Finite Group Databasebeta

← C29×#13093 #20307993

Subgroups — C29×#13093 #20307993

Order 7424.

752 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#413C211yesmaximal, characteristic, complemented
2C29×#2431C211yesmaximal, characteristic
3C2×C29×#355C212yesmaximal, complemented
4C29×#1785C211yesmaximal, characteristic, complemented
5C29×#1394C212yesmaximal, complemented
6C22×#41×C29C2211yescharacteristic
7C22×M16×C29—21no—
8C2×C29×#127C411yescharacteristic
9C2×C29×#124C2211yescharacteristic
10C2×C29×#121C411yescharacteristic
11C29×#413—24no—
12C2×C29×#101C2212yes—
13C2×C29×#101C2212yes—
14C2×C29×#100—21no—
15C2×C29×#100—21no—
16C29×#407—21no—
17C29×#392—21no—
18C29×#392—21no—
19C29×#391C2211yescharacteristic
20C29×#390C411yescharacteristic
21C29×#386—21no—
22C29×#386—21no—
23C4×C22⋊C4×C29C411yescharacteristic
24C29×#355—24no—
25C2×#41×C29—22no—
26C2×#41×C29—22no—
27C2×#41×C29—41no—
28C2×#41×C29—41no—
29C2×#41×C29—42no—
30C22×Q8×C29C2311yescharacteristic
31C22×D4×C29—21no—
32C22×D4×C29—21no—
33C22×D4×C29—21no—
34C22×D4×C29C2×C411yescharacteristic
35C22×D4×C29C2×C411yescharacteristic
36C22×D4×C29D411yescharacteristic
37C22×D4×C29D411yescharacteristic
38C23×C4×C29C2×C411yescharacteristic
39C23×C4×C29D411yescharacteristic
40C23×C4×C29D411yescharacteristic
41C2×M16×C29—24no—
42C2×M16×C29—22no—
43C2×M16×C29—22no—
44C2×M16×C29—42no—
45C2×M16×C29—41no—
46C22×C8×C29—41no—
47C29×#127—42no—
48C29×#124—22no—
49C29×#124—22no—
50C29×#121—41no—
51C29×#121—41no—
52C2×C4⋊C4×C29C2×C411yescharacteristic
53C2×C22⋊C4×C29—21no—
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29—21no—
56C2×C22⋊C4×C29—21no—
57C2×C22⋊C4×C29—21no—
58C2×C22⋊C4×C29—21no—
59C2×C42×C29C2×C411yescharacteristic
60C2×C42×C29C2×C411yescharacteristic
61C29×#101—22no—
62C29×#101—22no—
63C29×#101—22no—
64C29×#101D414yescomplemented
65C29×#100—24no—
66C29×#100—42no—
67C29×C22⋊C8—41no—
68C29×C22⋊C8—41no—
69C29×#95—21no—
70C29×#95—21no—
71C29×#95—21no—
72C24×C29—21no—
73C24×C29C22⋊C411yescharacteristic
74C24×C29C22⋊C411yescharacteristic
75C24×C29C22⋊C411yescharacteristic
76#41×C29—44no—
77#41×C29—44no—
78#41×C29—44no—
79#41×C29—44no—
80C2×Q8×C29—41no—
81C2×Q8×C29—41no—
82C2×Q8×C29C2×D412yes—
83C2×Q8×C29#4112yes—
84C2×D4×C29—22no—
85C2×D4×C29—22no—
86C2×D4×C29—22no—
87C2×D4×C29—22no—
88C2×D4×C29—21no—
89C2×D4×C29—22no—
90C2×D4×C29—21no—
91C2×D4×C29—41no—
92C2×D4×C29—41no—
93C2×D4×C29—41no—
94C2×D4×C29—41no—
95C2×D4×C29—41no—
96C2×D4×C29—41no—
97C2×D4×C29—42no—
98C2×D4×C29—42no—
99C2×D4×C29—42no—
100C2×D4×C29—42no—
101C2×D4×C29—42no—
102C2×D4×C29—81no—
103C2×D4×C29—81no—
104C2×D4×C29—81no—
105C2×D4×C29—81no—
106C22×C4×C29—22no—
107C22×C4×C29—21no—
108C22×C4×C29—21no—
109C22×C4×C29—21no—
110C22×C4×C29—21no—
111C22×C4×C29—21no—
112C22×C4×C29—21no—
113C22×C4×C29—21no—
114C22×C4×C29—21no—
115C22×C4×C29—21no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—21no—
119C22×C4×C29—21no—
120C22×C4×C29—41no—
121C22×C4×C29—41no—
122C22×C4×C29C22⋊C411yescharacteristic
123C22×C4×C29C22×C411yescharacteristic
124C22×C4×C29C2×D411yescharacteristic
125C22×C4×C29C2×D411yescharacteristic
126M16×C29—24no—
127M16×C29—44no—
128M16×C29—42no—
129M16×C29—42no—
130M16×C29—42no—
131C2×C8×C29—44no—
132C2×C8×C29—42no—
133C2×C8×C29—42no—
134C4⋊C4×C29—41no—
135C22⋊C4×C29—42no—
136C22⋊C4×C29—41no—
137C22⋊C4×C29—41no—
138C22⋊C4×C29—41no—
139C22⋊C4×C29—42no—
140C22⋊C4×C29—41no—
141C22⋊C4×C29—81no—
142C22⋊C4×C29—81no—
143C42×C29—22no—
144C42×C29—41no—
145#13093C2911yesmaximal, characteristic, direct product factor, Sylow
146C23×C29—21no—
147C23×C29—21no—
148C23×C29—21no—
149C23×C29—21no—
150C23×C29—21no—
151C23×C29—21no—
152C23×C29—21no—
153C23×C29—21no—
154C23×C29—41no—
155C23×C29—41no—
156C23×C29—41no—
157C23×C29—41no—
158C23×C29—41no—
159C23×C29—41no—
160C23×C29—41no—
161C23×C29—41no—
162C23×C29—41no—
163C23×C29—41no—
164C23×C29—41no—
165C23×C29—41no—
166C23×C29—41no—
167C23×C29#9912yes—
168C23×C29C2×C22⋊C411yescharacteristic
169Q8×C29—42no—
170Q8×C29—42no—
171D4×C29—44no—
172D4×C29—44no—
173D4×C29—42no—
174D4×C29—42no—
175D4×C29—82no—
176D4×C29—84no—
177D4×C29—84no—
178D4×C29—84no—
179C2×C4×C29—22no—
180C2×C4×C29—22no—
181C2×C4×C29—22no—
182C2×C4×C29—22no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—21no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—21no—
191C2×C4×C29—22no—
192C2×C4×C29—42no—
193C2×C4×C29—42no—
194C2×C4×C29—42no—
195C2×C4×C29—42no—
196C2×C4×C29—41no—
197C2×C4×C29—41no—
198C2×C4×C29—41no—
199C2×C4×C29—41no—
200C2×C4×C29—41no—
201C2×C4×C29—41no—
202C2×C4×C29—41no—
203C2×C4×C29—41no—
204C2×C4×C29#9911yescharacteristic
205C2×C4×C29#9911yescharacteristic
206C2×C4×C29C4×D412yes—
207C2×C4×C29#12011yescharacteristic
208C2×C4×C29#12112yes—
209C2×C4×C29#12311yescharacteristic
210C8×C29—44no—
211C8×C29—82no—
212C2×#413C2×C2911yescharacteristic, complemented
213#2431C2×C2911yescharacteristic
214C2×#355C2×C2912yescomplemented
215#1785C2×C2911yescharacteristic, complemented
216#1394C2×C2912yescomplemented
217C22×C29—21no—
218C22×C29—21no—
219C22×C29—22no—
220C22×C29—42no—
221C22×C29—42no—
222C22×C29—41no—
223C22×C29—41no—
224C22×C29—41no—
225C22×C29—41no—
226C22×C29—41no—
227C22×C29—41no—
228C22×C29—41no—
229C22×C29—41no—
230C22×C29—81no—
231C22×C29—81no—
232C22×C29—81no—
233C22×C29—81no—
234C22×C29—81no—
235C22×C29—81no—
236C22×C29—81no—
237C22×C29—81no—
238C22×C29—81no—
239C22×C29—81no—
240C22×C29—81no—
241C22×C29#38611yescharacteristic
242C22×C29C2×#9911yescharacteristic
243C22×C29C2×#9911yescharacteristic
244C4×C29—21no—
245C4×C29—22no—
246C4×C29—21no—
247C4×C29—21no—
248C4×C29—21no—
249C4×C29—22no—
250C4×C29—42no—
251C4×C29—81no—
252C4×C29—81no—
253C22×#41C22×C2911yescharacteristic
254C22×M16—21no—
255C2×#127C4×C2911yescharacteristic
256C2×#124C22×C2911yescharacteristic
257C2×#121C4×C2911yescharacteristic
258#413—24no—
259C2×#101C22×C2912yes—
260C2×#101C22×C2912yes—
261C2×#100—21no—
262C2×#100—21no—
263#407—21no—
264#392—21no—
265#392—21no—
266#391C22×C2911yescharacteristic
267#390C4×C2911yescharacteristic
268#386—21no—
269#386—21no—
270C4×C22⋊C4C4×C2911yescharacteristic
271#355—24no—
272C2×C29—21no—
273C2×C29—21no—
274C2×C29—42no—
275C2×C29—81no—
276C2×C29—81no—
277C2×C29—161no—
278C2×C29#189811yescharacteristic
279C2×C29#213211yescharacteristic
280C2×C29#213411yescharacteristic
281C2×#41—22no—
282C2×#41—22no—
283C2×#41—41no—
284C2×#41—41no—
285C2×#41—42no—
286C22×Q8C23×C2911yescharacteristic
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C2×C4×C2911yescharacteristic
291C22×D4C2×C4×C2911yescharacteristic
292C22×D4D4×C2911yescharacteristic
293C22×D4D4×C2911yescharacteristic
294C23×C4C2×C4×C2911yescharacteristic
295C23×C4D4×C2911yescharacteristic
296C23×C4D4×C2911yescharacteristic
297C2×M16—24no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—42no—
301C2×M16—41no—
302C22×C8—41no—
303#127—42no—
304#124—22no—
305#124—22no—
306#121—41no—
307#121—41no—
308C2×C4⋊C4C2×C4×C2911yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C42C2×C4×C2911yescharacteristic
316C2×C42C2×C4×C2911yescharacteristic
317#101—22no—
318#101—22no—
319#101—22no—
320#101D4×C2914yescomplemented
321#100—24no—
322#100—42no—
323C22⋊C8—41no—
324C22⋊C8—41no—
325#95—21no—
326#95—21no—
327#95—21no—
328C29#1309311yescharacteristic, direct product factor, Sylow
329C24—21no—
330C24C22⋊C4×C2911yescharacteristic
331C24C22⋊C4×C2911yescharacteristic
332C24C22⋊C4×C2911yescharacteristic
333#41—44no—
334#41—44no—
335#41—44no—
336#41—44no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×Q8C2×D4×C2912yes—
340C2×Q8#41×C2912yes—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—21no—
346C2×D4—22no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—81no—
360C2×D4—81no—
361C2×D4—81no—
362C2×D4—81no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4C22⋊C4×C2911yescharacteristic
380C22×C4C22×C4×C2911yescharacteristic
381C22×C4C2×D4×C2911yescharacteristic
382C22×C4C2×D4×C2911yescharacteristic
383M16—24no—
384M16—44no—
385M16—42no—
386M16—42no—
387M16—42no—
388C2×C8—44no—
389C2×C8—42no—
390C2×C8—42no—
391C4⋊C4—41no—
392C22⋊C4—42no—
393C22⋊C4—41no—
394C22⋊C4—42no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—81no—
399C22⋊C4—81no—
400C42—22no—
401C42—41no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23C29×#9912yes—
424C23C2×C22⋊C4×C2911yescharacteristic
425Q8—42no—
426Q8—42no—
427D4—44no—
428D4—44no—
429D4—42no—
430D4—42no—
431D4—82no—
432D4—84no—
433D4—84no—
434D4—84no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4C29×#9911yescharacteristic
461C2×C4C29×#9911yescharacteristic
462C2×C4C4×D4×C2912yes—
463C2×C4C29×#12011yescharacteristic
464C2×C4C29×#12112yes—
465C2×C4C29×#12311yescharacteristic
466C8—44no—
467C8—82no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—42no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22C29×#38611yescharacteristic
493C22C2×C29×#9911yescharacteristic
494C22C2×C29×#9911yescharacteristic
495C4—21no—
496C4—22no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—22no—
501C4—42no—
502C4—81no—
503C4—81no—
504C2—21no—
505C2—21no—
506C2—42no—
507C2—81no—
508C2—81no—
509C2—161no—
510C2C29×#189811yescharacteristic
511C2C29×#213211yescharacteristic
512C2C29×#213411yescharacteristic
subgroupG/H
center, socleC22×C29C2×#99
commutatorC22×C4C22×C4×C29
Frattini, cosocleC22×Q8C23×C29
prime radicalC29×#2431C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C22×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#413C2semidirect
3. C2×C29×#355C2semidirect
4. C29×#1785C2semidirect
5. C29×#1394C2semidirect
64. C29×#101D4semidirect
145. #13093C29direct (N × H)
212. C2×#413C2×C29semidirect
214. C2×#355C2×C29semidirect
215. #1785C2×C29semidirect
216. #1394C2×C29semidirect
320. #101D4×C29semidirect
328. C29#13093direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4132
C29×#24312
C2×C29×#3552
C29×#17852
C29×#13942
#1309329