Finite Group Databasebeta

← C29×#9937 #20304837

Subgroups — C29×#9937 #20304837

Order 7424.

526 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3195C211yesmaximal, characteristic
2C29×#3095C211yesmaximal, characteristic
3C29×#2625C211yesmaximal, characteristic
4C29×#1996C211yesmaximal, characteristic
5C29×#1826C211yesmaximal, characteristic
6C29×#1508C211yesmaximal, characteristic
7C29×#1305C211yesmaximal, characteristic
8C2×C29×C22⋊Q8C2211yescharacteristic
9C2×C29×C22⋊Q8C2211yescharacteristic
10C2×C29×#117C2211yescharacteristic
11C29×#485—22no—
12C29×#484—21no—
13C29×#483—21no—
14C29×#483—21no—
15C29×#483—21no—
16C29×#470—22no—
17C29×#451—21no—
18C29×#451—21no—
19C29×#428—21no—
20C29×#419—21no—
21C29×#407C2211yescharacteristic
22C29×#407C2211yescharacteristic
23C29×#400—21no—
24C29×#398—21no—
25C29×#397—22no—
26C29×#391—21no—
27C29×#389—21no—
28C29×#380C2211yescharacteristic
29C4×C22⋊C4×C29C2211yescharacteristic
30C29×#342—22no—
31C29×#339—22no—
32C29×#328—22no—
33C22×Q8×C29D411yescharacteristic
34C22×Q8×C29D411yescharacteristic
35C23×C4×C29C2311yescharacteristic
36C2×Q16×C29—22no—
37C2×M16×C29—21no—
38C2×M16×C29D412yes—
39C29×C22⋊Q8—21no—
40C29×C22⋊Q8—21no—
41C29×C22⋊Q8—21no—
42C29×C22⋊Q8—21no—
43C29×C22⋊Q8—21no—
44C29×C22⋊Q8—21no—
45C29×C22⋊Q8—21no—
46C29×C22⋊Q8—21no—
47C29×#117—21no—
48C29×#117—21no—
49C29×#117—21no—
50C29×#117—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29—22no—
55C2×C4⋊C4×C29D411yescharacteristic
56C2×C4⋊C4×C29D411yescharacteristic
57C2×C4⋊C4×C29D411yescharacteristic
58C2×C4⋊C4×C29D411yescharacteristic
59C2×C22⋊C4×C29—21no—
60C2×C22⋊C4×C29—21no—
61C2×C22⋊C4×C29—21no—
62C2×C22⋊C4×C29—21no—
63C2×C22⋊C4×C29D412yes—
64C2×C42×C29—21no—
65C2×C42×C29—21no—
66C29×#107—22no—
67C29×#106—22no—
68C29×#106—22no—
69C29×#103—22no—
70C29×#103—22no—
71C29×#103—22no—
72C29×#103—22no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8—21no—
76C29×C22⋊C8D412yes—
77C29×#95—22no—
78C29×#95—22no—
79C29×#95—22no—
80C29×#95—21no—
81C29×#95—21no—
82C24×C29C2×D411yescharacteristic
83C2×Q8×C29—21no—
84C2×Q8×C29—21no—
85C2×Q8×C29—21no—
86C2×Q8×C29—21no—
87C2×Q8×C29—42no—
88C2×Q8×C29—42no—
89C22×C4×C29—21no—
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—22no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—42no—
97C22×C4×C29—41no—
98C22×C4×C29C2×D411yescharacteristic
99C22×C4×C29C2×D411yescharacteristic
100C22×C4×C29C2×D411yescharacteristic
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29#4111yescharacteristic
104Q16×C29—82no—
105M16×C29—42no—
106M16×C29—42no—
107C2×C8×C29—22no—
108C2×C8×C29—22no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—42no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29—41no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29—82no—
123C22⋊C4×C29—22no—
124C22⋊C4×C29—41no—
125C22⋊C4×C29—41no—
126C22⋊C4×C29—41no—
127C22⋊C4×C29—41no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29—41no—
130C22⋊C4×C29—41no—
131C22⋊C4×C29—42no—
132C42×C29—42no—
133C42×C29—41no—
134C42×C29—41no—
135#9937C2911yesmaximal, characteristic, direct product factor, Sylow
136C23×C29—21no—
137C23×C29—21no—
138C23×C29—41no—
139C23×C29—41no—
140C23×C29#12011yescharacteristic
141C23×C29#12111yescharacteristic
142C23×C29#12711yescharacteristic
143Q8×C29—42no—
144Q8×C29—42no—
145Q8×C29—42no—
146Q8×C29—81no—
147C2×C4×C29—22no—
148C2×C4×C29—22no—
149C2×C4×C29—22no—
150C2×C4×C29—41no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—42no—
154C2×C4×C29—42no—
155C2×C4×C29—42no—
156C2×C4×C29—42no—
157C2×C4×C29—42no—
158C2×C4×C29—41no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—41no—
164C2×C4×C29—42no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—81no—
170C2×C4×C29—81no—
171C2×C4×C29—81no—
172C2×C4×C29—81no—
173C2×C4×C29#12011yescharacteristic
174C2×C4×C29#12011yescharacteristic
175C2×C4×C29#12111yescharacteristic
176C2×C4×C29#12111yescharacteristic
177C8×C29—42no—
178C8×C29—42no—
179#3195C2×C2911yescharacteristic
180#3095C2×C2911yescharacteristic
181#2625C2×C2911yescharacteristic
182#1996C2×C2911yescharacteristic
183#1826C2×C2911yescharacteristic
184#1508C2×C2911yescharacteristic
185#1305C2×C2911yescharacteristic
186C22×C29—21no—
187C22×C29—21no—
188C22×C29—21no—
189C22×C29—21no—
190C22×C29—21no—
191C22×C29—21no—
192C22×C29—21no—
193C22×C29—21no—
194C22×C29—81no—
195C22×C29—81no—
196C22×C29#39211yescharacteristic
197C22×C29#45511yescharacteristic
198C22×C29#45611yescharacteristic
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—82no—
203C4×C29—82no—
204C4×C29—81no—
205C4×C29—81no—
206C4×C29—81no—
207C4×C29—81no—
208C4×C29—81no—
209C4×C29—81no—
210C4×C29#45812yes—
211C2×C22⋊Q8C22×C2911yescharacteristic
212C2×C22⋊Q8C22×C2911yescharacteristic
213C2×#117C22×C2911yescharacteristic
214#485—22no—
215#484—21no—
216#483—21no—
217#483—21no—
218#483—21no—
219#470—22no—
220#451—21no—
221#451—21no—
222#428—21no—
223#419—21no—
224#407C22×C2911yescharacteristic
225#407C22×C2911yescharacteristic
226#400—21no—
227#398—21no—
228#397—22no—
229#391—21no—
230#389—21no—
231#380C22×C2911yescharacteristic
232C4×C22⋊C4C22×C2911yescharacteristic
233#342—22no—
234#339—22no—
235#328—22no—
236C2×C29—21no—
237C2×C29—21no—
238C2×C29—41no—
239C2×C29—41no—
240C2×C29#200711yescharacteristic
241C2×C29#200911yescharacteristic
242C2×C29#202211yescharacteristic
243C22×Q8D4×C2911yescharacteristic
244C22×Q8D4×C2911yescharacteristic
245C23×C4C23×C2911yescharacteristic
246C2×Q16—22no—
247C2×M16—21no—
248C2×M16D4×C2912yes—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257#117—21no—
258#117—21no—
259#117—21no—
260#117—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4D4×C2911yescharacteristic
266C2×C4⋊C4D4×C2911yescharacteristic
267C2×C4⋊C4D4×C2911yescharacteristic
268C2×C4⋊C4D4×C2911yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4D4×C2912yes—
274C2×C42—21no—
275C2×C42—21no—
276#107—22no—
277#106—22no—
278#106—22no—
279#103—22no—
280#103—22no—
281#103—22no—
282#103—22no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8D4×C2912yes—
287#95—22no—
288#95—22no—
289#95—22no—
290#95—21no—
291#95—21no—
292C29#993711yescharacteristic, direct product factor, Sylow
293C24C2×D4×C2911yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×Q8—42no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4C2×D4×C2911yescharacteristic
310C22×C4C2×D4×C2911yescharacteristic
311C22×C4C2×D4×C2911yescharacteristic
312C22×C4C2×D4×C2911yescharacteristic
313C22×C4C2×D4×C2911yescharacteristic
314C22×C4#41×C2911yescharacteristic
315Q16—82no—
316M16—42no—
317M16—42no—
318C2×C8—22no—
319C2×C8—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—82no—
334C22⋊C4—22no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C42—42no—
344C42—41no—
345C42—41no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23C29×#12011yescharacteristic
351C23C29×#12111yescharacteristic
352C23C29×#12711yescharacteristic
353Q8—42no—
354Q8—42no—
355Q8—42no—
356Q8—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C29×#12011yescharacteristic
384C2×C4C29×#12011yescharacteristic
385C2×C4C29×#12111yescharacteristic
386C2×C4C29×#12111yescharacteristic
387C8—42no—
388C8—42no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22C29×#39211yescharacteristic
400C22C29×#45511yescharacteristic
401C22C29×#45611yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—82no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4C29×#45812yes—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2C29×#200711yescharacteristic
419C2C29×#200911yescharacteristic
420C2C29×#202211yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC23×C4C23×C29
prime radicalC24×C29C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
135. #9937C29direct (N × H)
292. C29#9937direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31952
C29×#30952
C29×#26252
C29×#19962
C29×#18262
C29×#15082
C29×#13052
#993729