Finite Group Databasebeta

← C29×#13386 #20308286

Subgroups — C29×#13386 #20308286

Order 7424.

432 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3054C211yesmaximal, characteristic
2C29×#2159C211yesmaximal, characteristic, complemented
3C2×C29×#360C211yesmaximal, characteristic, complemented
4C29×#2139C211yesmaximal, characteristic, complemented
5C2×C29×#349C211yesmaximal, characteristic, complemented
6C29×#1809C211yesmaximal, characteristic, complemented
7C29×#1386C211yesmaximal, characteristic, complemented
8C2×C29×#135C2211yescharacteristic
9C22×M16×C29C2211yescharacteristic
10C29×#525—21no—
11C2×C29×M32C2211yescharacteristic
12C2×C29×M32C2211yescharacteristic
13C29×#470—21no—
14C29×#469—21no—
15C29×#468—21no—
16C29×#468—21no—
17C29×#427C2211yescharacteristic
18C2×C29×#107C2211yescharacteristic
19C2×C29×#106C2211yescharacteristic
20C29×#416—21no—
21C29×#380—21no—
22C29×#367—21no—
23C29×#366—21no—
24C29×#360—22no—
25C29×#358—21no—
26C29×#357—21no—
27C29×#349—22no—
28C29×#340—21no—
29C2×#41×C29—21no—
30C23×C4×C29D411yescharacteristic
31C29×#135—21no—
32C29×#135—21no—
33C29×#135—21no—
34C29×#135—21no—
35C2×Q16×C29D411yescharacteristic
36C2×SD16×C29—21no—
37C2×D8×C29D411yescharacteristic
38C2×M16×C29—21no—
39C2×M16×C29—21no—
40C2×M16×C29—21no—
41C2×M16×C29—21no—
42C2×M16×C29—21no—
43C2×M16×C29—21no—
44C22×C8×C29D411yescharacteristic
45C22×C8×C29C2311yescharacteristic
46C29×#123—41no—
47C29×C22⋊Q8—21no—
48C29×C22⋊Q8—21no—
49C29×#121—21no—
50C29×#121—21no—
51C29×#120—41no—
52C4×D4×C29—41no—
53C4×D4×C29—41no—
54C29×#117—21no—
55C2×C4⋊C4×C29—21no—
56C2×C4⋊C4×C29—21no—
57C2×C22⋊C4×C29—41no—
58C29×M32—21no—
59C29×M32—21no—
60C29×M32—21no—
61C29×M32D412yescomplemented
62C2×C16×C29—21no—
63C2×C16×C29—21no—
64C29×#107—21no—
65C29×#107—21no—
66C29×#107D411yescharacteristic
67C29×#107D411yescharacteristic
68C29×#106—21no—
69C29×#106—21no—
70C29×#106—21no—
71C29×#103—21no—
72C29×#103—21no—
73C29×#102—21no—
74C29×#102—21no—
75C29×#95—41no—
76C24×C29D811yescharacteristic
77#41×C29—41no—
78#41×C29—41no—
79#41×C29—41no—
80#41×C29—41no—
81C2×Q8×C29—21no—
82C2×D4×C29—21no—
83C2×D4×C29—41no—
84C2×D4×C29—41no—
85C2×D4×C29—41no—
86C22×C4×C29—21no—
87C22×C4×C29—21no—
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—41no—
93C22×C4×C29—41no—
94C22×C4×C29—41no—
95C22×C4×C29D811yescharacteristic
96C22×C4×C29C2×D411yescharacteristic
97Q16×C29—21no—
98Q16×C29—21no—
99SD16×C29—41no—
100SD16×C29—41no—
101D8×C29—21no—
102D8×C29—21no—
103M16×C29—41no—
104M16×C29—41no—
105M16×C29—41no—
106M16×C29—41no—
107C2×C8×C29—21no—
108C2×C8×C29—21no—
109C2×C8×C29—21no—
110C2×C8×C29C2×D411yescharacteristic
111C2×C8×C29C2×D411yescharacteristic
112C2×C8×C29C2×D411yescharacteristic
113C2×C8×C29#4111yescharacteristic
114C2×C8×C29#4111yescharacteristic
115C2×C8×C29#4111yescharacteristic
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29—41no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29—41no—
123C4⋊C4×C29—41no—
124C22⋊C4×C29—41no—
125C22⋊C4×C29—41no—
126C22⋊C4×C29—41no—
127C22⋊C4×C29—41no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29—82no—
130C42×C29—41no—
131C16×C29—22no—
132C16×C29—41no—
133#13386C2911yesmaximal, characteristic, direct product factor, Sylow
134C23×C29—21no—
135C23×C29—21no—
136C23×C29—21no—
137C23×C29—41no—
138C23×C29—41no—
139C23×C29—41no—
140C23×C29C2×D811yescharacteristic
141Q8×C29—41no—
142Q8×C29—41no—
143D4×C29—41no—
144D4×C29—41no—
145D4×C29—82no—
146D4×C29—82no—
147D4×C29—81no—
148D4×C29—81no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
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—81no—
160C2×C4×C29—81no—
161C2×C4×C29—81no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29—81no—
165C2×C4×C29—81no—
166C2×C4×C29—81no—
167C2×C4×C29#12011yescharacteristic
168C2×C4×C29#12111yescharacteristic
169C2×C4×C29#12311yescharacteristic
170C2×C4×C29#13511yescharacteristic
171C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C29#13711yescharacteristic
173C8×C29—41no—
174C8×C29#12111yescharacteristic
175C8×C29#12111yescharacteristic
176C8×C29#12311yescharacteristic
177C8×C29#12411yescharacteristic
178#3054C2×C2911yescharacteristic
179#2159C2×C2911yescharacteristic, complemented
180C2×#360C2×C2911yescharacteristic, complemented
181#2139C2×C2911yescharacteristic, complemented
182C2×#349C2×C2911yescharacteristic, complemented
183#1809C2×C2911yescharacteristic, complemented
184#1386C2×C2911yescharacteristic, complemented
185C22×C29—21no—
186C22×C29—21no—
187C22×C29—42no—
188C22×C29—41no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29—81no—
192C22×C29—81no—
193C22×C29—81no—
194C22×C29—81no—
195C22×C29#44711yescharacteristic
196C22×C29#46611yescharacteristic
197C22×C29#48011yescharacteristic
198C4×C29—41no—
199C4×C29—81no—
200C4×C29—81no—
201C4×C29—81no—
202C4×C29—161no—
203C4×C29—161no—
204C4×C29#39411yescharacteristic
205C4×C29#45211yescharacteristic
206C4×C29#46811yescharacteristic
207C4×C29#48211yescharacteristic
208C2×#135C22×C2911yescharacteristic
209C22×M16C22×C2911yescharacteristic
210#525—21no—
211C2×M32C22×C2911yescharacteristic
212C2×M32C22×C2911yescharacteristic
213#470—21no—
214#469—21no—
215#468—21no—
216#468—21no—
217#427C22×C2911yescharacteristic
218C2×#107C22×C2911yescharacteristic
219C2×#106C22×C2911yescharacteristic
220#416—21no—
221#380—21no—
222#367—21no—
223#366—21no—
224#360—22no—
225#358—21no—
226#357—21no—
227#349—22no—
228#340—21no—
229C2×C29—21no—
230C2×C29—21no—
231C2×C29—81no—
232C2×C29—161no—
233C2×C29#203311yescharacteristic
234C2×C29#219011yescharacteristic
235C2×C29#219111yescharacteristic
236C2×#41—21no—
237C23×C4D4×C2911yescharacteristic
238#135—21no—
239#135—21no—
240#135—21no—
241#135—21no—
242C2×Q16D4×C2911yescharacteristic
243C2×SD16—21no—
244C2×D8D4×C2911yescharacteristic
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C22×C8D4×C2911yescharacteristic
252C22×C8C23×C2911yescharacteristic
253#123—41no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256#121—21no—
257#121—21no—
258#120—41no—
259C4×D4—41no—
260C4×D4—41no—
261#117—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C22⋊C4—41no—
265M32—21no—
266M32—21no—
267M32—21no—
268M32D4×C2912yescomplemented
269C2×C16—21no—
270C2×C16—21no—
271#107—21no—
272#107—21no—
273#107D4×C2911yescharacteristic
274#107D4×C2911yescharacteristic
275#106—21no—
276#106—21no—
277#106—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282#95—41no—
283C29#1338611yescharacteristic, direct product factor, Sylow
284C24D8×C2911yescharacteristic
285#41—41no—
286#41—41no—
287#41—41no—
288#41—41no—
289C2×Q8—21no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4D8×C2911yescharacteristic
304C22×C4C2×D4×C2911yescharacteristic
305Q16—21no—
306Q16—21no—
307SD16—41no—
308SD16—41no—
309D8—21no—
310D8—21no—
311M16—41no—
312M16—41no—
313M16—41no—
314M16—41no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8C2×D4×C2911yescharacteristic
319C2×C8C2×D4×C2911yescharacteristic
320C2×C8C2×D4×C2911yescharacteristic
321C2×C8#41×C2911yescharacteristic
322C2×C8#41×C2911yescharacteristic
323C2×C8#41×C2911yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—82no—
338C42—41no—
339C16—22no—
340C16—41no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C2×D8×C2911yescharacteristic
348Q8—41no—
349Q8—41no—
350D4—41no—
351D4—41no—
352D4—82no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4C29×#12011yescharacteristic
375C2×C4C29×#12111yescharacteristic
376C2×C4C29×#12311yescharacteristic
377C2×C4C29×#13511yescharacteristic
378C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
379C2×C4C29×#13711yescharacteristic
380C8—41no—
381C8C29×#12111yescharacteristic
382C8C29×#12111yescharacteristic
383C8C29×#12311yescharacteristic
384C8C29×#12411yescharacteristic
385C22—21no—
386C22—21no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22C29×#44711yescharacteristic
396C22C29×#46611yescharacteristic
397C22C29×#48011yescharacteristic
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—161no—
403C4—161no—
404C4C29×#39411yescharacteristic
405C4C29×#45211yescharacteristic
406C4C29×#46811yescharacteristic
407C4C29×#48211yescharacteristic
408C2—21no—
409C2—21no—
410C2—81no—
411C2—161no—
412C2C29×#203311yescharacteristic
413C2C29×#219011yescharacteristic
414C2C29×#219111yescharacteristic
subgroupG/H
center, socleC22×C29#447
commutator, Frattini, cosocleC22×C8C23×C29
prime radicalC29×#3054C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C22×M16×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2159C2semidirect
3. C2×C29×#360C2semidirect
4. C29×#2139C2semidirect
5. C2×C29×#349C2semidirect
6. C29×#1809C2semidirect
7. C29×#1386C2semidirect
61. C29×M32D4semidirect
133. #13386C29direct (N × H)
179. #2159C2×C29semidirect
180. C2×#360C2×C29semidirect
181. #2139C2×C29semidirect
182. C2×#349C2×C29semidirect
183. #1809C2×C29semidirect
184. #1386C2×C29semidirect
268. M32D4×C29semidirect
283. C29#13386direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30542
C29×#21592
C2×C29×#3602
C29×#21392
C2×C29×#3492
C29×#18092
C29×#13862
#1338629