Finite Group Databasebeta

← C29×#9378 #20304278

Subgroups — C29×#9378 #20304278

Order 7424.

498 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3217C211yesmaximal, characteristic
2C29×#2992C211yesmaximal, characteristic, complemented
3C29×#1982C211yesmaximal, characteristic, complemented
4C29×#1555C211yesmaximal, characteristic, complemented
5C29×#1509C211yesmaximal, characteristic, complemented
6C29×#1290C211yesmaximal, characteristic, complemented
7C29×#1285C211yesmaximal, characteristic, complemented
8C2×C29×#127C2211yescharacteristic
9C29×#529C2211yescharacteristic
10C29×#496C412yescomplemented
11C29×#490C412yescomplemented
12C29×#460—21no—
13C29×#459—21no—
14C29×#450—21no—
15C29×#447—21no—
16C29×#446—21no—
17C29×#435—21no—
18C29×#435—21no—
19C8×D4×C29—21no—
20C29×#433—21no—
21C29×#432C2211yescharacteristic
22C29×#432C2211yescharacteristic
23C29×#432C2211yescharacteristic
24C29×#424—21no—
25C2×C29×C4⋊C8C2211yescharacteristic
26C2×C29×#102—21no—
27C2×C29×#102—21no—
28C4×C4⋊C4×C29C2211yescharacteristic
29C29×#331—21no—
30C29×#331—21no—
31C29×#328—21no—
32C29×#327—21no—
33C22×D4×C29—21no—
34C22×D4×C29—21no—
35C22×D4×C29—21no—
36C2×SD16×C29—22no—
37C2×D8×C29—22no—
38C2×M16×C29—21no—
39C22×C8×C29—21no—
40C22×C8×C29D411yescharacteristic
41C22×C8×C29D411yescharacteristic
42C29×#127—21no—
43C29×#127—21no—
44C29×#127—21no—
45C29×#127C2×C412yes—
46C29×#126—21no—
47C29×#125C2×C411yescharacteristic
48C29×#124C2×C411yescharacteristic
49C29×#123—21no—
50C29×C22⋊Q8D411yescharacteristic
51C29×#121D411yescharacteristic
52C4×Q8×C29D411yescharacteristic
53C4×D4×C29—21no—
54C4×D4×C29D411yescharacteristic
55C29×#117—21no—
56C2×C4⋊C4×C29—21no—
57C2×C42×C29—21no—
58C2×C42×C29C2311yescharacteristic
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8D411yescharacteristic
66C29×C4⋊C8D411yescharacteristic
67C29×#102—22no—
68C29×#102—22no—
69C29×#102—42no—
70C29×#102—42no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8—21no—
76C29×#97—21no—
77C29×#97—21no—
78C29×#97—21no—
79C29×#97C2×C412yes—
80C4×C8×C29—21no—
81C29×#95—21no—
82C24×C29—41no—
83C2×Q8×C29C22⋊C411yescharacteristic
84C2×D4×C29—21no—
85C2×D4×C29—22no—
86C2×D4×C29—22no—
87C2×D4×C29—22no—
88C2×D4×C29—41no—
89C2×D4×C29—41no—
90C2×D4×C29—41no—
91C2×D4×C29—41no—
92C2×D4×C29—41no—
93C2×D4×C29—41no—
94C2×D4×C29—41no—
95C2×D4×C29—81no—
96C2×D4×C29—81no—
97C2×D4×C29—82no—
98C2×D4×C29C22⋊C411yescharacteristic
99C22×C4×C29—21no—
100C22×C4×C29—41no—
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29#4111yescharacteristic
104SD16×C29—82no—
105D8×C29—82no—
106M16×C29—81no—
107C2×C8×C29—22no—
108C2×C8×C29—21no—
109C2×C8×C29—21no—
110C2×C8×C29—21no—
111C2×C8×C29—21no—
112C2×C8×C29—41no—
113C2×C8×C29—41no—
114C2×C8×C29—41no—
115C2×C8×C29—81no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—22no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29C22⋊C411yescharacteristic
123C4⋊C4×C29C22⋊C411yescharacteristic
124C22⋊C4×C29—21no—
125C22⋊C4×C29—21no—
126C22⋊C4×C29—21no—
127C22⋊C4×C29—21no—
128C22⋊C4×C29—21no—
129C42×C29—21no—
130C42×C29—81no—
131C42×C29C22×C411yescharacteristic
132C42×C29C2×D411yescharacteristic
133C42×C29C2×D411yescharacteristic
134C42×C29#4111yescharacteristic
135#9378C2911yesmaximal, characteristic, direct product factor, Sylow
136C23×C29—21no—
137C23×C29—42no—
138C23×C29—81no—
139C23×C29—81no—
140C23×C29—81no—
141C23×C29—81no—
142C23×C29—81no—
143C23×C29—81no—
144C23×C29#12111yescharacteristic
145Q8×C29—41no—
146D4×C29—41no—
147D4×C29—42no—
148D4×C29—42no—
149D4×C29—42no—
150D4×C29—42no—
151D4×C29—41no—
152D4×C29—41no—
153D4×C29—82no—
154D4×C29—82no—
155D4×C29—82no—
156D4×C29—81no—
157D4×C29—81no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—21no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—42no—
169C2×C4×C29—81no—
170C2×C4×C29—81no—
171C2×C4×C29C2×C22⋊C411yescharacteristic
172C2×C4×C29C4×D411yescharacteristic
173C2×C4×C29C4×D411yescharacteristic
174C2×C4×C29#12011yescharacteristic
175C2×C4×C29#12111yescharacteristic
176C2×C4×C29#12311yescharacteristic
177C8×C29—42no—
178C8×C29—41no—
179C8×C29—41no—
180C8×C29—41no—
181C8×C29—41no—
182C8×C29—81no—
183#3217C2×C2911yescharacteristic
184#2992C2×C2911yescharacteristic, complemented
185#1982C2×C2911yescharacteristic, complemented
186#1555C2×C2911yescharacteristic, complemented
187#1509C2×C2911yescharacteristic, complemented
188#1290C2×C2911yescharacteristic, complemented
189#1285C2×C2911yescharacteristic, complemented
190C22×C29—21no—
191C22×C29—21no—
192C22×C29—41no—
193C22×C29—41no—
194C22×C29—41no—
195C22×C29—82no—
196C22×C29—82no—
197C22×C29—82no—
198C22×C29—161no—
199C22×C29—161no—
200C22×C29—161no—
201C22×C29—161no—
202C22×C29#38611yescharacteristic
203C22×C29#47111yescharacteristic
204C22×C29#47211yescharacteristic
205C4×C29—21no—
206C4×C29—21no—
207C4×C29—21no—
208C4×C29—21no—
209C4×C29—21no—
210C4×C29—41no—
211C4×C29—41no—
212C4×C29—41no—
213C4×C29—82no—
214C4×C29#45311yescharacteristic
215C4×C29#45411yescharacteristic
216C2×#127C22×C2911yescharacteristic
217#529C22×C2911yescharacteristic
218#496C4×C2912yescomplemented
219#490C4×C2912yescomplemented
220#460—21no—
221#459—21no—
222#450—21no—
223#447—21no—
224#446—21no—
225#435—21no—
226#435—21no—
227C8×D4—21no—
228#433—21no—
229#432C22×C2911yescharacteristic
230#432C22×C2911yescharacteristic
231#432C22×C2911yescharacteristic
232#424—21no—
233C2×C4⋊C8C22×C2911yescharacteristic
234C2×#102—21no—
235C2×#102—21no—
236C4×C4⋊C4C22×C2911yescharacteristic
237#331—21no—
238#331—21no—
239#328—21no—
240#327—21no—
241C2×C29—21no—
242C2×C29—21no—
243C2×C29—81no—
244C2×C29—162no—
245C2×C29#188311yescharacteristic
246C2×C29#190711yescharacteristic
247C2×C29#191011yescharacteristic
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C2×SD16—22no—
252C2×D8—22no—
253C2×M16—21no—
254C22×C8—21no—
255C22×C8D4×C2911yescharacteristic
256C22×C8D4×C2911yescharacteristic
257#127—21no—
258#127—21no—
259#127—21no—
260#127C2×C4×C2912yes—
261#126—21no—
262#125C2×C4×C2911yescharacteristic
263#124C2×C4×C2911yescharacteristic
264#123—21no—
265C22⋊Q8D4×C2911yescharacteristic
266#121D4×C2911yescharacteristic
267C4×Q8D4×C2911yescharacteristic
268C4×D4—21no—
269C4×D4D4×C2911yescharacteristic
270#117—21no—
271C2×C4⋊C4—21no—
272C2×C42—21no—
273C2×C42C23×C2911yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8D4×C2911yescharacteristic
281C4⋊C8D4×C2911yescharacteristic
282#102—22no—
283#102—22no—
284#102—42no—
285#102—42no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291#97—21no—
292#97—21no—
293#97—21no—
294#97C2×C4×C2912yes—
295C4×C8—21no—
296#95—21no—
297C29#937811yescharacteristic, direct product factor, Sylow
298C24—41no—
299C2×Q8C22⋊C4×C2911yescharacteristic
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—81no—
312C2×D4—81no—
313C2×D4—82no—
314C2×D4C22⋊C4×C2911yescharacteristic
315C22×C4—21no—
316C22×C4—41no—
317C22×C4C2×D4×C2911yescharacteristic
318C22×C4C2×D4×C2911yescharacteristic
319C22×C4#41×C2911yescharacteristic
320SD16—82no—
321D8—82no—
322M16—81no—
323C2×C8—22no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—81no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4C22⋊C4×C2911yescharacteristic
339C4⋊C4C22⋊C4×C2911yescharacteristic
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42—21no—
346C42—81no—
347C42C22×C4×C2911yescharacteristic
348C42C2×D4×C2911yescharacteristic
349C42C2×D4×C2911yescharacteristic
350C42#41×C2911yescharacteristic
351C23—21no—
352C23—42no—
353C23—81no—
354C23—81no—
355C23—81no—
356C23—81no—
357C23—81no—
358C23—81no—
359C23C29×#12111yescharacteristic
360Q8—41no—
361D4—41no—
362D4—42no—
363D4—42no—
364D4—42no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—82no—
369D4—82no—
370D4—82no—
371D4—81no—
372D4—81no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4C2×C22⋊C4×C2911yescharacteristic
387C2×C4C4×D4×C2911yescharacteristic
388C2×C4C4×D4×C2911yescharacteristic
389C2×C4C29×#12011yescharacteristic
390C2×C4C29×#12111yescharacteristic
391C2×C4C29×#12311yescharacteristic
392C8—42no—
393C8—41no—
394C8—41no—
395C8—41no—
396C8—41no—
397C8—81no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—161no—
407C22—161no—
408C22—161no—
409C22—161no—
410C22C29×#38611yescharacteristic
411C22C29×#47111yescharacteristic
412C22C29×#47211yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4C29×#45311yescharacteristic
423C4C29×#45411yescharacteristic
424C2—21no—
425C2—21no—
426C2—81no—
427C2—162no—
428C2C29×#188311yescharacteristic
429C2C29×#190711yescharacteristic
430C2C29×#191011yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3217C2
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×#2992C2semidirect
3. C29×#1982C2semidirect
4. C29×#1555C2semidirect
5. C29×#1509C2semidirect
6. C29×#1290C2semidirect
7. C29×#1285C2semidirect
10. C29×#496C4semidirect
11. C29×#490C4semidirect
135. #9378C29direct (N × H)
184. #2992C2×C29semidirect
185. #1982C2×C29semidirect
186. #1555C2×C29semidirect
187. #1509C2×C29semidirect
188. #1290C2×C29semidirect
189. #1285C2×C29semidirect
218. #496C4×C29semidirect
219. #490C4×C29semidirect
297. C29#9378direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32172
C29×#29922
C29×#19822
C29×#15552
C29×#15092
C29×#12902
C29×#12852
#937829