Finite Group Databasebeta

← C29×#9941 #20304841

Subgroups — C29×#9941 #20304841

Order 7424.

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

normal subgroups only

This group has 600 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×#3094C211yesmaximal, characteristic
2C29×#2591C211yesmaximal, characteristic
3C29×#2484C211yesmaximal, characteristic, complemented
4C29×#1826C211yesmaximal, characteristic, complemented
5C29×#1510C211yesmaximal, characteristic
6C29×#1463C211yesmaximal, characteristic, complemented
7C29×#1284C211yesmaximal, characteristic, complemented
8C2×C29×#121C2211yescharacteristic
9C2×C29×#117C2211yescharacteristic
10C22×C4⋊C4×C29C2211yescharacteristic
11C29×#482—22no—
12C29×#481—21no—
13C29×#480—21no—
14C29×#428—21no—
15C29×#418—21no—
16C29×#407C2211yescharacteristic
17C29×#407C2211yescharacteristic
18C29×#400—21no—
19C29×#400—21no—
20C29×#398—21no—
21C29×#394—21no—
22C29×#388—22no—
23C29×#387—22no—
24C29×#386—21no—
25C29×#386—21no—
26C29×#385—21no—
27C29×#381—21no—
28C29×#381C2211yescharacteristic
29C4×C22⋊C4×C29C2211yescharacteristic
30C29×#339—22no—
31C29×#327—22no—
32C29×#324—22no—
33C22×D4×C29—21no—
34C22×D4×C29D411yescharacteristic
35C23×C4×C29D411yescharacteristic
36C23×C4×C29D411yescharacteristic
37C23×C4×C29C2311yescharacteristic
38C2×M16×C29—21no—
39C2×M16×C29—21no—
40C29×#121—21no—
41C29×#121—21no—
42C29×#121—21no—
43C29×#121—21no—
44C29×#117—21no—
45C29×#117—21no—
46C29×#117—21no—
47C29×#117—21no—
48C2×C4⋊C4×C29—22no—
49C2×C4⋊C4×C29—21no—
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29—21no—
55C2×C4⋊C4×C29D411yescharacteristic
56C2×C4⋊C4×C29D411yescharacteristic
57C2×C4⋊C4×C29D411yescharacteristic
58C2×C22⋊C4×C29—22no—
59C2×C22⋊C4×C29—21no—
60C2×C22⋊C4×C29—21no—
61C2×C22⋊C4×C29—21no—
62C2×C22⋊C4×C29—21no—
63C2×C22⋊C4×C29—22no—
64C2×C42×C29—21no—
65C2×C42×C29D412yes—
66C29×#107—22no—
67C29×#106—22no—
68C29×#102—22no—
69C29×#102—22no—
70C29×C22⋊C8—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8D412yes—
74C29×#95—22no—
75C29×#95—22no—
76C29×#95—22no—
77C29×#95—22no—
78C29×#95—22no—
79C29×#95—21no—
80C29×#95—21no—
81C29×#95D412yes—
82C24×C29—21no—
83C24×C29C2×D411yescharacteristic
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—42no—
87C2×D4×C29—44no—
88C2×D4×C29—41no—
89C2×D4×C29—41no—
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29—22no—
96C22×C4×C29—21no—
97C22×C4×C29—22no—
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29—42no—
102C22×C4×C29—42no—
103C22×C4×C29—42no—
104C22×C4×C29C2×D411yescharacteristic
105C22×C4×C29C2×D411yescharacteristic
106C22×C4×C29C2×D411yescharacteristic
107C22×C4×C29C2×D411yescharacteristic
108C22×C4×C29C2×D411yescharacteristic
109C22×C4×C29#4111yescharacteristic
110M16×C29—42no—
111M16×C29—42no—
112C2×C8×C29—22no—
113C2×C8×C29—41no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—44no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29—41no—
123C4⋊C4×C29—41no—
124C4⋊C4×C29—41no—
125C22⋊C4×C29—44no—
126C22⋊C4×C29—42no—
127C22⋊C4×C29—42no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29—41no—
130C22⋊C4×C29—41no—
131C22⋊C4×C29—41no—
132C22⋊C4×C29—82no—
133C42×C29—42no—
134C42×C29—41no—
135C42×C29—41no—
136#9941C2911yesmaximal, characteristic, direct product factor, Sylow
137C23×C29—22no—
138C23×C29—22no—
139C23×C29—41no—
140C23×C29—42no—
141C23×C29—42no—
142C23×C29—41no—
143C23×C29—42no—
144C23×C29#12011yescharacteristic
145C23×C29#12011yescharacteristic
146C23×C29#12111yescharacteristic
147D4×C29—42no—
148D4×C29—81no—
149D4×C29—82no—
150D4×C29—82no—
151C2×C4×C29—22no—
152C2×C4×C29—22no—
153C2×C4×C29—22no—
154C2×C4×C29—22no—
155C2×C4×C29—22no—
156C2×C4×C29—41no—
157C2×C4×C29—41no—
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—42no—
166C2×C4×C29—42no—
167C2×C4×C29—42no—
168C2×C4×C29—42no—
169C2×C4×C29—42no—
170C2×C4×C29—42no—
171C2×C4×C29—41no—
172C2×C4×C29—41no—
173C2×C4×C29—41no—
174C2×C4×C29—41no—
175C2×C4×C29—42no—
176C2×C4×C29—42no—
177C2×C4×C29—42no—
178C2×C4×C29—42no—
179C2×C4×C29—81no—
180C2×C4×C29#12011yescharacteristic
181C2×C4×C29#12111yescharacteristic
182C2×C4×C29#12111yescharacteristic
183C2×C4×C29#12711yescharacteristic
184C8×C29—42no—
185C8×C29—81no—
186#3094C2×C2911yescharacteristic
187#2591C2×C2911yescharacteristic
188#2484C2×C2911yescharacteristic, complemented
189#1826C2×C2911yescharacteristic, complemented
190#1510C2×C2911yescharacteristic
191#1463C2×C2911yescharacteristic, complemented
192#1284C2×C2911yescharacteristic, complemented
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—21no—
197C22×C29—21no—
198C22×C29—21no—
199C22×C29—21no—
200C22×C29—44no—
201C22×C29—84no—
202C22×C29—81no—
203C22×C29—81no—
204C22×C29—81no—
205C22×C29#39211yescharacteristic
206C22×C29#45412yes—
207C22×C29#45812yes—
208C4×C29—21no—
209C4×C29—21no—
210C4×C29—21no—
211C4×C29—21no—
212C4×C29—42no—
213C4×C29—82no—
214C4×C29—82no—
215C4×C29—81no—
216C4×C29—81no—
217C4×C29—81no—
218C4×C29—81no—
219C2×#121C22×C2911yescharacteristic
220C2×#117C22×C2911yescharacteristic
221C22×C4⋊C4C22×C2911yescharacteristic
222#482—22no—
223#481—21no—
224#480—21no—
225#428—21no—
226#418—21no—
227#407C22×C2911yescharacteristic
228#407C22×C2911yescharacteristic
229#400—21no—
230#400—21no—
231#398—21no—
232#394—21no—
233#388—22no—
234#387—22no—
235#386—21no—
236#386—21no—
237#385—21no—
238#381—21no—
239#381C22×C2911yescharacteristic
240C4×C22⋊C4C22×C2911yescharacteristic
241#339—22no—
242#327—22no—
243#324—22no—
244C2×C29—22no—
245C2×C29—22no—
246C2×C29—41no—
247C2×C29—161no—
248C2×C29#200311yescharacteristic
249C2×C29#201011yescharacteristic
250C2×C29#202211yescharacteristic
251C22×D4—21no—
252C22×D4D4×C2911yescharacteristic
253C23×C4D4×C2911yescharacteristic
254C23×C4D4×C2911yescharacteristic
255C23×C4C23×C2911yescharacteristic
256C2×M16—21no—
257C2×M16—21no—
258#121—21no—
259#121—21no—
260#121—21no—
261#121—21no—
262#117—21no—
263#117—21no—
264#117—21no—
265#117—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4D4×C2911yescharacteristic
274C2×C4⋊C4D4×C2911yescharacteristic
275C2×C4⋊C4D4×C2911yescharacteristic
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—22no—
282C2×C42—21no—
283C2×C42D4×C2912yes—
284#107—22no—
285#106—22no—
286#102—22no—
287#102—22no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8D4×C2912yes—
292#95—22no—
293#95—22no—
294#95—22no—
295#95—22no—
296#95—22no—
297#95—21no—
298#95—21no—
299#95D4×C2912yes—
300C29#994111yescharacteristic, direct product factor, Sylow
301C24—21no—
302C24C2×D4×C2911yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—44no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4C2×D4×C2911yescharacteristic
324C22×C4C2×D4×C2911yescharacteristic
325C22×C4C2×D4×C2911yescharacteristic
326C22×C4C2×D4×C2911yescharacteristic
327C22×C4C2×D4×C2911yescharacteristic
328C22×C4#41×C2911yescharacteristic
329M16—42no—
330M16—42no—
331C2×C8—22no—
332C2×C8—41no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—44no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—44no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—82no—
352C42—42no—
353C42—41no—
354C42—41no—
355C23—22no—
356C23—22no—
357C23—41no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—41no—
362C23C29×#12011yescharacteristic
363C23C29×#12011yescharacteristic
364C23C29×#12111yescharacteristic
365D4—42no—
366D4—81no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4C29×#12011yescharacteristic
399C2×C4C29×#12111yescharacteristic
400C2×C4C29×#12111yescharacteristic
401C2×C4C29×#12711yescharacteristic
402C8—42no—
403C8—81no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22C29×#39211yescharacteristic
417C22C29×#45412yes—
418C22C29×#45812yes—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—82no—
425C4—82no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4—81no—
430C2—22no—
431C2—22no—
432C2—41no—
433C2—161no—
434C2C29×#200311yescharacteristic
435C2C29×#201011yescharacteristic
436C2C29×#202211yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#121C22
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
3. C29×#2484C2semidirect
4. C29×#1826C2semidirect
6. C29×#1463C2semidirect
7. C29×#1284C2semidirect
136. #9941C29direct (N × H)
188. #2484C2×C29semidirect
189. #1826C2×C29semidirect
191. #1463C2×C29semidirect
192. #1284C2×C29semidirect
300. C29#9941direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30942
C29×#25912
C29×#24842
C29×#18262
C29×#15102
C29×#14632
C29×#12842
#994129