Finite Group Databasebeta

← #25123145

Subgroups — #25123145

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063321C211yesmaximal, characteristic
2#19134893C211yesmaximal, characteristic, complemented
3#19134891C211yesmaximal, characteristic, complemented
4#19134890C211yesmaximal, characteristic, complemented
5#19134890C211yesmaximal, characteristic, complemented
6#19134889C211yesmaximal, characteristic, complemented
7#19134889C211yesmaximal, characteristic, complemented
8#19134887C211yesmaximal, characteristic, complemented
9#19134887C211yesmaximal, characteristic, complemented
10#19134886C211yesmaximal, characteristic, complemented
11#19134884C211yesmaximal, characteristic, complemented
12#19134884C211yesmaximal, characteristic, complemented
13#19134737C211yesmaximal, characteristic, complemented
14#19134737C211yesmaximal, characteristic, complemented
15C43×#1869C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063321C411yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24C2×C4×C22⋊D43C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34#14582802C411yescharacteristic
35#14582800C411yescharacteristic
36#14582799C411yescharacteristic
37#14582799C411yescharacteristic
38#14582799C411yescharacteristic
39#14582799C411yescharacteristic
40#14582768C411yescharacteristic
41C42×Dic43C2211yescharacteristic
42#14582654C2211yescharacteristic
43#14582654C2211yescharacteristic
44#14582653C2211yescharacteristic
45#14582653C2211yescharacteristic
46#14582653C2211yescharacteristic
47#14582653C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C23×C8×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2×C411yescharacteristic
60C22×C22⋊D43C2×C411yescharacteristic
61C22×C22⋊D43C2×C411yescharacteristic
62C22×C22⋊D43C2×C411yescharacteristic
63C22×C22⋊D43C2×C411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621877—41no—
67C2×#10621877—41no—
68C2×#10621877—41no—
69C2×#10621872—41no—
70C2×#10621872—41no—
71C2×#10621872—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C2×C8×D43—41no—
77C2×C8×D43—41no—
78C2×C8×D43—41no—
79#13063321—24no—
80C4×D172—41no—
81C4×D172—41no—
82C4×C22⋊D43—41no—
83C4×C22⋊D43—41no—
84C4×C22⋊D43—41no—
85C4×C22⋊D43—41no—
86C4×C22⋊D43—41no—
87C4×C22⋊D43—41no—
88C4×C22⋊D43—41no—
89C4×C22⋊D43—41no—
90C2×C4⋊Dic43C2×C411yescharacteristic
91C2×Dic43⋊C4C2×C411yescharacteristic
92C2×Dic43⋊C4C2×C411yescharacteristic
93C2×Dic43⋊C4C2×C411yescharacteristic
94C2×Dic43⋊C4C2×C411yescharacteristic
95C2×C22⋊Dic43C2×C411yescharacteristic
96C2×C22⋊Dic43C2×C411yescharacteristic
97C2×C22⋊Dic43C2×C411yescharacteristic
98C2×C22⋊Dic43C2×C411yescharacteristic
99C2×(C2×D43)⋊C4C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43C2×C411yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111C22⋊(C43⋊C8)—41no—
112C22⋊(C43⋊C8)—41no—
113C22⋊(C43⋊C8)—41no—
114(C2×D43)⋊C8—41no—
115(C2×D43)⋊C8—41no—
116(C2×D43)⋊C8—41no—
117(C2×D43)⋊C8—41no—
118(C2×D43)⋊C8—41no—
119(C2×D43)⋊C8—41no—
120C22×D4×C43C2×C411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43—41no—
124C22×C8×C43—41no—
125C22×C8×C43—41no—
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C4×D4×C43—41no—
131C4×D4×C43—41no—
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43C2×C411yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C22⋊C8×C43—41no—
137C22⋊C8×C43—41no—
138C22⋊C8×C43—41no—
139C24×C43C22×C411yescharacteristic
140C24×C43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C23×D43C22×C411yescharacteristic
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—41no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—41no—
169C2×C22⋊D43—41no—
170C2×C22⋊D43—41no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43—41no—
174C2×C22⋊D43M1614yescomplemented
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C22×Dic43C22×C411yescharacteristic
180C22×Dic43C22×C411yescharacteristic
181C2×D172—22no—
182C2×D172—22no—
183C2×D172—41no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—44no—
209C4⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C42×C43—21no—
213C42×C43—21no—
214C22⋊Dic43—41no—
215C22⋊Dic43—41no—
216C22⋊Dic43—41no—
217C22⋊Dic43—41no—
218(C2×D43)⋊C4—41no—
219(C2×D43)⋊C4—41no—
220(C2×D43)⋊C4—41no—
221(C2×D43)⋊C4—41no—
222(C2×D43)⋊C4—41no—
223(C2×D43)⋊C4—41no—
224C4⋊Dic43—41no—
225Dic43⋊C4—41no—
226Dic43⋊C4—41no—
227Dic43⋊C4—41no—
228Dic43⋊C4—41no—
229C4×Dic43—22no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—22no—
235C4×Dic43—22no—
236C4×Dic43—41no—
237#10621877—44no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250#10621872—44no—
251C8×D43—44no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43C2×M1612yes—
266C23×C43C23×C411yescharacteristic
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43C2×M1612yes—
281D4×C43—44no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43#13112yes—
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C22⋊D43—44no—
309C22⋊D43—44no—
310C22⋊D43—44no—
311C22⋊D43—44no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43C2×M1612yes—
329C2×Dic43#13112yes—
330D172—44no—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—41no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C8×C43—41no—
340C8×C43—41no—
341C8×C43—41no—
342C8×C43—41no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346C43⋊C8—41no—
347#23356—431nomaximal, Sylow
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43#51811yescharacteristic
363C22×C43#51811yescharacteristic
364C22×C43#51811yescharacteristic
365C22×C43C22×M1611yescharacteristic
366C22×C43C2×#13111yescharacteristic
367C22×C43C2×#13111yescharacteristic
368C22×C43#56811yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C4×C43—22no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43#56011yescharacteristic
388C4×C43#56011yescharacteristic
389C4×C43#56011yescharacteristic
390C4×C43#56011yescharacteristic
391Dic43—22no—
392Dic43—22no—
393Dic43—41no—
394Dic43—41no—
395Dic43—41no—
396Dic43—41no—
397C4×#127—431no—
398#1870—431no—
399#1870—431no—
400#1870—431no—
401#1870—431no—
402#1870—431no—
403#1870—431no—
404#1869—431no—
405#1869—431no—
406#1869—431no—
407#1869—431no—
408#1869—431no—
409#1869D4311yescharacteristic, complemented
410#1839—431no—
411#1839—431no—
412C2×C43—42no—
413C2×C43—81no—
414C2×C43#238011yescharacteristic
415C2×C43#297311yescharacteristic
416C2×C43#297411yescharacteristic
417C2×C43#297411yescharacteristic
418C2×C43#297911yescharacteristic
419C2×C43#298111yescharacteristic
420C2×C43#298111yescharacteristic
421D43—42no—
422D43—81no—
423C22×M16—431no—
424C22×M16—431no—
425C23×C8—431no—
426C23×C8C2×D4311yescharacteristic
427C2×#127—431no—
428C2×C4×D4—431no—
429C2×C4×D4—431no—
430C2×C4×D4—431no—
431C2×C4×D4—431no—
432C2×C4×D4—431no—
433C2×C4×D4C2×D4311yescharacteristic
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8C2×D4311yescharacteristic
444C2×C22⋊C8C2×D4311yescharacteristic
445C2×C22⋊C8C2×D4311yescharacteristic
446#390—431no—
447#390—431no—
448#390—431no—
449#390—431no—
450#390—431no—
451#390—431no—
452#384—431no—
453C43—431no—
454#336—431no—
455#336—431no—
456#336—431no—
457#336—431no—
458#336—431no—
459#336—431no—
460#336—431no—
461#336—431no—
462#336—431no—
463#336—431no—
464#336C2×D4311yescharacteristic
465#336C2×D4311yescharacteristic
466C43#2335611yescharacteristic, complemented, Sylow
467C22×D4—431no—
468C22×D4—431no—
469C22×D4—431no—
470C22×D4—431no—
471C22×D4—431no—
472C22×D4C4×D4311yescharacteristic
473C23×C4—431no—
474C23×C4—431no—
475C23×C4C22×D4311yescharacteristic
476C23×C4C22×D4311yescharacteristic
477C2×M16—1721no—
478C2×M16—1721no—
479C2×M16—1721no—
480C2×M16—1721no—
481C2×M16—1721no—
482C2×M16—1721no—
483C22×C8—41no—
484C22×C8—41no—
485C22×C8—41no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8—1721no—
491C22×C8—1721no—
492C22×C8—1721no—
493C22×C8C22×D4311yescharacteristic
494C22×C8C22×D4311yescharacteristic
495C22×C8C22×D4311yescharacteristic
496C22×C8C22×D4311yescharacteristic
497#127—864no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—1721no—
501C4×D4—1721no—
502C4×D4—1721no—
503C4×D4—1721no—
504C4×D4—1721no—
505C4×D4—1721no—
506C4×D4—1721no—
507C4×D4—1721no—
508C4×D4—1721no—
509C4×D4—1721no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4C4×D4311yescharacteristic
516C2×C22⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4C4×D4311yescharacteristic
527C2×C22⋊C4C4×D4311yescharacteristic
528C2×C42—431no—
529C2×C42—431no—
530C2×C42—431no—
531C2×C42—431no—
532C2×C42—431no—
533C2×C42—431no—
534C2×C42C22×D4311yescharacteristic
535C22⋊C8—41no—
536C22⋊C8—41no—
537C22⋊C8—41no—
538C22⋊C8—1721no—
539C22⋊C8—1721no—
540C22⋊C8—1721no—
541C22⋊C8—1721no—
542C22⋊C8—1721no—
543C22⋊C8—1721no—
544C22⋊C8—1721no—
545C22⋊C8—1721no—
546C22⋊C8—1721no—
547C24—431no—
548C24—431no—
549C24C2×C4×D4311yescharacteristic
550C24C2×C4×D4311yescharacteristic
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—434no—
555C2×D4—862no—
556C2×D4—862no—
557C2×D4—862no—
558C2×D4—862no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—1721no—
563C2×D4—1721no—
564C2×D4—1721no—
565C2×D4—1721no—
566C2×D4—1721no—
567C2×D4—1721no—
568C2×D4—1721no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C2×C4×D4311yescharacteristic
601C22×C4C2×C4×D4311yescharacteristic
602C22×C4C2×C4×D4311yescharacteristic
603C22×C4C23×D4311yescharacteristic
604M16—1724no—
605M16—1724no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—44no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—1724no—
632C4⋊C4—41no—
633C4⋊C4—1721no—
634C4⋊C4—1721no—
635C4⋊C4—1721no—
636C4⋊C4—1721no—
637C4⋊C4—1721no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—1721no—
641C22⋊C4—1721no—
642C22⋊C4—1721no—
643C22⋊C4—1721no—
644C22⋊C4—1721no—
645C22⋊C4—1721no—
646C22⋊C4—1721no—
647C22⋊C4—1721no—
648C22⋊C4—1721no—
649C22⋊C4—1721no—
650C42—21no—
651C42—21no—
652C42—862no—
653C42—862no—
654C42—862no—
655C42—861no—
656C42—861no—
657C42—861no—
658C42—861no—
659C42—1721no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—432no—
674C23—861no—
675C23—861no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23—861no—
680C23—861no—
681C23—861no—
682C23—861no—
683C23—861no—
684C23—861no—
685C23—861no—
686C23—861no—
687C23M16×D4312yes—
688C23C22×C4×D4311yescharacteristic
689D4—44no—
690D4—1724no—
691D4—1724no—
692D4—1724no—
693D4—1724no—
694D4—1724no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—432no—
715C2×C4—432no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4#1306333112yes—
741C2×C4#1306337011yescharacteristic
742C2×C4#1306337011yescharacteristic
743C2×C4#1306337011yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337111yescharacteristic
746C2×C4#1306337111yescharacteristic
747C8—41no—
748C8—41no—
749C8—41no—
750C8—41no—
751C8—1721no—
752C8—1721no—
753C8—1721no—
754C8—1721no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—862no—
770C22—862no—
771C22—862no—
772C22—1721no—
773C22—1721no—
774C22—1721no—
775C22—1721no—
776C22—1721no—
777C22—1721no—
778C22—1721no—
779C22—1721no—
780C22—1721no—
781C22—1721no—
782C22—1721no—
783C22#1458337111yescharacteristic
784C22#1458337111yescharacteristic
785C22#1458337211yescharacteristic
786C22C2×M16×D4311yescharacteristic
787C22#131×D4311yescharacteristic
788C22C2×#1306333111yescharacteristic
789C22#1458366411yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—862no—
795C4—862no—
796C4—1721no—
797C4—1721no—
798C4—1721no—
799C4—1721no—
800C4#1458363711yescharacteristic
801C4#1458363711yescharacteristic
802C4#1458363811yescharacteristic
803C4#1458363911yescharacteristic
804C2—42no—
805C2—81no—
806C2—3441no—
807C2—1722no—
808C2#1913777011yescharacteristic
809C2#1914362011yescharacteristic
810C2#1914362511yescharacteristic
811C2#1914362611yescharacteristic
812C2#1914365811yescharacteristic
813C2#1914366811yescharacteristic
814C2#1914366911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1869C2
prime radicalC2×#13063321C4
cosocleC22×C4×C43C24
hypercenter#1869D43
hypocenterC43#23356
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #19134893C2semidirect
3. #19134891C2semidirect
4. #19134890C2semidirect
5. #19134890C2semidirect
6. #19134889C2semidirect
7. #19134889C2semidirect
8. #19134887C2semidirect
9. #19134887C2semidirect
10. #19134886C2semidirect
11. #19134884C2semidirect
12. #19134884C2semidirect
13. #19134737C2semidirect
14. #19134737C2semidirect
15. C43×#1869C2semidirect
174. C2×C22⋊D43M16semidirect
409. #1869D43semidirect
466. C43#23356semidirect

Maximal subgroups

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

subgroupindex
C4×#130633212
#191348932
#191348912
#191348902
#191348892
#191348872
#191348862
#191348842
#191347372
C43×#18692
#2335643