Finite Group Databasebeta

← C29×#8993 #20303893

Subgroups — C29×#8993 #20303893

Order 7424.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3076C211yesmaximal, characteristic
2C29×#2906C211yesmaximal, characteristic
3C29×#1493C211yesmaximal, characteristic, complemented
4C29×#1481C211yesmaximal, characteristic, complemented
5C29×#1476C211yesmaximal, characteristic
6C29×#1301C211yesmaximal, characteristic, complemented
7C29×#1277C211yesmaximal, characteristic, complemented
8C2×C29×#131—21no—
9C29×#533C2211yescharacteristic
10C4×#41×C29C2211yescharacteristic
11C29×#479—21no—
12C29×#478—21no—
13C29×#477C411yescharacteristic
14C29×#476C411yescharacteristic
15C29×#475C411yescharacteristic
16C29×#474C411yescharacteristic
17C29×#431C2211yescharacteristic
18C29×#427—21no—
19C29×#424—22no—
20C29×#424—21no—
21C29×#423—21no—
22C29×#423C2211yescharacteristic
23C2×C29×C4⋊C8—21no—
24C2×C29×C4⋊C8C2211yescharacteristic
25C2×C29×C4⋊C8C2211yescharacteristic
26C29×#416—21no—
27C2×C4×C8×C29C2211yescharacteristic
28C29×Q8⋊C8—21no—
29C29×Q8⋊C8—21no—
30C29×Q8⋊C8—22no—
31C29×Q8⋊C8—21no—
32C29×D4⋊C8—21no—
33C2×#41×C29D411yescharacteristic
34C29×#131—42no—
35C29×#131—42no—
36C2×M16×C29—22no—
37C2×M16×C29—21no—
38C22×C8×C29—22no—
39C22×C8×C29—21no—
40C22×C8×C29—21no—
41C22×C8×C29—21no—
42C29×C4⋊Q8C2×C411yescharacteristic
43C29×C4⋊Q8C2×C411yescharacteristic
44C29×#125—21no—
45C29×C22⋊Q8—21no—
46C29×C22⋊Q8—21no—
47C4×Q8×C29—21no—
48C4×Q8×C29—21no—
49C4×Q8×C29C2×C411yescharacteristic
50C4×Q8×C29D411yescharacteristic
51C4×D4×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29C2×C411yescharacteristic
54C4×D4×C29D411yescharacteristic
55C29×#117—21no—
56C29×#117—21no—
57C29×#117D411yescharacteristic
58C2×C42×C29—21no—
59C2×C42×C29C2311yescharacteristic
60C29×#107—21no—
61C29×#107—21no—
62C29×#106—21no—
63C29×#106—21no—
64C29×C4⋊C8—22no—
65C29×C4⋊C8—22no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×C4⋊C8—21no—
69C29×C4⋊C8—21no—
70C29×C4⋊C8C2×C411yescharacteristic
71C29×C4⋊C8C2×C411yescharacteristic
72C29×C4⋊C8D411yescharacteristic
73C29×C4⋊C8D411yescharacteristic
74C29×C4⋊C8D412yes—
75C29×#103—21no—
76C29×#103—21no—
77C29×#102—21no—
78C29×#102—21no—
79C29×C22⋊C8—21no—
80C4×C8×C29—21no—
81C4×C8×C29—21no—
82C4×C8×C29—21no—
83#41×C29—21no—
84#41×C29—21no—
85#41×C29SD1612yes—
86#41×C29Q1612yes—
87C2×Q8×C29—21no—
88C2×Q8×C29—21no—
89C2×Q8×C29C22⋊C411yescharacteristic
90C2×D4×C29—21no—
91C2×D4×C29C22⋊C411yescharacteristic
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29C2×D411yescharacteristic
96C22×C4×C29#4111yescharacteristic
97C22×C4×C29#4111yescharacteristic
98M16×C29—44no—
99M16×C29—41no—
100M16×C29—41no—
101C2×C8×C29—22no—
102C2×C8×C29—21no—
103C2×C8×C29—21no—
104C2×C8×C29—21no—
105C2×C8×C29—22no—
106C2×C8×C29—21no—
107C2×C8×C29—41no—
108C2×C8×C29—44no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C2×C8×C29—41no—
112C2×C8×C29—41no—
113C2×C8×C29—41no—
114C2×C8×C29—41no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29—41no—
123C4⋊C4×C29C22⋊C411yescharacteristic
124C4⋊C4×C29C22⋊C411yescharacteristic
125C22⋊C4×C29—21no—
126C22⋊C4×C29—21no—
127C22⋊C4×C29—21no—
128C22⋊C4×C29—41no—
129C42×C29—21no—
130C42×C29—21no—
131C42×C29—21no—
132C42×C29—41no—
133C42×C29C22×C411yescharacteristic
134C42×C29C2×D411yescharacteristic
135C42×C29C2×D411yescharacteristic
136C42×C29C2×D411yescharacteristic
137#8993C2911yesmaximal, characteristic, direct product factor, Sylow
138C23×C29—21no—
139C23×C29#12311yescharacteristic
140Q8×C29—21no—
141Q8×C29—42no—
142Q8×C29—41no—
143Q8×C29—41no—
144Q8×C29#10312yes—
145D4×C29—22no—
146D4×C29—22no—
147D4×C29—21no—
148D4×C29#10312yes—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—22no—
153C2×C4×C29—22no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—41no—
157C2×C4×C29—41no—
158C2×C4×C29—41no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—81no—
162C2×C4×C29C2×C22⋊C411yescharacteristic
163C2×C4×C29C4×D411yescharacteristic
164C2×C4×C29C4×D411yescharacteristic
165C2×C4×C29#12011yescharacteristic
166C2×C4×C29#12111yescharacteristic
167C2×C4×C29#12111yescharacteristic
168C2×C4×C29C2×SD1611yescharacteristic
169C2×C4×C29C2×Q1611yescharacteristic
170C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C29#13711yescharacteristic
172C8×C29—42no—
173C8×C29—41no—
174C8×C29—41no—
175C8×C29—41no—
176C8×C29—42no—
177C8×C29—41no—
178C8×C29—81no—
179#3076C2×C2911yescharacteristic
180#2906C2×C2911yescharacteristic
181#1493C2×C2911yescharacteristic, complemented
182#1481C2×C2911yescharacteristic, complemented
183#1476C2×C2911yescharacteristic
184#1301C2×C2911yescharacteristic, complemented
185#1277C2×C2911yescharacteristic, complemented
186C22×C29—21no—
187C22×C29—21no—
188C22×C29—22no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29#38611yescharacteristic
192C22×C29#48311yescharacteristic
193C22×C29#48411yescharacteristic
194C4×C29—22no—
195C4×C29—21no—
196C4×C29—21no—
197C4×C29—21no—
198C4×C29—41no—
199C4×C29—41no—
200C4×C29—81no—
201C4×C29—81no—
202C4×C29C2×#10311yescharacteristic
203C4×C29#41711yescharacteristic
204C4×C29#44311yescharacteristic
205C4×C29#44411yescharacteristic
206C4×C29#45011yescharacteristic
207C4×C29#45111yescharacteristic
208C2×#131—21no—
209#533C22×C2911yescharacteristic
210C4×#41C22×C2911yescharacteristic
211#479—21no—
212#478—21no—
213#477C4×C2911yescharacteristic
214#476C4×C2911yescharacteristic
215#475C4×C2911yescharacteristic
216#474C4×C2911yescharacteristic
217#431C22×C2911yescharacteristic
218#427—21no—
219#424—21no—
220#424—22no—
221#423—21no—
222#423C22×C2911yescharacteristic
223C2×C4⋊C8—21no—
224C2×C4⋊C8C22×C2911yescharacteristic
225C2×C4⋊C8C22×C2911yescharacteristic
226#416—21no—
227C2×C4×C8C22×C2911yescharacteristic
228Q8⋊C8—21no—
229Q8⋊C8—21no—
230Q8⋊C8—21no—
231Q8⋊C8—22no—
232D4⋊C8—21no—
233C2×C29—21no—
234C2×C29—21no—
235C2×C29—42no—
236C2×C29#187211yescharacteristic
237C2×C29#187611yescharacteristic
238C2×C29#188111yescharacteristic
239C2×#41D4×C2911yescharacteristic
240#131—42no—
241#131—42no—
242C2×M16—22no—
243C2×M16—21no—
244C22×C8—22no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C4⋊Q8C2×C4×C2911yescharacteristic
249C4⋊Q8C2×C4×C2911yescharacteristic
250#125—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8C2×C4×C2911yescharacteristic
256C4×Q8D4×C2911yescharacteristic
257C4×D4—21no—
258C4×D4—21no—
259C4×D4C2×C4×C2911yescharacteristic
260C4×D4D4×C2911yescharacteristic
261#117—21no—
262#117—21no—
263#117D4×C2911yescharacteristic
264C2×C42—21no—
265C2×C42C23×C2911yescharacteristic
266#107—21no—
267#107—21no—
268#106—21no—
269#106—21no—
270C4⋊C8—22no—
271C4⋊C8—22no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8C2×C4×C2911yescharacteristic
277C4⋊C8C2×C4×C2911yescharacteristic
278C4⋊C8D4×C2911yescharacteristic
279C4⋊C8D4×C2911yescharacteristic
280C4⋊C8D4×C2912yes—
281#103—21no—
282#103—21no—
283#102—21no—
284#102—21no—
285C22⋊C8—21no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8—21no—
289C29#899311yescharacteristic, direct product factor, Sylow
290#41—21no—
291#41—21no—
292#41SD16×C2912yes—
293#41Q16×C2912yes—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8C22⋊C4×C2911yescharacteristic
297C2×D4—21no—
298C2×D4C22⋊C4×C2911yescharacteristic
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4C2×D4×C2911yescharacteristic
303C22×C4#41×C2911yescharacteristic
304C22×C4#41×C2911yescharacteristic
305M16—44no—
306M16—41no—
307M16—41no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—44no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4C22⋊C4×C2911yescharacteristic
331C4⋊C4C22⋊C4×C2911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—41no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—41no—
340C42C22×C4×C2911yescharacteristic
341C42C2×D4×C2911yescharacteristic
342C42C2×D4×C2911yescharacteristic
343C42C2×D4×C2911yescharacteristic
344C23—21no—
345C23C29×#12311yescharacteristic
346Q8—21no—
347Q8—42no—
348Q8—41no—
349Q8—41no—
350Q8C29×#10312yes—
351D4—22no—
352D4—22no—
353D4—21no—
354D4C29×#10312yes—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4C2×C22⋊C4×C2911yescharacteristic
369C2×C4C4×D4×C2911yescharacteristic
370C2×C4C4×D4×C2911yescharacteristic
371C2×C4C29×#12011yescharacteristic
372C2×C4C29×#12111yescharacteristic
373C2×C4C29×#12111yescharacteristic
374C2×C4C2×SD16×C2911yescharacteristic
375C2×C4C2×Q16×C2911yescharacteristic
376C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
377C2×C4C29×#13711yescharacteristic
378C8—42no—
379C8—41no—
380C8—42no—
381C8—41no—
382C8—41no—
383C8—41no—
384C8—81no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22C29×#38611yescharacteristic
391C22C29×#48311yescharacteristic
392C22C29×#48411yescharacteristic
393C4—22no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4C2×C29×#10311yescharacteristic
402C4C29×#41711yescharacteristic
403C4C29×#44311yescharacteristic
404C4C29×#44411yescharacteristic
405C4C29×#45011yescharacteristic
406C4C29×#45111yescharacteristic
407C2—21no—
408C2—21no—
409C2—42no—
410C2C29×#187211yescharacteristic
411C2C29×#187611yescharacteristic
412C2C29×#188111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC2×#41×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1493C2semidirect
4. C29×#1481C2semidirect
6. C29×#1301C2semidirect
7. C29×#1277C2semidirect
137. #8993C29direct (N × H)
181. #1493C2×C29semidirect
182. #1481C2×C29semidirect
184. #1301C2×C29semidirect
185. #1277C2×C29semidirect
289. C29#8993direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30762
C29×#29062
C29×#14932
C29×#14812
C29×#14762
C29×#13012
C29×#12772
#899329