Finite Group Databasebeta

← C29×#8358 #20303258

Subgroups — C29×#8358 #20303258

Order 7424.

794 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3506C211yesmaximal, characteristic
2C29×#1954C211yesmaximal, characteristic, complemented
3C29×#1800C211yesmaximal, characteristic, complemented
4C29×#1550C211yesmaximal, characteristic, complemented
5C29×#1547C211yesmaximal, characteristic, complemented
6C29×#1493C211yesmaximal, characteristic, complemented
7C29×#1492C211yesmaximal, characteristic, complemented
8C29×#559—22no—
9C29×#556—21no—
10C29×#555—21no—
11C29×#553—22no—
12C29×#550—21no—
13C29×#547—21no—
14C29×#538C414yes—
15C29×#535—21no—
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C29×#525—22no—
19C29×#520—21no—
20C2×C4×D4×C29C2211yescharacteristic
21C29×#423C2211yescharacteristic
22C29×#423C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×#100—21no—
25C2×C29×C22⋊C8—22no—
26C2×C4×C8×C29C2211yescharacteristic
27C29×#343—21no—
28C29×#333—21no—
29C29×#332—21no—
30C29×#332—21no—
31C29×#331—21no—
32C29×Q8⋊C8—22no—
33C29×D4⋊C8—22no—
34C2×#41×C29—22no—
35C2×#41×C29—21no—
36C22×D4×C29D411yescharacteristic
37C23×C4×C29D412yes—
38C2×M16×C29—21no—
39C2×M16×C29—21no—
40C22×C8×C29—21no—
41C22×C8×C29—21no—
42C29×C4⋊Q8D411yescharacteristic
43C29×C4⋊Q8D411yescharacteristic
44C29×C4⋊Q8D411yescharacteristic
45C29×#127—22no—
46C29×#127D411yescharacteristic
47C29×#126—24no—
48C29×#125—21no—
49C29×#124—22no—
50C29×#124—24no—
51C29×#124—21no—
52C29×#123—24no—
53C29×#123—24no—
54C29×C22⋊Q8—22no—
55C29×C22⋊Q8—21no—
56C29×C22⋊Q8C2×C412yes—
57C29×#121—22no—
58C29×#121—22no—
59C29×#121—22no—
60C29×#121—24no—
61C29×#121—21no—
62C29×#121C2×C412yes—
63C29×#120—24no—
64C4×Q8×C29—22no—
65C4×Q8×C29—21no—
66C4×Q8×C29D412yes—
67C4×D4×C29—22no—
68C4×D4×C29—24no—
69C4×D4×C29—24no—
70C4×D4×C29—21no—
71C4×D4×C29—21no—
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C4×D4×C29—21no—
75C4×D4×C29D412yes—
76C29×#117—22no—
77C29×#117—22no—
78C29×#117—21no—
79C2×C4⋊C4×C29—22no—
80C2×C4⋊C4×C29D411yescharacteristic
81C2×C22⋊C4×C29C2×C412yes—
82C2×C42×C29C2311yescharacteristic
83C29×C4⋊C8—21no—
84C29×C4⋊C8—21no—
85C29×C4⋊C8—21no—
86C29×C4⋊C8—21no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8—21no—
89C29×#100—42no—
90C29×C22⋊C8—44no—
91C4×C8×C29—21no—
92C4×C8×C29—21no—
93C24×C29C22⋊C412yes—
94#41×C29—41no—
95#41×C29—41no—
96#41×C29—41no—
97#41×C29—41no—
98#41×C29—82no—
99#41×C29—82no—
100C2×Q8×C29—21no—
101C2×Q8×C29—21no—
102C2×Q8×C29C22⋊C412yes—
103C2×D4×C29—22no—
104C2×D4×C29—24no—
105C2×D4×C29—24no—
106C2×D4×C29—21no—
107C2×D4×C29—21no—
108C2×D4×C29—21no—
109C2×D4×C29—21no—
110C2×D4×C29—21no—
111C2×D4×C29—21no—
112C2×D4×C29—21no—
113C2×D4×C29—21no—
114C2×D4×C29C22⋊C412yes—
115C22×C4×C29—24no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—22no—
119C22×C4×C29—42no—
120C22×C4×C29—42no—
121C22×C4×C29C22⋊C412yes—
122C22×C4×C29C22×C411yescharacteristic
123C22×C4×C29C2×D411yescharacteristic
124C22×C4×C29C2×D411yescharacteristic
125M16×C29—41no—
126M16×C29—41no—
127M16×C29—41no—
128M16×C29—41no—
129C2×C8×C29—22no—
130C2×C8×C29—41no—
131C2×C8×C29—41no—
132C2×C8×C29—42no—
133C2×C8×C29—41no—
134C2×C8×C29—41no—
135C2×C8×C29—41no—
136C4⋊C4×C29—24no—
137C4⋊C4×C29—22no—
138C4⋊C4×C29—21no—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—22no—
145C4⋊C4×C29C22⋊C412yes—
146C4⋊C4×C29C22⋊C412yes—
147C22⋊C4×C29—24no—
148C22⋊C4×C29—24no—
149C22⋊C4×C29—24no—
150C22⋊C4×C29—22no—
151C22⋊C4×C29—22no—
152C22⋊C4×C29—22no—
153C22⋊C4×C29—22no—
154C22⋊C4×C29—22no—
155C42×C29—24no—
156C42×C29—22no—
157C42×C29C2×D411yescharacteristic
158C42×C29C2×D411yescharacteristic
159C42×C29C2×D411yescharacteristic
160C42×C29C2×D411yescharacteristic
161#8358C2911yesmaximal, characteristic, direct product factor, Sylow
162C23×C29—22no—
163C23×C29—22no—
164C23×C29—22no—
165C23×C29—22no—
166C23×C29—42no—
167C23×C29—42no—
168C23×C29C2×C22⋊C411yescharacteristic
169Q8×C29—42no—
170Q8×C29—41no—
171Q8×C29—41no—
172Q8×C29—41no—
173Q8×C29—41no—
174D4×C29—42no—
175D4×C29—42no—
176D4×C29—42no—
177D4×C29—41no—
178D4×C29—41no—
179D4×C29—41no—
180D4×C29—41no—
181D4×C29—41no—
182D4×C29—41no—
183D4×C29—41no—
184D4×C29—41no—
185D4×C29—84no—
186D4×C29—84no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—22no—
190C2×C4×C29—22no—
191C2×C4×C29—22no—
192C2×C4×C29—22no—
193C2×C4×C29—41no—
194C2×C4×C29—42no—
195C2×C4×C29—42no—
196C2×C4×C29—42no—
197C2×C4×C29—42no—
198C2×C4×C29—42no—
199C2×C4×C29—82no—
200C2×C4×C29—84no—
201C2×C4×C29C2×C22⋊C411yescharacteristic
202C2×C4×C29C2×C22⋊C411yescharacteristic
203C2×C4×C29#12011yescharacteristic
204C2×C4×C29#12011yescharacteristic
205C2×C4×C29#12011yescharacteristic
206C2×C4×C29#12011yescharacteristic
207C2×C4×C29#13511yescharacteristic
208C2×C4×C29#13511yescharacteristic
209C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C29#13711yescharacteristic
211C8×C29—42no—
212C8×C29—81no—
213C8×C29—81no—
214C8×C29—81no—
215#3506C2×C2911yescharacteristic
216#1954C2×C2911yescharacteristic, complemented
217#1800C2×C2911yescharacteristic, complemented
218#1550C2×C2911yescharacteristic, complemented
219#1547C2×C2911yescharacteristic, complemented
220#1493C2×C2911yescharacteristic, complemented
221#1492C2×C2911yescharacteristic, complemented
222C22×C29—21no—
223C22×C29—21no—
224C22×C29—44no—
225C22×C29—42no—
226C22×C29—42no—
227C22×C29—42no—
228C22×C29—42no—
229C22×C29—42no—
230C22×C29—42no—
231C22×C29—82no—
232C22×C29#37911yescharacteristic
233C22×C29#41611yescharacteristic
234C22×C29#41711yescharacteristic
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—42no—
239C4×C29—42no—
240C4×C29—42no—
241C4×C29—42no—
242C4×C29#44911yescharacteristic
243C4×C29#44911yescharacteristic
244C4×C29#45211yescharacteristic
245C4×C29#45211yescharacteristic
246C4×C29#45311yescharacteristic
247C4×C29#45511yescharacteristic
248#559—22no—
249#556—21no—
250#555—21no—
251#553—22no—
252#550—21no—
253#547—21no—
254#538C4×C2914yes—
255#535—21no—
256#533C22×C2911yescharacteristic
257#532C22×C2911yescharacteristic
258#525—22no—
259#520—21no—
260C2×C4×D4C22×C2911yescharacteristic
261#423C22×C2911yescharacteristic
262#423C22×C2911yescharacteristic
263C2×C4⋊C8C22×C2911yescharacteristic
264C2×#100—21no—
265C2×C22⋊C8—22no—
266C2×C4×C8C22×C2911yescharacteristic
267#343—21no—
268#333—21no—
269#332—21no—
270#332—21no—
271#331—21no—
272Q8⋊C8—22no—
273D4⋊C8—22no—
274C2×C29—21no—
275C2×C29—21no—
276C2×C29—82no—
277C2×C29—82no—
278C2×C29#178811yescharacteristic
279C2×C29#179111yescharacteristic
280C2×C29#179211yescharacteristic
281C2×#41—22no—
282C2×#41—21no—
283C22×D4D4×C2911yescharacteristic
284C23×C4D4×C2912yes—
285C2×M16—21no—
286C2×M16—21no—
287C22×C8—21no—
288C22×C8—21no—
289C4⋊Q8D4×C2911yescharacteristic
290C4⋊Q8D4×C2911yescharacteristic
291C4⋊Q8D4×C2911yescharacteristic
292#127—22no—
293#127D4×C2911yescharacteristic
294#126—24no—
295#125—21no—
296#124—22no—
297#124—24no—
298#124—21no—
299#123—24no—
300#123—24no—
301C22⋊Q8—22no—
302C22⋊Q8—21no—
303C22⋊Q8C2×C4×C2912yes—
304#121—22no—
305#121—22no—
306#121—22no—
307#121—24no—
308#121—21no—
309#121C2×C4×C2912yes—
310#120—24no—
311C4×Q8—22no—
312C4×Q8—21no—
313C4×Q8D4×C2912yes—
314C4×D4—22no—
315C4×D4—24no—
316C4×D4—24no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4D4×C2912yes—
323#117—22no—
324#117—22no—
325#117—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4D4×C2911yescharacteristic
328C2×C22⋊C4C2×C4×C2912yes—
329C2×C42C23×C2911yescharacteristic
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336#100—42no—
337C22⋊C8—44no—
338C4×C8—21no—
339C4×C8—21no—
340C29#835811yescharacteristic, direct product factor, Sylow
341C24C22⋊C4×C2912yes—
342#41—41no—
343#41—41no—
344#41—41no—
345#41—41no—
346#41—82no—
347#41—82no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8C22⋊C4×C2912yes—
351C2×D4—22no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C22⋊C4×C2912yes—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4C22⋊C4×C2912yes—
370C22×C4C22×C4×C2911yescharacteristic
371C22×C4C2×D4×C2911yescharacteristic
372C22×C4C2×D4×C2911yescharacteristic
373M16—41no—
374M16—41no—
375M16—41no—
376M16—41no—
377C2×C8—22no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—42no—
381C2×C8—41no—
382C2×C8—41no—
383C2×C8—41no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4C22⋊C4×C2912yes—
394C4⋊C4C22⋊C4×C2912yes—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C42—24no—
404C42—22no—
405C42C2×D4×C2911yescharacteristic
406C42C2×D4×C2911yescharacteristic
407C42C2×D4×C2911yescharacteristic
408C42C2×D4×C2911yescharacteristic
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—42no—
414C23—42no—
415C23C2×C22⋊C4×C2911yescharacteristic
416Q8—42no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—41no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—41no—
431D4—41no—
432D4—84no—
433D4—84no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4—84no—
448C2×C4C2×C22⋊C4×C2911yescharacteristic
449C2×C4C2×C22⋊C4×C2911yescharacteristic
450C2×C4C29×#12011yescharacteristic
451C2×C4C29×#12011yescharacteristic
452C2×C4C29×#12011yescharacteristic
453C2×C4C29×#12011yescharacteristic
454C2×C4C29×#13511yescharacteristic
455C2×C4C29×#13511yescharacteristic
456C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
457C2×C4C29×#13711yescharacteristic
458C8—42no—
459C8—81no—
460C8—81no—
461C8—81no—
462C22—21no—
463C22—21no—
464C22—44no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—82no—
472C22C29×#37911yescharacteristic
473C22C29×#41611yescharacteristic
474C22C29×#41711yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4C29×#44911yescharacteristic
483C4C29×#44911yescharacteristic
484C4C29×#45211yescharacteristic
485C4C29×#45211yescharacteristic
486C4C29×#45311yescharacteristic
487C4C29×#45511yescharacteristic
488C2—21no—
489C2—21no—
490C2—82no—
491C2—82no—
492C2C29×#178811yescharacteristic
493C2C29×#179111yescharacteristic
494C2C29×#179211yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3506C2
LCSG ▷ C22×C4 ▷ 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×#1954C2semidirect
3. C29×#1800C2semidirect
4. C29×#1550C2semidirect
5. C29×#1547C2semidirect
6. C29×#1493C2semidirect
7. C29×#1492C2semidirect
161. #8358C29direct (N × H)
216. #1954C2×C29semidirect
217. #1800C2×C29semidirect
218. #1550C2×C29semidirect
219. #1547C2×C29semidirect
220. #1493C2×C29semidirect
221. #1492C2×C29semidirect
340. C29#8358direct (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×#19542
C29×#18002
C29×#15502
C29×#15472
C29×#14932
C29×#14922
#835829