Finite Group Databasebeta

← C4×#16837633 #28595174

Subgroups — C4×#16837633 #28595174

Order 15104.

1138 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837633C211yesmaximal, characteristic
2C2×C4×#11745671C211yesmaximal, characteristic, complemented
3C22×C4×C59⋊C8C211yesmaximal, characteristic, complemented
4C4×#14273701C211yesmaximal, characteristic
5#21424953C211yesmaximal, characteristic, complemented
6#21424821C211yesmaximal, characteristic, complemented
7#21424778C211yesmaximal, characteristic, complemented
8#21424775C211yesmaximal, characteristic, complemented
9#21424522C211yesmaximal, characteristic
10#21424520C211yesmaximal, characteristic, complemented
11#21424119C211yesmaximal, characteristic, complemented
12C4×#14273658C211yesmaximal, characteristic, complemented
13C4×#14273651C211yesmaximal, characteristic, complemented
14C4×#14273647C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C59C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×C4×C22⋊D59—21no—
22#16837633C418yesdirect product factor
23C4×#11745671—24no—
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×C4×C59⋊C8—24no—
34C2×C4×C59⋊C8C2211yescharacteristic
35C2×C4×C59⋊C8C2211yescharacteristic
36C2×C4×C59⋊C8C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837300C2211yescharacteristic
40#16837293—21no—
41#16837281—21no—
42#16837262C2211yescharacteristic
43C4×C4⋊Dic59C2211yescharacteristic
44C4×(C2×D59)⋊C4—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51C2×C22⋊Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C22×C42×C59C2211yescharacteristic
54C59×#391C2211yescharacteristic
55C59×#389C2211yescharacteristic
56C59×#387—21no—
57C59×#385—21no—
58C59×#380C2211yescharacteristic
59C4×C4⋊C4×C59—21no—
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C22⋊C4×C59—21no—
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C4×D59—21no—
65C2×#11745671—22no—
66C2×#11745671—22no—
67C2×#11745671C2×C414yescomplemented
68C22×C59⋊C8—22no—
69C22×C59⋊C8—22no—
70C22×C59⋊C8—22no—
71C22×C59⋊C8—22no—
72C22×C59⋊C8—22no—
73C22×C59⋊C8C2×C414yescomplemented
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78#14273701—22no—
79#14273701C2×C414yes—
80C4×D236—22no—
81C4×D236—22no—
82C4×C22⋊D59—44no—
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×Dic59⋊C4—21no—
87C2×C22⋊Dic59—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×C4×Dic59—21no—
93#14273658—22no—
94#14273658—22no—
95#14273658C2×C414yescomplemented
96#14273651—22no—
97#14273651—22no—
98#14273651C2×C414yescomplemented
99#14273647—22no—
100#14273647—22no—
101#14273647C2×C414yescomplemented
102C4×C59⋊C8—22no—
103C4×C59⋊C8—22no—
104C4×C59⋊C8—22no—
105C4×C59⋊C8D414yescomplemented
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C22×Q8×C59C2311yescharacteristic
110C23×C4×C59D411yescharacteristic
111C23×C4×C59D411yescharacteristic
112C23×C4×C59C2311yescharacteristic
113C22⋊Q8×C59—22no—
114C22⋊Q8×C59C2×C414yescomplemented
115C4×Q8×C59—22no—
116C4×Q8×C59—22no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C42×C59—22no—
126C2×C42×C59—22no—
127C2×C42×C59—21no—
128C2×C42×C59—21no—
129C2×C42×C59D411yescharacteristic
130C2×C42×C59D411yescharacteristic
131C2×C42×C59C2311yescharacteristic
132C2×C42×C59C2311yescharacteristic
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137#95×C59—21no—
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59C22×C412yes—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59SD1614yescomplemented
160C22×C4×C59C22×C412yes—
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59#4112yes—
167C22×C4×C59C2411yescharacteristic
168C2×C22⋊D59—24no—
169C2×C22⋊D59—42no—
170C2×C22⋊D59—42no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236C22×C412yes—
180C2×C4×D59—42no—
181C2×C4×D59—42no—
182C2×C4×D59—42no—
183C4⋊C4×C59—24no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—42no—
190C4⋊C4×C59—42no—
191C4⋊C4×C59C22×C412yes—
192C22⋊C4×C59—24no—
193C22⋊C4×C59—42no—
194C42×C59—22no—
195C42×C59—22no—
196C42×C59—21no—
197C42×C59—21no—
198C42×C59—42no—
199C42×C59—42no—
200C42×C59C2×D412yes—
201C42×C59#4112yes—
202C22⋊Dic59—42no—
203#11745671—28no—
204(C2×D59)⋊C4—24no—
205(C2×D59)⋊C4—42no—
206(C2×D59)⋊C4—42no—
207(C2×D59)⋊C4—42no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59C22×C412yes—
214Dic59⋊C4—42no—
215C4×Dic59—42no—
216C2×C59⋊C8—28no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—28no—
224C2×C59⋊C8C22×C412yes—
225C2×C59⋊C8C22×C412yes—
226C2×C59⋊C8C2×D412yes—
227C2×C59⋊C8C2×D412yes—
228C2×C59⋊C8#4112yes—
229C2×C59⋊C8#4112yes—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59C4×D412yes—
235C23×C59C2×SD1612yes—
236C23×C59#13512yes—
237C23×C59C22×D411yescharacteristic
238C22×D59—22no—
239C22×D59—41no—
240C22×D59—41no—
241C22×D59—41no—
242C22×D59—41no—
243C22×D59—41no—
244C22×D59—41no—
245Q8×C59—22no—
246Q8×C59—22no—
247Q8×C59—41no—
248Q8×C59—41no—
249C2×C4×C59—28no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—28no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59C4×D412yes—
276C2×C4×C59#12112yes—
277C2×C4×C59#12112yes—
278C2×C4×C59C2×SD1612yes—
279C2×C4×C59C2×SD1612yes—
280C2×C4×C59#13512yes—
281C2×C4×C59#13512yes—
282C2×C4×C59C23×C411yescharacteristic
283C2×C4×C59C22×D411yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59C2×#4111yescharacteristic
287C2×C4×C59C2×#4111yescharacteristic
288C22⋊D59—48no—
289C2×Dic59—22no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298D236—22no—
299D236—22no—
300D236—41no—
301D236—41no—
302C4×D59—84no—
303C59⋊C8—22no—
304C59⋊C8—22no—
305C59⋊C8—22no—
306C59⋊C8C4×D414yescomplemented
307C4×#465—591nomaximal, Sylow
308C22×C59—22no—
309C22×C59—22no—
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59C4×SD1614yescomplemented
315C22×C59C2×C4×D411yescharacteristic
316C22×C59C2×#12111yescharacteristic
317C22×C59#53211yescharacteristic
318C22×C59C22×SD1611yescharacteristic
319C22×C59C2×#13511yescharacteristic
320C22×C59C2×#13511yescharacteristic
321C22×C59C2×#13511yescharacteristic
322C2×D59—42no—
323C2×D59—42no—
324C2×D59—42no—
325C2×D59—81no—
326C2×D59—81no—
327C2×D59—81no—
328C2×D59—81no—
329C4×C59—22no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—42no—
334C4×C59—42no—
335C4×C59—81no—
336C4×C59—81no—
337C4×C59#46514yescomplemented
338C4×C59C2×C4×D411yescharacteristic
339C4×C59C4×#4111yescharacteristic
340C4×C59#52511yescharacteristic
341C4×C59#52911yescharacteristic
342Dic59—42no—
343Dic59—81no—
344Dic59—81no—
345C2×#465—591no—
346C2×C4×SD16—591no—
347C22×C4×C8—591no—
348C4×C22⋊Q8D5911yescharacteristic, complemented
349C4×#121—591no—
350#1968—591no—
351#1941—591no—
352#1934—591no—
353#1933—591no—
354#1893—591no—
355#1892—591no—
356#1807—591no—
357C4×#106—591no—
358C4×#103—591no—
359C4×#102—591no—
360C2×C59—24no—
361C2×C59C4×#12111yescharacteristic
362C2×C59C2×C4×SD1611yescharacteristic
363C2×C59C4×#13511yescharacteristic
364C2×C59C2×#46511yescharacteristic
365C2×C59#305011yescharacteristic
366C2×C59#316711yescharacteristic
367C2×C59#316811yescharacteristic
368D59—82no—
369C22×SD16—591no—
370C23×C8—591no—
371C23×C8—591no—
372C2×C22⋊Q8C2×D5911yescharacteristic
373C2×#121—591no—
374C2×C4×Q8C2×D5911yescharacteristic
375C2×C4×D4—591no—
376C2×C4×D4—1181no—
377C22×C42C2×D5911yescharacteristic
378#465—598no—
379C4×SD16—1184no—
380C2×#106—591no—
381C2×#106—591no—
382C2×#106—591no—
383C2×#103—591no—
384C2×#103—591no—
385C2×#103—591no—
386C2×#102—591no—
387C2×#102—591no—
388C2×#102—591no—
389C2×C4×C8—591no—
390C2×C4×C8—591no—
391C2×C4×C8—591no—
392C2×C4×C8—591no—
393C2×C4×C8—1184no—
394#391C2×D5911yescharacteristic
395#390—591no—
396#389—591no—
397#389C2×D5911yescharacteristic
398#388—1181no—
399#387—21no—
400#386—1181no—
401#385—21no—
402#380—591no—
403#380C2×D5911yescharacteristic
404C4×C4⋊C4—21no—
405C4×C4⋊C4—591no—
406C4×C4⋊C4C2×D5911yescharacteristic
407C4×C22⋊C4—21no—
408C4×C22⋊C4—1181no—
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415C59C4×#46511yescharacteristic, complemented, Sylow
416C22×Q8C22×D5911yescharacteristic
417C22×D4—591no—
418C22×D4—1181no—
419C23×C4—1181no—
420C23×C4C22⋊D5911yescharacteristic
421C23×C4C22⋊D5911yescharacteristic
422C23×C4C22×D5911yescharacteristic
423C2×SD16—594no—
424C2×SD16—1182no—
425C2×SD16—1182no—
426C22×C8—591no—
427C22×C8—594no—
428C22×C8—591no—
429C22×C8—591no—
430C22×C8—591no—
431C22×C8—1182no—
432C22×C8—1182no—
433C22×C8—1182no—
434C22×C8—1182no—
435C22×C8—1182no—
436C22⋊Q8—22no—
437C22⋊Q8C4×D5914yescomplemented
438#121—594no—
439#121—1182no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×D4—1182no—
443C4×D4—1182no—
444C4×D4—2364no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—591no—
449C2×C4⋊C4—591no—
450C2×C4⋊C4—591no—
451C2×C4⋊C4—1181no—
452C2×C4⋊C4C22×D5911yescharacteristic
453C2×C4⋊C4C22×D5911yescharacteristic
454C2×C4⋊C4C22×D5911yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4—1181no—
459C2×C22⋊C4—1181no—
460C2×C22⋊C4—1181no—
461C2×C22⋊C4—1181no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—1181no—
467C2×C42C22⋊D5911yescharacteristic
468C2×C42C22⋊D5911yescharacteristic
469C2×C42C22×D5911yescharacteristic
470C2×C42C22×D5911yescharacteristic
471#106—594no—
472#106—1182no—
473#106—1182no—
474#103—594no—
475#103—1182no—
476#103—1182no—
477#102—594no—
478#102—1182no—
479#102—1182no—
480C4×C8—594no—
481C4×C8—1182no—
482C4×C8—1182no—
483C4×C8—1182no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—1181no—
490#95—1181no—
491#95—1181no—
492C24—1181no—
493C24C2×C22⋊D5911yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D5912yes—
500C2×D4—592no—
501C2×D4—1184no—
502C2×D4—1181no—
503C2×D4—1181no—
504C2×D4—1181no—
505C2×D4—1181no—
506C2×D4—1181no—
507C2×D4—2362no—
508C2×D4—2362no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
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—1181no—
523C22×C4—1181no—
524C22×C4—1181no—
525C22×C4—2362no—
526C22×C4—2362no—
527C22×C4—2362no—
528C22×C4#1174567114yescomplemented
529C22×C4C2×C4×D5912yes—
530C22×C4#1174568512yes—
531C22×C4C2×C22⋊D5911yescharacteristic
532C22×C4C2×C22⋊D5911yescharacteristic
533C22×C4C2×C22⋊D5911yescharacteristic
534C22×C4C2×C22⋊D5911yescharacteristic
535C22×C4C2×C22⋊D5911yescharacteristic
536C22×C4C23×D5911yescharacteristic
537SD16—1188no—
538C2×C8—592no—
539C2×C8—592no—
540C2×C8—592no—
541C2×C8—592no—
542C2×C8—592no—
543C2×C8—592no—
544C2×C8—1188no—
545C2×C8—1188no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—592no—
561C4⋊C4—1181no—
562C4⋊C4—1181no—
563C4⋊C4—1181no—
564C4⋊C4—1181no—
565C4⋊C4—1181no—
566C4⋊C4—2362no—
567C4⋊C4C2×C4×D5912yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—1184no—
571C22⋊C4—2362no—
572C22⋊C4—2362no—
573C22⋊C4—2362no—
574C22⋊C4—2362no—
575C42—22no—
576C42—22no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—2362no—
582C42D4×D5912yes—
583C42#1174568712yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—1182no—
589C23—2361no—
590C23—2361no—
591C23—2361no—
592C23—2361no—
593C23—2361no—
594C23—2361no—
595C23C4×C22⋊D5912yes—
596C23C2×#1174567112yes—
597C23#1427374712yes—
598C23C22×C22⋊D5911yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—1182no—
604D4—1182no—
605D4—2368no—
606D4—2361no—
607D4—2361no—
608C2×C4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—28no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—41no—
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—1182no—
635C2×C4—4724no—
636C2×C4—2361no—
637C2×C4—2361no—
638C2×C4—2361no—
639C2×C4—2361no—
640C2×C4—2361no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4C4×C22⋊D5912yes—
645C2×C4#1427369912yes—
646C2×C4#1427369912yes—
647C2×C4C2×#1174567112yes—
648C2×C4C2×#1174567112yes—
649C2×C4#1427374712yes—
650C2×C4#1427374712yes—
651C2×C4C22×C4×D5911yescharacteristic
652C2×C4C2×D4×D5911yescharacteristic
653C2×C4#41×D5911yescharacteristic
654C2×C4#41×D5911yescharacteristic
655C2×C4C2×#1174568711yescharacteristic
656C2×C4C2×#1174568511yescharacteristic
657C8—594no—
658C8—1182no—
659C8—1182no—
660C8—1182no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—4721no—
668C22—4721no—
669C22—4721no—
670C22—4721no—
671C22—2362no—
672C22—2362no—
673C22—2362no—
674C22C4×#1174567114yescomplemented
675C22C2×C4×C22⋊D5911yescharacteristic
676C22C2×#1427369911yescharacteristic
677C22#1683794811yescharacteristic
678C22C22×#1174567111yescharacteristic
679C22C2×#1427374711yescharacteristic
680C22C2×#1427374711yescharacteristic
681C22C2×#1427374711yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—42no—
688C4—81no—
689C4—81no—
690C4—4721no—
691C4—4721no—
692C4—2362no—
693C4#1683763314yesdirect product factor
694C4C4×D4×D5911yescharacteristic
695C4C4×#1174568711yescharacteristic
696C4#1683791111yescharacteristic
697C4#1683793211yescharacteristic
698C2—24no—
699C2—4722no—
700C2C4×#1427369911yescharacteristic
701C2C2×C4×#1174567111yescharacteristic
702C2C4×#1427374711yescharacteristic
703C2C2×#1683763311yescharacteristic
704C2#2143367411yescharacteristic
705C2#2143465611yescharacteristic
706C2#2143466011yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×C22⋊Q8×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenterC4×C22⋊Q8D59
hypocenterC59C4×#465
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745671C2semidirect
3. C22×C4×C59⋊C8C2semidirect
5. #21424953C2semidirect
6. #21424821C2semidirect
7. #21424778C2semidirect
8. #21424775C2semidirect
10. #21424520C2semidirect
11. #21424119C2semidirect
12. C4×#14273658C2semidirect
13. C4×#14273651C2semidirect
14. C4×#14273647C2semidirect
15. C4×C22⋊Q8×C59C2semidirect
22. #16837633C4direct (N × H)
67. C2×#11745671C2×C4semidirect
73. C22×C59⋊C8C2×C4semidirect
95. #14273658C2×C4semidirect
98. #14273651C2×C4semidirect
101. #14273647C2×C4semidirect
105. C4×C59⋊C8D4semidirect
114. C22⋊Q8×C59C2×C4semidirect
159. C22×C4×C59SD16semidirect
306. C59⋊C8C4×D4semidirect
314. C22×C59C4×SD16semidirect
337. C4×C59#465semidirect
348. C4×C22⋊Q8D59semidirect
415. C59C4×#465semidirect
437. C22⋊Q8C4×D59semidirect
528. C22×C4#11745671semidirect
674. C22C4×#11745671semidirect
693. C4#16837633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168376332
C2×C4×#117456712
C22×C4×C59⋊C82
C4×#142737012
#214249532
#214248212
#214247782
#214247752
#214245222
#214245202
#214241192
C4×#142736582
C4×#142736512
C4×#142736472
C4×C22⋊Q8×C592
C4×#46559