Finite Group Databasebeta

← #25028015

Subgroups — #25028015

Order 11008.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063303C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic
3C2×#14582820C211yesmaximal, characteristic, complemented
4C2×#14582819C211yesmaximal, characteristic, complemented
5C2×#14582773C211yesmaximal, characteristic
6C2×#14582770C211yesmaximal, characteristic
7#19132859C211yesmaximal, characteristic, complemented
8#19132858C211yesmaximal, characteristic, complemented
9#19132858C211yesmaximal, characteristic, complemented
10#19132847C211yesmaximal, characteristic, complemented
11#19132846C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic
13(C2×D43)⋊#95C211yesmaximal, characteristic
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C43×#1444C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063303—24no—
21C2×#13063303—24no—
22C2×#13063303—24no—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C2×C4⋊C4×D43—24no—
32C2×C4⋊C4×D43—24no—
33C2×C4⋊C4×D43—24no—
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38#14582820—24no—
39#14582819—24no—
40#14582773—24no—
41#14582770—24no—
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C24×D43C2311yescharacteristic
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—41no—
68C22×Dic86—41no—
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—22no—
87C22×C4×D43—22no—
88C22×C4×D43—22no—
89C22×C4×D43—22no—
90C22×C4×D43—22no—
91C22×C4×D43—41no—
92C22×C4×D43—41no—
93C22×C4×D43—41no—
94C22×C4×D43—41no—
95C22×C4×D43D414yes—
96C22×C4×D43Q814yescomplemented
97#13063303—232no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43—22no—
100C2×C4⋊Dic43—22no—
101C2×C4⋊Dic43—22no—
102C2×C4⋊Dic43—41no—
103C2×C4⋊Dic43D414yes—
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4—22no—
109C2×Dic43⋊C4—22no—
110C2×Dic43⋊C4—22no—
111C2×Dic43⋊C4—22no—
112C2×Dic43⋊C4—22no—
113C2×Dic43⋊C4—22no—
114C2×Dic43⋊C4—22no—
115C2×Dic43⋊C4—22no—
116C2×Dic43⋊C4—22no—
117C2×Dic43⋊C4—22no—
118C2×Dic43⋊C4—22no—
119C2×Dic43⋊C4—41no—
120C2×Dic43⋊C4—41no—
121C2×Dic43⋊C4D414yes—
122C4⋊C4×D43—232no—
123C2×(C2×D43)⋊C4—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—22no—
126C2×(C2×D43)⋊C4—22no—
127C2×(C2×D43)⋊C4—22no—
128C2×(C2×D43)⋊C4—22no—
129C2×(C2×D43)⋊C4—22no—
130C2×(C2×D43)⋊C4—22no—
131C2×(C2×D43)⋊C4D414yes—
132C2×(C2×D43)⋊C4D414yes—
133C2×(C2×D43)⋊C4Q814yescomplemented
134C2×(C2×D43)⋊C4Q814yescomplemented
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—22no—
143C43⋊#95—22no—
144C43⋊#95—22no—
145C43⋊#95—22no—
146C43⋊#95—41no—
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43—22no—
155C2×C4⋊C4×C43—22no—
156C2×C4⋊C4×C43—22no—
157C2×C4⋊C4×C43—22no—
158C2×C4⋊C4×C43—22no—
159C2×C4⋊C4×C43—22no—
160C2×C4⋊C4×C43—22no—
161C2×C4⋊C4×C43—22no—
162C2×C4⋊C4×C43—41no—
163#95×C43—22no—
164#95×C43—22no—
165#95×C43—22no—
166#95×C43—41no—
167C24×C43C2411yescharacteristic
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43C2×D412yes—
177C23×D43C2×D412yes—
178C23×D43C2×D412yes—
179C23×D43C2×Q812yes—
180C23×D43C2×Q812yes—
181C23×D43C2×Q812yes—
182C23×D43#4112yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43C2×D412yes—
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×Q812yes—
229C22×C4×C43C2×Q812yes—
230C22×C4×C43C2×Q812yes—
231C22×C4×C43#4112yes—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43C2×D412yes—
271C22×Dic43C2×D412yes—
272C22×Dic43C2×D412yes—
273C22×Dic43C2×D412yes—
274C22×Dic43C2×D412yes—
275C22×Dic43C2×D412yes—
276C22×Dic43C2×D412yes—
277C22×Dic43C2×Q812yes—
278C22×Dic43C2×Q812yes—
279C22×Dic43C2×Q812yes—
280C22×Dic43#4112yes—
281C2×C4×D43—28no—
282C2×C4×D43—28no—
283C2×C4×D43—28no—
284C2×C4×D43—28no—
285C2×C4×D43—28no—
286C2×C4×D43—28no—
287C2×C4×D43—28no—
288C2×C4×D43—28no—
289C2×C4×D43—28no—
290C2×C4×D43—28no—
291C2×C4×D43—44no—
292C2×C4×D43—44no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C2×Dic86—28no—
303C2×Dic86—44no—
304C2×Dic86—44no—
305C2×Dic86—44no—
306C2×Dic86—44no—
307C2×Dic86—44no—
308C2×Dic86—44no—
309C4⋊C4×C43—28no—
310C4⋊C4×C43—28no—
311C4⋊C4×C43—44no—
312(C2×D43)⋊C4—28no—
313(C2×D43)⋊C4—28no—
314(C2×D43)⋊C4—28no—
315(C2×D43)⋊C4—28no—
316C4⋊Dic43—28no—
317C4⋊Dic43—44no—
318Dic43⋊C4—28no—
319Dic43⋊C4—28no—
320Dic43⋊C4—28no—
321Dic43⋊C4—28no—
322Dic43⋊C4—44no—
323Dic43⋊C4—44no—
324C23×C43C22×D411yescharacteristic
325C23×C43C22×D411yescharacteristic
326C23×C43C22×D411yescharacteristic
327C23×C43C22×D411yescharacteristic
328C23×C43C22×D411yescharacteristic
329C23×C43C22×Q811yescharacteristic
330C23×C43C22×Q811yescharacteristic
331C23×C43C22×Q811yescharacteristic
332C23×C43C2×#4111yescharacteristic
333C23×C43C2×#4111yescharacteristic
334C23×C43C2×#4111yescharacteristic
335C23×C43H(5,𝔽2)11yescharacteristic
336C23×C43H(5,𝔽2)11yescharacteristic
337C23×C432−1+411yescharacteristic
338C23×C432−1+411yescharacteristic
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43#12014yes—
368C22×D43C22⋊Q814yes—
369C22×D43C22⋊Q814yes—
370C22×D43C22⋊Q814yes—
371C22×D43C4⋊Q814yes—
372C22×D43C4⋊Q814yes—
373C22×D43C4⋊Q814yes—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43C22⋊Q814yescomplemented
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—22no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—22no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—41no—
451C2×Dic43—41no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43#12014yes—
471C2×Dic43C22⋊Q814yescomplemented
472C4×D43—232no—
473C4×D43—416no—
474C4×D43—416no—
475Dic86—416no—
476#14720—431nomaximal, Sylow
477C22×C43C2×#12011yescharacteristic
478C22×C43C2×#12011yescharacteristic
479C22×C43C2×C22⋊Q811yescharacteristic
480C22×C43C2×C22⋊Q811yescharacteristic
481C22×C43C2×C22⋊Q811yescharacteristic
482C22×C43C2×C22⋊Q811yescharacteristic
483C22×C43C2×C22⋊Q811yescharacteristic
484C22×C43#52511yescharacteristic
485C22×C43#52511yescharacteristic
486C22×C43#52511yescharacteristic
487C22×C43C2×C4⋊Q811yescharacteristic
488C22×C43C2×C4⋊Q811yescharacteristic
489C22×C43C2×C4⋊Q811yescharacteristic
490C22×C43#53411yescharacteristic
491C22×C43#53611yescharacteristic
492C22×C43#53911yescharacteristic
493C22×C43#53911yescharacteristic
494C22×C43#54411yescharacteristic
495C22×C43#54411yescharacteristic
496C22×C43D4211yescharacteristic
497C22×C43D4211yescharacteristic
498C22×C43D4211yescharacteristic
499C22×C43D4211yescharacteristic
500C22×C43#54711yescharacteristic
501C22×C43#54711yescharacteristic
502C22×C43#54711yescharacteristic
503C22×C43#54711yescharacteristic
504C22×C43D4×Q811yescharacteristic
505C22×C43D4×Q811yescharacteristic
506C22×C43D4×Q811yescharacteristic
507C22×C43D4×Q811yescharacteristic
508C22×C43#55411yescharacteristic
509C22×C43#55411yescharacteristic
510C22×C43#55411yescharacteristic
511C22×C43#55411yescharacteristic
512C2×D43—24no—
513C2×D43—24no—
514C2×D43—24no—
515C2×D43—24no—
516C2×D43—24no—
517C2×D43—24no—
518C2×D43—24no—
519C2×D43—24no—
520C2×D43—24no—
521C2×D43—24no—
522C2×D43—24no—
523C2×D43—24no—
524C2×D43—24no—
525C2×D43—24no—
526C2×D43#39518yescomplemented
527C4×C43—24no—
528C4×C43—42no—
529C4×C43—42no—
530C4×C43—42no—
531C4×C43—42no—
532C4×C43—42no—
533C4×C43—42no—
534Dic43—24no—
535Dic43—24no—
536Dic43—42no—
537Dic43—42no—
538Dic43—42no—
539Dic43—42no—
540Dic43—42no—
541C22×C22⋊Q8—431no—
542C23×C4⋊C4—431no—
543C2×#395—431no—
544C2×#395—431no—
545C2×#385—431no—
546C2×#385—431no—
547#1444—431no—
548#1444—431no—
549#1444—431no—
550#1444D4311yescharacteristic, complemented
551#1441—431no—
552#1441—431no—
553C22⋊#95—431no—
554C22⋊#95—431no—
555C22⋊#95—431no—
556C2×C43C2×#39511yescharacteristic
557C2×C43#240311yescharacteristic
558C2×C43#240611yescharacteristic
559C2×C43#243411yescharacteristic
560C2×C43#244011yescharacteristic
561C2×C43#244011yescharacteristic
562C2×C43#244011yescharacteristic
563C2×C43#244011yescharacteristic
564C2×C43#244911yescharacteristic
565C2×C43#244911yescharacteristic
566C2×C43#244911yescharacteristic
567C2×C43#244911yescharacteristic
568C2×C43#258311yescharacteristic
569C2×C43#262711yescharacteristic
570C2×C43#284811yescharacteristic
571D43—28no—
572C23×Q8—431no—
573C24×C4—431no—
574C24×C4—431no—
575C24×C4—431no—
576C2×C22⋊Q8—864no—
577C2×C22⋊Q8—864no—
578C2×C22⋊Q8—864no—
579C22×C4⋊C4—431no—
580C22×C4⋊C4—431no—
581C22×C4⋊C4—431no—
582C22×C4⋊C4—431no—
583C22×C4⋊C4—431no—
584C22×C4⋊C4—431no—
585C22×C4⋊C4—431no—
586C22×C4⋊C4—431no—
587C22×C4⋊C4—864no—
588C22×C4⋊C4—864no—
589C22×C4⋊C4—864no—
590C22×C4⋊C4C2×D4311yescharacteristic
591C22×C4⋊C4C2×D4311yescharacteristic
592C22×C4⋊C4C2×D4311yescharacteristic
593C22×C22⋊C4—431no—
594C22×C22⋊C4—431no—
595C22×C22⋊C4—431no—
596C22×C22⋊C4—431no—
597#395—864no—
598#395—864no—
599#385—864no—
600#385—864no—
601C2×#95—431no—
602C2×#95—431no—
603C2×#95—431no—
604C2×#95—431no—
605C2×#95—431no—
606C2×#95—431no—
607C2×#95—431no—
608C2×#95—431no—
609C2×#95—431no—
610C2×#95—431no—
611C2×#95—431no—
612C2×#95—431no—
613C2×#95C2×D4311yescharacteristic
614C2×#95C2×D4311yescharacteristic
615C2×#95C2×D4311yescharacteristic
616C2×#95C2×D4311yescharacteristic
617C43#1472011yescharacteristic, complemented, Sylow
618C25—431no—
619C22×Q8—862no—
620C22×Q8—862no—
621C22×Q8—862no—
622C22×Q8—862no—
623C22×Q8—862no—
624C22×Q8—1721no—
625C22×Q8—1721no—
626C23×C4—431no—
627C23×C4—431no—
628C23×C4—431no—
629C23×C4—431no—
630C23×C4—431no—
631C23×C4—431no—
632C23×C4—431no—
633C23×C4—434no—
634C23×C4—434no—
635C23×C4—862no—
636C23×C4—862no—
637C23×C4—862no—
638C23×C4—862no—
639C23×C4—862no—
640C23×C4—862no—
641C23×C4—862no—
642C23×C4—862no—
643C23×C4—862no—
644C23×C4—862no—
645C23×C4—862no—
646C23×C4—862no—
647C23×C4—862no—
648C23×C4—862no—
649C23×C4—862no—
650C23×C4—1721no—
651C23×C4—1721no—
652C23×C4—1721no—
653C23×C4—1721no—
654C23×C4C22×D4311yescharacteristic
655C23×C4C22×D4311yescharacteristic
656C23×C4C22×D4311yescharacteristic
657C23×C4C22×D4311yescharacteristic
658C23×C4C22×D4311yescharacteristic
659C23×C4C22×D4311yescharacteristic
660C23×C4C22×D4311yescharacteristic
661C22⋊Q8—8632no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—434no—
672C2×C4⋊C4—434no—
673C2×C4⋊C4—8632no—
674C2×C4⋊C4—862no—
675C2×C4⋊C4—862no—
676C2×C4⋊C4—862no—
677C2×C4⋊C4—862no—
678C2×C4⋊C4—862no—
679C2×C4⋊C4—862no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—862no—
684C2×C4⋊C4—862no—
685C2×C4⋊C4—862no—
686C2×C4⋊C4—862no—
687C2×C4⋊C4—862no—
688C2×C4⋊C4—862no—
689C2×C4⋊C4—862no—
690C2×C4⋊C4—862no—
691C2×C4⋊C4—862no—
692C2×C4⋊C4—862no—
693C2×C4⋊C4—1721no—
694C2×C4⋊C4—1721no—
695C2×C4⋊C4—1721no—
696C2×C22⋊C4—434no—
697C2×C22⋊C4—434no—
698C2×C22⋊C4—434no—
699C2×C22⋊C4—434no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—862no—
702C2×C22⋊C4—862no—
703C2×C22⋊C4—862no—
704C2×C22⋊C4—862no—
705C2×C22⋊C4—862no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708#95—22no—
709#95—22no—
710#95—22no—
711#95—41no—
712#95—862no—
713#95—862no—
714#95—862no—
715#95—862no—
716#95—862no—
717#95—862no—
718#95—862no—
719#95—862no—
720#95—862no—
721#95—862no—
722#95—862no—
723#95—1721no—
724C24—432no—
725C24—432no—
726C24—432no—
727C24—432no—
728C24—432no—
729C24—432no—
730C24—432no—
731C24—861no—
732C24—861no—
733C24—861no—
734C24—861no—
735C24—861no—
736C24—861no—
737C24—861no—
738C24—861no—
739C24C23×D4311yescharacteristic
740C2×Q8—868no—
741C2×Q8—1724no—
742C2×Q8—1724no—
743C2×Q8—1724no—
744C2×Q8—1724no—
745C2×Q8—1724no—
746C2×Q8—1724no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—432no—
788C22×C4—432no—
789C22×C4—432no—
790C22×C4—432no—
791C22×C4—432no—
792C22×C4—432no—
793C22×C4—432no—
794C22×C4—432no—
795C22×C4—432no—
796C22×C4—432no—
797C22×C4—432no—
798C22×C4—868no—
799C22×C4—868no—
800C22×C4—868no—
801C22×C4—868no—
802C22×C4—868no—
803C22×C4—868no—
804C22×C4—868no—
805C22×C4—868no—
806C22×C4—868no—
807C22×C4—861no—
808C22×C4—861no—
809C22×C4—861no—
810C22×C4—861no—
811C22×C4—861no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—868no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—1724no—
847C22×C4—1724no—
848C22×C4—1724no—
849C22×C4—1724no—
850C22×C4—1724no—
851C22×C4—1724no—
852C22×C4—1724no—
853C22×C4—1724no—
854C22×C4—1724no—
855C22×C4—1724no—
856C22×C4—1724no—
857C22×C4#1062189812yes—
858C22×C4D4×D4312yes—
859C22×C4D4×D4312yes—
860C22×C4D4×D4312yes—
861C22×C4D4×D4312yes—
862C22×C4D4×D4312yes—
863C22×C4Q8×D4312yes—
864C22×C4Q8×D4312yes—
865C22×C4Q8×D4312yes—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—44no—
869C4⋊C4—868no—
870C4⋊C4—868no—
871C4⋊C4—868no—
872C4⋊C4—868no—
873C4⋊C4—868no—
874C4⋊C4—1724no—
875C4⋊C4—1724no—
876C4⋊C4—1724no—
877C22⋊C4—868no—
878C22⋊C4—868no—
879C22⋊C4—868no—
880C22⋊C4—868no—
881C23—434no—
882C23—434no—
883C23—434no—
884C23—434no—
885C23—434no—
886C23—434no—
887C23—434no—
888C23—862no—
889C23—862no—
890C23—862no—
891C23—862no—
892C23—862no—
893C23—862no—
894C23—862no—
895C23—862no—
896C23—862no—
897C23—862no—
898C23—862no—
899C23—862no—
900C23—862no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—862no—
911C23—862no—
912C23—862no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23C2×D4×D4311yescharacteristic
917C23C2×D4×D4311yescharacteristic
918C23C2×D4×D4311yescharacteristic
919C23C2×D4×D4311yescharacteristic
920C23C2×D4×D4311yescharacteristic
921C23C2×Q8×D4311yescharacteristic
922C23C2×Q8×D4311yescharacteristic
923C23C2×Q8×D4311yescharacteristic
924C23#41×D4311yescharacteristic
925C23#41×D4311yescharacteristic
926C23C2×#1062189811yescharacteristic
927C23#1306337011yescharacteristic
928C23#1306337111yescharacteristic
929C23#1306337211yescharacteristic
930C23#1306337311yescharacteristic
931Q8—17216no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—434no—
981C2×C4—434no—
982C2×C4—8632no—
983C2×C4—862no—
984C2×C4—862no—
985C2×C4—862no—
986C2×C4—862no—
987C2×C4—862no—
988C2×C4—862no—
989C2×C4—862no—
990C2×C4—862no—
991C2×C4—862no—
992C2×C4—862no—
993C2×C4—862no—
994C2×C4—862no—
995C2×C4—862no—
996C2×C4—862no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—17216no—
1011C2×C4—17216no—
1012C2×C4—1721no—
1013C2×C4—1721no—
1014C2×C4—1721no—
1015C2×C4—1721no—
1016C2×C4—1721no—
1017C2×C4—1721no—
1018C2×C4—1721no—
1019C2×C4—1721no—
1020C2×C4—1721no—
1021C2×C4—1721no—
1022C2×C4—1721no—
1023C2×C4—1721no—
1024C2×C4—1721no—
1025C2×C4—1721no—
1026C2×C4—1721no—
1027C2×C4—1721no—
1028C2×C4—1721no—
1029C2×C4—1721no—
1030C2×C4—1721no—
1031C2×C4—1721no—
1032C2×C4#1306330314yescomplemented
1033C22—438no—
1034C22—864no—
1035C22—864no—
1036C22—864no—
1037C22—864no—
1038C22—864no—
1039C22—864no—
1040C22—864no—
1041C22—864no—
1042C22—864no—
1043C22—864no—
1044C22—864no—
1045C22—864no—
1046C22—864no—
1047C22—864no—
1048C22#120×D4311yescharacteristic
1049C22#120×D4311yescharacteristic
1050C22C22⋊Q8×D4311yescharacteristic
1051C22C22⋊Q8×D4311yescharacteristic
1052C22C22⋊Q8×D4311yescharacteristic
1053C22C22⋊Q8×D4311yescharacteristic
1054C22C2×#1306330311yescharacteristic
1055C22#1458340711yescharacteristic
1056C22#1458340811yescharacteristic
1057C22#1458340811yescharacteristic
1058C22C4⋊Q8×D4311yescharacteristic
1059C22C4⋊Q8×D4311yescharacteristic
1060C22C4⋊Q8×D4311yescharacteristic
1061C22#1458345711yescharacteristic
1062C22#1458347211yescharacteristic
1063C22#1458349211yescharacteristic
1064C22#1458349711yescharacteristic
1065C22#1458352611yescharacteristic
1066C22#1458352911yescharacteristic
1067C22#1458353111yescharacteristic
1068C22#1458353311yescharacteristic
1069C22#1458353311yescharacteristic
1070C22#1458353411yescharacteristic
1071C22#1458354711yescharacteristic
1072C22#1458355011yescharacteristic
1073C22#1458355111yescharacteristic
1074C22#1458355411yescharacteristic
1075C22#1458356211yescharacteristic
1076C22#1458356211yescharacteristic
1077C22#1458356411yescharacteristic
1078C22#1458356411yescharacteristic
1079C22#1458360311yescharacteristic
1080C22#1458360411yescharacteristic
1081C22#1458360511yescharacteristic
1082C22#1458360911yescharacteristic
1083C4—24no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—864no—
1091C4—864no—
1092C4—1722no—
1093C4—1722no—
1094C4—1722no—
1095C4—1722no—
1096C4—1722no—
1097C2—868no—
1098C2#395×D4311yescharacteristic
1099C2#1913790411yescharacteristic
1100C2#1913792811yescharacteristic
1101C2#1913823411yescharacteristic
1102C2#1913829011yescharacteristic
1103C2#1913829211yescharacteristic
1104C2#1913829911yescharacteristic
1105C2#1913830011yescharacteristic
1106C2#1913839911yescharacteristic
1107C2#1913840311yescharacteristic
1108C2#1913840711yescharacteristic
1109C2#1913841111yescharacteristic
1110C2#1913997311yescharacteristic
1111C2#1914041311yescharacteristic
1112C2#1914288111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC43×#1444C2
prime radicalC24×D43C23
hypercenter#1444D43
hypocenterC43#14720
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. C2×#14582820C2semidirect
4. C2×#14582819C2semidirect
7. #19132859C2semidirect
8. #19132858C2semidirect
9. #19132858C2semidirect
10. #19132847C2semidirect
11. #19132846C2semidirect
15. C43×#1444C2semidirect
96. C22×C4×D43Q8semidirect
133. C2×(C2×D43)⋊C4Q8semidirect
134. C2×(C2×D43)⋊C4Q8semidirect
422. C2×C4×C43C22⋊Q8semidirect
471. C2×Dic43C22⋊Q8semidirect
526. C2×D43#395semidirect
550. #1444D43semidirect
617. C43#14720semidirect
1032. C2×C4#13063303semidirect

Maximal subgroups

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

subgroupindex
C22×#130633032
C22×C4⋊C4×D432
C2×#145828202
C2×#145828192
C2×#145827732
C2×#145827702
#191328592
#191328582
#191328472
#191328462
(C2×D43)⋊#952
C43×#14442
#1472043