Finite Group Databasebeta

← C29×#8557 #20303457

Subgroups — C29×#8557 #20303457

Order 7424.

898 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
1C2×C4×C22⋊C4×C29C211yesmaximal, characteristic
2C29×#1797C212yesmaximal, complemented
3C2×C29×#323C212yesmaximal
4C29×#1280C212yesmaximal, complemented
5C24×C4×C29C411yescharacteristic
6C22×C22⋊C4×C29C411yescharacteristic
7C22×C22⋊C4×C29C2211yescharacteristic
8C22×C42×C29C411yescharacteristic
9C22×C42×C29C2211yescharacteristic
10C2×C29×C4⋊C8—22no—
11C2×C29×C22⋊C8C2214yes—
12C4×C22⋊C4×C29—22no—
13C4×C22⋊C4×C29—22no—
14C2×C29×#95C411yescharacteristic
15C2×C29×#95C2211yescharacteristic
16C29×#336—22no—
17C29×#323—24no—
18C25×C29C2×C411yescharacteristic
19C23×C4×C29—21no—
20C23×C4×C29—21no—
21C23×C4×C29—22no—
22C23×C4×C29—42no—
23C23×C4×C29—42no—
24C23×C4×C29C814yescomplemented
25C23×C4×C29C2×C411yescharacteristic
26C23×C4×C29C2×C411yescharacteristic
27C23×C4×C29C2×C411yescharacteristic
28C23×C4×C29C2×C411yescharacteristic
29C23×C4×C29C2×C411yescharacteristic
30C23×C4×C29C2311yescharacteristic
31C22×C8×C29—24no—
32C2×C22⋊C4×C29—22no—
33C2×C22⋊C4×C29—22no—
34C2×C22⋊C4×C29—22no—
35C2×C22⋊C4×C29—22no—
36C2×C22⋊C4×C29—22no—
37C2×C22⋊C4×C29D412yes—
38C2×C22⋊C4×C29Q812yes—
39C2×C42×C29—21no—
40C2×C42×C29—21no—
41C2×C42×C29—42no—
42C2×C42×C29—42no—
43C2×C42×C29D412yes—
44C2×C42×C29D412yes—
45C29×C4⋊C8—44no—
46C29×C22⋊C8—24no—
47C29×C22⋊C8—24no—
48C29×#95—22no—
49C29×#95—22no—
50C24×C29—21no—
51C24×C29—21no—
52C24×C29—21no—
53C24×C29—21no—
54C24×C29—41no—
55C24×C29—41no—
56C24×C29—41no—
57C24×C29—41no—
58C24×C29C4⋊C412yes—
59C24×C29C2×C812yes—
60C24×C29M1612yes—
61C24×C29C22×C411yescharacteristic
62C22×C4×C29—22no—
63C22×C4×C29—22no—
64C22×C4×C29—21no—
65C22×C4×C29—21no—
66C22×C4×C29—21no—
67C22×C4×C29—21no—
68C22×C4×C29—21no—
69C22×C4×C29—21no—
70C22×C4×C29—21no—
71C22×C4×C29—21no—
72C22×C4×C29—24no—
73C22×C4×C29—24no—
74C22×C4×C29—41no—
75C22×C4×C29—41no—
76C22×C4×C29—41no—
77C22×C4×C29—41no—
78C22×C4×C29—42no—
79C22×C4×C29—42no—
80C22×C4×C29—48no—
81C22×C4×C29—48no—
82C22×C4×C29—42no—
83C22×C4×C29—42no—
84C22×C4×C29—41no—
85C22×C4×C29—41no—
86C22×C4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29—41no—
90C22×C4×C29C22⋊C412yes—
91C22×C4×C29C22⋊C411yescharacteristic
92C22×C4×C29C22⋊C411yescharacteristic
93C22×C4×C29C4⋊C412yes—
94C22×C4×C29C2×C812yes—
95C22×C4×C29C2×C812yes—
96C22×C4×C29M1612yes—
97C22×C4×C29M1612yes—
98C22×C4×C29C2×D412yes—
99C22×C4×C29C2×D411yescharacteristic
100C22×C4×C29C2×Q811yescharacteristic
101C22×C4×C29#4112yes—
102C2×C8×C29—44no—
103C2×C8×C29—44no—
104C2×C8×C29—44no—
105C22⋊C4×C29—28no—
106C22⋊C4×C29—24no—
107C22⋊C4×C29—24no—
108C42×C29—24no—
109C42×C29—42no—
110C42×C29—42no—
111C42×C29—42no—
112#8557C2911yesmaximal, characteristic, direct product factor, Sylow
113C23×C29—21no—
114C23×C29—21no—
115C23×C29—21no—
116C23×C29—21no—
117C23×C29—22no—
118C23×C29—22no—
119C23×C29—22no—
120C23×C29—22no—
121C23×C29—22no—
122C23×C29—22no—
123C23×C29—42no—
124C23×C29—42no—
125C23×C29—42no—
126C23×C29—42no—
127C23×C29—42no—
128C23×C29—42no—
129C23×C29—42no—
130C23×C29—42no—
131C23×C29—42no—
132C23×C29—42no—
133C23×C29—42no—
134C23×C29—42no—
135C23×C29—41no—
136C23×C29—41no—
137C23×C29—41no—
138C23×C29—41no—
139C23×C29C4⋊C814yescomplemented
140C23×C29C2×C22⋊C411yescharacteristic
141C23×C29C2×C4⋊C411yescharacteristic
142C23×C29#11711yescharacteristic
143C23×C29C22×C811yescharacteristic
144C23×C29C2×M1611yescharacteristic
145C23×C29C2×M1611yescharacteristic
146C23×C29C2×M1611yescharacteristic
147C2×C4×C29—22no—
148C2×C4×C29—21no—
149C2×C4×C29—22no—
150C2×C4×C29—21no—
151C2×C4×C29—24no—
152C2×C4×C29—24no—
153C2×C4×C29—22no—
154C2×C4×C29—22no—
155C2×C4×C29—22no—
156C2×C4×C29—22no—
157C2×C4×C29—22no—
158C2×C4×C29—22no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—42no—
162C2×C4×C29—48no—
163C2×C4×C29—42no—
164C2×C4×C29—42no—
165C2×C4×C29—42no—
166C2×C4×C29—42no—
167C2×C4×C29—42no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—41no—
173C2×C4×C29—41no—
174C2×C4×C29—48no—
175C2×C4×C29—42no—
176C2×C4×C29—42no—
177C2×C4×C29—42no—
178C2×C4×C29C22⋊C812yes—
179C2×C4×C29C22⋊C812yes—
180C2×C4×C29#9912yes—
181C2×C4×C29#10012yes—
182C2×C4×C29#12112yes—
183C2×C4×C29C22⋊Q812yes—
184C8×C29—84no—
185C2×C4×C22⋊C4C2×C2911yescharacteristic
186#1797C2×C2912yescomplemented
187C2×#323C2×C2912yes—
188#1280C2×C2912yescomplemented
189C22×C29—21no—
190C22×C29—21no—
191C22×C29—21no—
192C22×C29—21no—
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—21no—
197C22×C29—21no—
198C22×C29—21no—
199C22×C29—21no—
200C22×C29—21no—
201C22×C29—24no—
202C22×C29—44no—
203C22×C29—44no—
204C22×C29—44no—
205C22×C29—44no—
206C22×C29—42no—
207C22×C29—42no—
208C22×C29—42no—
209C22×C29—42no—
210C22×C29—42no—
211C22×C29—42no—
212C22×C29#38011yescharacteristic
213C22×C29C2×C22⋊C811yescharacteristic
214C22×C29#40711yescharacteristic
215C22×C29C2×#9911yescharacteristic
216C22×C29#41011yescharacteristic
217C22×C29C2×#10011yescharacteristic
218C22×C29#41311yescharacteristic
219C22×C29C2×C4⋊C811yescharacteristic
220C22×C29#42311yescharacteristic
221C22×C29#43111yescharacteristic
222C22×C29#43211yescharacteristic
223C4×C29—22no—
224C4×C29—22no—
225C4×C29—22no—
226C4×C29—42no—
227C4×C29—42no—
228C4×C29—42no—
229C4×C29—42no—
230C4×C29#32314yescomplemented
231C24×C4C4×C2911yescharacteristic
232C22×C22⋊C4C4×C2911yescharacteristic
233C22×C22⋊C4C22×C2911yescharacteristic
234C22×C42C4×C2911yescharacteristic
235C22×C42C22×C2911yescharacteristic
236C2×C4⋊C8—22no—
237C2×C22⋊C8C22×C2914yes—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C2×#95C4×C2911yescharacteristic
241C2×#95C22×C2911yescharacteristic
242#336—22no—
243#323—24no—
244C2×C29—21no—
245C2×C29—21no—
246C2×C29—21no—
247C2×C29—21no—
248C2×C29—44no—
249C2×C29C2×#32311yescharacteristic
250C2×C29#145811yescharacteristic
251C2×C29#146511yescharacteristic
252C2×C29#146611yescharacteristic
253C2×C29#179711yescharacteristic
254C2×C29#179911yescharacteristic
255C2×C29#180011yescharacteristic
256C25C2×C4×C2911yescharacteristic
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—22no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4C8×C2914yescomplemented
263C23×C4C2×C4×C2911yescharacteristic
264C23×C4C2×C4×C2911yescharacteristic
265C23×C4C2×C4×C2911yescharacteristic
266C23×C4C2×C4×C2911yescharacteristic
267C23×C4C2×C4×C2911yescharacteristic
268C23×C4C23×C2911yescharacteristic
269C22×C8—24no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4D4×C2912yes—
276C2×C22⋊C4Q8×C2912yes—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—42no—
280C2×C42—42no—
281C2×C42D4×C2912yes—
282C2×C42D4×C2912yes—
283C4⋊C8—44no—
284C22⋊C8—24no—
285C22⋊C8—24no—
286#95—22no—
287#95—22no—
288C29#855711yescharacteristic, direct product factor, Sylow
289C24—21no—
290C24—21no—
291C24—21no—
292C24—21no—
293C24—41no—
294C24—41no—
295C24—41no—
296C24—41no—
297C24C4⋊C4×C2912yes—
298C24C2×C8×C2912yes—
299C24M16×C2912yes—
300C24C22×C4×C2911yescharacteristic
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—48no—
320C22×C4—48no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4C22⋊C4×C2912yes—
330C22×C4C22⋊C4×C2911yescharacteristic
331C22×C4C22⋊C4×C2911yescharacteristic
332C22×C4C4⋊C4×C2912yes—
333C22×C4C2×C8×C2912yes—
334C22×C4C2×C8×C2912yes—
335C22×C4M16×C2912yes—
336C22×C4M16×C2912yes—
337C22×C4C2×D4×C2912yes—
338C22×C4C2×D4×C2911yescharacteristic
339C22×C4C2×Q8×C2911yescharacteristic
340C22×C4#41×C2912yes—
341C2×C8—44no—
342C2×C8—44no—
343C2×C8—44no—
344C22⋊C4—28no—
345C22⋊C4—24no—
346C22⋊C4—24no—
347C42—24no—
348C42—42no—
349C42—42no—
350C42—42no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23C29×C4⋊C814yescomplemented
378C23C2×C22⋊C4×C2911yescharacteristic
379C23C2×C4⋊C4×C2911yescharacteristic
380C23C29×#11711yescharacteristic
381C23C22×C8×C2911yescharacteristic
382C23C2×M16×C2911yescharacteristic
383C23C2×M16×C2911yescharacteristic
384C23C2×M16×C2911yescharacteristic
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—48no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—48no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4C29×C22⋊C812yes—
417C2×C4C29×C22⋊C812yes—
418C2×C4C29×#9912yes—
419C2×C4C29×#10012yes—
420C2×C4C29×#12112yes—
421C2×C4C29×C22⋊Q812yes—
422C8—84no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—44no—
437C22—44no—
438C22—44no—
439C22—44no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22C29×#38011yescharacteristic
447C22C2×C29×C22⋊C811yescharacteristic
448C22C29×#40711yescharacteristic
449C22C2×C29×#9911yescharacteristic
450C22C29×#41011yescharacteristic
451C22C2×C29×#10011yescharacteristic
452C22C29×#41311yescharacteristic
453C22C2×C29×C4⋊C811yescharacteristic
454C22C29×#42311yescharacteristic
455C22C29×#43111yescharacteristic
456C22C29×#43211yescharacteristic
457C4—22no—
458C4—22no—
459C4—22no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4C29×#32314yescomplemented
465C2—21no—
466C2—21no—
467C2—21no—
468C2—21no—
469C2—44no—
470C2C2×C29×#32311yescharacteristic
471C2C29×#145811yescharacteristic
472C2C29×#146511yescharacteristic
473C2C29×#146611yescharacteristic
474C2C29×#179711yescharacteristic
475C2C29×#179911yescharacteristic
476C2C29×#180011yescharacteristic
subgroupG/H
center, socleC23×C29C2×C22⋊C4
commutatorC23C22×C8×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC25×C29C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C22×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1797C2semidirect
4. C29×#1280C2semidirect
24. C23×C4×C29C8semidirect
112. #8557C29direct (N × H)
139. C23×C29C4⋊C8semidirect
186. #1797C2×C29semidirect
188. #1280C2×C29semidirect
230. C4×C29#323semidirect
262. C23×C4C8×C29semidirect
288. C29#8557direct (N × H)
377. C23C29×C4⋊C8semidirect
464. C4C29×#323semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊C4×C292
C29×#17972
C2×C29×#3232
C29×#12802
#855729