8×C29—41no—
72C2×Q8×C29—41no—
73C2×Q8×C29—41no—
74C2×Q8×C29—41no—
75C2×Q8×C29—41no—
76C2×D4×C29—21no—
77C2×D4×C29—21no—
78C2×D4×C29—21no—
79C2×D4×C29C22⋊C412yes—
80C2×D4×C29SD1612yes—
81C2×D4×C29Q1612yes—
82C22×C4×C29—21no—
83C22×C4×C29—22no—
84C22×C4×C29—22no—
85C22×C4×C29—41no—
86C22×C4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29—41no—
90C22×C4×C29—41no—
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29C2×D411yescharacteristic
93C22×C4×C29#4111yescharacteristic
94C2×C8×C29—21no—
95C2×C8×C29—21no—
96C2×C8×C29—22no—
97C2×C8×C29—22no—
98C2×C8×C29—21no—
99C2×C8×C29—21no—
100C2×C8×C29—21no—
101C2×C8×C29—48no—
102C2×C8×C29—41no—
103C2×C8×C29—41no—
104C2×C8×C29—41no—
105C2×C8×C29—41no—
106C2×C8×C29—41no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29D812yes—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—22no—
112C4⋊C4×C29—22no—
113C4⋊C4×C29—41no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29—41no—
116C4⋊C4×C29—41no—
117C4⋊C4×C29—41no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—81no—
120C4⋊C4×C29C22⋊C412yes—
121C22⋊C4×C29—22no—
122C22⋊C4×C29—22no—
123C42×C29C22×C411yescharacteristic
124C42×C29C2×D411yescharacteristic
125C42×C29C2×D411yescharacteristic
126C42×C29#4111yescharacteristic
127#9219C2911yesmaximal, characteristic, direct product factor, Sylow
128C23×C29—22no—
129C23×C29—22no—
130C23×C29—22no—
131C23×C29—41no—
132C23×C29—41no—
133C23×C29—41no—
134C23×C29—41no—
135C23×C29#12111yescharacteristic
136Q8×C29—42no—
137Q8×C29—42no—
138Q8×C29—81no—
139Q8×C29—81no—
140D4×C29—22no—
141D4×C29—22no—
142D4×C29—22no—
143D4×C29#10314yescomplemented
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—22no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—42no—
150C2×C4×C29—42no—
151C2×C4×C29—42no—
152C2×C4×C29—42no—
153C2×C4×C29—42no—
154C2×C4×C29—81no—
155C2×C4×C29—81no—
156C2×C4×C29—81no—
157C2×C4×C29—81no—
158C2×C4×C29—81no—
159C2×C4×C29C2×C22⋊C411yescharacteristic
160C2×C4×C29C4×D411yescharacteristic
161C2×C4×C29C4×D411yescharacteristic
162C2×C4×C29#12011yescharacteristic
163C2×C4×C29#12111yescharacteristic
164C2×C4×C29#12311yescharacteristic
165C2×C4×C29C2×D811yescharacteristic
166C2×C4×C29C2×SD1611yescharacteristic
167C2×C4×C29C2×Q1611yescharacteristic
168C2×C4×C29#13511yescharacteristic
169C2×C4×C29#13511yescharacteristic
170C2×C4×C29#13511yescharacteristic
171C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
173C8×C29—22no—
174C8×C29—42no—
175C8×C29—42no—
176C8×C29—41no—
177C8×C29—81no—
178C2×#474C2×C2911yescharacteristic
179C2×C8×D4C2×C2911yescharacteristic
180#1956C2×C2911yescharacteristic, complemented
181#1802C2×C2911yescharacteristic
182C2×#332C2×C2911yescharacteristic, complemented
183#1296C2×C2911yescharacteristic, complemented
184#1277C2×C2911yescharacteristic, complemented
185C22×C29—24no—
186C22×C29—42no—
187C22×C29—42no—
188C22×C29—42no—
189C22×C29—42no—
190C22×C29—42no—
191C22×C29—42no—
192C22×C29#38611yescharacteristic
193C22×C29#45911yescharacteristic
194C22×C29#46311yescharacteristic
195C22×C29#46511yescharacteristic
196C22×C29#46711yescharacteristic
197C22×C29#47111yescharacteristic
198C22×C29#47311yescharacteristic
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—42no—
202C4×C29—82no—
203C4×C29—161no—
204C4×C29C2×#10311yescharacteristic
205C4×C29#41611yescharacteristic
206C4×C29C4×D811yescharacteristic
207C4×C29#44211yescharacteristic
208C4×C29#44711yescharacteristic
209C4×C29#44911yescharacteristic
210C4×C29#46511yescharacteristic
211C4×C29#46711yescharacteristic
212C23×C8—21no—
213C2×C4⋊Q8C22×C2911yescharacteristic
214C2×C4×D4C22×C2911yescharacteristic
215#474—22no—
216#474C4×C2914yescomplemented
217C8×D4—22no—
218C8×D4—22no—
219C2×#107—21no—
220C2×C4⋊C8C22×C2911yescharacteristic
221C2×C4⋊C8C22×C2911yescharacteristic
222C2×C4⋊C8C22×C2911yescharacteristic
223C2×#103—21no—
224C2×#103—21no—
225C2×#102—21no—
226C2×#102—21no—
227C2×C22⋊C8—21no—
228C2×C4×C8C22×C2911yescharacteristic
229#384C22×C2911yescharacteristic
230#340—21no—
231#332—22no—
232C2×C29—44no—
233C2×C29#166511yescharacteristic
234C2×C29#166911yescharacteristic
235C2×C29#167911yescharacteristic
236C2×C29#168311yescharacteristic
237C2×C29#187911yescharacteristic
238C2×C29#189211yescharacteristic
239C2×C29#190811yescharacteristic
240C22×Q8—21no—
241C22×D4D4×C2911yescharacteristic
242C23×C4—21no—
243C22×C8—24no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—42no—
248C22×C8—42no—
249C22×C8D4×C2911yescharacteristic
250C22×C8D4×C2911yescharacteristic
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8C2×C4×C2912yes—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4C2×C4×C2912yes—
258C4×D4D4×C2912yes—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4D4×C2911yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C23×C2911yescharacteristic
267#107—24no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8C2×C4×C2912yes—
273C4⋊C8D4×C2912yes—
274#103—42no—
275#103—42no—
276#102—24no—
277#102—42no—
278C22⋊C8—24no—
279C4×C8—21no—
280C4×C8—21no—
281C29#921911yescharacteristic, direct product factor, Sylow
282C24—21no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4C22⋊C4×C2912yes—
293C2×D4SD16×C2912yes—
294C2×D4Q16×C2912yes—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4C2×D4×C2911yescharacteristic
305C22×C4C2×D4×C2911yescharacteristic
306C22×C4#41×C2911yescharacteristic
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—48no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8D8×C2912yes—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—81no—
333C4⋊C4C22⋊C4×C2912yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C42C22×C4×C2911yescharacteristic
337C42C2×D4×C2911yescharacteristic
338C42C2×D4×C2911yescharacteristic
339C42#41×C2911yescharacteristic
340C23—22no—
341C23—22no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C29×#12111yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—22no—
353D4—22no—
354D4—22no—
355D4C29×#10314yescomplemented
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4C2×C22⋊C4×C2911yescharacteristic
372C2×C4C4×D4×C2911yescharacteristic
373C2×C4C4×D4×C2911yescharacteristic
374C2×C4C29×#12011yescharacteristic
375C2×C4C29×#12111yescharacteristic
376C2×C4C29×#12311yescharacteristic
377C2×C4C2×D8×C2911yescharacteristic
378C2×C4C2×SD16×C2911yescharacteristic
379C2×C4C2×Q16×C2911yescharacteristic
380C2×C4C29×#13511yescharacteristic
381C2×C4C29×#13511yescharacteristic
382C2×C4C29×#13511yescharacteristic
383C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
384C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
385C8—22no—
386C8—42no—
387C8—41no—
388C8—42no—
389C8—81no—
390C22—24no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22C29×#38611yescharacteristic
398C22C29×#45911yescharacteristic
399C22C29×#46311yescharacteristic
400C22C29×#46511yescharacteristic
401C22C29×#46711yescharacteristic
402C22C29×#47111yescharacteristic
403C22C29×#47311yescharacteristic
404C4—21no—
405C4—21no—
406C4—42no—
407C4—82no—
408C4—161no—
409C4C2×C29×#10311yescharacteristic
410C4C29×#41611yescharacteristic
411C4C4×D8×C2911yescharacteristic
412C4C29×#44211yescharacteristic
413C4C29×#44711yescharacteristic
414C4C29×#44911yescharacteristic
415C4C29×#46511yescharacteristic
416C4C29×#46711yescharacteristic
417C2—44no—
418C2C29×#166511yescharacteristic
419C2C29×#166911yescharacteristic
420C2C29×#167911yescharacteristic
421C2C29×#168311yescharacteristic
422C2C29×#187911yescharacteristic
423C2C29×#189211yescharacteristic
424C2C29×#190811yescharacteristic
subgroupG/H
center, socleC23×C29#121
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1956C2semidirect
5. C2×C29×#332C2semidirect
6. C29×#1296C2semidirect
7. C29×#1277C2semidirect
12. C29×#474C4semidirect
127. #9219C29direct (N × H)
143. D4×C29#103semidirect
180. #1956C2×C29semidirect
182. C2×#332C2×C29semidirect
183. #1296C2×C29semidirect
184. #1277C2×C29semidirect
216. #474C4×C29semidirect
281. C29#9219direct (N × H)
355. D4C29×#103semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#4742
C2×C8×D4×C292
C29×#19562
C29×#18022
C2×C29×#3322
C29×#12962
C29×#12772
#921929