Finite Group Databasebeta

← C29×#8434 #20303334

Subgroups — C29×#8434 #20303334

Order 7424.

760 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3506C211yesmaximal, characteristic
2C29×#1804C211yesmaximal, characteristic, complemented
3C29×#1542C211yesmaximal, characteristic, complemented
4C29×#1518C211yesmaximal, characteristic, complemented
5C29×#1517C211yesmaximal, characteristic, complemented
6C29×#1480C211yesmaximal, characteristic, complemented
7C29×#1478C211yesmaximal, characteristic, complemented
8C29×#559—22no—
9C29×#556C412yescomplemented
10C29×#555—21no—
11C29×#553—22no—
12C29×#550C412yescomplemented
13C29×#547—21no—
14C29×#538—22no—
15C29×#535—21no—
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C29×#525—22no—
19C29×#520—21no—
20C2×C4×D4×C29C2211yescharacteristic
21C29×#431C2211yescharacteristic
22C29×#431C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×#102—21no—
25C29×#382C2211yescharacteristic
26C29×#340—21no—
27C29×#333—21no—
28C29×#332—21no—
29C29×#328—22no—
30C29×#327—22no—
31C29×D4⋊C8—22no—
32C29×D4⋊C8—22no—
33C2×#41×C29—22no—
34C2×#41×C29—21no—
35C22×D4×C29D411yescharacteristic
36C23×C4×C29—21no—
37C22×C8×C29—21no—
38C29×C4⋊Q8C2×C411yescharacteristic
39C29×C4⋊Q8D411yescharacteristic
40C29×C4⋊Q8D411yescharacteristic
41C29×#127—22no—
42C29×#127C2×C411yescharacteristic
43C29×#126—24no—
44C29×#125—21no—
45C29×#124—24no—
46C29×#124—22no—
47C29×#124—21no—
48C29×#123—24no—
49C29×#123—24no—
50C29×C22⋊Q8—22no—
51C29×C22⋊Q8—21no—
52C29×C22⋊Q8D412yes—
53C29×#121—22no—
54C29×#121—22no—
55C29×#121—24no—
56C29×#121—21no—
57C29×#121—22no—
58C29×#121D412yes—
59C29×#120—24no—
60C4×Q8×C29—22no—
61C4×Q8×C29—21no—
62C4×Q8×C29C2×C412yes—
63C4×D4×C29—24no—
64C4×D4×C29—24no—
65C4×D4×C29—22no—
66C4×D4×C29—21no—
67C4×D4×C29—21no—
68C4×D4×C29—21no—
69C4×D4×C29C2×C412yes—
70C4×D4×C29D412yes—
71C4×D4×C29D412yes—
72C29×#117—22no—
73C29×#117—21no—
74C29×#117—22no—
75C2×C4⋊C4×C29—22no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29D411yescharacteristic
78C2×C22⋊C4×C29—21no—
79C2×C42×C29C2311yescharacteristic
80C29×C4⋊C8—21no—
81C29×C4⋊C8—21no—
82C29×C4⋊C8—21no—
83C29×C4⋊C8—21no—
84C29×#102—42no—
85C29×C22⋊C8—21no—
86C29×C22⋊C8—21no—
87C4×C8×C29—21no—
88C4×C8×C29—21no—
89C29×#95—21no—
90C29×#95—21no—
91C24×C29—21no—
92#41×C29—41no—
93#41×C29—41no—
94#41×C29—41no—
95#41×C29—41no—
96#41×C29—84no—
97C2×Q8×C29—21no—
98C2×Q8×C29—21no—
99C2×Q8×C29C22⋊C412yes—
100C2×D4×C29—22no—
101C2×D4×C29—24no—
102C2×D4×C29—24no—
103C2×D4×C29—21no—
104C2×D4×C29—21no—
105C2×D4×C29—21no—
106C2×D4×C29—21no—
107C2×D4×C29—21no—
108C2×D4×C29—21no—
109C2×D4×C29—21no—
110C2×D4×C29C22⋊C412yes—
111C2×D4×C29C22⋊C412yes—
112C22×C4×C29—24no—
113C22×C4×C29—21no—
114C22×C4×C29—22no—
115C22×C4×C29—22no—
116C22×C4×C29—22no—
117C22×C4×C29—41no—
118C22×C4×C29—82no—
119C22×C4×C29C2×D411yescharacteristic
120C22×C4×C29C2×D411yescharacteristic
121C22×C4×C29C2×D411yescharacteristic
122C2×C8×C29—41no—
123C2×C8×C29—41no—
124C2×C8×C29—41no—
125C2×C8×C29—41no—
126C2×C8×C29—41no—
127C4⋊C4×C29—24no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—22no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—21no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—22no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—41no—
136C4⋊C4×C29—41no—
137C4⋊C4×C29C22⋊C412yes—
138C4⋊C4×C29C22⋊C412yes—
139C4⋊C4×C29C22⋊C412yes—
140C22⋊C4×C29—24no—
141C22⋊C4×C29—24no—
142C22⋊C4×C29—24no—
143C22⋊C4×C29—22no—
144C22⋊C4×C29—22no—
145C22⋊C4×C29—22no—
146C22⋊C4×C29—22no—
147C22⋊C4×C29—22no—
148C42×C29—24no—
149C42×C29—22no—
150C42×C29C22×C411yescharacteristic
151C42×C29C2×D411yescharacteristic
152C42×C29C2×D411yescharacteristic
153C42×C29C2×D411yescharacteristic
154#8434C2911yesmaximal, characteristic, direct product factor, Sylow
155C23×C29—22no—
156C23×C29—22no—
157C23×C29—41no—
158C23×C29—41no—
159C23×C29—81no—
160C23×C29—81no—
161C23×C29#12011yescharacteristic
162Q8×C29—42no—
163Q8×C29—41no—
164Q8×C29—41no—
165Q8×C29—81no—
166D4×C29—22no—
167D4×C29—22no—
168D4×C29—42no—
169D4×C29—42no—
170D4×C29—42no—
171D4×C29—42no—
172D4×C29—41no—
173D4×C29—41no—
174D4×C29—41no—
175D4×C29—41no—
176D4×C29—84no—
177D4×C29—84no—
178C2×C4×C29—22no—
179C2×C4×C29—22no—
180C2×C4×C29—22no—
181C2×C4×C29—22no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—44no—
185C2×C4×C29—42no—
186C2×C4×C29—42no—
187C2×C4×C29—82no—
188C2×C4×C29—81no—
189C2×C4×C29—84no—
190C2×C4×C29—81no—
191C2×C4×C29—81no—
192C2×C4×C29—81no—
193C2×C4×C29C2×C22⋊C411yescharacteristic
194C2×C4×C29C2×C22⋊C411yescharacteristic
195C2×C4×C29C2×C22⋊C411yescharacteristic
196C2×C4×C29#12011yescharacteristic
197C2×C4×C29#12011yescharacteristic
198C2×C4×C29#12011yescharacteristic
199C2×C4×C29#13511yescharacteristic
200C2×C4×C29#13511yescharacteristic
201C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C29#13711yescharacteristic
203C8×C29—81no—
204C8×C29—81no—
205C8×C29—81no—
206#3506C2×C2911yescharacteristic
207#1804C2×C2911yescharacteristic, complemented
208#1542C2×C2911yescharacteristic, complemented
209#1518C2×C2911yescharacteristic, complemented
210#1517C2×C2911yescharacteristic, complemented
211#1480C2×C2911yescharacteristic, complemented
212#1478C2×C2911yescharacteristic, complemented
213C22×C29—21no—
214C22×C29—21no—
215C22×C29—42no—
216C22×C29—42no—
217C22×C29—42no—
218C22×C29—42no—
219C22×C29—42no—
220C22×C29—42no—
221C22×C29—82no—
222C22×C29—82no—
223C22×C29#37911yescharacteristic
224C22×C29#44911yescharacteristic
225C22×C29#45211yescharacteristic
226C4×C29—21no—
227C4×C29—21no—
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—42no—
231C4×C29—42no—
232C4×C29—42no—
233C4×C29—42no—
234C4×C29—161no—
235C4×C29#41611yescharacteristic
236C4×C29#41711yescharacteristic
237C4×C29#44911yescharacteristic
238C4×C29#45211yescharacteristic
239#559—22no—
240#556C4×C2912yescomplemented
241#555—21no—
242#553—22no—
243#550C4×C2912yescomplemented
244#547—21no—
245#538—22no—
246#535—21no—
247#533C22×C2911yescharacteristic
248#532C22×C2911yescharacteristic
249#525—22no—
250#520—21no—
251C2×C4×D4C22×C2911yescharacteristic
252#431C22×C2911yescharacteristic
253#431C22×C2911yescharacteristic
254C2×C4⋊C8C22×C2911yescharacteristic
255C2×#102—21no—
256#382C22×C2911yescharacteristic
257#340—21no—
258#333—21no—
259#332—21no—
260#328—22no—
261#327—22no—
262D4⋊C8—22no—
263D4⋊C8—22no—
264C2×C29—21no—
265C2×C29—21no—
266C2×C29—82no—
267C2×C29—82no—
268C2×C29#178811yescharacteristic
269C2×C29#179411yescharacteristic
270C2×C29#179511yescharacteristic
271C2×#41—22no—
272C2×#41—21no—
273C22×D4D4×C2911yescharacteristic
274C23×C4—21no—
275C22×C8—21no—
276C4⋊Q8C2×C4×C2911yescharacteristic
277C4⋊Q8D4×C2911yescharacteristic
278C4⋊Q8D4×C2911yescharacteristic
279#127—22no—
280#127C2×C4×C2911yescharacteristic
281#126—24no—
282#125—21no—
283#124—24no—
284#124—22no—
285#124—21no—
286#123—24no—
287#123—24no—
288C22⋊Q8—22no—
289C22⋊Q8—21no—
290C22⋊Q8D4×C2912yes—
291#121—22no—
292#121—22no—
293#121—24no—
294#121—21no—
295#121—22no—
296#121D4×C2912yes—
297#120—24no—
298C4×Q8—22no—
299C4×Q8—21no—
300C4×Q8C2×C4×C2912yes—
301C4×D4—24no—
302C4×D4—24no—
303C4×D4—22no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4C2×C4×C2912yes—
308C4×D4D4×C2912yes—
309C4×D4D4×C2912yes—
310#117—22no—
311#117—21no—
312#117—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4D4×C2911yescharacteristic
316C2×C22⋊C4—21no—
317C2×C42C23×C2911yescharacteristic
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322#102—42no—
323C22⋊C8—21no—
324C22⋊C8—21no—
325C4×C8—21no—
326C4×C8—21no—
327#95—21no—
328#95—21no—
329C29#843411yescharacteristic, direct product factor, Sylow
330C24—21no—
331#41—41no—
332#41—41no—
333#41—41no—
334#41—41no—
335#41—84no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8C22⋊C4×C2912yes—
339C2×D4—22no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4C22⋊C4×C2912yes—
350C2×D4C22⋊C4×C2912yes—
351C22×C4—24no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—41no—
357C22×C4—82no—
358C22×C4C2×D4×C2911yescharacteristic
359C22×C4C2×D4×C2911yescharacteristic
360C22×C4C2×D4×C2911yescharacteristic
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C22⋊C4×C2912yes—
377C4⋊C4C22⋊C4×C2912yes—
378C4⋊C4C22⋊C4×C2912yes—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—24no—
388C42—22no—
389C42C22×C4×C2911yescharacteristic
390C42C2×D4×C2911yescharacteristic
391C42C2×D4×C2911yescharacteristic
392C42C2×D4×C2911yescharacteristic
393C23—22no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—81no—
398C23—81no—
399C23C29×#12011yescharacteristic
400Q8—42no—
401Q8—41no—
402Q8—41no—
403Q8—81no—
404D4—22no—
405D4—22no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—84no—
415D4—84no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—82no—
426C2×C4—81no—
427C2×C4—84no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4C2×C22⋊C4×C2911yescharacteristic
432C2×C4C2×C22⋊C4×C2911yescharacteristic
433C2×C4C2×C22⋊C4×C2911yescharacteristic
434C2×C4C29×#12011yescharacteristic
435C2×C4C29×#12011yescharacteristic
436C2×C4C29×#12011yescharacteristic
437C2×C4C29×#13511yescharacteristic
438C2×C4C29×#13511yescharacteristic
439C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
440C2×C4C29×#13711yescharacteristic
441C8—81no—
442C8—81no—
443C8—81no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—82no—
453C22—82no—
454C22C29×#37911yescharacteristic
455C22C29×#44911yescharacteristic
456C22C29×#45211yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—161no—
466C4C29×#41611yescharacteristic
467C4C29×#41711yescharacteristic
468C4C29×#44911yescharacteristic
469C4C29×#45211yescharacteristic
470C2—21no—
471C2—21no—
472C2—82no—
473C2—82no—
474C2C29×#178811yescharacteristic
475C2C29×#179411yescharacteristic
476C2C29×#179511yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3506C2
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×#1804C2semidirect
3. C29×#1542C2semidirect
4. C29×#1518C2semidirect
5. C29×#1517C2semidirect
6. C29×#1480C2semidirect
7. C29×#1478C2semidirect
9. C29×#556C4semidirect
12. C29×#550C4semidirect
154. #8434C29direct (N × H)
207. #1804C2×C29semidirect
208. #1542C2×C29semidirect
209. #1518C2×C29semidirect
210. #1517C2×C29semidirect
211. #1480C2×C29semidirect
212. #1478C2×C29semidirect
240. #556C4×C29semidirect
243. #550C4×C29semidirect
329. C29#8434direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35062
C29×#18042
C29×#15422
C29×#15182
C29×#15172
C29×#14802
C29×#14782
#843429