Finite Group Databasebeta

← C2×#20252129 #27080185

Subgroups — C2×#20252129 #27080185

Order 12032.

2850 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094032C211yesmaximal, characteristic, complemented
2C22×#13094030C211yesmaximal, characteristic, complemented
3C2×#15689670C211yesmaximal, characteristic
4#20252129C2116yesmaximal, direct product factor
5C2×#15689199C211yesmaximal, characteristic, complemented
6C2×#15689198C211yesmaximal, characteristic, complemented
7C2×#15689196C211yesmaximal, characteristic, complemented
8C2×#15689195C211yesmaximal, characteristic, complemented
9C2×#15689193C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
11C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
12C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
13C2×#15689088C211yesmaximal, characteristic, complemented
14C2×#15689088C211yesmaximal, characteristic, complemented
15C2×#15689075C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C2×#13094032—28no—
20C2×#13094032C2218yescomplemented
21C2×#13094030—28no—
22C2×#13094030C2218yescomplemented
23C22×#10625329C2211yescharacteristic
24C22×#10625324C2211yescharacteristic
25C22×#10625324C2211yescharacteristic
26C22×#10625324C2211yescharacteristic
27C22×#10625324C2211yescharacteristic
28C23×C47⋊C8C2211yescharacteristic
29C22×C8×D47C2211yescharacteristic
30C22×C8×D47C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic
32C22×C8×D47C2211yescharacteristic
33#15689670C418yes—
34#15689670C2218yes—
35C2×#13094023C411yescharacteristic
36C2×#13094020C411yescharacteristic
37C2×#13094010C411yescharacteristic
38C2×#13094010C411yescharacteristic
39C2×#13093999C411yescharacteristic
40C2×#13093997C411yescharacteristic
41C2×#13093997C411yescharacteristic
42C2×#13093995C411yescharacteristic
43C2×C4×D188C2211yescharacteristic
44C2×C4×C22⋊D47C2211yescharacteristic
45C2×C4×C22⋊D47C2211yescharacteristic
46C2×C42×D47C2211yescharacteristic
47#15689199C2218yescomplemented
48#15689198C2218yescomplemented
49#15689196C2218yescomplemented
50#15689195C2218yescomplemented
51#15689193C2218yescomplemented
52C8×C22⋊D47C2218yescomplemented
53(C22⋊D47)⋊C8C2218yescomplemented
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57C4⋊C8×D47C2218yescomplemented
58#15689088C2218yescomplemented
59#15689088C2218yescomplemented
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×(C2×D47)⋊C8C2211yescharacteristic
63C2×(C2×D47)⋊C8C2211yescharacteristic
64C2×(C2×D47)⋊C8C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66#15689075C2218yescomplemented
67C2×#13093935C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C8×Dic47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C23×C8×C47C2211yescharacteristic
72C2×C4×D4×C47C2211yescharacteristic
73C47×#435C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#97×C47C2211yescharacteristic
78C2×#10625350—24no—
79C2×#10625350—24no—
80C2×#10625350—24no—
81C2×#10625350—24no—
82C2×#10625350C2×C414yes—
83C2×#10625350C2×C414yes—
84C2×#10625350C2314yes—
85C2×#10625350C2314yes—
86C22×Dic94C2×C411yescharacteristic
87C22×Dic94C2×C411yescharacteristic
88C22×D188C2×C411yescharacteristic
89C22×D188C2×C411yescharacteristic
90C22×D188C2×C411yescharacteristic
91C22×C22⋊D47C2×C411yescharacteristic
92C22×C22⋊D47C2×C411yescharacteristic
93C22×C22⋊D47C2×C411yescharacteristic
94C22×C22⋊D47C2×C411yescharacteristic
95C22×C22⋊D47C2×C411yescharacteristic
96C22×C22⋊D47C2×C411yescharacteristic
97C22×C4×D47C2×C411yescharacteristic
98C22×C4×D47C2×C411yescharacteristic
99C22×C4×D47C2311yescharacteristic
100C22×C4×D47C2311yescharacteristic
101C22×C4×D47C2311yescharacteristic
102#13094032—232no—
103#13094030—232no—
104C2×#10625329—24no—
105C2×#10625329C2314yes—
106C2×#10625324—24no—
107C2×#10625324—24no—
108C2×#10625324—24no—
109C2×#10625324D418yescomplemented
110C2×#10625324C2314yes—
111C2×#10625324C2314yes—
112C2×#10625324C2314yes—
113C2×#10625324C2314yes—
114C22×C47⋊C8—24no—
115C22×C47⋊C8C2311yescharacteristic
116C22×C47⋊C8C2311yescharacteristic
117C22×C47⋊C8C2311yescharacteristic
118C22×C47⋊C8C2314yes—
119C22×C47⋊C8C2311yescharacteristic
120C2×C8×D47—24no—
121C2×C8×D47—24no—
122C2×C8×D47—24no—
123C2×C8×D47—24no—
124C2×C8×D47C2314yes—
125C2×C8×D47C2314yes—
126C2×C8×D47C2314yes—
127C2×C8×D47C2314yes—
128#13094023C2×C418yes—
129#13094020C2×C418yes—
130#13094010C2×C418yes—
131#13094010C2×C418yes—
132#13093999C2×C418yes—
133#13093997C2×C418yes—
134#13093997C2×C418yes—
135#13093995C2×C418yes—
136C4×D188C2×C414yes—
137C4×D188C2314yes—
138C4×C22⋊D47C2×C414yes—
139C4×C22⋊D47C2×C414yes—
140C4×C22⋊D47C2314yes—
141C4×C22⋊D47C2314yes—
142C2×C4⋊Dic47C2×C411yescharacteristic
143C2×Dic47⋊C4C2×C411yescharacteristic
144C2×Dic47⋊C4C2×C411yescharacteristic
145C2×C22⋊Dic47C2×C411yescharacteristic
146C2×C22⋊Dic47C2×C411yescharacteristic
147C2×(C2×D47)⋊C4C2×C411yescharacteristic
148C2×(C2×D47)⋊C4C2×C411yescharacteristic
149C2×(C2×D47)⋊C4C2×C411yescharacteristic
150C2×(C2×D47)⋊C4C2×C411yescharacteristic
151C2×C4×Dic47C2×C411yescharacteristic
152C2×C4×Dic47C2×C411yescharacteristic
153C2×C4×Dic47C2311yescharacteristic
154C42×D47C2×C414yes—
155C42×D47C2314yes—
156C4⋊(C47⋊C8)C2314yes—
157Dic47⋊C8C2314yes—
158Dic47⋊C8C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164(C2×D47)⋊C8C2314yes—
165#13093935C2314yes—
166C8×Dic47C2314yes—
167C8×Dic47C2314yes—
168C22×D4×C47C2×C411yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C23×C4×C47C2311yescharacteristic
171C2×M16×C47—24no—
172C2×M16×C47C2314yes—
173C22×C8×C47—24no—
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2314yes—
177C22×C8×C47C2311yescharacteristic
178C22×C8×C47C2311yescharacteristic
179C4×D4×C47C2×C414yes—
180C4×D4×C47C2314yes—
181C2×C4⋊C4×C47C2×C411yescharacteristic
182C2×C22⋊C4×C47C2×C411yescharacteristic
183C2×C22⋊C4×C47C2×C411yescharacteristic
184C2×C42×C47C2311yescharacteristic
185C4⋊C8×C47C2314yes—
186C22⋊C8×C47C2314yes—
187C22⋊C8×C47C2314yes—
188#97×C47C2314yes—
189C24×C47C22×C411yescharacteristic
190C24×C47C22×C411yescharacteristic
191C23×D47C22×C411yescharacteristic
192C23×D47C22×C411yescharacteristic
193C23×D47C22×C411yescharacteristic
194C2×D4×C47—42no—
195C2×D4×C47C22×C414yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47C22×C411yescharacteristic
201C22×C4×C47C22×C411yescharacteristic
202C22×C4×C47C22×C411yescharacteristic
203C22×C4×C47C22×C411yescharacteristic
204C22×C4×C47C22×C412yes—
205C22×C4×C47C22×C412yes—
206C22×C4×C47C2412yes—
207C22×C4×C47C2412yes—
208C22×C4×C47C2411yescharacteristic
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—24no—
212C2×C22⋊D47—24no—
213C2×C22⋊D47—24no—
214C2×C22⋊D47—24no—
215C2×C22⋊D47C22×C414yes—
216C2×C22⋊D47C22×C414yes—
217C2×C22⋊D47C22×C414yes—
218C2×C22⋊D47C22×C414yes—
219C2×C22⋊D47C22×C414yes—
220C2×C22⋊D47C22×C414yes—
221C22×Dic47C22×C411yescharacteristic
222C22×Dic47C22×C411yescharacteristic
223C22×Dic47C22×C411yescharacteristic
224C22×Dic47C22×C411yescharacteristic
225C22×Dic47C22×C411yescharacteristic
226#10625350—216no—
227#10625350—216no—
228#10625350—28no—
229#10625350—28no—
230#10625350—28no—
231#10625350—28no—
232C2×D188—24no—
233C2×D188—24no—
234C2×D188—42no—
235C2×D188C22×C414yes—
236C2×D188C22×C414yes—
237C2×D188C22×C414yes—
238C2×C4×D47—22no—
239C2×C4×D47—22no—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—24no—
243C2×C4×D47—42no—
244C2×C4×D47C22×C414yes—
245C2×C4×D47C22×C412yes—
246C2×C4×D47C22×C412yes—
247C2×C4×D47C22×C414yes—
248C2×C4×D47C22×C412yes—
249C2×C4×D47C2×D414yes—
250C2×C4×D47#4114yes—
251C2×C4×D47C2412yes—
252C2×C4×D47C2412yes—
253C2×C4×D47C2412yes—
254C2×Dic94—24no—
255C2×Dic94—24no—
256C2×Dic94C22×C414yes—
257C2×Dic94C22×C414yes—
258M16×C47—28no—
259C2×C8×C47—22no—
260C2×C8×C47—22no—
261C2×C8×C47—22no—
262C2×C8×C47—28no—
263C2×C8×C47C2×D414yes—
264C2×C8×C47C2412yes—
265C2×C8×C47C2412yes—
266C2×C8×C47C2412yes—
267C2×C8×C47C2412yes—
268C4⋊C4×C47C22×C414yes—
269C22⋊C4×C47C22×C414yes—
270C22⋊C4×C47C22×C414yes—
271C42×C47C22×C412yes—
272C42×C47C2412yes—
273C22⋊Dic47C22×C414yes—
274C22⋊Dic47C22×C414yes—
275(C2×D47)⋊C4C22×C414yes—
276(C2×D47)⋊C4C22×C414yes—
277(C2×D47)⋊C4C22×C414yes—
278(C2×D47)⋊C4C22×C414yes—
279C4⋊Dic47C22×C414yes—
280Dic47⋊C4C22×C414yes—
281Dic47⋊C4C22×C414yes—
282C4×Dic47C22×C412yes—
283C4×Dic47C22×C414yes—
284C4×Dic47C22×C414yes—
285C4×Dic47C2412yes—
286#10625329—28no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8—28no—
291C2×C47⋊C8C2×D414yes—
292C2×C47⋊C8C2412yes—
293C2×C47⋊C8C2412yes—
294C2×C47⋊C8C2412yes—
295C2×C47⋊C8C2412yes—
296#10625324—28no—
297#10625324—28no—
298#10625324—28no—
299#10625324C2×D4116yescomplemented
300C8×D47—28no—
301C8×D47—28no—
302C8×D47—28no—
303C8×D47—28no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47C23×C412yes—
311C23×C47C23×C412yes—
312C23×C47C23×C411yescharacteristic
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47C4×D414yes—
322C22×D47C23×C412yes—
323C22×D47C23×C412yes—
324C22×D47C23×C412yes—
325D4×C47—44no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—24no—
331C2×C4×C47—24no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47C23×C412yes—
337C2×C4×C47C23×C412yes—
338C2×C4×C47C23×C412yes—
339C2×C4×C47C23×C412yes—
340C2×C4×C47C23×C411yescharacteristic
341C2×C4×C47C22×D412yes—
342C2×C4×C47C2×#4112yes—
343C2×C4×C47C2511yescharacteristic
344C22⋊D47—28no—
345C22⋊D47—28no—
346C22⋊D47—28no—
347C22⋊D47—28no—
348C22⋊D47—28no—
349C22⋊D47—28no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47C4×D414yes—
354C2×Dic47#13114yescomplemented
355C2×Dic47C23×C412yes—
356C2×Dic47C23×C412yes—
357C2×Dic47C23×C412yes—
358C2×Dic47C23×C412yes—
359C2×Dic47C23×C412yes—
360D188—28no—
361D188—28no—
362D188—44no—
363C4×D47—24no—
364C4×D47—24no—
365C4×D47—22no—
366C4×D47—22no—
367C4×D47—22no—
368C4×D47—22no—
369C4×D47—28no—
370C4×D47—44no—
371C4×D47C4×D418yes—
372C4×D47C22×D414yes—
373C4×D47C2×#4114yes—
374Dic94—28no—
375Dic94—28no—
376C8×C47—22no—
377C8×C47—22no—
378C8×C47—22no—
379C8×C47C22×D414yes—
380C47⋊C8—22no—
381C47⋊C8—22no—
382C47⋊C8—22no—
383C47⋊C8C22×D414yes—
384C2×#2935—471nomaximal, Sylow
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—22no—
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—44no—
392C22×C47—44no—
393C22×C47C2×C4×D412yes—
394C22×C47C2×#13112yes—
395C22×C47#56812yes—
396C22×C47C24×C411yescharacteristic
397C2×D47—28no—
398C2×D47—22no—
399C2×D47—22no—
400C2×D47—22no—
401C2×D47—22no—
402C2×D47—22no—
403C2×D47—22no—
404C2×D47—22no—
405C2×D47—22no—
406C2×D47—44no—
407C2×D47—44no—
408C2×D47C2×C4×D414yes—
409C4×C47—22no—
410C4×C47—22no—
411C4×C47—22no—
412C4×C47—22no—
413C4×C47C2×C4×D412yes—
414C4×C47C23×D411yescharacteristic
415C4×C47C22×#4111yescharacteristic
416Dic47—22no—
417Dic47—22no—
418Dic47—22no—
419Dic47C2×C4×D414yes—
420Dic47C2×#13114yescomplemented
421C22×#131—471no—
422C22×#131—471no—
423C2×#532—471no—
424#2935—4716no—
425C2×#436—471no—
426C2×#436—471no—
427C2×#435—471no—
428C2×#435—471no—
429C2×#435—471no—
430C2×#435D4711yescharacteristic, complemented
431C2×C8×D4—471no—
432C2×C8×D4—471no—
433C22×C4⋊C8—471no—
434C2×#408—471no—
435C2×#408—471no—
436C2×C4×M16—471no—
437C2×C47—42no—
438C2×C47—42no—
439C2×C47#293514yescomplemented
440C2×C47C22×C4×D411yescharacteristic
441C2×C47C22×#13111yescharacteristic
442C2×C47C2×#56811yescharacteristic
443D47—24no—
444D47—42no—
445D47—42no—
446C22×#41—471no—
447C22×#41—471no—
448C2×#131—478no—
449C2×#131—478no—
450C2×#131—948no—
451C2×#131—948no—
452C22×M16—471no—
453C22×M16—471no—
454C22×M16—471no—
455C22×M16—471no—
456C22×M16—471no—
457C22×M16C2×D4711yescharacteristic
458C23×C8—471no—
459C23×C8—471no—
460C23×C8—471no—
461C23×C8—471no—
462C23×C8—471no—
463C23×C8C2×D4711yescharacteristic
464#532—478no—
465#532—478no—
466C2×C4⋊Q8—471no—
467C2×#127—471no—
468C2×#124—471no—
469C2×#124—471no—
470C2×#121—471no—
471C2×#121—471no—
472C2×#121—471no—
473C2×#121—471no—
474C2×C4×D4—471no—
475C2×C4×D4—471no—
476C2×C4×D4—471no—
477C2×C4×D4C2×D4711yescharacteristic
478C22×C42—471no—
479#436—478no—
480#436—478no—
481#435—478no—
482#435—478no—
483#435—478no—
484#435C2×D4718yescomplemented
485C8×D4—478no—
486C8×D4—478no—
487C2×C4⋊C8—471no—
488C2×C4⋊C8—471no—
489C2×C4⋊C8—471no—
490C2×C4⋊C8—478no—
491C2×C4⋊C8C2×D4711yescharacteristic
492#408—478no—
493#408—478no—
494C2×C22⋊C8—471no—
495C2×C22⋊C8—471no—
496C2×C22⋊C8—471no—
497C2×C22⋊C8—471no—
498C2×C22⋊C8—471no—
499C2×C22⋊C8—471no—
500C2×C22⋊C8C2×D4711yescharacteristic
501C2×C22⋊C8C2×D4711yescharacteristic
502C4×M16—478no—
503C2×#97—471no—
504C2×#97C2×D4711yescharacteristic
505C2×C4×C8—471no—
506C2×C4×C8—471no—
507C47C2×#293511yescharacteristic, complemented, Sylow
508C2×#41—474no—
509C2×#41—474no—
510C2×#41—474no—
511C2×#41—474no—
512C2×#41—944no—
513C2×#41—944no—
514C2×#41—944no—
515C2×#41—944no—
516C22×Q8—471no—
517C22×Q8—471no—
518C22×D4—471no—
519C22×D4—471no—
520C22×D4—471no—
521C22×D4—471no—
522C22×D4—471no—
523C22×D4—471no—
524C22×D4—471no—
525C22×D4—471no—
526C22×D4—471no—
527C22×D4C4×D4711yescharacteristic
528C23×C4—471no—
529C23×C4—471no—
530C23×C4—471no—
531C23×C4—471no—
532C23×C4—471no—
533C23×C4C22×D4711yescharacteristic
534C23×C4C22×D4711yescharacteristic
535#131—9432no—
536#131—9432no—
537C2×M16—24no—
538C2×M16—474no—
539C2×M16—478no—
540C2×M16—474no—
541C2×M16—474no—
542C2×M16—474no—
543C2×M16—474no—
544C2×M16—944no—
545C2×M16—944no—
546C2×M16—944no—
547C2×M16—944no—
548C2×M16C22×D4714yes—
549C22×C8—24no—
550C22×C8—471no—
551C22×C8—474no—
552C22×C8—471no—
553C22×C8—471no—
554C22×C8—471no—
555C22×C8—474no—
556C22×C8—474no—
557C22×C8—474no—
558C22×C8—474no—
559C22×C8—944no—
560C22×C8—944no—
561C22×C8—944no—
562C22×C8—944no—
563C22×C8—944no—
564C22×C8C22×D4714yes—
565C22×C8C22×D4711yescharacteristic
566C22×C8C22×D4711yescharacteristic
567C22×C8C22×D4711yescharacteristic
568C22×C8C22×D4711yescharacteristic
569C4⋊Q8—478no—
570#127—478no—
571#124—478no—
572#124—478no—
573#121—478no—
574#121—478no—
575#121—478no—
576#121—478no—
577C4×D4—474no—
578C4×D4—474no—
579C4×D4—474no—
580C4×D4—474no—
581C4×D4—474no—
582C4×D4—474no—
583C4×D4C4×D4714yes—
584C4×D4C22×D4714yes—
585C2×C4⋊C4—471no—
586C2×C4⋊C4—471no—
587C2×C4⋊C4—471no—
588C2×C4⋊C4C4×D4711yescharacteristic
589C2×C22⋊C4—471no—
590C2×C22⋊C4—471no—
591C2×C22⋊C4—471no—
592C2×C22⋊C4—471no—
593C2×C22⋊C4—471no—
594C2×C22⋊C4—471no—
595C2×C22⋊C4C4×D4711yescharacteristic
596C2×C22⋊C4C4×D4711yescharacteristic
597C2×C42—471no—
598C2×C42—471no—
599C2×C42—471no—
600C2×C42—474no—
601C2×C42—474no—
602C2×C42C22×D4711yescharacteristic
603C4⋊C8—474no—
604C4⋊C8—474no—
605C4⋊C8—474no—
606C4⋊C8C22×D4714yes—
607C22⋊C8—474no—
608C22⋊C8—474no—
609C22⋊C8—474no—
610C22⋊C8—474no—
611C22⋊C8—474no—
612C22⋊C8—474no—
613C22⋊C8C22×D4714yes—
614C22⋊C8C22×D4714yes—
615#97—474no—
616#97C22×D4714yes—
617C4×C8—474no—
618C4×C8—474no—
619C24—471no—
620C24—471no—
621C24—471no—
622C24C2×C4×D4711yescharacteristic
623C24C2×C4×D4711yescharacteristic
624#41—948no—
625#41—948no—
626#41—9416no—
627#41—9416no—
628#41—948no—
629#41—948no—
630C2×Q8—474no—
631C2×Q8—474no—
632C2×Q8—944no—
633C2×Q8—944no—
634C2×D4—42no—
635C2×D4—474no—
636C2×D4—474no—
637C2×D4—474no—
638C2×D4—474no—
639C2×D4—474no—
640C2×D4—474no—
641C2×D4—474no—
642C2×D4—474no—
643C2×D4—474no—
644C2×D4—944no—
645C2×D4—944no—
646C2×D4—944no—
647C2×D4—944no—
648C2×D4—944no—
649C2×D4—944no—
650C2×D4—944no—
651C2×D4—944no—
652C2×D4—1882no—
653C2×D4C2×C4×D4714yes—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—471no—
659C22×C4—471no—
660C22×C4—472no—
661C22×C4—474no—
662C22×C4—474no—
663C22×C4—472no—
664C22×C4—471no—
665C22×C4—471no—
666C22×C4—471no—
667C22×C4—474no—
668C22×C4—472no—
669C22×C4—472no—
670C22×C4—472no—
671C22×C4—472no—
672C22×C4—474no—
673C22×C4—944no—
674C22×C4—942no—
675C22×C4—942no—
676C22×C4—942no—
677C22×C4—942no—
678C22×C4—1882no—
679C22×C4C2×C4×D4711yescharacteristic
680C22×C4C2×C4×D4711yescharacteristic
681C22×C4C2×C4×D4711yescharacteristic
682C22×C4C2×C4×D4711yescharacteristic
683C22×C4C2×C4×D4712yes—
684C22×C4C2×C4×D4712yes—
685C22×C4C23×D4712yes—
686C22×C4C23×D4712yes—
687C22×C4C23×D4711yescharacteristic
688M16—28no—
689M16—4716no—
690M16—948no—
691M16—948no—
692M16—948no—
693M16—948no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—28no—
698C2×C8—474no—
699C2×C8—472no—
700C2×C8—472no—
701C2×C8—472no—
702C2×C8—472no—
703C2×C8—948no—
704C2×C8—948no—
705C2×C8—948no—
706C2×C8—948no—
707C2×C8—942no—
708C2×C8—942no—
709C2×C8—942no—
710C2×C8—948no—
711C2×C8D4×D4714yes—
712C2×C8C23×D4712yes—
713C2×C8C23×D4712yes—
714C2×C8C23×D4712yes—
715C2×C8C23×D4712yes—
716C4⋊C4—474no—
717C4⋊C4—474no—
718C4⋊C4—474no—
719C4⋊C4C2×C4×D4714yes—
720C22⋊C4—474no—
721C22⋊C4—474no—
722C22⋊C4—474no—
723C22⋊C4—474no—
724C22⋊C4—474no—
725C22⋊C4—474no—
726C22⋊C4C2×C4×D4714yes—
727C22⋊C4C2×C4×D4714yes—
728C42—472no—
729C42—474no—
730C42—474no—
731C42—472no—
732C42C2×C4×D4712yes—
733C42C23×D4712yes—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—474no—
741C23—472no—
742C23—472no—
743C23—472no—
744C23—942no—
745C23—942no—
746C23—942no—
747C23—942no—
748C23—942no—
749C23—942no—
750C23—942no—
751C23—942no—
752C23C22×C4×D4712yes—
753C23C22×C4×D4712yes—
754C23C22×C4×D4711yescharacteristic
755Q8—948no—
756Q8—948no—
757D4—44no—
758D4—948no—
759D4—948no—
760D4—948no—
761D4—948no—
762D4—948no—
763D4—948no—
764D4—948no—
765D4—948no—
766D4—1884no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—474no—
778C2×C4—474no—
779C2×C4—472no—
780C2×C4—472no—
781C2×C4—478no—
782C2×C4—474no—
783C2×C4—474no—
784C2×C4—472no—
785C2×C4—472no—
786C2×C4—472no—
787C2×C4—948no—
788C2×C4—942no—
789C2×C4—942no—
790C2×C4—942no—
791C2×C4—944no—
792C2×C4—944no—
793C2×C4—942no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—942no—
797C2×C4—1884no—
798C2×C4C22×C4×D4712yes—
799C2×C4C22×C4×D4712yes—
800C2×C4C22×C4×D4712yes—
801C2×C4C22×C4×D4712yes—
802C2×C4C22×C4×D4711yescharacteristic
803C2×C4C2×D4×D4712yes—
804C2×C4#41×D4712yes—
805C2×C4C24×D4711yescharacteristic
806C8—22no—
807C8—22no—
808C8—22no—
809C8—474no—
810C8—942no—
811C8—942no—
812C8—942no—
813C8C2×D4×D4714yes—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—44no—
821C22—44no—
822C22—474no—
823C22—942no—
824C22—942no—
825C22—948no—
826C22—942no—
827C22—942no—
828C22—942no—
829C22—942no—
830C22—942no—
831C22—942no—
832C22—1884no—
833C22—1884no—
834C22C4×D4×D4712yes—
835C22#131×D4712yes—
836C22#1568988912yes—
837C22C23×C4×D4711yescharacteristic
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—474no—
843C4—474no—
844C4—942no—
845C4—942no—
846C4—942no—
847C4C4×D4×D4712yes—
848C4C22×D4×D4711yescharacteristic
849C4C2×#41×D4711yescharacteristic
850C2—42no—
851C2—42no—
852C2—944no—
853C2—1882no—
854C2—1882no—
855C2#2025212914yesdirect product factor
856C2C2×C4×D4×D4711yescharacteristic
857C2C2×#131×D4711yescharacteristic
858C2C2×#1568988911yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C23×C4
prime radicalC2×#15689670C2
cosocleC2×C4×C47C25
hypercenterC2×#435D47
hypocenterC47C2×#2935
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#13094032C2semidirect
2. C22×#13094030C2semidirect
4. #20252129C2direct (N × H)
5. C2×#15689199C2semidirect
6. C2×#15689198C2semidirect
7. C2×#15689196C2semidirect
8. C2×#15689195C2semidirect
9. C2×#15689193C2semidirect
10. C2×C8×C22⋊D47C2semidirect
11. C2×(C22⋊D47)⋊C8C2semidirect
12. C2×C4⋊C8×D47C2semidirect
13. C2×#15689088C2semidirect
14. C2×#15689088C2semidirect
15. C2×#15689075C2semidirect
16. C2×C47×#435C2semidirect
20. C2×#13094032C22semidirect
22. C2×#13094030C22semidirect
47. #15689199C22semidirect
48. #15689198C22semidirect
49. #15689196C22semidirect
50. #15689195C22semidirect
51. #15689193C22semidirect
52. C8×C22⋊D47C22semidirect
53. (C22⋊D47)⋊C8C22semidirect
57. C4⋊C8×D47C22semidirect
58. #15689088C22semidirect
59. #15689088C22semidirect
66. #15689075C22semidirect
73. C47×#435C22semidirect
109. C2×#10625324D4semidirect
299. #10625324C2×D4semidirect
354. C2×Dic47#131semidirect
420. Dic47C2×#131semidirect
430. C2×#435D47semidirect
439. C2×C47#2935semidirect
484. #435C2×D47semidirect
507. C47C2×#2935semidirect
855. C2#20252129direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940322
C22×#130940302
C2×#156896702
#202521292
C2×#156891992
C2×#156891982
C2×#156891962
C2×#156891952
C2×#156891932
C2×C8×C22⋊D472
C2×(C22⋊D47)⋊C82
C2×C4⋊C8×D472
C2×#156890882
C2×#156890752
C2×C47×#4352
C2×#293547