Finite Group Databasebeta

← C29×#26989 #20321889

Subgroups — C29×#26989 #20321889

Order 7424.

866 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#468C211yesmaximal, characteristic
2C2×C29×#441C211yesmaximal, characteristic, complemented
3C29×#2426C211yesmaximal, characteristic
4C29×#2421C211yesmaximal, characteristic, complemented
5C29×#2085C211yesmaximal, characteristic, complemented
6C29×#2034C211yesmaximal, characteristic
7C29×#2015C211yesmaximal, characteristic, complemented
8C29×#2001C211yesmaximal, characteristic, complemented
9C29×#1958C211yesmaximal, characteristic, complemented
10C29×#1936C211yesmaximal, characteristic, complemented
11C29×#1933C211yesmaximal, characteristic, complemented
12C29×#1894C211yesmaximal, characteristic, complemented
13C29×#1880C211yesmaximal, characteristic, complemented
14C29×#1863C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic, complemented
16C22×Q16×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic
19C2×C29×#124C2211yescharacteristic
20C2×C29×C22⋊Q8C2211yescharacteristic
21C2×C29×C22⋊Q8C2211yescharacteristic
22C2×C29×#121C2211yescharacteristic
23C2×C4×Q8×C29C2211yescharacteristic
24C2×C4×Q8×C29C2211yescharacteristic
25C29×#468—24no—
26C29×#441—24no—
27C2×C29×#107C2211yescharacteristic
28C2×C29×#106C2211yescharacteristic
29C2×C29×#103C2211yescharacteristic
30C2×C29×#103C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#103C2211yescharacteristic
33C2×C29×#103C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×#102C2211yescharacteristic
36C2×C29×#102C2211yescharacteristic
37C2×C29×C22⋊C8C2211yescharacteristic
38C2×C29×#97C2211yescharacteristic
39C2×C4×C8×C29C2211yescharacteristic
40C29×#400—21no—
41C29×#397—21no—
42C29×#396—21no—
43C29×#394—21no—
44C29×#391C2211yescharacteristic
45C29×#390—21no—
46C29×#390C2211yescharacteristic
47C29×#389C2211yescharacteristic
48C29×#389C2211yescharacteristic
49C29×#388—21no—
50C29×#388—21no—
51C29×#387—21no—
52C29×#382C2211yescharacteristic
53C29×#380C2211yescharacteristic
54C4×C22⋊C4×C29C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C22×Q8×C29C2311yescharacteristic
62C22×Q8×C29C2311yescharacteristic
63C22×D4×C29—21no—
64C22×D4×C29C2311yescharacteristic
65C23×C4×C29C2311yescharacteristic
66C2×Q16×C29—22no—
67C2×Q16×C29—22no—
68C2×Q16×C29—22no—
69C2×SD16×C29—22no—
70C2×SD16×C29—22no—
71C2×SD16×C29—41no—
72C2×M16×C29—22no—
73C2×M16×C29—22no—
74C2×M16×C29—41no—
75C22×C8×C29C2311yescharacteristic
76C22×C8×C29C2311yescharacteristic
77C22×C8×C29C2311yescharacteristic
78C22×C8×C29C2311yescharacteristic
79C29×#124—22no—
80C29×#124—41no—
81C29×C22⋊Q8—22no—
82C29×C22⋊Q8—22no—
83C29×C22⋊Q8—41no—
84C29×C22⋊Q8—41no—
85C29×#121—22no—
86C29×#121—41no—
87C4×Q8×C29—22no—
88C4×Q8×C29—22no—
89C4×Q8×C29—41no—
90C4×Q8×C29—41no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—21no—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29—21no—
95C2×C4⋊C4×C29—21no—
96C2×C4⋊C4×C29—21no—
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C4⋊C4×C29C2311yescharacteristic
100C2×C4⋊C4×C29C2311yescharacteristic
101C2×C4⋊C4×C29C2311yescharacteristic
102C2×C22⋊C4×C29—21no—
103C2×C22⋊C4×C29—21no—
104C2×C22⋊C4×C29—21no—
105C2×C22⋊C4×C29—21no—
106C2×C22⋊C4×C29—21no—
107C2×C22⋊C4×C29—21no—
108C2×C22⋊C4×C29—21no—
109C2×C22⋊C4×C29—21no—
110C2×C22⋊C4×C29D411yescharacteristic
111C2×C22⋊C4×C29D411yescharacteristic
112C2×C42×C29—21no—
113C2×C42×C29—21no—
114C2×C42×C29C2311yescharacteristic
115C2×C42×C29C2311yescharacteristic
116C29×#107—22no—
117C29×#106—22no—
118C29×#103—22no—
119C29×#103—22no—
120C29×#103—41no—
121C29×#103—41no—
122C29×#103D414yes—
123C29×#102—22no—
124C29×#102—22no—
125C29×#102—41no—
126C29×C22⋊C8—22no—
127C29×#97—22no—
128C4×C8×C29—41no—
129C29×#95—21no—
130C29×#95—21no—
131C29×#95—21no—
132C29×#95—21no—
133C29×#95—21no—
134C29×#95—21no—
135C29×#95—21no—
136C29×#95D411yescharacteristic
137C29×#95D411yescharacteristic
138C24×C29—21no—
139C24×C29C2×D411yescharacteristic
140C2×Q8×C29—21no—
141C2×Q8×C29—21no—
142C2×Q8×C29—21no—
143C2×Q8×C29—21no—
144C2×Q8×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C2×D412yes—
151C2×Q8×C29#4112yes—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—42no—
159C2×D4×C29—42no—
160C2×D4×C29—81no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D411yescharacteristic
177C22×C4×C29C2×D411yescharacteristic
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29C2411yescharacteristic
180Q16×C29—28no—
181SD16×C29—44no—
182M16×C29—44no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29C2×D412yes—
193C2×C8×C29#4112yes—
194C2×C8×C29#4112yes—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—42no—
205C4⋊C4×C29—42no—
206C4⋊C4×C29—42no—
207C4⋊C4×C29—42no—
208C4⋊C4×C29—42no—
209C4⋊C4×C29—81no—
210C4⋊C4×C29C2×D412yes—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C22⋊C4×C29—42no—
214C22⋊C4×C29—42no—
215C22⋊C4×C29—42no—
216C22⋊C4×C29—42no—
217C22⋊C4×C29—42no—
218C22⋊C4×C29—42no—
219C22⋊C4×C29—42no—
220C22⋊C4×C29—81no—
221C42×C29—21no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—21no—
225C42×C29—42no—
226C42×C29—42no—
227#26989C2911yesmaximal, characteristic, direct product factor, Sylow
228C23×C29—21no—
229C23×C29—21no—
230C23×C29—21no—
231C23×C29—21no—
232C23×C29—21no—
233C23×C29—21no—
234C23×C29—21no—
235C23×C29—41no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29—41no—
242C23×C29C22×D411yescharacteristic
243Q8×C29—22no—
244Q8×C29—22no—
245Q8×C29—22no—
246Q8×C29—22no—
247Q8×C29—41no—
248Q8×C29—41no—
249Q8×C29—41no—
250Q8×C29—41no—
251D4×C29—41no—
252D4×C29—41no—
253D4×C29—41no—
254D4×C29—41no—
255D4×C29—84no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—21no—
259C2×C4×C29—22no—
260C2×C4×C29—22no—
261C2×C4×C29—21no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—22no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
269C2×C4×C29—21no—
270C2×C4×C29—21no—
271C2×C4×C29—21no—
272C2×C4×C29—21no—
273C2×C4×C29—21no—
274C2×C4×C29—41no—
275C2×C4×C29—41no—
276C2×C4×C29—41no—
277C2×C4×C29—41no—
278C2×C4×C29—41no—
279C2×C4×C29—41no—
280C2×C4×C29—41no—
281C2×C4×C29—41no—
282C2×C4×C29—41no—
283C2×C4×C29—41no—
284C2×C4×C29—41no—
285C2×C4×C29—41no—
286C2×C4×C29—41no—
287C2×C4×C29—41no—
288C2×C4×C29—41no—
289C2×C4×C29—41no—
290C2×C4×C29—41no—
291C2×C4×C29—41no—
292C2×C4×C29—41no—
293C2×C4×C29—41no—
294C2×C4×C29—41no—
295C2×C4×C29—41no—
296C2×C4×C29C22×D411yescharacteristic
297C2×C4×C29C2×#4111yescharacteristic
298C2×C4×C29C2×#4111yescharacteristic
299C2×C4×C29C2×#4111yescharacteristic
300C2×C4×C29H(5,𝔽2)11yescharacteristic
301C2×C4×C29H(5,𝔽2)11yescharacteristic
302C8×C29—22no—
303C8×C29—22no—
304C8×C29—22no—
305C8×C29—41no—
306C2×#468C2×C2911yescharacteristic
307C2×#441C2×C2911yescharacteristic, complemented
308#2426C2×C2911yescharacteristic
309#2421C2×C2911yescharacteristic, complemented
310#2085C2×C2911yescharacteristic, complemented
311#2034C2×C2911yescharacteristic
312#2015C2×C2911yescharacteristic, complemented
313#2001C2×C2911yescharacteristic, complemented
314#1958C2×C2911yescharacteristic, complemented
315#1936C2×C2911yescharacteristic, complemented
316#1933C2×C2911yescharacteristic, complemented
317#1894C2×C2911yescharacteristic, complemented
318#1880C2×C2911yescharacteristic, complemented
319#1863C2×C2911yescharacteristic, complemented
320#1753C2×C2911yescharacteristic, complemented
321C22×C29—41no—
322C22×C29—41no—
323C22×C29—41no—
324C22×C29—41no—
325C22×C29—41no—
326C22×C29—41no—
327C22×C29—41no—
328C22×C29—81no—
329C22×C29—81no—
330C22×C29—81no—
331C22×C29—81no—
332C22×C29—81no—
333C22×C29—81no—
334C22×C29—81no—
335C22×C29#53211yescharacteristic
336C22×C29D4211yescharacteristic
337C22×C29#54611yescharacteristic
338C22×C29#57511yescharacteristic
339C22×C29#57511yescharacteristic
340C22×C29#57711yescharacteristic
341C22×C29#57811yescharacteristic
342C4×C29—41no—
343C4×C29—42no—
344C4×C29—42no—
345C4×C29—41no—
346C4×C29—42no—
347C4×C29—41no—
348C4×C29—41no—
349C4×C29—41no—
350C4×C29—81no—
351C4×C29—81no—
352C4×C29—81no—
353C4×C29—81no—
354C4×C29#52511yescharacteristic
355C4×C29#54011yescharacteristic
356C4×C29#54611yescharacteristic
357C4×C29#55311yescharacteristic
358C22×Q16C22×C2911yescharacteristic
359C22×SD16C22×C2911yescharacteristic
360C22×M16C22×C2911yescharacteristic
361C2×#124C22×C2911yescharacteristic
362C2×C22⋊Q8C22×C2911yescharacteristic
363C2×C22⋊Q8C22×C2911yescharacteristic
364C2×#121C22×C2911yescharacteristic
365C2×C4×Q8C22×C2911yescharacteristic
366C2×C4×Q8C22×C2911yescharacteristic
367#468—24no—
368#441—24no—
369C2×#107C22×C2911yescharacteristic
370C2×#106C22×C2911yescharacteristic
371C2×#103C22×C2911yescharacteristic
372C2×#103C22×C2911yescharacteristic
373C2×#103C22×C2911yescharacteristic
374C2×#103C22×C2911yescharacteristic
375C2×#103C22×C2911yescharacteristic
376C2×#102C22×C2911yescharacteristic
377C2×#102C22×C2911yescharacteristic
378C2×#102C22×C2911yescharacteristic
379C2×C22⋊C8C22×C2911yescharacteristic
380C2×#97C22×C2911yescharacteristic
381C2×C4×C8C22×C2911yescharacteristic
382#400—21no—
383#397—21no—
384#396—21no—
385#394—21no—
386#391C22×C2911yescharacteristic
387#390—21no—
388#390C22×C2911yescharacteristic
389#389C22×C2911yescharacteristic
390#389C22×C2911yescharacteristic
391#388—21no—
392#388—21no—
393#387—21no—
394#382C22×C2911yescharacteristic
395#380C22×C2911yescharacteristic
396C4×C22⋊C4C22×C2911yescharacteristic
397#340C22×C2911yescharacteristic
398#340C22×C2911yescharacteristic
399#340C22×C2911yescharacteristic
400#340C22×C2911yescharacteristic
401#336C22×C2911yescharacteristic
402#336C22×C2911yescharacteristic
403C2×C29—81no—
404C2×C29—161no—
405C2×C29#246411yescharacteristic
406C2×C29#317811yescharacteristic
407C2×C29#318311yescharacteristic
408C2×C29#327511yescharacteristic
409C2×C29#327711yescharacteristic
410C2×C29#331311yescharacteristic
411C2×C29#331711yescharacteristic
412C22×Q8C23×C2911yescharacteristic
413C22×Q8C23×C2911yescharacteristic
414C22×D4—21no—
415C22×D4C23×C2911yescharacteristic
416C23×C4C23×C2911yescharacteristic
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16—22no—
420C2×SD16—22no—
421C2×SD16—22no—
422C2×SD16—41no—
423C2×M16—22no—
424C2×M16—22no—
425C2×M16—41no—
426C22×C8C23×C2911yescharacteristic
427C22×C8C23×C2911yescharacteristic
428C22×C8C23×C2911yescharacteristic
429C22×C8C23×C2911yescharacteristic
430#124—22no—
431#124—41no—
432C22⋊Q8—22no—
433C22⋊Q8—22no—
434C22⋊Q8—41no—
435C22⋊Q8—41no—
436#121—22no—
437#121—41no—
438C4×Q8—22no—
439C4×Q8—22no—
440C4×Q8—41no—
441C4×Q8—41no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4C23×C2911yescharacteristic
449C2×C4⋊C4C23×C2911yescharacteristic
450C2×C4⋊C4C23×C2911yescharacteristic
451C2×C4⋊C4C23×C2911yescharacteristic
452C2×C4⋊C4C23×C2911yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C2911yescharacteristic
462C2×C22⋊C4D4×C2911yescharacteristic
463C2×C42—21no—
464C2×C42—21no—
465C2×C42C23×C2911yescharacteristic
466C2×C42C23×C2911yescharacteristic
467#107—22no—
468#106—22no—
469#103—22no—
470#103—22no—
471#103—41no—
472#103—41no—
473#103D4×C2914yes—
474#102—22no—
475#102—22no—
476#102—41no—
477C22⋊C8—22no—
478#97—22no—
479C4×C8—41no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95D4×C2911yescharacteristic
488#95D4×C2911yescharacteristic
489C29#2698911yescharacteristic, direct product factor, Sylow
490C24—21no—
491C24C2×D4×C2911yescharacteristic
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8C2×D4×C2912yes—
503C2×Q8#41×C2912yes—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4C2×D4×C2911yescharacteristic
527C22×C4C2×D4×C2911yescharacteristic
528C22×C4C2×D4×C2911yescharacteristic
529C22×C4C2×D4×C2911yescharacteristic
530C22×C4C2×D4×C2911yescharacteristic
531C22×C4C24×C2911yescharacteristic
532Q16—28no—
533SD16—44no—
534M16—44no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C2×D4×C2912yes—
545C2×C8#41×C2912yes—
546C2×C8#41×C2912yes—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4C2×D4×C2912yes—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—42no—
578C42—42no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C22×D4×C2911yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4C22×D4×C2911yescharacteristic
648C2×C4C2×#41×C2911yescharacteristic
649C2×C4C2×#41×C2911yescharacteristic
650C2×C4C2×#41×C2911yescharacteristic
651C2×C4C29×H(5,𝔽2)11yescharacteristic
652C2×C4C29×H(5,𝔽2)11yescharacteristic
653C8—22no—
654C8—22no—
655C8—22no—
656C8—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22C29×#53211yescharacteristic
672C22D42×C2911yescharacteristic
673C22C29×#54611yescharacteristic
674C22C29×#57511yescharacteristic
675C22C29×#57511yescharacteristic
676C22C29×#57711yescharacteristic
677C22C29×#57811yescharacteristic
678C4—41no—
679C4—42no—
680C4—42no—
681C4—41no—
682C4—42no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4C29×#52511yescharacteristic
691C4C29×#54011yescharacteristic
692C4C29×#54611yescharacteristic
693C4C29×#55311yescharacteristic
694C2—81no—
695C2—161no—
696C2C29×#246411yescharacteristic
697C2C29×#317811yescharacteristic
698C2C29×#318311yescharacteristic
699C2C29×#327511yescharacteristic
700C2C29×#327711yescharacteristic
701C2C29×#331311yescharacteristic
702C2C29×#331711yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#441C2semidirect
4. C29×#2421C2semidirect
5. C29×#2085C2semidirect
7. C29×#2015C2semidirect
8. C29×#2001C2semidirect
9. C29×#1958C2semidirect
10. C29×#1936C2semidirect
11. C29×#1933C2semidirect
12. C29×#1894C2semidirect
13. C29×#1880C2semidirect
14. C29×#1863C2semidirect
15. C29×#1753C2semidirect
227. #26989C29direct (N × H)
307. C2×#441C2×C29semidirect
309. #2421C2×C29semidirect
310. #2085C2×C29semidirect
312. #2015C2×C29semidirect
313. #2001C2×C29semidirect
314. #1958C2×C29semidirect
315. #1936C2×C29semidirect
316. #1933C2×C29semidirect
317. #1894C2×C29semidirect
318. #1880C2×C29semidirect
319. #1863C2×C29semidirect
320. #1753C2×C29semidirect
489. C29#26989direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4682
C2×C29×#4412
C29×#24262
C29×#24212
C29×#20852
C29×#20342
C29×#20152
C29×#20012
C29×#19582
C29×#19362
C29×#19332
C29×#18942
C29×#18802
C29×#18632
C29×#17532
#2698929