Finite Group Databasebeta

← C29×#61838 #20356738

Subgroups — C29×#61838 #20356738

Order 7424.

1700 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3523C211yesmaximal, characteristic
2C2×Q82×C29C211yesmaximal, characteristic, complemented
3C29×#3387C216yesmaximal, complemented
4Q8×SD16×C29C212yesmaximal, complemented
5C29×#3369C216yesmaximal, complemented
6C29×#3363C212yesmaximal, complemented
7C29×#3238C213yesmaximal
8C29×#3229C213yesmaximal, complemented
9C29×#3113C213yesmaximal, complemented
10C29×#3108C213yesmaximal
11C29×#2984C211yesmaximal, characteristic, complemented
12Q82×C29—21no—
13Q82×C29—23no—
14Q82×C29C2212yes—
15Q82×C29C2216yes—
16C29×#557C2211yescharacteristic
17C29×#557C2213yes—
18C29×#556C2213yes—
19C29×#552—23no—
20D4×Q8×C29—21no—
21D4×Q8×C29C2211yescharacteristic
22C29×#541—23no—
23C29×#533C2213yes—
24C2×C29×C4⋊Q8—23no—
25C2×C29×C4⋊Q8C2213yes—
26C29×#529C2213yes—
27C29×#519—21no—
28C2×C4×Q8×C29—21no—
29C2×C4×Q8×C29C2213yes—
30C2×C4×Q8×C29C2211yescharacteristic
31C29×#501C2216yes—
32C29×#498C2216yes—
33C29×#489C2216yes—
34C29×#487C2216yes—
35C29×#483C2213yes—
36C29×#483C2216yes—
37C29×#480C2213yes—
38C29×#479C2216yes—
39C29×#477C2216yes—
40C29×#476C2216yes—
41C29×#475C22112yes—
42C29×#475C2216yes—
43C29×#464C2216yes—
44C29×#462C2216yes—
45C29×#451C2213yes—
46C29×#448C2211yescharacteristic
47C29×#446C2216yes—
48C8×Q8×C29C2212yes—
49C29×#441C22112yes—
50C4×Q16×C29C2216yes—
51C4×SD16×C29C2216yes—
52C29×#432C2213yes—
53C29×#431C2213yes—
54C22×Q8×C29—21no—
55C22×Q8×C29—23no—
56C22×Q8×C29D411yescharacteristic
57C22×Q8×C29C2311yescharacteristic
58C2×Q16×C29C2316yes—
59C2×SD16×C29C2312yes—
60C29×C4⋊Q8—23no—
61C29×C4⋊Q8—26no—
62C29×C4⋊Q8—26no—
63C29×C4⋊Q8—212no—
64C29×C4⋊Q8—23no—
65C29×C4⋊Q8—23no—
66C29×C4⋊Q8C2313yes—
67C29×C4⋊Q8C2316yes—
68C29×C4⋊Q8C2313yes—
69C29×C4⋊Q8C2316yes—
70C29×#126—26no—
71C29×#126—23no—
72C29×#125—26no—
73C29×#125—23no—
74C29×#125—23no—
75C29×#125C2313yes—
76C29×#124C2313yes—
77C29×#123—23no—
78C29×C22⋊Q8—23no—
79C29×C22⋊Q8—23no—
80C29×C22⋊Q8—23no—
81C29×C22⋊Q8C2313yes—
82C29×#121C2311yescharacteristic
83C4×Q8×C29—26no—
84C4×Q8×C29—22no—
85C4×Q8×C29—21no—
86C4×Q8×C29—23no—
87C4×Q8×C29—23no—
88C4×Q8×C29—23no—
89C4×Q8×C29—23no—
90C4×Q8×C29D411yescharacteristic
91C4×Q8×C29D413yes—
92C4×Q8×C29C2316yes—
93C4×Q8×C29C2313yes—
94C4×Q8×C29C2316yes—
95C4×Q8×C29C2316yes—
96C4×Q8×C29C2311yescharacteristic
97C4×Q8×C29C2313yes—
98C4×D4×C29—23no—
99C4×D4×C29C2313yes—
100C29×#117—23no—
101C29×#117—23no—
102C29×#117—23no—
103C2×C4⋊C4×C29—23no—
104C2×C4⋊C4×C29—23no—
105C2×C4⋊C4×C29D413yes—
106C2×C4⋊C4×C29C2313yes—
107C2×C42×C29—23no—
108C2×C42×C29C2313yes—
109C29×#107C2316yes—
110C29×#106C2316yes—
111C29×#106C23112yes—
112C29×C4⋊C8C2316yes—
113C29×C4⋊C8C2316yes—
114C29×#103C2316yes—
115C29×#103C2312yes—
116C29×#103C2316yes—
117C29×#103C23112yes—
118C29×#102C2316yes—
119C29×C22⋊C8C2311yescharacteristic
120C29×C22⋊C8C2313yes—
121C29×#97C2316yes—
122C4×C8×C29C2316yes—
123C2×Q8×C29—24no—
124C2×Q8×C29—24no—
125C2×Q8×C29—21no—
126C2×Q8×C29—23no—
127C2×Q8×C29—26no—
128C2×Q8×C29—26no—
129C2×Q8×C29—44no—
130C2×Q8×C29—86no—
131C2×Q8×C29C2×D413yes—
132C2×Q8×C29C2×D411yescharacteristic
133C2×Q8×C29C2413yes—
134C2×Q8×C29C2412yes—
135C2×D4×C29—21no—
136C2×D4×C29C2411yescharacteristic
137C22×C4×C29—21no—
138C22×C4×C29—23no—
139C22×C4×C29—23no—
140C22×C4×C29C2×D413yes—
141C22×C4×C29C2×D413yes—
142C22×C4×C29C2411yescharacteristic
143Q16×C29—212no—
144SD16×C29—24no—
145C2×C8×C29C2412yes—
146C2×C8×C29C2416yes—
147C4⋊C4×C29—26no—
148C4⋊C4×C29—26no—
149C4⋊C4×C29—26no—
150C4⋊C4×C29—26no—
151C4⋊C4×C29—23no—
152C4⋊C4×C29—23no—
153C4⋊C4×C29—23no—
154C4⋊C4×C29—23no—
155C4⋊C4×C29—23no—
156C4⋊C4×C29—23no—
157C4⋊C4×C29—23no—
158C4⋊C4×C29—26no—
159C4⋊C4×C29—23no—
160C4⋊C4×C29C2×D413yes—
161C4⋊C4×C29C2×D413yes—
162C4⋊C4×C29C2×D416yes—
163C4⋊C4×C29C2416yes—
164C4⋊C4×C29C2413yes—
165C4⋊C4×C29C2411yescharacteristic
166C22⋊C4×C29—23no—
167C22⋊C4×C29—21no—
168C22⋊C4×C29—23no—
169C22⋊C4×C29—23no—
170C22⋊C4×C29—23no—
171C42×C29—26no—
172C42×C29—26no—
173C42×C29—26no—
174C42×C29—23no—
175C42×C29C2×D413yes—
176C42×C29C2×D413yes—
177C42×C29C2413yes—
178C42×C29C2413yes—
179#61838C2911yesmaximal, characteristic, direct product factor, Sylow
180C23×C29—21no—
181C23×C29C22×D411yescharacteristic
182Q8×C29—24no—
183Q8×C29—26no—
184Q8×C29—22no—
185Q8×C29—26no—
186Q8×C29—46no—
187Q8×C29—86no—
188Q8×C29—86no—
189Q8×C29#13714yes—
190Q8×C292−1+414yes—
191D4×C29—22no—
192D4×C29—42no—
193C2×C4×C29—24no—
194C2×C4×C29—26no—
195C2×C4×C29—22no—
196C2×C4×C29—26no—
197C2×C4×C29—22no—
198C2×C4×C29—23no—
199C2×C4×C29—21no—
200C2×C4×C29—23no—
201C2×C4×C29—26no—
202C2×C4×C29—46no—
203C2×C4×C29—46no—
204C2×C4×C29C22×D413yes—
205C2×C4×C29C22×D413yes—
206C2×C4×C29C22×D411yescharacteristic
207C2×C4×C29C22×D413yes—
208C2×C4×C29C22×D413yes—
209C2×C4×C29C2511yescharacteristic
210C8×C29—22no—
211C8×C29—26no—
212#3523C2×C2911yescharacteristic
213C2×Q82C2×C2911yescharacteristic, complemented
214#3387C2×C2916yescomplemented
215Q8×SD16C2×C2912yescomplemented
216#3369C2×C2916yescomplemented
217#3363C2×C2912yescomplemented
218#3238C2×C2913yes—
219#3229C2×C2913yescomplemented
220#3113C2×C2913yescomplemented
221#3108C2×C2913yes—
222#2984C2×C2911yescharacteristic, complemented
223C22×C29—21no—
224C22×C29—21no—
225C22×C29—41no—
226C22×C29—41no—
227C22×C29—41no—
228C22×C29#57712yes—
229C22×C29C23×D411yescharacteristic
230C4×C29—24no—
231C4×C29—21no—
232C4×C29—23no—
233C4×C29—23no—
234C4×C29—23no—
235C4×C29—43no—
236C4×C29—43no—
237C4×C29—46no—
238C4×C29—41no—
239C4×C29C2×#13716yes—
240C4×C29C2×2−1+412yes—
241Q82—21no—
242Q82—23no—
243Q82C22×C2912yes—
244Q82C22×C2916yes—
245#557C22×C2911yescharacteristic
246#557C22×C2913yes—
247#556C22×C2913yes—
248#552—23no—
249D4×Q8—21no—
250D4×Q8C22×C2911yescharacteristic
251#541—23no—
252#533C22×C2913yes—
253C2×C4⋊Q8—23no—
254C2×C4⋊Q8C22×C2913yes—
255#529C22×C2913yes—
256#519—21no—
257C2×C4×Q8—21no—
258C2×C4×Q8C22×C2913yes—
259C2×C4×Q8C22×C2911yescharacteristic
260#501C22×C2916yes—
261#498C22×C2916yes—
262#489C22×C2916yes—
263#487C22×C2916yes—
264#483C22×C2913yes—
265#483C22×C2916yes—
266#480C22×C2913yes—
267#479C22×C2916yes—
268#477C22×C2916yes—
269#476C22×C2916yes—
270#475C22×C2916yes—
271#475C22×C29112yes—
272#464C22×C2916yes—
273#462C22×C2916yes—
274#451C22×C2913yes—
275#448C22×C2911yescharacteristic
276#446C22×C2916yes—
277C8×Q8C22×C2912yes—
278#441C22×C29112yes—
279C4×Q16C22×C2916yes—
280C4×SD16C22×C2916yes—
281#432C22×C2913yes—
282#431C22×C2913yes—
283C2×C29—22no—
284C2×C29—81no—
285C2×C29#348611yescharacteristic
286C2×C29C22×#13711yescharacteristic
287C2×C29C2×#57711yescharacteristic
288C22×Q8—21no—
289C22×Q8—23no—
290C22×Q8D4×C2911yescharacteristic
291C22×Q8C23×C2911yescharacteristic
292C2×Q16C23×C2916yes—
293C2×SD16C23×C2912yes—
294C4⋊Q8—23no—
295C4⋊Q8—26no—
296C4⋊Q8—26no—
297C4⋊Q8—212no—
298C4⋊Q8—23no—
299C4⋊Q8—23no—
300C4⋊Q8C23×C2913yes—
301C4⋊Q8C23×C2916yes—
302C4⋊Q8C23×C2916yes—
303C4⋊Q8C23×C2913yes—
304#126—26no—
305#126—23no—
306#125—26no—
307#125—23no—
308#125—23no—
309#125C23×C2913yes—
310#124C23×C2913yes—
311#123—23no—
312C22⋊Q8—23no—
313C22⋊Q8—23no—
314C22⋊Q8—23no—
315C22⋊Q8C23×C2913yes—
316#121C23×C2911yescharacteristic
317C4×Q8—26no—
318C4×Q8—22no—
319C4×Q8—21no—
320C4×Q8—23no—
321C4×Q8—23no—
322C4×Q8—23no—
323C4×Q8—23no—
324C4×Q8D4×C2911yescharacteristic
325C4×Q8D4×C2913yes—
326C4×Q8C23×C2916yes—
327C4×Q8C23×C2916yes—
328C4×Q8C23×C2913yes—
329C4×Q8C23×C2916yes—
330C4×Q8C23×C2911yescharacteristic
331C4×Q8C23×C2913yes—
332C4×D4—23no—
333C4×D4C23×C2913yes—
334#117—23no—
335#117—23no—
336#117—23no—
337C2×C4⋊C4—23no—
338C2×C4⋊C4—23no—
339C2×C4⋊C4D4×C2913yes—
340C2×C4⋊C4C23×C2913yes—
341C2×C42—23no—
342C2×C42C23×C2913yes—
343#107C23×C2916yes—
344#106C23×C2916yes—
345#106C23×C29112yes—
346C4⋊C8C23×C2916yes—
347C4⋊C8C23×C2916yes—
348#103C23×C2916yes—
349#103C23×C2912yes—
350#103C23×C2916yes—
351#103C23×C29112yes—
352#102C23×C2916yes—
353C22⋊C8C23×C2911yescharacteristic
354C22⋊C8C23×C2913yes—
355#97C23×C2916yes—
356C4×C8C23×C2916yes—
357C29#6183811yescharacteristic, direct product factor, Sylow
358C2×Q8—24no—
359C2×Q8—24no—
360C2×Q8—21no—
361C2×Q8—23no—
362C2×Q8—26no—
363C2×Q8—26no—
364C2×Q8—44no—
365C2×Q8—86no—
366C2×Q8C2×D4×C2913yes—
367C2×Q8C2×D4×C2911yescharacteristic
368C2×Q8C24×C2913yes—
369C2×Q8C24×C2912yes—
370C2×D4—21no—
371C2×D4C24×C2911yescharacteristic
372C22×C4—21no—
373C22×C4—23no—
374C22×C4—23no—
375C22×C4C2×D4×C2913yes—
376C22×C4C2×D4×C2913yes—
377C22×C4C24×C2911yescharacteristic
378Q16—212no—
379SD16—24no—
380C2×C8C24×C2912yes—
381C2×C8C24×C2916yes—
382C4⋊C4—26no—
383C4⋊C4—26no—
384C4⋊C4—26no—
385C4⋊C4—26no—
386C4⋊C4—23no—
387C4⋊C4—23no—
388C4⋊C4—23no—
389C4⋊C4—23no—
390C4⋊C4—23no—
391C4⋊C4—23no—
392C4⋊C4—23no—
393C4⋊C4—26no—
394C4⋊C4—23no—
395C4⋊C4C2×D4×C2913yes—
396C4⋊C4C2×D4×C2913yes—
397C4⋊C4C2×D4×C2916yes—
398C4⋊C4C24×C2916yes—
399C4⋊C4C24×C2913yes—
400C4⋊C4C24×C2911yescharacteristic
401C22⋊C4—23no—
402C22⋊C4—21no—
403C22⋊C4—23no—
404C22⋊C4—23no—
405C22⋊C4—23no—
406C42—26no—
407C42—26no—
408C42—26no—
409C42—23no—
410C42C2×D4×C2913yes—
411C42C2×D4×C2913yes—
412C42C24×C2913yes—
413C42C24×C2913yes—
414C23—21no—
415C23C22×D4×C2911yescharacteristic
416Q8—24no—
417Q8—26no—
418Q8—22no—
419Q8—26no—
420Q8—46no—
421Q8—86no—
422Q8—86no—
423Q8C29×#13714yes—
424Q8C29×2−1+414yes—
425D4—22no—
426D4—42no—
427C2×C4—24no—
428C2×C4—26no—
429C2×C4—22no—
430C2×C4—26no—
431C2×C4—22no—
432C2×C4—23no—
433C2×C4—21no—
434C2×C4—23no—
435C2×C4—26no—
436C2×C4—46no—
437C2×C4—46no—
438C2×C4C22×D4×C2913yes—
439C2×C4C22×D4×C2913yes—
440C2×C4C22×D4×C2911yescharacteristic
441C2×C4C22×D4×C2913yes—
442C2×C4C22×D4×C2913yes—
443C2×C4C25×C2911yescharacteristic
444C8—22no—
445C8—26no—
446C22—21no—
447C22—21no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22C29×#57712yes—
452C22C23×D4×C2911yescharacteristic
453C4—24no—
454C4—21no—
455C4—23no—
456C4—23no—
457C4—23no—
458C4—43no—
459C4—43no—
460C4—46no—
461C4—41no—
462C4C2×C29×#13716yes—
463C4C2×C29×2−1+412yes—
464C2—22no—
465C2—81no—
466C2C29×#348611yescharacteristic
467C2C22×C29×#13711yescharacteristic
468C2C2×C29×#57711yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC29×#121C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C4×Q8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×Q82×C29C2semidirect
3. C29×#3387C2semidirect
4. Q8×SD16×C29C2semidirect
5. C29×#3369C2semidirect
6. C29×#3363C2semidirect
8. C29×#3229C2semidirect
9. C29×#3113C2semidirect
11. C29×#2984C2semidirect
179. #61838C29direct (N × H)
213. C2×Q82C2×C29semidirect
214. #3387C2×C29semidirect
215. Q8×SD16C2×C29semidirect
216. #3369C2×C29semidirect
217. #3363C2×C29semidirect
219. #3229C2×C29semidirect
220. #3113C2×C29semidirect
222. #2984C2×C29semidirect
357. C29#61838direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35232
C2×Q82×C292
C29×#33872
Q8×SD16×C292
C29×#33692
C29×#33632
C29×#32382
C29×#32292
C29×#31132
C29×#31082
C29×#29842
#6183829