Finite Group Databasebeta

← C2×C29×#3388 #20356262

Subgroups — C2×C29×#3388 #20356262

Order 7424.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#557C211yesmaximal, characteristic, complemented
2C2×C29×#554C211yesmaximal, characteristic
3C29×#3388C2116yesmaximal, direct product factor
4C2×C29×#501C211yesmaximal, characteristic, complemented
5C2×C29×#501C211yesmaximal, characteristic, complemented
6C2×C29×#499C211yesmaximal, characteristic, complemented
7C2×C29×#479C211yesmaximal, characteristic, complemented
8C2×C29×#479C211yesmaximal, characteristic, complemented
9C2×C29×#475C211yesmaximal, characteristic, complemented
10C2×C29×#478C211yesmaximal, characteristic
11C2×C29×#478C211yesmaximal, characteristic
12C2×C29×#476C211yesmaximal, characteristic
13C2×C29×#446C211yesmaximal, characteristic, complemented
14C2×C29×#440C211yesmaximal, characteristic
15C2×C29×#440C211yesmaximal, characteristic
16C2×C4×SD16×C29C211yesmaximal, characteristic
17C22×SD16×C29C2211yescharacteristic
18C29×#557—24no—
19C29×#557C2218yescomplemented
20C29×#554—24no—
21C29×#554C2218yes—
22C2×C29×C4⋊Q8—21no—
23C2×C29×C4⋊Q8C2211yescharacteristic
24C2×C29×C4⋊Q8C2211yescharacteristic
25C2×C29×#125—21no—
26C2×C29×#125—21no—
27C2×C29×#125C2211yescharacteristic
28C2×C29×#125C2211yescharacteristic
29C2×C29×#125C2211yescharacteristic
30C2×C29×#125C2211yescharacteristic
31C2×C29×C22⋊Q8—21no—
32C2×C29×C22⋊Q8—21no—
33C2×C29×C22⋊Q8—21no—
34C2×C4×Q8×C29—21no—
35C2×C4×Q8×C29C2211yescharacteristic
36C2×C4×Q8×C29C2211yescharacteristic
37C2×C4×Q8×C29C2211yescharacteristic
38C2×C4×Q8×C29C2211yescharacteristic
39C2×C4×D4×C29C2211yescharacteristic
40C2×C4×D4×C29C2211yescharacteristic
41C2×C4×D4×C29C2211yescharacteristic
42C22×C4⋊C4×C29—21no—
43C29×#501C2218yescomplemented
44C29×#501C2218yescomplemented
45C29×#499C2218yescomplemented
46C29×#479C2218yescomplemented
47C29×#479C2218yescomplemented
48C29×#478C2218yes—
49C29×#478C2218yes—
50C29×#476C2218yes—
51C29×#475C2218yescomplemented
52C29×#446C2218yescomplemented
53C29×#440C2218yes—
54C29×#440C2218yes—
55C4×SD16×C29C2218yes—
56C2×C29×#107C2211yescharacteristic
57C2×C29×#107C2211yescharacteristic
58C2×C29×#107C2211yescharacteristic
59C2×C29×#107C2211yescharacteristic
60C2×C29×#106C2211yescharacteristic
61C2×C29×#106C2211yescharacteristic
62C2×C29×#106C2211yescharacteristic
63C2×C29×#106C2211yescharacteristic
64C2×C29×#106C2211yescharacteristic
65C2×C29×C4⋊C8C2211yescharacteristic
66C2×C29×C4⋊C8C2211yescharacteristic
67C2×C29×C4⋊C8C2211yescharacteristic
68C2×C29×#103C2211yescharacteristic
69C2×C29×#103C2211yescharacteristic
70C2×C29×#103C2211yescharacteristic
71C2×C29×#102C2211yescharacteristic
72C2×C29×#102C2211yescharacteristic
73C2×C29×#102C2211yescharacteristic
74C2×C29×#97C2211yescharacteristic
75C2×C29×#97C2211yescharacteristic
76C2×C4×C8×C29C2211yescharacteristic
77C22×Q8×C29—21no—
78C22×Q8×C29—21no—
79C22×Q8×C29D411yescharacteristic
80C22×Q8×C29C2311yescharacteristic
81C22×D4×C29C2311yescharacteristic
82C23×C4×C29—21no—
83C23×C4×C29—21no—
84C23×C4×C29—21no—
85C2×SD16×C29Q818yescomplemented
86C2×SD16×C29C2314yes—
87C22×C8×C29C2311yescharacteristic
88C22×C8×C29C2311yescharacteristic
89C22×C8×C29C2311yescharacteristic
90C22×C8×C29C2311yescharacteristic
91C29×C4⋊Q8—28no—
92C29×C4⋊Q8—22no—
93C29×C4⋊Q8—22no—
94C29×C4⋊Q8C2314yes—
95C29×C4⋊Q8C2314yes—
96C29×#125—28no—
97C29×#125—28no—
98C29×#125—22no—
99C29×#125—22no—
100C29×#125—22no—
101C29×#125—22no—
102C29×#125C2314yes—
103C29×#125C2314yes—
104C29×#125C2314yes—
105C29×#125C2314yes—
106C29×C22⋊Q8—28no—
107C29×C22⋊Q8—28no—
108C29×C22⋊Q8—28no—
109C4×Q8×C29—28no—
110C4×Q8×C29—22no—
111C4×Q8×C29—22no—
112C4×Q8×C29—22no—
113C4×Q8×C29D414yes—
114C4×Q8×C29C2314yes—
115C4×Q8×C29C2314yes—
116C4×Q8×C29C2314yes—
117C4×Q8×C29C2314yes—
118C4×D4×C29—22no—
119C4×D4×C29—22no—
120C4×D4×C29—22no—
121C4×D4×C29C2314yes—
122C4×D4×C29C2314yes—
123C4×D4×C29C2314yes—
124C2×C4⋊C4×C29—21no—
125C2×C4⋊C4×C29—21no—
126C2×C4⋊C4×C29—21no—
127C2×C4⋊C4×C29—21no—
128C2×C4⋊C4×C29—21no—
129C2×C4⋊C4×C29—21no—
130C2×C4⋊C4×C29—21no—
131C2×C4⋊C4×C29—21no—
132C2×C4⋊C4×C29—21no—
133C2×C4⋊C4×C29—21no—
134C2×C4⋊C4×C29—21no—
135C2×C4⋊C4×C29—21no—
136C2×C4⋊C4×C29—21no—
137C2×C4⋊C4×C29—28no—
138C2×C4⋊C4×C29D411yescharacteristic
139C2×C4⋊C4×C29D411yescharacteristic
140C2×C4⋊C4×C29D411yescharacteristic
141C2×C4⋊C4×C29C2311yescharacteristic
142C2×C4⋊C4×C29C2311yescharacteristic
143C2×C4⋊C4×C29C2311yescharacteristic
144C2×C4⋊C4×C29C2311yescharacteristic
145C2×C4⋊C4×C29C2311yescharacteristic
146C2×C4⋊C4×C29C2311yescharacteristic
147C2×C22⋊C4×C29—21no—
148C2×C22⋊C4×C29—21no—
149C2×C22⋊C4×C29—21no—
150C2×C42×C29—21no—
151C2×C42×C29—21no—
152C2×C42×C29—21no—
153C2×C42×C29C2311yescharacteristic
154C2×C42×C29C2311yescharacteristic
155C2×C42×C29C2311yescharacteristic
156C29×#107C2314yes—
157C29×#107C2314yes—
158C29×#107C2314yes—
159C29×#107C2314yes—
160C29×#106C2314yes—
161C29×#106C2314yes—
162C29×#106C2314yes—
163C29×#106C2314yes—
164C29×#106C2314yes—
165C29×C4⋊C8C2314yes—
166C29×C4⋊C8C2314yes—
167C29×C4⋊C8C2314yes—
168C29×#103C2314yes—
169C29×#103C2314yes—
170C29×#103C2314yes—
171C29×#102C2314yes—
172C29×#102C2314yes—
173C29×#102C2314yes—
174C29×#97C2314yes—
175C29×#97C2314yes—
176C4×C8×C29C2314yes—
177C24×C29—21no—
178C2×Q8×C29—21no—
179C2×Q8×C29—24no—
180C2×Q8×C29—24no—
181C2×Q8×C29—22no—
182C2×Q8×C29—42no—
183C2×Q8×C29—44no—
184C2×Q8×C29—82no—
185C2×Q8×C29C2×D414yes—
186C2×Q8×C29C2×Q814yes—
187C2×Q8×C29C2412yes—
188C2×D4×C29—21no—
189C2×D4×C29—22no—
190C2×D4×C29C2×Q814yes—
191C2×D4×C29C2412yes—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—21no—
195C22×C4×C29—21no—
196C22×C4×C29—21no—
197C22×C4×C29—21no—
198C22×C4×C29—21no—
199C22×C4×C29—24no—
200C22×C4×C29—24no—
201C22×C4×C29—24no—
202C22×C4×C29—44no—
203C22×C4×C29—82no—
204C22×C4×C29—82no—
205C22×C4×C29C2×D411yescharacteristic
206C22×C4×C29C2×D411yescharacteristic
207C22×C4×C29C2×D411yescharacteristic
208C22×C4×C29C2×D411yescharacteristic
209C22×C4×C29C2×D411yescharacteristic
210C22×C4×C29C2×D411yescharacteristic
211C22×C4×C29C2411yescharacteristic
212SD16×C29C2×Q8116yescomplemented
213C2×C8×C29—22no—
214C2×C8×C29—22no—
215C2×C8×C29—22no—
216C2×C8×C29C2×Q814yes—
217C2×C8×C29C2412yes—
218C2×C8×C29C2412yes—
219C2×C8×C29C2412yes—
220C2×C8×C29C2412yes—
221C4⋊C4×C29—24no—
222C4⋊C4×C29—24no—
223C4⋊C4×C29—24no—
224C4⋊C4×C29—24no—
225C4⋊C4×C29—24no—
226C4⋊C4×C29—24no—
227C4⋊C4×C29—24no—
228C4⋊C4×C29—24no—
229C4⋊C4×C29—24no—
230C4⋊C4×C29—24no—
231C4⋊C4×C29—24no—
232C4⋊C4×C29—24no—
233C4⋊C4×C29—24no—
234C4⋊C4×C29—21no—
235C4⋊C4×C29—21no—
236C4⋊C4×C29—21no—
237C4⋊C4×C29—21no—
238C4⋊C4×C29—21no—
239C4⋊C4×C29—21no—
240C4⋊C4×C29C2×D414yes—
241C4⋊C4×C29C2×D414yes—
242C4⋊C4×C29C2×D414yes—
243C4⋊C4×C29C2412yes—
244C4⋊C4×C29C2412yes—
245C4⋊C4×C29C2412yes—
246C4⋊C4×C29C2412yes—
247C4⋊C4×C29C2412yes—
248C4⋊C4×C29C2412yes—
249C22⋊C4×C29—24no—
250C22⋊C4×C29—24no—
251C22⋊C4×C29—24no—
252C42×C29—24no—
253C42×C29—24no—
254C42×C29—24no—
255C42×C29C2×D412yes—
256C42×C29C2×D412yes—
257C42×C29C2×D412yes—
258C42×C29C2412yes—
259C42×C29C2412yes—
260C42×C29C2412yes—
261C2×#3388C2911yesmaximal, characteristic, direct product factor, Sylow
262C23×C29—24no—
263C23×C29—22no—
264C23×C29—42no—
265C23×C29—42no—
266C23×C29C22×D411yescharacteristic
267Q8×C29—24no—
268Q8×C29—22no—
269Q8×C29—44no—
270Q8×C29—48no—
271Q8×C29—84no—
272Q8×C29C22×Q814yes—
273D4×C29—24no—
274D4×C29—22no—
275D4×C29C22×Q814yes—
276C2×C4×C29—24no—
277C2×C4×C29—22no—
278C2×C4×C29—22no—
279C2×C4×C29—22no—
280C2×C4×C29—22no—
281C2×C4×C29—22no—
282C2×C4×C29—22no—
283C2×C4×C29—22no—
284C2×C4×C29—22no—
285C2×C4×C29—22no—
286C2×C4×C29—22no—
287C2×C4×C29—22no—
288C2×C4×C29—22no—
289C2×C4×C29—22no—
290C2×C4×C29—48no—
291C2×C4×C29—42no—
292C2×C4×C29—42no—
293C2×C4×C29—42no—
294C2×C4×C29—42no—
295C2×C4×C29—42no—
296C2×C4×C29—42no—
297C2×C4×C29—84no—
298C2×C4×C29—84no—
299C2×C4×C29C22×D412yes—
300C2×C4×C29C22×D412yes—
301C2×C4×C29C22×D412yes—
302C2×C4×C29C22×D412yes—
303C2×C4×C29C22×D412yes—
304C2×C4×C29C22×D412yes—
305C2×C4×C29C22×D411yescharacteristic
306C2×C4×C29C22×Q812yes—
307C2×C4×C292−1+412yes—
308C2×C4×C29C2511yescharacteristic
309C8×C29—22no—
310C8×C29—22no—
311C8×C29—22no—
312C8×C29C22×Q814yes—
313C2×#557C2×C2911yescharacteristic, complemented
314C2×#554C2×C2911yescharacteristic
315#3388C2×C29116yesdirect product factor
316C2×#501C2×C2911yescharacteristic, complemented
317C2×#501C2×C2911yescharacteristic, complemented
318C2×#499C2×C2911yescharacteristic, complemented
319C2×#479C2×C2911yescharacteristic, complemented
320C2×#479C2×C2911yescharacteristic, complemented
321C2×#475C2×C2911yescharacteristic, complemented
322C2×#478C2×C2911yescharacteristic
323C2×#478C2×C2911yescharacteristic
324C2×#476C2×C2911yescharacteristic
325C2×#446C2×C2911yescharacteristic, complemented
326C2×#440C2×C2911yescharacteristic
327C2×#440C2×C2911yescharacteristic
328C2×C4×SD16C2×C2911yescharacteristic
329C22×C29—24no—
330C22×C29—48no—
331C22×C29—42no—
332C22×C29—42no—
333C22×C29D4×Q812yes—
334C22×C29#57512yes—
335C22×C29#57712yes—
336C22×C29C23×D411yescharacteristic
337C4×C29—24no—
338C4×C29—22no—
339C4×C29—22no—
340C4×C29—22no—
341C4×C29—22no—
342C4×C29—22no—
343C4×C29—22no—
344C4×C29—42no—
345C4×C29—42no—
346C4×C29—42no—
347C4×C29—42no—
348C4×C29—42no—
349C4×C29—42no—
350C4×C29D4×Q812yes—
351C4×C29C23×Q811yescharacteristic
352C4×C29C2×2−1+411yescharacteristic
353C22×SD16C22×C2911yescharacteristic
354#557—24no—
355#557C22×C2918yescomplemented
356#554—24no—
357#554C22×C2918yes—
358C2×C4⋊Q8—21no—
359C2×C4⋊Q8C22×C2911yescharacteristic
360C2×C4⋊Q8C22×C2911yescharacteristic
361C2×#125—21no—
362C2×#125—21no—
363C2×#125C22×C2911yescharacteristic
364C2×#125C22×C2911yescharacteristic
365C2×#125C22×C2911yescharacteristic
366C2×#125C22×C2911yescharacteristic
367C2×C22⋊Q8—21no—
368C2×C22⋊Q8—21no—
369C2×C22⋊Q8—21no—
370C2×C4×Q8—21no—
371C2×C4×Q8C22×C2911yescharacteristic
372C2×C4×Q8C22×C2911yescharacteristic
373C2×C4×Q8C22×C2911yescharacteristic
374C2×C4×Q8C22×C2911yescharacteristic
375C2×C4×D4C22×C2911yescharacteristic
376C2×C4×D4C22×C2911yescharacteristic
377C2×C4×D4C22×C2911yescharacteristic
378C22×C4⋊C4—21no—
379#501C22×C2918yescomplemented
380#501C22×C2918yescomplemented
381#499C22×C2918yescomplemented
382#479C22×C2918yescomplemented
383#479C22×C2918yescomplemented
384#478C22×C2918yes—
385#478C22×C2918yes—
386#476C22×C2918yes—
387#475C22×C2918yescomplemented
388#446C22×C2918yescomplemented
389#440C22×C2918yes—
390#440C22×C2918yes—
391C4×SD16C22×C2918yes—
392C2×#107C22×C2911yescharacteristic
393C2×#107C22×C2911yescharacteristic
394C2×#107C22×C2911yescharacteristic
395C2×#107C22×C2911yescharacteristic
396C2×#106C22×C2911yescharacteristic
397C2×#106C22×C2911yescharacteristic
398C2×#106C22×C2911yescharacteristic
399C2×#106C22×C2911yescharacteristic
400C2×#106C22×C2911yescharacteristic
401C2×C4⋊C8C22×C2911yescharacteristic
402C2×C4⋊C8C22×C2911yescharacteristic
403C2×C4⋊C8C22×C2911yescharacteristic
404C2×#103C22×C2911yescharacteristic
405C2×#103C22×C2911yescharacteristic
406C2×#103C22×C2911yescharacteristic
407C2×#102C22×C2911yescharacteristic
408C2×#102C22×C2911yescharacteristic
409C2×#102C22×C2911yescharacteristic
410C2×#97C22×C2911yescharacteristic
411C2×#97C22×C2911yescharacteristic
412C2×C4×C8C22×C2911yescharacteristic
413C2×C29—44no—
414C2×C29#338814yesdirect product factor
415C2×C29C2×D4×Q811yescharacteristic
416C2×C29C2×#57511yescharacteristic
417C2×C29C2×#57711yescharacteristic
418C22×Q8—21no—
419C22×Q8—21no—
420C22×Q8D4×C2911yescharacteristic
421C22×Q8C23×C2911yescharacteristic
422C22×D4C23×C2911yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—21no—
426C2×SD16Q8×C2918yescomplemented
427C2×SD16C23×C2914yes—
428C22×C8C23×C2911yescharacteristic
429C22×C8C23×C2911yescharacteristic
430C22×C8C23×C2911yescharacteristic
431C22×C8C23×C2911yescharacteristic
432C4⋊Q8—28no—
433C4⋊Q8—22no—
434C4⋊Q8—22no—
435C4⋊Q8C23×C2914yes—
436C4⋊Q8C23×C2914yes—
437#125—28no—
438#125—28no—
439#125—22no—
440#125—22no—
441#125—22no—
442#125—22no—
443#125C23×C2914yes—
444#125C23×C2914yes—
445#125C23×C2914yes—
446#125C23×C2914yes—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450C4×Q8—28no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8D4×C2914yes—
455C4×Q8C23×C2914yes—
456C4×Q8C23×C2914yes—
457C4×Q8C23×C2914yes—
458C4×Q8C23×C2914yes—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4C23×C2914yes—
463C4×D4C23×C2914yes—
464C4×D4C23×C2914yes—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4D4×C2911yescharacteristic
480C2×C4⋊C4D4×C2911yescharacteristic
481C2×C4⋊C4D4×C2911yescharacteristic
482C2×C4⋊C4C23×C2911yescharacteristic
483C2×C4⋊C4C23×C2911yescharacteristic
484C2×C4⋊C4C23×C2911yescharacteristic
485C2×C4⋊C4C23×C2911yescharacteristic
486C2×C4⋊C4C23×C2911yescharacteristic
487C2×C4⋊C4C23×C2911yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42C23×C2911yescharacteristic
495C2×C42C23×C2911yescharacteristic
496C2×C42C23×C2911yescharacteristic
497#107C23×C2914yes—
498#107C23×C2914yes—
499#107C23×C2914yes—
500#107C23×C2914yes—
501#106C23×C2914yes—
502#106C23×C2914yes—
503#106C23×C2914yes—
504#106C23×C2914yes—
505#106C23×C2914yes—
506C4⋊C8C23×C2914yes—
507C4⋊C8C23×C2914yes—
508C4⋊C8C23×C2914yes—
509#103C23×C2914yes—
510#103C23×C2914yes—
511#103C23×C2914yes—
512#102C23×C2914yes—
513#102C23×C2914yes—
514#102C23×C2914yes—
515#97C23×C2914yes—
516#97C23×C2914yes—
517C4×C8C23×C2914yes—
518C29C2×#338811yescharacteristic, direct product factor, Sylow
519C24—21no—
520C2×Q8—21no—
521C2×Q8—24no—
522C2×Q8—24no—
523C2×Q8—22no—
524C2×Q8—42no—
525C2×Q8—44no—
526C2×Q8—82no—
527C2×Q8C2×D4×C2914yes—
528C2×Q8C2×Q8×C2914yes—
529C2×Q8C24×C2912yes—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4C2×Q8×C2914yes—
533C2×D4C24×C2912yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—44no—
545C22×C4—82no—
546C22×C4—82no—
547C22×C4C2×D4×C2911yescharacteristic
548C22×C4C2×D4×C2911yescharacteristic
549C22×C4C2×D4×C2911yescharacteristic
550C22×C4C2×D4×C2911yescharacteristic
551C22×C4C2×D4×C2911yescharacteristic
552C22×C4C2×D4×C2911yescharacteristic
553C22×C4C24×C2911yescharacteristic
554SD16C2×Q8×C29116yescomplemented
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8C2×Q8×C2914yes—
559C2×C8C24×C2912yes—
560C2×C8C24×C2912yes—
561C2×C8C24×C2912yes—
562C2×C8C24×C2912yes—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4C2×D4×C2914yes—
583C4⋊C4C2×D4×C2914yes—
584C4⋊C4C2×D4×C2914yes—
585C4⋊C4C24×C2912yes—
586C4⋊C4C24×C2912yes—
587C4⋊C4C24×C2912yes—
588C4⋊C4C24×C2912yes—
589C4⋊C4C24×C2912yes—
590C4⋊C4C24×C2912yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C42—24no—
595C42—24no—
596C42—24no—
597C42C2×D4×C2912yes—
598C42C2×D4×C2912yes—
599C42C2×D4×C2912yes—
600C42C24×C2912yes—
601C42C24×C2912yes—
602C42C24×C2912yes—
603C23—24no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23C22×D4×C2911yescharacteristic
608Q8—24no—
609Q8—22no—
610Q8—44no—
611Q8—48no—
612Q8—84no—
613Q8C22×Q8×C2914yes—
614D4—24no—
615D4—22no—
616D4C22×Q8×C2914yes—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—48no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4C22×D4×C2912yes—
641C2×C4C22×D4×C2912yes—
642C2×C4C22×D4×C2912yes—
643C2×C4C22×D4×C2912yes—
644C2×C4C22×D4×C2912yes—
645C2×C4C22×D4×C2912yes—
646C2×C4C22×D4×C2911yescharacteristic
647C2×C4C22×Q8×C2912yes—
648C2×C4C29×2−1+412yes—
649C2×C4C25×C2911yescharacteristic
650C8—22no—
651C8—22no—
652C8—22no—
653C8C22×Q8×C2914yes—
654C22—24no—
655C22—42no—
656C22—42no—
657C22—48no—
658C22D4×Q8×C2912yes—
659C22C29×#57512yes—
660C22C29×#57712yes—
661C22C23×D4×C2911yescharacteristic
662C4—24no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4D4×Q8×C2912yes—
676C4C23×Q8×C2911yescharacteristic
677C4C2×C29×2−1+411yescharacteristic
678C2—44no—
679C2C29×#338814yesdirect product factor
680C2C2×D4×Q8×C2911yescharacteristic
681C2C2×C29×#57511yescharacteristic
682C2C2×C29×#57711yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC22×D4×C29C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C4×Q8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#557C2semidirect
3. C29×#3388C2direct (N × H)
4. C2×C29×#501C2semidirect
5. C2×C29×#501C2semidirect
6. C2×C29×#499C2semidirect
7. C2×C29×#479C2semidirect
8. C2×C29×#479C2semidirect
9. C2×C29×#475C2semidirect
13. C2×C29×#446C2semidirect
19. C29×#557C22semidirect
43. C29×#501C22semidirect
44. C29×#501C22semidirect
45. C29×#499C22semidirect
46. C29×#479C22semidirect
47. C29×#479C22semidirect
51. C29×#475C22semidirect
52. C29×#446C22semidirect
85. C2×SD16×C29Q8semidirect
212. SD16×C29C2×Q8semidirect
261. C2×#3388C29direct (N × H)
313. C2×#557C2×C29semidirect
315. #3388C2×C29direct (N × H)
316. C2×#501C2×C29semidirect
317. C2×#501C2×C29semidirect
318. C2×#499C2×C29semidirect
319. C2×#479C2×C29semidirect
320. C2×#479C2×C29semidirect
321. C2×#475C2×C29semidirect
325. C2×#446C2×C29semidirect
355. #557C22×C29semidirect
379. #501C22×C29semidirect
380. #501C22×C29semidirect
381. #499C22×C29semidirect
382. #479C22×C29semidirect
383. #479C22×C29semidirect
387. #475C22×C29semidirect
388. #446C22×C29semidirect
414. C2×C29#3388direct (N × H)
426. C2×SD16Q8×C29semidirect
518. C29C2×#3388direct (N × H)
554. SD16C2×Q8×C29semidirect
679. C2C29×#3388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5572
C2×C29×#5542
C29×#33882
C2×C29×#5012
C2×C29×#4992
C2×C29×#4792
C2×C29×#4752
C2×C29×#4782
C2×C29×#4762
C2×C29×#4462
C2×C29×#4402
C2×C4×SD16×C292
C2×#338829