Finite Group Databasebeta

← C2×C29×#1612 #20313019

Subgroups — C2×C29×#1612 #20313019

Order 7424.

1156 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#538C211yesmaximal, characteristic
2C2×C29×#483C211yesmaximal, characteristic, complemented
3C2×C29×#480C211yesmaximal, characteristic, complemented
4C2×C29×#397C211yesmaximal, characteristic, complemented
5C29×#1612C218yesmaximal, direct product factor
6C2×C29×#328C211yesmaximal, characteristic, complemented
7C2×C29×#327C211yesmaximal, characteristic, complemented
8C2×C29×#323C211yesmaximal, characteristic, complemented
9C29×#538—22no—
10C29×#538—22no—
11C29×#538—22no—
12C29×#538C2214yes—
13C2×C29×#126—21no—
14C2×C29×#124—21no—
15C2×C29×#123—21no—
16C2×C29×C22⋊Q8C2211yescharacteristic
17C2×C29×#121—21no—
18C2×C29×#121C2211yescharacteristic
19C2×C29×#120—21no—
20C2×C4×D4×C29—21no—
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29—21no—
23C22×C22⋊C4×C29C2211yescharacteristic
24C29×#483—22no—
25C29×#483C2214yescomplemented
26C29×#480—22no—
27C29×#480C2214yescomplemented
28C2×C29×#107—21no—
29C2×C29×#106—21no—
30C2×C29×#103—21no—
31C2×C29×#102—21no—
32C2×C29×C22⋊C8C2211yescharacteristic
33C2×C29×C22⋊C8C2211yescharacteristic
34C29×#397—22no—
35C29×#397C2214yescomplemented
36C2×C29×#95—21no—
37C2×C29×#95C2211yescharacteristic
38C29×#328C2214yescomplemented
39C29×#327C2214yescomplemented
40C29×#323C2214yescomplemented
41C25×C29D411yescharacteristic
42C22×Q8×C29D411yescharacteristic
43C22×D4×C29—21no—
44C22×D4×C29—21no—
45C22×D4×C29—21no—
46C22×D4×C29D411yescharacteristic
47C23×C4×C29—21no—
48C23×C4×C29—21no—
49C23×C4×C29—21no—
50C23×C4×C29D411yescharacteristic
51C23×C4×C29C2311yescharacteristic
52C22×C8×C29—21no—
53C22×C8×C29—21no—
54C29×#126—24no—
55C29×#126—24no—
56C29×#124—24no—
57C29×#124—24no—
58C29×#123—24no—
59C29×#123—24no—
60C29×C22⋊Q8—21no—
61C29×C22⋊Q8—21no—
62C29×C22⋊Q8D412yes—
63C29×C22⋊Q8C2312yes—
64C29×#121—24no—
65C29×#121—24no—
66C29×#121—21no—
67C29×#121—21no—
68C29×#121D412yes—
69C29×#121C2312yes—
70C29×#120—24no—
71C29×#120—24no—
72C4×D4×C29—24no—
73C4×D4×C29—24no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29D411yescharacteristic
82C2×C4⋊C4×C29D411yescharacteristic
83C2×C4⋊C4×C29C2312yes—
84C2×C22⋊C4×C29—21no—
85C2×C22⋊C4×C29—21no—
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—24no—
94C2×C22⋊C4×C29—44no—
95C2×C22⋊C4×C29D412yes—
96C2×C22⋊C4×C29C2312yes—
97C2×C42×C29—21no—
98C29×#107—24no—
99C29×#106—24no—
100C29×#103—24no—
101C29×#102—24no—
102C29×C22⋊C8—21no—
103C29×C22⋊C8—21no—
104C29×C22⋊C8C2312yes—
105C29×C22⋊C8C2312yes—
106C29×#95—24no—
107C29×#95—21no—
108C29×#95C2312yes—
109C24×C29—21no—
110C24×C29—21no—
111C24×C29—22no—
112C24×C29—21no—
113C24×C29—22no—
114C24×C29—42no—
115C24×C29—42no—
116C24×C29C2×D411yescharacteristic
117C24×C29C2×D412yes—
118C2×Q8×C29—21no—
119C2×Q8×C29—42no—
120C2×Q8×C29C2×D412yes—
121C2×D4×C29—22no—
122C2×D4×C29—22no—
123C2×D4×C29—24no—
124C2×D4×C29—24no—
125C2×D4×C29—21no—
126C2×D4×C29—42no—
127C2×D4×C29—42no—
128C2×D4×C29—42no—
129C2×D4×C29—82no—
130C2×D4×C29—82no—
131C2×D4×C29C2×D412yes—
132C22×C4×C29—21no—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—21no—
136C22×C4×C29—24no—
137C22×C4×C29—21no—
138C22×C4×C29—22no—
139C22×C4×C29—22no—
140C22×C4×C29—42no—
141C22×C4×C29—42no—
142C22×C4×C29—42no—
143C22×C4×C29—42no—
144C22×C4×C29—41no—
145C22×C4×C29—41no—
146C22×C4×C29—42no—
147C22×C4×C29—42no—
148C22×C4×C29—42no—
149C22×C4×C29—82no—
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D412yes—
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2×D411yescharacteristic
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2411yescharacteristic
157C2×C8×C29—22no—
158C2×C8×C29—22no—
159C2×C8×C29—42no—
160C2×C8×C29—42no—
161C4⋊C4×C29—24no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—21no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—41no—
169C4⋊C4×C29—41no—
170C4⋊C4×C29C2×D412yes—
171C4⋊C4×C29C2×D412yes—
172C22⋊C4×C29—24no—
173C22⋊C4×C29—24no—
174C22⋊C4×C29—24no—
175C22⋊C4×C29—22no—
176C22⋊C4×C29—22no—
177C22⋊C4×C29—22no—
178C22⋊C4×C29—22no—
179C22⋊C4×C29—22no—
180C22⋊C4×C29—22no—
181C22⋊C4×C29—22no—
182C22⋊C4×C29—22no—
183C22⋊C4×C29—48no—
184C42×C29—24no—
185C2×#1612C2911yesmaximal, characteristic, direct product factor, Sylow
186C23×C29—22no—
187C23×C29—22no—
188C23×C29—22no—
189C23×C29—22no—
190C23×C29—22no—
191C23×C29—22no—
192C23×C29—42no—
193C23×C29—42no—
194C23×C29—48no—
195C23×C29—42no—
196C23×C29—42no—
197C23×C29—42no—
198C23×C29—42no—
199C23×C29—42no—
200C23×C29—42no—
201C23×C29—42no—
202C23×C29—81no—
203C23×C29—81no—
204C23×C29—84no—
205C23×C29#12011yescharacteristic
206C23×C29#12011yescharacteristic
207C23×C29#13512yes—
208C23×C29AGL(1,ℤ/8)12yes—
209C23×C29C22×D411yescharacteristic
210Q8×C29—42no—
211Q8×C29—81no—
212D4×C29—42no—
213D4×C29—42no—
214D4×C29—42no—
215D4×C29—44no—
216D4×C29—81no—
217D4×C29—84no—
218D4×C29—84no—
219C2×C4×C29—22no—
220C2×C4×C29—22no—
221C2×C4×C29—22no—
222C2×C4×C29—22no—
223C2×C4×C29—22no—
224C2×C4×C29—22no—
225C2×C4×C29—41no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—42no—
230C2×C4×C29—42no—
231C2×C4×C29—42no—
232C2×C4×C29—42no—
233C2×C4×C29—42no—
234C2×C4×C29—42no—
235C2×C4×C29—42no—
236C2×C4×C29—42no—
237C2×C4×C29—42no—
238C2×C4×C29—42no—
239C2×C4×C29—42no—
240C2×C4×C29—81no—
241C2×C4×C29—84no—
242C2×C4×C29—84no—
243C2×C4×C29—82no—
244C2×C4×C29—82no—
245C2×C4×C29#12011yescharacteristic
246C2×C4×C29#12011yescharacteristic
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29C22×D411yescharacteristic
249C8×C29—42no—
250C8×C29—42no—
251C2×#538C2×C2911yescharacteristic
252C2×#483C2×C2911yescharacteristic, complemented
253C2×#480C2×C2911yescharacteristic, complemented
254C2×#397C2×C2911yescharacteristic, complemented
255#1612C2×C2918yesdirect product factor
256C2×#328C2×C2911yescharacteristic, complemented
257C2×#327C2×C2911yescharacteristic, complemented
258C2×#323C2×C2911yescharacteristic, complemented
259C22×C29—24no—
260C22×C29—24no—
261C22×C29—21no—
262C22×C29—21no—
263C22×C29—21no—
264C22×C29—21no—
265C22×C29—44no—
266C22×C29—42no—
267C22×C29—42no—
268C22×C29—42no—
269C22×C29—42no—
270C22×C29—42no—
271C22×C29—42no—
272C22×C29—82no—
273C22×C29—84no—
274C22×C29—84no—
275C22×C29—84no—
276C22×C29#44912yes—
277C22×C29#44912yes—
278C22×C29#45512yes—
279C22×C29#45812yes—
280C22×C29C2×#12011yescharacteristic
281C22×C29C2×#13511yescharacteristic
282C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C29—21no—
284C4×C29—21no—
285C4×C29—21no—
286C4×C29—21no—
287C4×C29—42no—
288C4×C29—42no—
289C4×C29—42no—
290C4×C29—42no—
291C4×C29—82no—
292C4×C29—82no—
293#538—22no—
294#538—22no—
295#538—22no—
296#538C22×C2914yes—
297C2×#126—21no—
298C2×#124—21no—
299C2×#123—21no—
300C2×C22⋊Q8C22×C2911yescharacteristic
301C2×#121—21no—
302C2×#121C22×C2911yescharacteristic
303C2×#120—21no—
304C2×C4×D4—21no—
305C22×C4⋊C4C22×C2911yescharacteristic
306C22×C22⋊C4—21no—
307C22×C22⋊C4C22×C2911yescharacteristic
308#483—22no—
309#483C22×C2914yescomplemented
310#480—22no—
311#480C22×C2914yescomplemented
312C2×#107—21no—
313C2×#106—21no—
314C2×#103—21no—
315C2×#102—21no—
316C2×C22⋊C8C22×C2911yescharacteristic
317C2×C22⋊C8C22×C2911yescharacteristic
318#397—22no—
319#397C22×C2914yescomplemented
320C2×#95—21no—
321C2×#95C22×C2911yescharacteristic
322#328C22×C2914yescomplemented
323#327C22×C2914yescomplemented
324#323C22×C2914yescomplemented
325C2×C29—21no—
326C2×C29—21no—
327C2×C29—22no—
328C2×C29—82no—
329C2×C29—82no—
330C2×C29#161214yesdirect product factor
331C2×C29C2×#44911yescharacteristic
332C2×C29C2×#45511yescharacteristic
333C2×C29C2×#45811yescharacteristic
334C25D4×C2911yescharacteristic
335C22×Q8D4×C2911yescharacteristic
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4D4×C2911yescharacteristic
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4D4×C2911yescharacteristic
344C23×C4C23×C2911yescharacteristic
345C22×C8—21no—
346C22×C8—21no—
347#126—24no—
348#126—24no—
349#124—24no—
350#124—24no—
351#123—24no—
352#123—24no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8D4×C2912yes—
356C22⋊Q8C23×C2912yes—
357#121—24no—
358#121—24no—
359#121—21no—
360#121—21no—
361#121D4×C2912yes—
362#121C23×C2912yes—
363#120—24no—
364#120—24no—
365C4×D4—24no—
366C4×D4—24no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C2911yescharacteristic
375C2×C4⋊C4D4×C2911yescharacteristic
376C2×C4⋊C4C23×C2912yes—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4D4×C2912yes—
389C2×C22⋊C4C23×C2912yes—
390C2×C42—21no—
391#107—24no—
392#106—24no—
393#103—24no—
394#102—24no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8C23×C2912yes—
398C22⋊C8C23×C2912yes—
399#95—24no—
400#95—21no—
401#95C23×C2912yes—
402C29C2×#161211yescharacteristic, direct product factor, Sylow
403C24—21no—
404C24—21no—
405C24—22no—
406C24—21no—
407C24—22no—
408C24—42no—
409C24—42no—
410C24C2×D4×C2911yescharacteristic
411C24C2×D4×C2912yes—
412C2×Q8—21no—
413C2×Q8—42no—
414C2×Q8C2×D4×C2912yes—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—21no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4C2×D4×C2912yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—82no—
444C22×C4C2×D4×C2911yescharacteristic
445C22×C4C2×D4×C2911yescharacteristic
446C22×C4C2×D4×C2912yes—
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4C2×D4×C2911yescharacteristic
450C22×C4C24×C2911yescharacteristic
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—42no—
454C2×C8—42no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C2912yes—
465C4⋊C4C2×D4×C2912yes—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—48no—
478C42—24no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23—48no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23—84no—
498C23C29×#12011yescharacteristic
499C23C29×#12011yescharacteristic
500C23C29×#13512yes—
501C23C29×AGL(1,ℤ/8)12yes—
502C23C22×D4×C2911yescharacteristic
503Q8—42no—
504Q8—81no—
505D4—42no—
506D4—44no—
507D4—42no—
508D4—42no—
509D4—81no—
510D4—84no—
511D4—84no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—84no—
535C2×C4—84no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4C29×#12011yescharacteristic
539C2×C4C29×#12011yescharacteristic
540C2×C4C22×D4×C2911yescharacteristic
541C2×C4C22×D4×C2911yescharacteristic
542C8—42no—
543C8—42no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—24no—
549C22—24no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—82no—
558C22—84no—
559C22—84no—
560C22—84no—
561C22C29×#44912yes—
562C22C29×#44912yes—
563C22C29×#45512yes—
564C22C29×#45812yes—
565C22C2×C29×#12011yescharacteristic
566C22C2×C29×#13511yescharacteristic
567C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—82no—
577C4—82no—
578C2—21no—
579C2—22no—
580C2—21no—
581C2—82no—
582C2—82no—
583C2C29×#161214yesdirect product factor
584C2C2×C29×#44911yescharacteristic
585C2C2×C29×#45511yescharacteristic
586C2C2×C29×#45811yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#538C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#483C2semidirect
3. C2×C29×#480C2semidirect
4. C2×C29×#397C2semidirect
5. C29×#1612C2direct (N × H)
6. C2×C29×#328C2semidirect
7. C2×C29×#327C2semidirect
8. C2×C29×#323C2semidirect
25. C29×#483C22semidirect
27. C29×#480C22semidirect
35. C29×#397C22semidirect
38. C29×#328C22semidirect
39. C29×#327C22semidirect
40. C29×#323C22semidirect
185. C2×#1612C29direct (N × H)
252. C2×#483C2×C29semidirect
253. C2×#480C2×C29semidirect
254. C2×#397C2×C29semidirect
255. #1612C2×C29direct (N × H)
256. C2×#328C2×C29semidirect
257. C2×#327C2×C29semidirect
258. C2×#323C2×C29semidirect
309. #483C22×C29semidirect
311. #480C22×C29semidirect
319. #397C22×C29semidirect
322. #328C22×C29semidirect
323. #327C22×C29semidirect
324. #323C22×C29semidirect
330. C2×C29#1612direct (N × H)
402. C29C2×#1612direct (N × H)
583. C2C29×#1612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5382
C2×C29×#4832
C2×C29×#4802
C2×C29×#3972
C29×#16122
C2×C29×#3282
C2×C29×#3272
C2×C29×#3232
C2×#161229