Finite Group Databasebeta

← C29×#9956 #20304856

Subgroups — C29×#9956 #20304856

Order 7424.

770 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3187C211yesmaximal, characteristic
2C2×C29×#451C211yesmaximal, characteristic, complemented
3C29×#2436C211yesmaximal, characteristic
4C29×#1996C211yesmaximal, characteristic, complemented
5C29×#1787C211yesmaximal, characteristic, complemented
6C29×#1519C211yesmaximal, characteristic
7C29×#1282C211yesmaximal, characteristic, complemented
8C23×Q8×C29C2211yescharacteristic
9C22×Q16×C29—21no—
10C2×C29×#124—21no—
11C2×C29×C22⋊Q8C2211yescharacteristic
12C2×C29×#121C2211yescharacteristic
13C29×#483—21no—
14C29×#481—21no—
15C29×#465—22no—
16C29×#451—22no—
17C29×#451—22no—
18C29×#450—21no—
19C29×#448—21no—
20C2×C29×#103—22no—
21C2×C29×#103—21no—
22C2×C29×C22⋊C8C2211yescharacteristic
23C2×C29×C22⋊C8C2211yescharacteristic
24C29×#393—22no—
25C29×#391—21no—
26C29×#386—22no—
27C29×#380C2211yescharacteristic
28C4×C22⋊C4×C29C2211yescharacteristic
29C29×#342—22no—
30C29×#327—22no—
31C22×Q8×C29—21no—
32C22×Q8×C29—21no—
33C22×Q8×C29—21no—
34C22×Q8×C29—21no—
35C22×Q8×C29—21no—
36C22×Q8×C29—44no—
37C22×Q8×C29D411yescharacteristic
38C22×Q8×C29D412yes—
39C22×D4×C29—21no—
40C22×D4×C29D411yescharacteristic
41C23×C4×C29—21no—
42C23×C4×C29C2311yescharacteristic
43C2×Q16×C29—24no—
44C2×Q16×C29—44no—
45C2×SD16×C29—22no—
46C22×C8×C29—21no—
47C22×C8×C29D412yes—
48C29×#124—44no—
49C29×C22⋊Q8—21no—
50C29×C22⋊Q8—21no—
51C29×C22⋊Q8—21no—
52C29×C22⋊Q8—21no—
53C29×#121—21no—
54C29×#121—21no—
55C29×#121—21no—
56C29×#121—21no—
57C2×C4⋊C4×C29—21no—
58C2×C4⋊C4×C29—21no—
59C2×C4⋊C4×C29D411yescharacteristic
60C2×C4⋊C4×C29D411yescharacteristic
61C2×C22⋊C4×C29—24no—
62C2×C22⋊C4×C29—21no—
63C2×C22⋊C4×C29—21no—
64C2×C22⋊C4×C29—21no—
65C2×C22⋊C4×C29D412yes—
66C2×C42×C29—21no—
67C29×#106—22no—
68C29×#103—22no—
69C29×#103—24no—
70C29×#103—44no—
71C29×#102—22no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8D412yes—
76C29×#95—24no—
77C29×#95—21no—
78C29×#95—21no—
79C24×C29—21no—
80C24×C29C2×D411yescharacteristic
81C2×Q8×C29—24no—
82C2×Q8×C29—24no—
83C2×Q8×C29—24no—
84C2×Q8×C29—22no—
85C2×Q8×C29—21no—
86C2×Q8×C29—21no—
87C2×Q8×C29—22no—
88C2×Q8×C29—44no—
89C2×Q8×C29—42no—
90C2×Q8×C29—42no—
91C2×Q8×C29—42no—
92C2×Q8×C29—42no—
93C2×Q8×C29—44no—
94C2×Q8×C29—44no—
95C2×Q8×C29—41no—
96C2×Q8×C29—41no—
97C2×D4×C29—21no—
98C2×D4×C29—21no—
99C2×D4×C29—42no—
100C2×D4×C29—41no—
101C2×D4×C29—41no—
102C2×D4×C29—42no—
103C2×D4×C29—42no—
104C22×C4×C29—22no—
105C22×C4×C29—22no—
106C22×C4×C29—21no—
107C22×C4×C29—21no—
108C22×C4×C29—21no—
109C22×C4×C29—42no—
110C22×C4×C29—44no—
111C22×C4×C29—41no—
112C22×C4×C29—41no—
113C22×C4×C29—41no—
114C22×C4×C29C2×D411yescharacteristic
115C22×C4×C29C2×D411yescharacteristic
116C22×C4×C29C2×D411yescharacteristic
117C22×C4×C29C2×D411yescharacteristic
118C22×C4×C29C2×D411yescharacteristic
119C22×C4×C29#4111yescharacteristic
120Q16×C29—48no—
121SD16×C29—82no—
122C2×C8×C29—22no—
123C2×C8×C29—22no—
124C2×C8×C29—42no—
125C2×C8×C29—42no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—21no—
130C4⋊C4×C29—42no—
131C4⋊C4×C29—41no—
132C4⋊C4×C29—41no—
133C22⋊C4×C29—22no—
134C22⋊C4×C29—22no—
135C22⋊C4×C29—48no—
136C22⋊C4×C29—41no—
137C22⋊C4×C29—41no—
138C22⋊C4×C29—41no—
139C22⋊C4×C29—41no—
140C22⋊C4×C29—42no—
141C42×C29—42no—
142#9956C2911yesmaximal, characteristic, direct product factor, Sylow
143C23×C29—41no—
144C23×C29—41no—
145C23×C29—42no—
146C23×C29—42no—
147C23×C29—41no—
148C23×C29—42no—
149C23×C29#12011yescharacteristic
150C23×C29#12111yescharacteristic
151C23×C29#12711yescharacteristic
152C23×C29#13512yes—
153C23×C29#13712yes—
154Q8×C29—24no—
155Q8×C29—24no—
156Q8×C29—42no—
157Q8×C29—44no—
158Q8×C29—42no—
159Q8×C29—42no—
160Q8×C29—44no—
161Q8×C29—42no—
162D4×C29—42no—
163D4×C29—81no—
164D4×C29—82no—
165D4×C29—81no—
166D4×C29—81no—
167C2×C4×C29—22no—
168C2×C4×C29—22no—
169C2×C4×C29—22no—
170C2×C4×C29—24no—
171C2×C4×C29—41no—
172C2×C4×C29—41no—
173C2×C4×C29—41no—
174C2×C4×C29—42no—
175C2×C4×C29—44no—
176C2×C4×C29—44no—
177C2×C4×C29—42no—
178C2×C4×C29—42no—
179C2×C4×C29—42no—
180C2×C4×C29—41no—
181C2×C4×C29—41no—
182C2×C4×C29—41no—
183C2×C4×C29—42no—
184C2×C4×C29—42no—
185C2×C4×C29—81no—
186C2×C4×C29—81no—
187C2×C4×C29—81no—
188C2×C4×C29—81no—
189C2×C4×C29—81no—
190C2×C4×C29#12011yescharacteristic
191C2×C4×C29#12011yescharacteristic
192C2×C4×C29#12111yescharacteristic
193C2×C4×C29#12111yescharacteristic
194C8×C29—42no—
195C8×C29—42no—
196#3187C2×C2911yescharacteristic
197C2×#451C2×C2911yescharacteristic, complemented
198#2436C2×C2911yescharacteristic
199#1996C2×C2911yescharacteristic, complemented
200#1787C2×C2911yescharacteristic, complemented
201#1519C2×C2911yescharacteristic
202#1282C2×C2911yescharacteristic, complemented
203C22×C29—21no—
204C22×C29—21no—
205C22×C29—21no—
206C22×C29—21no—
207C22×C29—21no—
208C22×C29—21no—
209C22×C29—42no—
210C22×C29—42no—
211C22×C29—84no—
212C22×C29—81no—
213C22×C29—81no—
214C22×C29—81no—
215C22×C29#39211yescharacteristic
216C22×C29#45212yes—
217C22×C29#46412yes—
218C22×C29#49511yescharacteristic
219C22×C29#49711yescharacteristic
220C4×C29—21no—
221C4×C29—21no—
222C4×C29—21no—
223C4×C29—44no—
224C4×C29—82no—
225C4×C29—81no—
226C4×C29—81no—
227C4×C29—81no—
228C4×C29—161no—
229C4×C29B(4,𝔽2)12yes—
230C23×Q8C22×C2911yescharacteristic
231C22×Q16—21no—
232C2×#124—21no—
233C2×C22⋊Q8C22×C2911yescharacteristic
234C2×#121C22×C2911yescharacteristic
235#483—21no—
236#481—21no—
237#465—22no—
238#451—22no—
239#451—22no—
240#450—21no—
241#448—21no—
242C2×#103—21no—
243C2×#103—22no—
244C2×C22⋊C8C22×C2911yescharacteristic
245C2×C22⋊C8C22×C2911yescharacteristic
246#393—22no—
247#391—21no—
248#386—22no—
249#380C22×C2911yescharacteristic
250C4×C22⋊C4C22×C2911yescharacteristic
251#342—22no—
252#327—22no—
253C2×C29—22no—
254C2×C29—21no—
255C2×C29—22no—
256C2×C29—21no—
257C2×C29—161no—
258C2×C29#200911yescharacteristic
259C2×C29#201511yescharacteristic
260C2×C29#202111yescharacteristic
261C22×Q8—21no—
262C22×Q8—21no—
263C22×Q8—21no—
264C22×Q8—21no—
265C22×Q8—21no—
266C22×Q8—44no—
267C22×Q8D4×C2911yescharacteristic
268C22×Q8D4×C2912yes—
269C22×D4—21no—
270C22×D4D4×C2911yescharacteristic
271C23×C4—21no—
272C23×C4C23×C2911yescharacteristic
273C2×Q16—24no—
274C2×Q16—44no—
275C2×SD16—22no—
276C22×C8—21no—
277C22×C8D4×C2912yes—
278#124—44no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283#121—21no—
284#121—21no—
285#121—21no—
286#121—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4D4×C2911yescharacteristic
290C2×C4⋊C4D4×C2911yescharacteristic
291C2×C22⋊C4—24no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4D4×C2912yes—
296C2×C42—21no—
297#106—22no—
298#103—24no—
299#103—22no—
300#103—44no—
301#102—22no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8D4×C2912yes—
306#95—24no—
307#95—21no—
308#95—21no—
309C29#995611yescharacteristic, direct product factor, Sylow
310C24—21no—
311C24C2×D4×C2911yescharacteristic
312C2×Q8—24no—
313C2×Q8—24no—
314C2×Q8—24no—
315C2×Q8—22no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—44no—
320C2×Q8—42no—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8—44no—
325C2×Q8—44no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—42no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—44no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4C2×D4×C2911yescharacteristic
346C22×C4C2×D4×C2911yescharacteristic
347C22×C4C2×D4×C2911yescharacteristic
348C22×C4C2×D4×C2911yescharacteristic
349C22×C4C2×D4×C2911yescharacteristic
350C22×C4#41×C2911yescharacteristic
351Q16—48no—
352SD16—82no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—42no—
356C2×C8—42no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—42no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—48no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—42no—
372C42—42no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—41no—
379C23C29×#12011yescharacteristic
380C23C29×#12111yescharacteristic
381C23C29×#12711yescharacteristic
382C23C29×#13512yes—
383C23C29×#13712yes—
384Q8—24no—
385Q8—24no—
386Q8—42no—
387Q8—44no—
388Q8—42no—
389Q8—42no—
390Q8—44no—
391Q8—42no—
392D4—42no—
393D4—81no—
394D4—82no—
395D4—81no—
396D4—81no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4C29×#12011yescharacteristic
421C2×C4C29×#12011yescharacteristic
422C2×C4C29×#12111yescharacteristic
423C2×C4C29×#12111yescharacteristic
424C8—42no—
425C8—42no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—42no—
433C22—42no—
434C22—84no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22C29×#39211yescharacteristic
439C22C29×#45212yes—
440C22C29×#46412yes—
441C22C29×#49511yescharacteristic
442C22C29×#49711yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—44no—
447C4—82no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—161no—
452C4C29×B(4,𝔽2)12yes—
453C2—22no—
454C2—21no—
455C2—22no—
456C2—21no—
457C2—161no—
458C2C29×#200911yescharacteristic
459C2C29×#201511yescharacteristic
460C2C29×#202111yescharacteristic
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
2. C2×C29×#451C2semidirect
4. C29×#1996C2semidirect
5. C29×#1787C2semidirect
7. C29×#1282C2semidirect
142. #9956C29direct (N × H)
197. C2×#451C2×C29semidirect
199. #1996C2×C29semidirect
200. #1787C2×C29semidirect
202. #1282C2×C29semidirect
309. C29#9956direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31872
C2×C29×#4512
C29×#24362
C29×#19962
C29×#17872
C29×#15192
C29×#12822
#995629