Finite Group Databasebeta

← #25017763

Subgroups — #25017763

Order 11008.

2782 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D43C211yesmaximal, characteristic
2C2×#14582773C211yesmaximal, characteristic
3C2×#14582770C211yesmaximal, characteristic
4C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
5C2×#14582750C211yesmaximal, characteristic, complemented
6C2×#14582746C211yesmaximal, characteristic
7C2×#14582746C211yesmaximal, characteristic
8#19132829C211yesmaximal, characteristic, complemented
9#19132828C211yesmaximal, characteristic, complemented
10#19132826C211yesmaximal, characteristic, complemented
11(C2×D43)⋊#95C211yesmaximal, characteristic
12(C2×D43)⋊#95C211yesmaximal, characteristic
13#95×Dic43C211yesmaximal, characteristic, complemented
14#95×Dic43C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C2×C42×D43—24no—
34C2×C42×D43—24no—
35C2×C42×D43—24no—
36#14582773C418yescomplemented
37#14582770C418yescomplemented
38C4⋊C4×Dic43—24no—
39#14582750—24no—
40#14582746—24no—
41#14582746C418yescomplemented
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
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C22×C4×D43—22no—
69C22×C4×D43—22no—
70C22×C4×D43—22no—
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
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×D43C2×C414yes—
85C22×C4×D43C2×C414yes—
86C22×C4×D43C2×C414yes—
87C22×C4×D43D414yes—
88C22×C4×D43Q814yes—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43C2×C414yescomplemented
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4C2×C414yescomplemented
97C2×Dic43⋊C4C2×C414yescomplemented
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4C2×C414yes—
105C2×(C2×D43)⋊C4C2×C414yes—
106C2×(C2×D43)⋊C4C2×C414yes—
107C2×(C2×D43)⋊C4C2×C414yes—
108C2×(C2×D43)⋊C4C2×C414yes—
109C2×(C2×D43)⋊C4C2×C414yes—
110C2×C4×Dic43—22no—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—22no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—22no—
122C2×C4×Dic43—22no—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43C2×C414yescomplemented
128C2×C4×Dic43C2×C414yescomplemented
129C2×C4×Dic43D414yes—
130C2×C4×Dic43D414yes—
131C42×D43—232no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95C2×C414yescomplemented
140C43⋊#95C2×C414yescomplemented
141C43⋊#95C2×C414yescomplemented
142C43⋊#95C2×C414yescomplemented
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43—22no—
151C2×C4⋊C4×C43—22no—
152C2×C4⋊C4×C43C2×C414yescomplemented
153C2×C42×C43—22no—
154C2×C42×C43—22no—
155C2×C42×C43—22no—
156#95×C43—22no—
157#95×C43—22no—
158#95×C43—22no—
159#95×C43C2×C414yescomplemented
160#95×C43C2×C414yescomplemented
161C24×C43C2411yescharacteristic
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43C22×C412yes—
171C23×D43C22×C412yes—
172C23×D43C22×C412yes—
173C23×D43C2×D412yes—
174C23×D43C2×Q812yes—
175C23×D43#4112yes—
176C23×D43#4112yes—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
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×C43C22×C412yes—
212C22×C4×C43C22×C412yes—
213C22×C4×C43C22×C412yes—
214C22×C4×C43C22×C412yes—
215C22×C4×C43C22×C412yes—
216C22×C4×C43C22×C412yes—
217C22×C4×C43C22×C412yes—
218C22×C4×C43C22×C412yes—
219C22×C4×C43C22×C412yes—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2×Q812yes—
224C22×C4×C43#4112yes—
225C22×C4×C43#4112yes—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
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×Dic43C22×C412yes—
257C22×Dic43C22×C412yes—
258C22×Dic43C22×C412yes—
259C22×Dic43C22×C412yes—
260C22×Dic43C22×C412yes—
261C22×Dic43C22×C412yes—
262C22×Dic43C22×C412yes—
263C22×Dic43C22×C412yes—
264C22×Dic43C22×C412yes—
265C22×Dic43C2×D412yes—
266C22×Dic43C2×D412yes—
267C22×Dic43C2×D412yes—
268C22×Dic43C2×D412yes—
269C22×Dic43C2×D412yes—
270C22×Dic43C2×Q812yes—
271C22×Dic43#4112yes—
272C22×Dic43#4112yes—
273C22×Dic43#4112yes—
274C22×Dic43#4112yes—
275C2×C4×D43—28no—
276C2×C4×D43—28no—
277C2×C4×D43—28no—
278C2×C4×D43—28no—
279C2×C4×D43—28no—
280C2×C4×D43—28no—
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—28no—
292C2×C4×D43—28no—
293C2×C4×D43—28no—
294C2×C4×D43—28no—
295C2×C4×D43C4⋊C4116yescomplemented
296C4⋊C4×C43—28no—
297C42×C43—28no—
298(C2×D43)⋊C4—28no—
299(C2×D43)⋊C4—28no—
300(C2×D43)⋊C4—28no—
301(C2×D43)⋊C4C42116yescomplemented
302C4⋊Dic43—28no—
303Dic43⋊C4—28no—
304Dic43⋊C4—28no—
305C4×Dic43—28no—
306C4×Dic43—28no—
307C4×Dic43—28no—
308C4×Dic43—28no—
309C4×Dic43—28no—
310C4×Dic43—44no—
311C4×Dic43—44no—
312C23×C43C23×C411yescharacteristic
313C23×C43C23×C411yescharacteristic
314C23×C43C23×C411yescharacteristic
315C23×C43C22×D411yescharacteristic
316C23×C43C22×D411yescharacteristic
317C23×C43C22×D411yescharacteristic
318C23×C43C22×Q811yescharacteristic
319C23×C43C2×#4111yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C23×C43C2×#4111yescharacteristic
322C23×C43C2×#4111yescharacteristic
323C23×C43C2×#4111yescharacteristic
324C23×C43C2×#4111yescharacteristic
325C23×C43C2×#4111yescharacteristic
326C23×C43C2×#4111yescharacteristic
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
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×D43C2×C4214yes—
356C22×D43C2×C4⋊C414yes—
357C22×D43#11714yes—
358C22×D43C4×D414yes—
359C22×D43C4×D414yes—
360C22×D43C4×Q814yes—
361C22×D43C4×Q814yes—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
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—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
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×C43C2×C4214yescomplemented
408C2×C4×C43C2×C4⋊C414yes—
409C2×C4×C43C4×D414yes—
410C2×C4×C43C4×D414yes—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—22no—
416C2×Dic43—22no—
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—22no—
421C2×Dic43—22no—
422C2×Dic43—22no—
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—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43—41no—
442C2×Dic43—41no—
443C2×Dic43—41no—
444C2×Dic43—41no—
445C2×Dic43—41no—
446C2×Dic43—41no—
447C2×Dic43—41no—
448C2×Dic43—41no—
449C2×Dic43—41no—
450C2×Dic43C2×C4214yescomplemented
451C2×Dic43C2×C4⋊C414yes—
452C2×Dic43C4×D414yes—
453C2×Dic43C4×D414yes—
454C2×Dic43C4×D414yes—
455C2×Dic43C4×D414yes—
456C2×Dic43#12014yes—
457C2×Dic43C22⋊Q814yes—
458C2×Dic43C22⋊Q814yes—
459C2×Dic43#12314yes—
460C4×D43—232no—
461C4×D43—232no—
462C4×D43—232no—
463C4×#385—431nomaximal, Sylow
464C22×C43C22×C4211yescharacteristic
465C22×C43C22×C4⋊C411yescharacteristic
466C22×C43C2×#11711yescharacteristic
467C22×C43C2×C4×D411yescharacteristic
468C22×C43C2×C4×D411yescharacteristic
469C22×C43C2×C4×D411yescharacteristic
470C22×C43C2×C4×D411yescharacteristic
471C22×C43C2×C4×D411yescharacteristic
472C22×C43C2×C4×D411yescharacteristic
473C22×C43C2×C4×D411yescharacteristic
474C22×C43C2×C4×D411yescharacteristic
475C22×C43C2×C4×Q811yescharacteristic
476C22×C43C2×C4×Q811yescharacteristic
477C22×C43C4×#4111yescharacteristic
478C22×C43C4×#4111yescharacteristic
479C22×C43C4×#4111yescharacteristic
480C22×C43C4×#4111yescharacteristic
481C22×C43C4×#4111yescharacteristic
482C22×C43C4×#4111yescharacteristic
483C22×C43C2×#12011yescharacteristic
484C22×C43C2×C22⋊Q811yescharacteristic
485C22×C43C2×C22⋊Q811yescharacteristic
486C22×C43C2×#12311yescharacteristic
487C22×C43#52511yescharacteristic
488C22×C43#52511yescharacteristic
489C22×C43#52511yescharacteristic
490C22×C43#52511yescharacteristic
491C22×C43#52511yescharacteristic
492C22×C43#52511yescharacteristic
493C22×C43#52911yescharacteristic
494C22×C43#52911yescharacteristic
495C22×C43#52911yescharacteristic
496C22×C43#52911yescharacteristic
497C22×C43#53311yescharacteristic
498C22×C43#53311yescharacteristic
499C2×D43—24no—
500C2×D43—24no—
501C2×D43—24no—
502C2×D43—24no—
503C2×D43—24no—
504C2×D43—24no—
505C2×D43—24no—
506C2×D43—24no—
507C2×D43—24no—
508C2×D43—24no—
509C2×D43—24no—
510C2×D43—24no—
511C2×D43—24no—
512C2×D43—24no—
513C2×D43C4×C4⋊C418yescomplemented
514C4×C43—24no—
515C4×C43—24no—
516C4×C43—24no—
517C4×C43—24no—
518C4×C43—42no—
519C4×C43—42no—
520C4×C43—42no—
521Dic43—24no—
522Dic43—24no—
523Dic43—24no—
524Dic43—42no—
525Dic43—42no—
526Dic43—42no—
527Dic43#38518yescomplemented
528C23×C42—431no—
529C2×#385—431no—
530C2×#385—431no—
531C2×C4×C4⋊C4—431no—
532C2×C4×C4⋊C4—431no—
533C2×C4×C22⋊C4—431no—
534C2×C4×C22⋊C4—431no—
535#1436—431no—
536#1436—431no—
537#1436—431no—
538#1436D4311yescharacteristic, complemented
539C22⋊#95—431no—
540C22⋊#95—431no—
541C4×#95—431no—
542C4×#95—431no—
543C2×C43C2×C4×C4⋊C411yescharacteristic
544C2×C43C42×D411yescharacteristic
545C2×C43C42×D411yescharacteristic
546C2×C43C2×#38511yescharacteristic
547C2×C43#229011yescharacteristic
548C2×C43#229011yescharacteristic
549C2×C43#229611yescharacteristic
550C2×C43C4×#12011yescharacteristic
551C2×C43C4×#12011yescharacteristic
552C2×C43C4×#12311yescharacteristic
553C2×C43C4×#12311yescharacteristic
554C2×C43C4×C22⋊Q811yescharacteristic
555C2×C43C4×C22⋊Q811yescharacteristic
556C2×C43C4×C22⋊Q811yescharacteristic
557C2×C43C4×C22⋊Q811yescharacteristic
558D43—28no—
559C24×C4—431no—
560C24×C4—431no—
561C24×C4—431no—
562C22×C4⋊C4—431no—
563C22×C4⋊C4—431no—
564C22×C4⋊C4—431no—
565C22×C4⋊C4C2×D4311yescharacteristic
566C22×C22⋊C4—431no—
567C22×C22⋊C4—431no—
568C22×C22⋊C4—431no—
569C22×C22⋊C4—431no—
570C22×C42—431no—
571C22×C42—431no—
572C22×C42—431no—
573C22×C42—431no—
574C22×C42—431no—
575C22×C42—431no—
576C22×C42—431no—
577C22×C42—864no—
578C22×C42—864no—
579C22×C42—864no—
580C22×C42C2×D4311yescharacteristic
581#385—438no—
582#385—438no—
583C4×C4⋊C4—864no—
584C4×C4⋊C4—864no—
585C4×C22⋊C4—438no—
586C4×C22⋊C4—864no—
587C2×#95—431no—
588C2×#95—431no—
589C2×#95—431no—
590C2×#95—431no—
591C2×#95—431no—
592C2×#95—431no—
593C2×#95—431no—
594C2×#95—431no—
595C2×#95—431no—
596C2×#95—431no—
597C2×#95—431no—
598C2×#95C2×D4311yescharacteristic
599C2×#95C2×D4311yescharacteristic
600C2×#95C2×D4311yescharacteristic
601C2×#95C2×D4311yescharacteristic
602C2×#95C2×D4311yescharacteristic
603C43C4×#38511yescharacteristic, complemented, Sylow
604C25—431no—
605C23×C4—431no—
606C23×C4—431no—
607C23×C4—431no—
608C23×C4—431no—
609C23×C4—434no—
610C23×C4—434no—
611C23×C4—434no—
612C23×C4—431no—
613C23×C4—431no—
614C23×C4—431no—
615C23×C4—434no—
616C23×C4—434no—
617C23×C4—862no—
618C23×C4—862no—
619C23×C4—862no—
620C23×C4—862no—
621C23×C4—862no—
622C23×C4—862no—
623C23×C4—862no—
624C23×C4—862no—
625C23×C4—862no—
626C23×C4—862no—
627C23×C4—862no—
628C23×C4—862no—
629C23×C4—862no—
630C23×C4—862no—
631C23×C4—862no—
632C23×C4—862no—
633C23×C4C22×D4311yescharacteristic
634C23×C4C22×D4311yescharacteristic
635C23×C4C22×D4311yescharacteristic
636C23×C4C22×D4311yescharacteristic
637C23×C4C22×D4311yescharacteristic
638C23×C4C22×D4311yescharacteristic
639C23×C4C22×D4311yescharacteristic
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—434no—
643C2×C4⋊C4—434no—
644C2×C4⋊C4—434no—
645C2×C4⋊C4—862no—
646C2×C4⋊C4—862no—
647C2×C4⋊C4—862no—
648C2×C4⋊C4—862no—
649C2×C4⋊C4—862no—
650C2×C4⋊C4—862no—
651C2×C4⋊C4C4×D4314yescomplemented
652C2×C22⋊C4—434no—
653C2×C22⋊C4—434no—
654C2×C22⋊C4—434no—
655C2×C22⋊C4—434no—
656C2×C22⋊C4—434no—
657C2×C22⋊C4—434no—
658C2×C22⋊C4—862no—
659C2×C22⋊C4—862no—
660C2×C22⋊C4—862no—
661C2×C22⋊C4—862no—
662C2×C22⋊C4—862no—
663C2×C22⋊C4—862no—
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—434no—
668C2×C42—434no—
669C2×C42—434no—
670C2×C42—434no—
671C2×C42—8632no—
672C2×C42—862no—
673C2×C42—862no—
674C2×C42—862no—
675C2×C42—862no—
676C2×C42—862no—
677C2×C42—862no—
678C2×C42—862no—
679C2×C42—862no—
680C2×C42—862no—
681C2×C42—862no—
682C2×C42—862no—
683C2×C42—862no—
684C2×C42—862no—
685C2×C42—862no—
686C2×C42—862no—
687C2×C42—862no—
688C2×C42—862no—
689#95—22no—
690#95—22no—
691#95—22no—
692#95—434no—
693#95—434no—
694#95—434no—
695#95—434no—
696#95—862no—
697#95—862no—
698#95—862no—
699#95—862no—
700#95—862no—
701#95—862no—
702#95—862no—
703#95C4×D4314yescomplemented
704#95C4×D4314yescomplemented
705C24—432no—
706C24—432no—
707C24—432no—
708C24—432no—
709C24—432no—
710C24—432no—
711C24—432no—
712C24—861no—
713C24—861no—
714C24—861no—
715C24—861no—
716C24—861no—
717C24—861no—
718C24—861no—
719C24—861no—
720C24C23×D4311yescharacteristic
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
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—432no—
756C22×C4—432no—
757C22×C4—432no—
758C22×C4—432no—
759C22×C4—432no—
760C22×C4—432no—
761C22×C4—432no—
762C22×C4—432no—
763C22×C4—432no—
764C22×C4—432no—
765C22×C4—432no—
766C22×C4—432no—
767C22×C4—432no—
768C22×C4—432no—
769C22×C4—432no—
770C22×C4—432no—
771C22×C4—4316no—
772C22×C4—432no—
773C22×C4—432no—
774C22×C4—432no—
775C22×C4—868no—
776C22×C4—868no—
777C22×C4—868no—
778C22×C4—868no—
779C22×C4—868no—
780C22×C4—868no—
781C22×C4—868no—
782C22×C4—868no—
783C22×C4—868no—
784C22×C4—868no—
785C22×C4—868no—
786C22×C4—868no—
787C22×C4—868no—
788C22×C4—868no—
789C22×C4—868no—
790C22×C4—868no—
791C22×C4—868no—
792C22×C4—868no—
793C22×C4—861no—
794C22×C4—861no—
795C22×C4—861no—
796C22×C4—861no—
797C22×C4—861no—
798C22×C4—861no—
799C22×C4—861no—
800C22×C4—861no—
801C22×C4—861no—
802C22×C4—861no—
803C22×C4—861no—
804C22×C4—861no—
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—861no—
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×C4C2×C4×D4312yes—
826C22×C4C2×C4×D4312yes—
827C22×C4C2×C4×D4312yes—
828C22×C4C2×C4×D4312yes—
829C22×C4C2×C4×D4312yes—
830C22×C4C2×C4×D4312yes—
831C22×C4C2×C4×D4312yes—
832C22×C4C2×C4×D4312yes—
833C22×C4C2×C4×D4312yes—
834C22×C4D4×D4312yes—
835C22×C4D4×D4312yes—
836C22×C4D4×D4312yes—
837C22×C4#1062190012yes—
838C22×C4Q8×D4312yes—
839C22×C4#1062190212yes—
840C4⋊C4—28no—
841C4⋊C4—868no—
842C4⋊C4—868no—
843C4⋊C4—868no—
844C22⋊C4—4316no—
845C22⋊C4—868no—
846C22⋊C4—868no—
847C22⋊C4—868no—
848C42—28no—
849C42—868no—
850C42—868no—
851C42—868no—
852C42—868no—
853C42—868no—
854C42—1724no—
855C42—1724no—
856C23—434no—
857C23—434no—
858C23—434no—
859C23—434no—
860C23—434no—
861C23—434no—
862C23—434no—
863C23—862no—
864C23—862no—
865C23—862no—
866C23—862no—
867C23—862no—
868C23—862no—
869C23—862no—
870C23—862no—
871C23—862no—
872C23—862no—
873C23—862no—
874C23—862no—
875C23—862no—
876C23—862no—
877C23—862no—
878C23—862no—
879C23—862no—
880C23—862no—
881C23—862no—
882C23—862no—
883C23—862no—
884C23—862no—
885C23—862no—
886C23—862no—
887C23—862no—
888C23—862no—
889C23—862no—
890C23—862no—
891C23C22×C4×D4311yescharacteristic
892C23C22×C4×D4311yescharacteristic
893C23C22×C4×D4311yescharacteristic
894C23C2×D4×D4311yescharacteristic
895C23C2×D4×D4311yescharacteristic
896C23C2×D4×D4311yescharacteristic
897C23C2×Q8×D4311yescharacteristic
898C23#41×D4311yescharacteristic
899C23#41×D4311yescharacteristic
900C23#41×D4311yescharacteristic
901C23#41×D4311yescharacteristic
902C23#41×D4311yescharacteristic
903C23#41×D4311yescharacteristic
904C23C2×#1062190011yescharacteristic
905C23C2×#1062190211yescharacteristic
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—434no—
952C2×C4—434no—
953C2×C4—434no—
954C2×C4—434no—
955C2×C4—434no—
956C2×C4—434no—
957C2×C4—434no—
958C2×C4—434no—
959C2×C4—434no—
960C2×C4—434no—
961C2×C4—8632no—
962C2×C4—8632no—
963C2×C4—8632no—
964C2×C4—862no—
965C2×C4—862no—
966C2×C4—862no—
967C2×C4—862no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—862no—
971C2×C4—862no—
972C2×C4—862no—
973C2×C4—862no—
974C2×C4—862no—
975C2×C4—862no—
976C2×C4—862no—
977C2×C4—862no—
978C2×C4—862no—
979C2×C4—862no—
980C2×C4—862no—
981C2×C4—862no—
982C2×C4—862no—
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—1721no—
992C2×C4—1721no—
993C2×C4—1721no—
994C2×C4—1721no—
995C2×C4—1721no—
996C2×C4—1721no—
997C2×C4—1721no—
998C2×C4—1721no—
999C2×C4—1721no—
1000C2×C4—1721no—
1001C2×C4—1721no—
1002C2×C4—1721no—
1003C2×C4C42×D4314yescomplemented
1004C2×C4C4⋊C4×D4314yes—
1005C2×C4(C22⋊D43)⋊C414yes—
1006C2×C4#1306328714yes—
1007C22—438no—
1008C22—864no—
1009C22—864no—
1010C22—864no—
1011C22—864no—
1012C22—864no—
1013C22—864no—
1014C22—864no—
1015C22—864no—
1016C22—864no—
1017C22—864no—
1018C22—864no—
1019C22—864no—
1020C22—864no—
1021C22—864no—
1022C22C2×C42×D4311yescharacteristic
1023C22C2×C4⋊C4×D4311yescharacteristic
1024C22#117×D4311yescharacteristic
1025C22C4×D4×D4311yescharacteristic
1026C22C4×D4×D4311yescharacteristic
1027C22C4×D4×D4311yescharacteristic
1028C22C4×D4×D4311yescharacteristic
1029C22C4×D4×D4311yescharacteristic
1030C22C4×D4×D4311yescharacteristic
1031C22C2×(C22⋊D43)⋊C411yescharacteristic
1032C22C2×#1306328711yescharacteristic
1033C22C4×Q8×D4311yescharacteristic
1034C22C4×Q8×D4311yescharacteristic
1035C22C4×#1062190011yescharacteristic
1036C22C4×#1062190011yescharacteristic
1037C22#1458336711yescharacteristic
1038C22#1458336711yescharacteristic
1039C22C4×#1062190211yescharacteristic
1040C22C4×#1062190211yescharacteristic
1041C22#120×D4311yescharacteristic
1042C22C22⋊Q8×D4311yescharacteristic
1043C22C22⋊Q8×D4311yescharacteristic
1044C22#123×D4311yescharacteristic
1045C22#1458340711yescharacteristic
1046C22#1458340711yescharacteristic
1047C22#1458340911yescharacteristic
1048C22#1458340911yescharacteristic
1049C22#1458341211yescharacteristic
1050C22#1458341211yescharacteristic
1051C22#1458342811yescharacteristic
1052C22#1458343211yescharacteristic
1053C22#1458343211yescharacteristic
1054C22#1458343411yescharacteristic
1055C22#1458345411yescharacteristic
1056C22#1458345511yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—24no—
1061C4—42no—
1062C4—42no—
1063C4—42no—
1064C4—438no—
1065C4—864no—
1066C4—864no—
1067C4—864no—
1068C4—1722no—
1069C4—1722no—
1070C4—1722no—
1071C2—868no—
1072C2C4×C4⋊C4×D4311yescharacteristic
1073C2C4×(C22⋊D43)⋊C411yescharacteristic
1074C2C4×#1306328711yescharacteristic
1075C2#385×D4311yescharacteristic
1076C2#1913703311yescharacteristic
1077C2#1913703711yescharacteristic
1078C2#1913707611yescharacteristic
1079C2#1913709611yescharacteristic
1080C2#1913710011yescharacteristic
1081C2#1913711611yescharacteristic
1082C2#1913712211yescharacteristic
1083C2#1913712511yescharacteristic
1084C2#1913712911yescharacteristic
1085C2#1913712911yescharacteristic
1086C2#1913713311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1436D43
hypocenterC43C4×#385
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic43C2semidirect
5. C2×#14582750C2semidirect
8. #19132829C2semidirect
9. #19132828C2semidirect
10. #19132826C2semidirect
13. #95×Dic43C2semidirect
14. #95×Dic43C2semidirect
15. C43×#1436C2semidirect
36. #14582773C4semidirect
37. #14582770C4semidirect
41. #14582746C4semidirect
91. C2×C4⋊Dic43C2×C4semidirect
96. C2×Dic43⋊C4C2×C4semidirect
97. C2×Dic43⋊C4C2×C4semidirect
127. C2×C4×Dic43C2×C4semidirect
128. C2×C4×Dic43C2×C4semidirect
139. C43⋊#95C2×C4semidirect
140. C43⋊#95C2×C4semidirect
141. C43⋊#95C2×C4semidirect
142. C43⋊#95C2×C4semidirect
152. C2×C4⋊C4×C43C2×C4semidirect
159. #95×C43C2×C4semidirect
160. #95×C43C2×C4semidirect
295. C2×C4×D43C4⋊C4semidirect
301. (C2×D43)⋊C4C42semidirect
407. C2×C4×C43C2×C42semidirect
450. C2×Dic43C2×C42semidirect
513. C2×D43C4×C4⋊C4semidirect
527. Dic43#385semidirect
538. #1436D43semidirect
603. C43C4×#385semidirect
651. C2×C4⋊C4C4×D43semidirect
703. #95C4×D43semidirect
704. #95C4×D43semidirect
1003. C2×C4C42×D43semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D432
C2×#145827732
C2×#145827702
C2×C4⋊C4×Dic432
C2×#145827502
C2×#145827462
#191328292
#191328282
#191328262
(C2×D43)⋊#952
#95×Dic432
C43×#14362
C4×#38543