Finite Group Databasebeta

← C22×#15689870 #27123155

Subgroups — C22×#15689870 #27123155

Order 12032.

8102 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689870C2148yesmaximal, direct product factor
2C22×#13094015C211yesmaximal, characteristic, complemented
3C22×#13094010C211yesmaximal, characteristic, complemented
4C22×#13094010C211yesmaximal, characteristic, complemented
5C22×#13094009C211yesmaximal, characteristic, complemented
6C22×#13094008C211yesmaximal, characteristic, complemented
7C22×#13094006C211yesmaximal, characteristic, complemented
8C22×#13094004C211yesmaximal, characteristic, complemented
9C22×#13094003C211yesmaximal, characteristic, complemented
10C22×#13094002C211yesmaximal, characteristic, complemented
11C22×#13094001C211yesmaximal, characteristic, complemented
12C22×#13093998C211yesmaximal, characteristic, complemented
13C22×#13093997C211yesmaximal, characteristic, complemented
14C22×#13093996C211yesmaximal, characteristic, complemented
15C22×#13093995C211yesmaximal, characteristic, complemented
16C22×#123×C47C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C22⋊D47C2211yescharacteristic
22C23×C22⋊D47C2211yescharacteristic
23C23×C22⋊D47C2211yescharacteristic
24C24×Dic47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27#15689870C221256yesdirect product factor
28C2×#13094015C22124yescomplemented
29C2×#13094010C22124yescomplemented
30C2×#13094010C22124yescomplemented
31C2×#13094009C22124yescomplemented
32C2×#13094008C22124yescomplemented
33C2×#13094006C22124yescomplemented
34C2×#13094004C22124yescomplemented
35C2×#13094003C22124yescomplemented
36C2×#13094002C22124yescomplemented
37C2×#13094001C22124yescomplemented
38C2×#13093998C22124yescomplemented
39C2×#13093997C22124yescomplemented
40C2×#13093996C22124yescomplemented
41C2×#13093995C22124yescomplemented
42C22×C4⋊Dic47C2211yescharacteristic
43C22×C4⋊Dic47C2211yescharacteristic
44C22×C4⋊Dic47C2211yescharacteristic
45C22×C4⋊Dic47C2211yescharacteristic
46C22×Dic47⋊C4C2211yescharacteristic
47C22×Dic47⋊C4C2211yescharacteristic
48C22×Dic47⋊C4C2211yescharacteristic
49C22×Dic47⋊C4C2211yescharacteristic
50C22×C22⋊Dic47C2211yescharacteristic
51C22×C22⋊Dic47C2211yescharacteristic
52C22×C22⋊Dic47C2211yescharacteristic
53C22×(C2×D47)⋊C4C2211yescharacteristic
54C22×(C2×D47)⋊C4C2211yescharacteristic
55C22×(C2×D47)⋊C4C2211yescharacteristic
56C22×(C2×D47)⋊C4C2211yescharacteristic
57C22×(C2×D47)⋊C4C2211yescharacteristic
58C22×(C2×D47)⋊C4C2211yescharacteristic
59C22×C4×Dic47C2211yescharacteristic
60C23×D4×C47C2211yescharacteristic
61C24×C4×C47C2211yescharacteristic
62C2×#123×C47C22124yescomplemented
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C24×D47C2311yescharacteristic
69C24×D47C2311yescharacteristic
70C22×Dic94—44no—
71C22×Dic94—44no—
72C22×Dic94C23112yes—
73C22×Dic94C23112yes—
74C22×D188—44no—
75C22×D188C23112yes—
76C22×C22⋊D47—44no—
77C22×C22⋊D47—44no—
78C22×C22⋊D47—44no—
79C22×C22⋊D47—44no—
80C22×C22⋊D47C23112yes—
81C22×C22⋊D47C23112yes—
82C22×C22⋊D47C23112yes—
83C22×C22⋊D47C23112yes—
84C23×Dic47—44no—
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C23×Dic47C23112yes—
92C22×C4×D47—44no—
93C22×C4×D47—44no—
94C22×C4×D47C23112yes—
95C22×C4×D47C23112yes—
96#13094015C23164yescomplemented
97#13094010C23164yescomplemented
98#13094010C23164yescomplemented
99#13094009C23164yescomplemented
100#13094008C23164yescomplemented
101#13094006C23164yescomplemented
102#13094004C23164yescomplemented
103#13094003C23164yescomplemented
104#13094002C23164yescomplemented
105#13094001C23164yescomplemented
106#13093998C23164yescomplemented
107#13093997C23164yescomplemented
108#13093996C23164yescomplemented
109#13093995C23164yescomplemented
110C2×C4⋊Dic47C23112yes—
111C2×C4⋊Dic47C23112yes—
112C2×C4⋊Dic47C23112yes—
113C2×C4⋊Dic47C23112yes—
114C2×Dic47⋊C4C23112yes—
115C2×Dic47⋊C4C23112yes—
116C2×Dic47⋊C4C23112yes—
117C2×Dic47⋊C4C23112yes—
118C2×C22⋊Dic47C23112yes—
119C2×C22⋊Dic47C23112yes—
120C2×C22⋊Dic47C23112yes—
121C2×(C2×D47)⋊C4C23112yes—
122C2×(C2×D47)⋊C4C23112yes—
123C2×(C2×D47)⋊C4C23112yes—
124C2×(C2×D47)⋊C4C23112yes—
125C2×(C2×D47)⋊C4C23112yes—
126C2×(C2×D47)⋊C4C23112yes—
127C2×C4×Dic47C23112yes—
128C25×C47C2311yescharacteristic
129C25×C47C2311yescharacteristic
130C22×D4×C47—44no—
131C22×D4×C47C23112yes—
132C23×C4×C47—44no—
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C23112yes—
139#123×C47C23164yescomplemented
140C2×C4⋊C4×C47C23112yes—
141C2×C4⋊C4×C47C23112yes—
142C2×C22⋊C4×C47C23112yes—
143C2×C22⋊C4×C47C23112yes—
144C2×C22⋊C4×C47C23112yes—
145C24×C47—24no—
146C24×C47—24no—
147C24×C47—24no—
148C24×C47—24no—
149C24×C47—24no—
150C24×C47—24no—
151C24×C47C2416yes—
152C24×C47C2416yes—
153C24×C47C2411yescharacteristic
154C23×D47—24no—
155C23×D47—24no—
156C23×D47—24no—
157C23×D47—24no—
158C23×D47—24no—
159C23×D47—24no—
160C23×D47C2416yes—
161C23×D47C2416yes—
162C2×D4×C47—424no—
163C2×D4×C47C24116yes—
164C22×C4×C47—24no—
165C22×C4×C47—24no—
166C22×C4×C47—24no—
167C22×C4×C47—24no—
168C22×C4×C47—24no—
169C22×C4×C47—424no—
170C22×C4×C47C2416yes—
171C22×C4×C47C2416yes—
172C22×C4×C47C2416yes—
173C22×C4×C47C2416yes—
174C22×C4×C47C2416yes—
175C22×C4×C47C24116yes—
176C2×C22⋊D47—424no—
177C2×C22⋊D47—424no—
178C2×C22⋊D47—424no—
179C2×C22⋊D47—424no—
180C2×C22⋊D47C24116yes—
181C2×C22⋊D47C24116yes—
182C2×C22⋊D47C24116yes—
183C2×C22⋊D47C24116yes—
184C22×Dic47—24no—
185C22×Dic47—24no—
186C22×Dic47—24no—
187C22×Dic47—24no—
188C22×Dic47—24no—
189C22×Dic47—24no—
190C22×Dic47—424no—
191C22×Dic47C2416yes—
192C22×Dic47C2416yes—
193C22×Dic47C2416yes—
194C22×Dic47C2416yes—
195C22×Dic47C2416yes—
196C22×Dic47C2416yes—
197C22×Dic47C24116yes—
198C2×D188—424no—
199C2×D188C24116yes—
200C2×C4×D47—424no—
201C2×C4×D47—424no—
202C2×C4×D47C24116yes—
203C2×C4×D47C24116yes—
204C2×Dic94—424no—
205C2×Dic94—424no—
206C2×Dic94C24116yes—
207C2×Dic94C24116yes—
208C4⋊C4×C47C24116yes—
209C4⋊C4×C47C24116yes—
210C22⋊C4×C47C24116yes—
211C22⋊C4×C47C24116yes—
212C22⋊C4×C47C24116yes—
213C22⋊Dic47C24116yes—
214C22⋊Dic47C24116yes—
215C22⋊Dic47C24116yes—
216(C2×D47)⋊C4C24116yes—
217(C2×D47)⋊C4C24116yes—
218(C2×D47)⋊C4C24116yes—
219(C2×D47)⋊C4C24116yes—
220(C2×D47)⋊C4C24116yes—
221(C2×D47)⋊C4C24116yes—
222C4⋊Dic47C24116yes—
223C4⋊Dic47C24116yes—
224C4⋊Dic47C24116yes—
225C4⋊Dic47C24116yes—
226Dic47⋊C4C24116yes—
227Dic47⋊C4C24116yes—
228Dic47⋊C4C24116yes—
229Dic47⋊C4C24116yes—
230C4×Dic47C24116yes—
231C23×C47—212no—
232C23×C47—212no—
233C23×C47—212no—
234C23×C47—212no—
235C23×C47—212no—
236C23×C47—212no—
237C23×C47—416no—
238C23×C47—416no—
239C23×C47H(5,𝔽2)14yes—
240C23×C47H(5,𝔽2)14yes—
241C23×C472−1+414yes—
242C23×C47C2514yes—
243C23×C47C2514yes—
244C23×C47C2513yes—
245C22×D47—212no—
246C22×D47—212no—
247C22×D47—212no—
248C22×D47—212no—
249C22×D47—212no—
250C22×D47—212no—
251C22×D47—416no—
252C22×D47—416no—
253C22×D47C2514yes—
254C22×D47C2514yes—
255D4×C47—416no—
256C2×C4×C47—212no—
257C2×C4×C47—212no—
258C2×C4×C47—212no—
259C2×C4×C47—212no—
260C2×C4×C47—212no—
261C2×C4×C47—416no—
262C2×C4×C47C2514yes—
263C2×C4×C47C2514yes—
264C2×C4×C47C2514yes—
265C2×C4×C47C2514yes—
266C2×C4×C47C2514yes—
267C22⋊D47—416no—
268C22⋊D47—416no—
269C22⋊D47—416no—
270C22⋊D47—416no—
271C2×Dic47—212no—
272C2×Dic47—212no—
273C2×Dic47—212no—
274C2×Dic47—212no—
275C2×Dic47—212no—
276C2×Dic47—212no—
277C2×Dic47—416no—
278C2×Dic47C2514yes—
279C2×Dic47C2514yes—
280C2×Dic47C2514yes—
281C2×Dic47C2514yes—
282C2×Dic47C2514yes—
283C2×Dic47C2514yes—
284D188—416no—
285C4×D47—416no—
286C4×D47—416no—
287Dic94—416no—
288Dic94—416no—
289C22×#562—471nomaximal, Sylow
290C22×C47—24no—
291C22×C47—24no—
292C22×C47—24no—
293C22×C47—24no—
294C22×C47—24no—
295C22×C47—24no—
296C22×C47—424no—
297C22×C47—424no—
298C22×C47#562116yescomplemented
299C22×C47C2×H(5,𝔽2)16yes—
300C22×C47C2×H(5,𝔽2)16yes—
301C22×C47C2×2−1+416yes—
302C22×C47C2611yescharacteristic
303C2×D47—24no—
304C2×D47—24no—
305C2×D47—24no—
306C2×D47—24no—
307C2×D47—24no—
308C2×D47—24no—
309C2×D47—424no—
310C2×D47—424no—
311C4×C47—24no—
312C4×C47—24no—
313C4×C47—24no—
314C4×C47—24no—
315C4×C47—24no—
316Dic47—24no—
317Dic47—24no—
318Dic47—24no—
319Dic47—24no—
320Dic47—24no—
321Dic47—24no—
322C2×#562—4748no—
323C22×#125—471no—
324C22×#124—471no—
325C22×#124—471no—
326C22×#123—471no—
327C22×#123—471no—
328C22×#123—471no—
329C22×#123D4711yescharacteristic, complemented
330C22×C22⋊Q8—471no—
331C22×C22⋊Q8—471no—
332C22×C22⋊Q8—471no—
333C22×C22⋊Q8—471no—
334C22×#121—471no—
335C22×#121—471no—
336C22×#121—471no—
337C22×#121—471no—
338C2×C47—44no—
339C2×C47—44no—
340C2×C47C2×#562112yescomplemented
341C2×C47C22×H(5,𝔽2)11yescharacteristic
342C2×C47C22×H(5,𝔽2)11yescharacteristic
343C2×C47C22×2−1+411yescharacteristic
344D47—44no—
345D47—44no—
346C23×Q8—471no—
347C23×Q8—471no—
348C23×D4—471no—
349C23×D4—471no—
350C23×D4—471no—
351C23×D4—471no—
352C23×D4—471no—
353C23×D4C2×D4711yescharacteristic
354C24×C4—471no—
355C24×C4—471no—
356C24×C4—471no—
357C24×C4C2×D4711yescharacteristic
358#562—47256no—
359C2×#125—4724no—
360C2×#124—4724no—
361C2×#124—4724no—
362C2×#123—4724no—
363C2×#123—4724no—
364C2×#123—4724no—
365C2×#123C2×D47124yescomplemented
366C2×C22⋊Q8—4724no—
367C2×C22⋊Q8—4724no—
368C2×C22⋊Q8—4724no—
369C2×C22⋊Q8—4724no—
370C2×#121—4724no—
371C2×#121—4724no—
372C2×#121—4724no—
373C2×#121—4724no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4—471no—
376C22×C4⋊C4—471no—
377C22×C4⋊C4—471no—
378C22×C4⋊C4—471no—
379C22×C4⋊C4—471no—
380C22×C4⋊C4—471no—
381C22×C4⋊C4—471no—
382C22×C4⋊C4C2×D4711yescharacteristic
383C22×C4⋊C4C2×D4711yescharacteristic
384C22×C22⋊C4—471no—
385C22×C22⋊C4—471no—
386C22×C22⋊C4—471no—
387C22×C22⋊C4—471no—
388C22×C22⋊C4—471no—
389C22×C22⋊C4—471no—
390C22×C22⋊C4—471no—
391C22×C22⋊C4—471no—
392C22×C22⋊C4—471no—
393C22×C22⋊C4C2×D4711yescharacteristic
394C22×C22⋊C4C2×D4711yescharacteristic
395C22×C22⋊C4C2×D4711yescharacteristic
396C22×C42—471no—
397C47C22×#56211yescharacteristic, complemented, Sylow
398C25—471no—
399C25—471no—
400C25C22×D4711yescharacteristic
401C25C22×D4711yescharacteristic
402C22×Q8—4712no—
403C22×Q8—4712no—
404C22×Q8—1884no—
405C22×Q8—1884no—
406C22×D4—44no—
407C22×D4—4712no—
408C22×D4—4712no—
409C22×D4—4712no—
410C22×D4—4712no—
411C22×D4—4712no—
412C22×D4—1884no—
413C22×D4—1884no—
414C22×D4—1884no—
415C22×D4—1884no—
416C22×D4—1884no—
417C22×D4C22×D47112yes—
418C23×C4—44no—
419C23×C4—471no—
420C23×C4—471no—
421C23×C4—471no—
422C23×C4—471no—
423C23×C4—471no—
424C23×C4—471no—
425C23×C4—4712no—
426C23×C4—4712no—
427C23×C4—4712no—
428C23×C4—1884no—
429C23×C4—1884no—
430C23×C4—1884no—
431C23×C4C22×D4711yescharacteristic
432C23×C4C22×D4711yescharacteristic
433C23×C4C22×D4711yescharacteristic
434C23×C4C22×D4711yescharacteristic
435C23×C4C22×D4711yescharacteristic
436C23×C4C22×D47112yes—
437#125—4764no—
438#124—4764no—
439#124—4764no—
440#123—4764no—
441#123—4764no—
442#123—4764no—
443#123C22×D47164yescomplemented
444C22⋊Q8—4764no—
445C22⋊Q8—4764no—
446C22⋊Q8—4764no—
447C22⋊Q8—4764no—
448#121—4764no—
449#121—4764no—
450#121—4764no—
451#121—4764no—
452C2×C4⋊C4—4712no—
453C2×C4⋊C4—4712no—
454C2×C4⋊C4—4712no—
455C2×C4⋊C4—4712no—
456C2×C4⋊C4—4712no—
457C2×C4⋊C4—4712no—
458C2×C4⋊C4—4712no—
459C2×C4⋊C4—4712no—
460C2×C4⋊C4C22×D47112yes—
461C2×C4⋊C4C22×D47112yes—
462C2×C22⋊C4—4712no—
463C2×C22⋊C4—4712no—
464C2×C22⋊C4—4712no—
465C2×C22⋊C4—4712no—
466C2×C22⋊C4—4712no—
467C2×C22⋊C4—4712no—
468C2×C22⋊C4—4712no—
469C2×C22⋊C4—4712no—
470C2×C22⋊C4—4712no—
471C2×C22⋊C4C22×D47112yes—
472C2×C22⋊C4C22×D47112yes—
473C2×C22⋊C4C22×D47112yes—
474C2×C42—4712no—
475C24—24no—
476C24—24no—
477C24—24no—
478C24—24no—
479C24—24no—
480C24—24no—
481C24—476no—
482C24—476no—
483C24—944no—
484C24—944no—
485C24—944no—
486C24—944no—
487C24—944no—
488C24—944no—
489C24C23×D4716yes—
490C24C23×D4716yes—
491C24C23×D4711yescharacteristic
492C2×Q8—4716no—
493C2×Q8—4716no—
494C2×Q8—18824no—
495C2×Q8—18824no—
496C2×D4—424no—
497C2×D4—4716no—
498C2×D4—4716no—
499C2×D4—4716no—
500C2×D4—4716no—
501C2×D4—4716no—
502C2×D4—18824no—
503C2×D4—18824no—
504C2×D4—18824no—
505C2×D4—18824no—
506C2×D4—18824no—
507C2×D4C23×D47116yes—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—424no—
514C22×C4—476no—
515C22×C4—476no—
516C22×C4—476no—
517C22×C4—476no—
518C22×C4—476no—
519C22×C4—476no—
520C22×C4—4716no—
521C22×C4—4716no—
522C22×C4—4716no—
523C22×C4—944no—
524C22×C4—944no—
525C22×C4—944no—
526C22×C4—944no—
527C22×C4—944no—
528C22×C4—944no—
529C22×C4—18824no—
530C22×C4—18824no—
531C22×C4—18824no—
532C22×C4C23×D4716yes—
533C22×C4C23×D4716yes—
534C22×C4C23×D4716yes—
535C22×C4C23×D4716yes—
536C22×C4C23×D4716yes—
537C22×C4C23×D47116yes—
538C4⋊C4—4716no—
539C4⋊C4—4716no—
540C4⋊C4—4716no—
541C4⋊C4—4716no—
542C4⋊C4—4716no—
543C4⋊C4—4716no—
544C4⋊C4—4716no—
545C4⋊C4—4716no—
546C4⋊C4C23×D47116yes—
547C4⋊C4C23×D47116yes—
548C22⋊C4—4716no—
549C22⋊C4—4716no—
550C22⋊C4—4716no—
551C22⋊C4—4716no—
552C22⋊C4—4716no—
553C22⋊C4—4716no—
554C22⋊C4—4716no—
555C22⋊C4—4716no—
556C22⋊C4—4716no—
557C22⋊C4C23×D47116yes—
558C22⋊C4C23×D47116yes—
559C22⋊C4C23×D47116yes—
560C42—4716no—
561C23—212no—
562C23—212no—
563C23—212no—
564C23—212no—
565C23—212no—
566C23—212no—
567C23—416no—
568C23—416no—
569C23—474no—
570C23—474no—
571C23—9412no—
572C23—9412no—
573C23—9412no—
574C23—9412no—
575C23—9412no—
576C23—9412no—
577C23—18816no—
578C23—18816no—
579C23#1309406914yes—
580C23#1309407014yes—
581C23#1309407114yes—
582C23C24×D4714yes—
583C23C24×D4714yes—
584C23C24×D4713yes—
585Q8—18816no—
586Q8—18816no—
587D4—416no—
588D4—18816no—
589D4—18816no—
590D4—18816no—
591D4—18816no—
592D4—18816no—
593C2×C4—212no—
594C2×C4—212no—
595C2×C4—212no—
596C2×C4—212no—
597C2×C4—212no—
598C2×C4—416no—
599C2×C4—474no—
600C2×C4—474no—
601C2×C4—474no—
602C2×C4—474no—
603C2×C4—474no—
604C2×C4—474no—
605C2×C4—9412no—
606C2×C4—9412no—
607C2×C4—9412no—
608C2×C4—9412no—
609C2×C4—9412no—
610C2×C4—9412no—
611C2×C4—18816no—
612C2×C4—18816no—
613C2×C4—18816no—
614C2×C4C24×D4714yes—
615C2×C4C24×D4714yes—
616C2×C4C24×D4714yes—
617C2×C4C24×D4714yes—
618C2×C4C24×D4714yes—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—24no—
625C22—424no—
626C22—424no—
627C22—944no—
628C22—944no—
629C22—944no—
630C22—944no—
631C22—944no—
632C22—944no—
633C22—18824no—
634C22—18824no—
635C22#15689870116yesdirect product factor
636C22C2×#1309406916yes—
637C22C2×#1309407016yes—
638C22C2×#1309407116yes—
639C22C25×D4711yescharacteristic
640C4—24no—
641C4—24no—
642C4—24no—
643C4—24no—
644C4—24no—
645C4—944no—
646C4—944no—
647C4—944no—
648C4—944no—
649C4—944no—
650C4—944no—
651C2—44no—
652C2—44no—
653C2—1884no—
654C2—1884no—
655C2C2×#15689870112yesdirect product factor
656C2C22×#1309406911yescharacteristic
657C2C22×#1309407011yescharacteristic
658C2C22×#1309407111yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC22×#123×C47C2
socleC24×C47C24
hypercenterC22×#123D47
hypocenterC47C22×#562
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#15689870C2direct (N × H)
2. C22×#13094015C2semidirect
3. C22×#13094010C2semidirect
4. C22×#13094010C2semidirect
5. C22×#13094009C2semidirect
6. C22×#13094008C2semidirect
7. C22×#13094006C2semidirect
8. C22×#13094004C2semidirect
9. C22×#13094003C2semidirect
10. C22×#13094002C2semidirect
11. C22×#13094001C2semidirect
12. C22×#13093998C2semidirect
13. C22×#13093997C2semidirect
14. C22×#13093996C2semidirect
15. C22×#13093995C2semidirect
16. C22×#123×C47C2semidirect
27. #15689870C22direct (N × H)
28. C2×#13094015C22semidirect
29. C2×#13094010C22semidirect
30. C2×#13094010C22semidirect
31. C2×#13094009C22semidirect
32. C2×#13094008C22semidirect
33. C2×#13094006C22semidirect
34. C2×#13094004C22semidirect
35. C2×#13094003C22semidirect
36. C2×#13094002C22semidirect
37. C2×#13094001C22semidirect
38. C2×#13093998C22semidirect
39. C2×#13093997C22semidirect
40. C2×#13093996C22semidirect
41. C2×#13093995C22semidirect
62. C2×#123×C47C22semidirect
96. #13094015C23semidirect
97. #13094010C23semidirect
98. #13094010C23semidirect
99. #13094009C23semidirect
100. #13094008C23semidirect
101. #13094006C23semidirect
102. #13094004C23semidirect
103. #13094003C23semidirect
104. #13094002C23semidirect
105. #13094001C23semidirect
106. #13093998C23semidirect
107. #13093997C23semidirect
108. #13093996C23semidirect
109. #13093995C23semidirect
139. #123×C47C23semidirect
298. C22×C47#562semidirect
329. C22×#123D47semidirect
340. C2×C47C2×#562semidirect
365. C2×#123C2×D47semidirect
397. C47C22×#562semidirect
443. #123C22×D47semidirect
635. C22#15689870direct (N × H)
655. C2C2×#15689870direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898702
C22×#130940152
C22×#130940102
C22×#130940092
C22×#130940082
C22×#130940062
C22×#130940042
C22×#130940032
C22×#130940022
C22×#130940012
C22×#130939982
C22×#130939972
C22×#130939962
C22×#130939952
C22×#123×C472
C22×#56247