Finite Group Databasebeta

← #25113521

Subgroups — #25113521

Order 11008.

1212 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582950C211yesmaximal, characteristic, complemented
2C2×#14582862C211yesmaximal, characteristic
3C4×C22⋊C4×D43C211yesmaximal, characteristic
4#19135208C211yesmaximal, characteristic, complemented
5#19135206C211yesmaximal, characteristic, complemented
6#19135201C211yesmaximal, characteristic, complemented
7#19135199C211yesmaximal, characteristic, complemented
8#19134778C211yesmaximal, characteristic, complemented
9#19134777C211yesmaximal, characteristic, complemented
10#19134662C211yesmaximal, characteristic, complemented
11#19134574C211yesmaximal, characteristic, complemented
12#19134504C211yesmaximal, characteristic
13#19134379C211yesmaximal, characteristic, complemented
14#19134358C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×C22⋊C4×D43C411yescharacteristic
19C2×C22⋊C4×D43C411yescharacteristic
20C2×C42×D43C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
22#14582950—24no—
23C2×Dic43⋊C8C2211yescharacteristic, complemented
24C2×Dic43⋊C8C2211yescharacteristic, complemented
25C2×Dic43⋊C8C2211yescharacteristic, complemented
26C2×Dic43⋊C8C2211yescharacteristic, complemented
27#14582862—24no—
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×#13063236C2211yescharacteristic, complemented
38C2×C4×C43⋊C8C2211yescharacteristic, complemented
39C22⋊C4×Dic43C411yescharacteristic
40C22⋊C4×Dic43C411yescharacteristic
41C4×(C2×D43)⋊C4C2211yescharacteristic
42C4×(C2×D43)⋊C4C2211yescharacteristic
43C4×C22⋊Dic43C2211yescharacteristic
44#14582746C411yescharacteristic
45#14582746C411yescharacteristic
46#95×D43C411yescharacteristic
47#95×D43C411yescharacteristic
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50#14582653C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C22×M16×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic, complemented
57C2×C4×C8×C43C2211yescharacteristic, complemented
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C24×D43C2×C411yescharacteristic
62C23×Dic43C2×C411yescharacteristic
63C22×C4×D43—22no—
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—41no—
68C22×C4×D43—41no—
69C22×C4×D43C2×C411yescharacteristic
70C22×C4×D43C2×C411yescharacteristic
71C22×C4×D43C2×C411yescharacteristic
72C22×C4×D43C2×C411yescharacteristic
73C22×C4×D43C2×C411yescharacteristic
74C22×C4×D43C2×C411yescharacteristic
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621877—22no—
78C2×#10621877—22no—
79C2×#10621877—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C2×C22⋊Dic43C2×C411yescharacteristic
85C2×C22⋊Dic43C2×C411yescharacteristic
86C2×(C2×D43)⋊C4C2×C411yescharacteristic
87C2×(C2×D43)⋊C4C2×C411yescharacteristic
88C2×(C2×D43)⋊C4C2×C411yescharacteristic
89C2×(C2×D43)⋊C4C2×C411yescharacteristic
90C22⋊C4×D43—24no—
91C22⋊C4×D43—24no—
92C2×C4×Dic43C2×C411yescharacteristic
93C2×C4×Dic43C2×C411yescharacteristic
94C2×C4×Dic43C2×C411yescharacteristic
95C2×C4×Dic43C2×C411yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98C42×D43—22no—
99C42×D43—22no—
100C42×D43—41no—
101C42×D43—41no—
102Dic43⋊C8—22no—
103Dic43⋊C8—22no—
104Dic43⋊C8—41no—
105Dic43⋊C8—41no—
106C22⋊(C43⋊C8)—22no—
107(C2×D43)⋊C8—22no—
108(C2×D43)⋊C8—22no—
109(C2×D43)⋊C8—22no—
110(C2×D43)⋊C8—22no—
111(C2×D43)⋊C8—22no—
112(C2×D43)⋊C8—41no—
113(C2×D43)⋊C8—41no—
114(C2×D43)⋊C8D414yes—
115#13063236—41no—
116C4×C43⋊C8—22no—
117C43⋊#95C2×C411yescharacteristic
118C43⋊#95C2×C411yescharacteristic
119C43⋊#95C2×C411yescharacteristic
120C43⋊#95C2×C411yescharacteristic
121C43⋊#95C2×C411yescharacteristic
122C43⋊#95C2×C411yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—22no—
125C2×M16×C43—22no—
126C2×M16×C43—41no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C2×C22⋊C4×C43C2×C411yescharacteristic
132C2×C22⋊C4×C43C2×C411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C22⋊C8×C43—22no—
136#97×C43—41no—
137C4×C8×C43—22no—
138#95×C43C2×C411yescharacteristic
139#95×C43C2×C411yescharacteristic
140C24×C43C22×C411yescharacteristic
141C23×D43—22no—
142C23×D43—22no—
143C23×D43—22no—
144C23×D43—22no—
145C23×D43—22no—
146C23×D43—41no—
147C23×D43—41no—
148C23×D43C22×C411yescharacteristic
149C23×D43C22×C411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43#4112yes—
160C22×C4×C43#4112yes—
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—41no—
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C22×Dic43C22×C411yescharacteristic
168C22×Dic43C22×C411yescharacteristic
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43—22no—
190C2×C4×D43—22no—
191C2×C4×D43—22no—
192C2×C4×D43—41no—
193C2×C4×D43—41no—
194C2×C4×D43—41no—
195C2×C4×D43—41no—
196C2×C4×D43—41no—
197C2×C4×D43—41no—
198C2×C4×D43—44no—
199C2×C4×D43—44no—
200C2×C4×D43—44no—
201C2×C4×D43—44no—
202C2×C4×D43M1614yescomplemented
203C2×C4×D43C2×D412yes—
204C2×C4×D43#4112yes—
205M16×C43—44no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43C2×D412yes—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—21no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4M1614yescomplemented
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—22no—
235C4×Dic43—22no—
236C4×Dic43—41no—
237C4×Dic43—41no—
238#10621877—44no—
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—
250C2×C43⋊C8C2×D412yes—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43#11712yes—
258C23×C43C23×C411yescharacteristic
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—28no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—44no—
271C22×D43—44no—
272C22×D43—44no—
273C22×D43—44no—
274C22×D43—44no—
275C22×D43—44no—
276C22×D43C4×D412yes—
277C22×D43C2×M1612yes—
278C22×D43C2×M1612yes—
279C22×D43#13112yes—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43#11712yes—
297C2×C4×C43C2×M1612yes—
298C2×C4×C43C2×M1612yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
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—44no—
321C2×Dic43C4×D412yes—
322C2×Dic43C2×M1612yes—
323C2×Dic43C2×M1612yes—
324C4×D43—28no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—44no—
330C4×D43—44no—
331C4×D43—44no—
332C4×D43—44no—
333C4×D43—44no—
334C4×D43—41no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C8×C43—22no—
339C8×C43—41no—
340C8×C43—41no—
341C8×C43—41no—
342C43⋊C8—22no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346#22553—431nomaximal, Sylow
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43C2×#11711yescharacteristic
355C22×C43C2×C4×D411yescharacteristic
356C22×C43#51811yescharacteristic
357C22×C43C22×M1611yescharacteristic
358C22×C43C22×M1611yescharacteristic
359C22×C43C2×#13111yescharacteristic
360C22×C43#56811yescharacteristic
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—416no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43#43514yes—
376C4×C43—22no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43#54611yescharacteristic
382C4×C43#54611yescharacteristic
383C4×C43#55111yescharacteristic
384C4×C43#55111yescharacteristic
385Dic43—22no—
386Dic43—22no—
387Dic43—22no—
388Dic43—41no—
389Dic43—41no—
390Dic43—41no—
391C2×#431—431no—
392C2×#407—431no—
393C2×C4×C22⋊C4—431no—
394#1924—431no—
395#1924—431no—
396#1923—431no—
397#1923—431no—
398#1851—431no—
399#1851—431no—
400#1817—431no—
401#1797—431no—
402#1779—431no—
403#1753—431no—
404#1753D4311yescharacteristic, complemented
405#1749—431no—
406C2×C43—42no—
407C2×C43#234211yescharacteristic
408C2×C43#292011yescharacteristic
409C2×C43#292411yescharacteristic
410C2×C43C2×#43511yescharacteristic
411C2×C43D4×M1611yescharacteristic
412C2×C43#297411yescharacteristic
413C2×C43#297511yescharacteristic
414D43—24no—
415D43—42no—
416C24×C4—431no—
417C22×M16—431no—
418C22×M16C2×D4311yescharacteristic
419C22×C22⋊C4—431no—
420C22×C22⋊C4—431no—
421C22×C42—431no—
422C22×C42—431no—
423#431—864no—
424C2×C4⋊C8—431no—
425C2×C4⋊C8—431no—
426C2×C4⋊C8—431no—
427C2×C4⋊C8—431no—
428#407—864no—
429C2×C22⋊C8—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8—431no—
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×C22⋊C8—431no—
438C2×C22⋊C8C2×D4311yescharacteristic
439C2×#97—431no—
440C2×#97C2×D4311yescharacteristic, complemented
441C2×C4×C8—431no—
442C2×C4×C8C2×D4311yescharacteristic, complemented
443C4×C22⋊C4—431no—
444C4×C22⋊C4—431no—
445C4×C22⋊C4—431no—
446C4×C22⋊C4—431no—
447C4×C22⋊C4—431no—
448C4×C22⋊C4—431no—
449C4×C22⋊C4—431no—
450C4×C22⋊C4C2×D4311yescharacteristic
451C2×#95—431no—
452C2×#95—431no—
453#336—431no—
454#336—431no—
455#336—431no—
456#336—431no—
457#336—431no—
458#336—431no—
459#336C2×D4311yescharacteristic, complemented
460#336C2×D4311yescharacteristic, complemented
461C43#2255311yescharacteristic, complemented, Sylow
462C25—431no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—862no—
473C23×C4—862no—
474C23×C4—862no—
475C23×C4—862no—
476C23×C4—1721no—
477C23×C4—1721no—
478C23×C4C22×D4311yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C2×M16—862no—
483C2×M16—862no—
484C2×M16—1721no—
485C22×C8—431no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8C22×D4311yescharacteristic
490C22×C8C22×D4311yescharacteristic
491C22×C8C22×D4311yescharacteristic
492C22×C8C22×D4311yescharacteristic
493C2×C22⋊C4—431no—
494C2×C22⋊C4—431no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—431no—
498C2×C22⋊C4—431no—
499C2×C22⋊C4—864no—
500C2×C22⋊C4—864no—
501C2×C22⋊C4C4×D4311yescharacteristic
502C2×C22⋊C4C4×D4311yescharacteristic
503C2×C42—431no—
504C2×C42—431no—
505C2×C42—431no—
506C2×C42—431no—
507C2×C42—431no—
508C2×C42—431no—
509C2×C42—862no—
510C2×C42—862no—
511C2×C42—1721no—
512C2×C42—1721no—
513C2×C42C22×D4311yescharacteristic
514C2×C42C22×D4311yescharacteristic
515C4⋊C8—862no—
516C4⋊C8—862no—
517C4⋊C8—1721no—
518C4⋊C8—1721no—
519C22⋊C8—22no—
520C22⋊C8—434no—
521C22⋊C8—862no—
522C22⋊C8—862no—
523C22⋊C8—862no—
524C22⋊C8—862no—
525C22⋊C8—862no—
526C22⋊C8—862no—
527C22⋊C8—1721no—
528C22⋊C8—1721no—
529#97—41no—
530#97—1721no—
531C4×C8—22no—
532C4×C8—862no—
533#95—431no—
534#95—431no—
535#95—431no—
536#95—431no—
537#95—431no—
538#95—431no—
539#95C4×D4311yescharacteristic
540#95C4×D4311yescharacteristic
541C24—431no—
542C24—431no—
543C24—862no—
544C24—862no—
545C24—862no—
546C24—862no—
547C24—862no—
548C24—1721no—
549C24—1721no—
550C24C2×C4×D4311yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—434no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—1721no—
588C22×C4—1721no—
589C22×C4—1721no—
590C22×C4—1721no—
591C22×C4—1721no—
592C22×C4—1721no—
593C22×C4—1724no—
594C22×C4—1724no—
595C22×C4—1724no—
596C22×C4—1724no—
597C22×C4—1721no—
598C22×C4C2×C4×D4311yescharacteristic
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C2×C4×D4311yescharacteristic
601C22×C4C2×C4×D4311yescharacteristic
602C22×C4C2×C4×D4311yescharacteristic
603C22×C4#1062189812yes—
604C22×C4#1062189812yes—
605C22×C4C23×D4311yescharacteristic
606M16—44no—
607M16—1724no—
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—21no—
619C2×C8—432no—
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×C8D4×D4312yes—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—434no—
635C22⋊C4—862no—
636C22⋊C4—862no—
637C22⋊C4—862no—
638C22⋊C4—862no—
639C22⋊C4—862no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—862no—
645C42—862no—
646C42—861no—
647C42—861no—
648C42—861no—
649C42—861no—
650C42—1721no—
651C42—1721no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—432no—
659C23—432no—
660C23—432no—
661C23—432no—
662C23—868no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—1724no—
674C23—1724no—
675C23—1724no—
676C23—1724no—
677C23—1724no—
678C23—1724no—
679C23#1306328212yes—
680C23C22×C4×D4311yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—432no—
700C2×C4—868no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—1724no—
721C2×C4—1724no—
722C2×C4—1724no—
723C2×C4—1724no—
724C2×C4—1724no—
725C2×C4—1724no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4#1306328212yes—
731C2×C4M16×D4312yes—
732C2×C4M16×D4312yes—
733C2×C4C2×D4×D4311yescharacteristic
734C2×C4#41×D4311yescharacteristic
735C2×C4C2×#1062189811yescharacteristic
736C2×C4C2×#1062189811yescharacteristic
737C2×C4#1306337011yescharacteristic
738C2×C4#1306337111yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—862no—
744C8—1721no—
745C8—1721no—
746C8—1721no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—434no—
755C22—862no—
756C22—862no—
757C22—862no—
758C22—862no—
759C22—862no—
760C22—862no—
761C22—862no—
762C22—862no—
763C22—862no—
764C22—17216no—
765C22—1721no—
766C22—1721no—
767C22—1721no—
768C22—1721no—
769C22C2×#1306328211yescharacteristic
770C22C4×D4×D4311yescharacteristic
771C22#1458337111yescharacteristic
772C22C2×M16×D4311yescharacteristic
773C22C2×M16×D4311yescharacteristic
774C22#131×D4311yescharacteristic
775C22#1458366411yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—862no—
782C4—862no—
783C4—862no—
784C4—1721no—
785C4—1721no—
786C4—1721no—
787C4#1458353911yescharacteristic
788C4#1458354511yescharacteristic
789C4#1458357311yescharacteristic
790C4#1458357811yescharacteristic
791C2—42no—
792C2—864no—
793C2—1722no—
794C2#1913743811yescharacteristic
795C2#1914322611yescharacteristic
796C2#1914325011yescharacteristic
797C2#435×D4311yescharacteristic
798C2#1914332811yescharacteristic
799C2#1914362711yescharacteristic
800C2#1914363311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1753C2
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1753D43
hypocenterC43#22553
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#14582950C2semidirect
4. #19135208C2semidirect
5. #19135206C2semidirect
6. #19135201C2semidirect
7. #19135199C2semidirect
8. #19134778C2semidirect
9. #19134777C2semidirect
10. #19134662C2semidirect
11. #19134574C2semidirect
13. #19134379C2semidirect
14. #19134358C2semidirect
15. C43×#1753C2semidirect
23. C2×Dic43⋊C8C22semidirect
24. C2×Dic43⋊C8C22semidirect
25. C2×Dic43⋊C8C22semidirect
26. C2×Dic43⋊C8C22semidirect
37. C2×#13063236C22semidirect
38. C2×C4×C43⋊C8C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
50. #14582653C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
56. C2×#97×C43C22semidirect
57. C2×C4×C8×C43C22semidirect
59. C43×#336C22semidirect
60. C43×#336C22semidirect
202. C2×C4×D43M16semidirect
229. (C2×D43)⋊C4M16semidirect
404. #1753D43semidirect
440. C2×#97C2×D43semidirect
442. C2×C4×C8C2×D43semidirect
459. #336C2×D43semidirect
460. #336C2×D43semidirect
461. C43#22553semidirect

Maximal subgroups

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

subgroupindex
C2×#145829502
C2×#145828622
C4×C22⋊C4×D432
#191352082
#191352062
#191352012
#191351992
#191347782
#191347772
#191346622
#191345742
#191345042
#191343792
#191343582
C43×#17532
#2255343