Finite Group Databasebeta

← #25111883

Subgroups — #25111883

Order 11008.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582974C211yesmaximal, characteristic, complemented
3C2×#14582973C211yesmaximal, characteristic, complemented
4C2×#14582864C211yesmaximal, characteristic, complemented
5C2×#14582863C211yesmaximal, characteristic, complemented
6#19135391C211yesmaximal, characteristic, complemented
7#19135387C211yesmaximal, characteristic, complemented
8#19134890C211yesmaximal, characteristic, complemented
9#19134890C211yesmaximal, characteristic, complemented
10#19134889C211yesmaximal, characteristic, complemented
11#19134884C211yesmaximal, characteristic, complemented
12#19134577C211yesmaximal, characteristic, complemented
13#19134506C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1779C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621872C2211yescharacteristic, complemented
20C22×C8×D43C2211yescharacteristic, complemented
21#14583410—24no—
22#14583410—24no—
23C2×#13063308C411yescharacteristic
24C2×#13063308C411yescharacteristic
25C2×#13063304C411yescharacteristic
26C2×#13063304C411yescharacteristic
27C2×#13063299C411yescharacteristic
28C2×#13063299C411yescharacteristic
29C2×#13063294C411yescharacteristic
30C2×#13063294C411yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×#13063284C2211yescharacteristic
36#14582974—24no—
37#14582973—24no—
38C2×Dic43⋊C8C2211yescharacteristic, complemented
39C2×Dic43⋊C8C2211yescharacteristic, complemented
40#14582864—24no—
41#14582863—24no—
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
47C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
48C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
49C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
50C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×#13063235C2211yescharacteristic, complemented
53C2×C8×Dic43C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58C24×C4×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic
64C2×C22⋊C8×C43C2211yescharacteristic
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—41no—
70C2×#10621898—41no—
71C22×Dic86C2×C411yescharacteristic
72C22×D172C2×C411yescharacteristic
73C22×C22⋊D43C2×C411yescharacteristic
74C22×C22⋊D43C2×C411yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C2×#10621877—22no—
82C2×#10621877—22no—
83C2×#10621877—22no—
84C2×#10621877—22no—
85C2×#10621877—41no—
86C2×#10621877—41no—
87C2×#10621872—22no—
88C2×#10621872—22no—
89C2×#10621872—41no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C2×C8×D43—22no—
95C2×C8×D43—22no—
96C2×C8×D43—41no—
97#13063308—24no—
98#13063308—24no—
99#13063304—24no—
100#13063304—24no—
101#13063299—24no—
102#13063299—24no—
103#13063294—24no—
104#13063294—24no—
105C4×C22⋊D43—22no—
106C4×C22⋊D43—22no—
107C4×C22⋊D43—22no—
108C4×C22⋊D43—22no—
109C4×C22⋊D43—22no—
110C4×C22⋊D43—22no—
111C4×C22⋊D43D414yes—
112C4×C22⋊D43D414yes—
113#13063284—22no—
114#13063284—22no—
115C2×C4⋊Dic43C2×C411yescharacteristic
116C2×C4⋊Dic43C2×C411yescharacteristic
117C2×Dic43⋊C4C2×C411yescharacteristic
118C2×Dic43⋊C4C2×C411yescharacteristic
119C2×Dic43⋊C4C2×C411yescharacteristic
120C2×Dic43⋊C4C2×C411yescharacteristic
121C2×C22⋊Dic43C2×C411yescharacteristic
122C2×C22⋊Dic43C2×C411yescharacteristic
123C2×C22⋊Dic43C2×C411yescharacteristic
124C2×C22⋊Dic43C2×C411yescharacteristic
125C2×C22⋊Dic43C2×C411yescharacteristic
126C2×C22⋊Dic43C2×C411yescharacteristic
127C2×(C2×D43)⋊C4C2×C411yescharacteristic
128C2×(C2×D43)⋊C4C2×C411yescharacteristic
129C2×(C2×D43)⋊C4C2×C411yescharacteristic
130C2×(C2×D43)⋊C4C2×C411yescharacteristic
131C2×C4×Dic43C2311yescharacteristic
132C2×C4×Dic43C2311yescharacteristic
133Dic43⋊C8—22no—
134Dic43⋊C8—22no—
135C22⋊(C43⋊C8)—22no—
136C22⋊(C43⋊C8)—22no—
137C22⋊(C43⋊C8)—22no—
138C22⋊(C43⋊C8)D414yescomplemented
139(C2×D43)⋊C8—22no—
140(C2×D43)⋊C8—22no—
141(C2×D43)⋊C8—22no—
142(C2×D43)⋊C8—22no—
143(C2×D43)⋊C8—41no—
144(C2×D43)⋊C8—41no—
145#13063235—22no—
146C8×Dic43—22no—
147C25×C43C2×C411yescharacteristic
148C23×C4×C43—22no—
149C23×C4×C43—22no—
150C23×C4×C43—22no—
151C23×C4×C43—22no—
152C23×C4×C43—41no—
153C23×C4×C43—41no—
154C23×C4×C43C2×C411yescharacteristic
155C23×C4×C43C2×C411yescharacteristic
156C23×C4×C43C2×C411yescharacteristic
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22⋊C8×C43—22no—
165C22⋊C8×C43—22no—
166C22⋊C8×C43—22no—
167C22⋊C8×C43—22no—
168C22⋊C8×C43—41no—
169C22⋊C8×C43—41no—
170C24×C43—22no—
171C24×C43—22no—
172C24×C43—22no—
173C24×C43—41no—
174C24×C43—41no—
175C24×C43—41no—
176C24×C43—41no—
177C24×C43C22×C411yescharacteristic
178C24×C43C22×C411yescharacteristic
179C24×C43C22×C411yescharacteristic
180C23×D43C22×C411yescharacteristic
181C23×D43C22×C411yescharacteristic
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—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
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—22no—
201C22×C4×C43—22no—
202C22×C4×C43—41no—
203C22×C4×C43—41no—
204C22×C4×C43—41no—
205C22×C4×C43—44no—
206C22×C4×C43—44no—
207C22×C4×C43—44no—
208C22×C4×C43—44no—
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D412yes—
215C22×C4×C43#4112yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—22no—
218C2×C22⋊D43—22no—
219C2×C22⋊D43—22no—
220C2×C22⋊D43—22no—
221C2×C22⋊D43—22no—
222C2×C22⋊D43—22no—
223C2×C22⋊D43—22no—
224C2×C22⋊D43—22no—
225C2×C22⋊D43—22no—
226C2×C22⋊D43—41no—
227C2×C22⋊D43—41no—
228C2×C22⋊D43—41no—
229C2×C22⋊D43—41no—
230C2×C22⋊D43—41no—
231C2×C22⋊D43—41no—
232C2×C22⋊D43—41no—
233C2×C22⋊D43—41no—
234C2×C22⋊D43C22⋊C414yes—
235C22×Dic43C22×C411yescharacteristic
236C22×Dic43C22×C411yescharacteristic
237C22×Dic43C22×C411yescharacteristic
238C22×Dic43C22×C411yescharacteristic
239C22×Dic43C22×C411yescharacteristic
240C22×Dic43C22×C411yescharacteristic
241#10621898—44no—
242#10621898—44no—
243#10621898—44no—
244#10621898—44no—
245C2×D172—22no—
246C2×D172—22no—
247C2×D172—41no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×C4×D43C2×D412yes—
259C2×C4×D43C2×D412yes—
260C2×Dic86—22no—
261C2×Dic86—22no—
262C2×Dic86—41no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—21no—
275C22⋊Dic43—22no—
276C22⋊Dic43—22no—
277C22⋊Dic43—22no—
278C22⋊Dic43—22no—
279C22⋊Dic43—22no—
280C22⋊Dic43C22⋊C414yes—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4—22no—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4C22⋊C414yes—
285C4⋊Dic43—22no—
286C4⋊Dic43—22no—
287Dic43⋊C4—22no—
288Dic43⋊C4—22no—
289Dic43⋊C4—22no—
290Dic43⋊C4C22⋊C414yes—
291C4×Dic43—21no—
292C4×Dic43—21no—
293C4×Dic43C2×D412yes—
294C4×Dic43C2×D412yes—
295#10621877—44no—
296#10621877—44no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—21no—
302C2×C43⋊C8—21no—
303C2×C43⋊C8—21no—
304C2×C43⋊C8—21no—
305C2×C43⋊C8—21no—
306C2×C43⋊C8—21no—
307C2×C43⋊C8C2×D412yes—
308C2×C43⋊C8C2×D412yes—
309#10621872—44no—
310C8×D43—44no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43—21no—
325C23×C43—21no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—21no—
329C23×C43—44no—
330C23×C43—44no—
331C23×C43—44no—
332C23×C43—44no—
333C23×C43—44no—
334C23×C43—44no—
335C23×C43—44no—
336C23×C43C2×C22⋊C412yes—
337C23×C43C4×D412yes—
338C23×C43#13112yes—
339C23×C43C23×C411yescharacteristic
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—21no—
348C22×D43—21no—
349C22×D43—21no—
350C22×D43—21no—
351C22×D43—21no—
352C22×D43—21no—
353C22×D43C2×C22⋊C412yes—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—44no—
370C2×C4×C43—44no—
371C2×C4×C43—44no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43C2×C22⋊C412yes—
377C2×C4×C43C4×D412yes—
378C2×C4×C43C22×D411yescharacteristic
379C2×C4×C43C22×D411yescharacteristic
380C2×C4×C43C22×D411yescharacteristic
381C2×C4×C43C2×#4111yescharacteristic
382C2×C4×C43H(5,𝔽2)11yescharacteristic
383C2×C4×C43H(5,𝔽2)11yescharacteristic
384C22⋊D43—44no—
385C22⋊D43—44no—
386C22⋊D43—44no—
387C22⋊D43—44no—
388C22⋊D43—44no—
389C22⋊D43—44no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—21no—
398C2×Dic43—21no—
399C2×Dic43—21no—
400C2×Dic43—21no—
401C2×Dic43—21no—
402C2×Dic43—21no—
403C2×Dic43—21no—
404C2×Dic43—21no—
405C2×Dic43C2×C22⋊C412yes—
406C2×Dic43C2×C22⋊C412yes—
407C2×Dic43C2×C22⋊C412yes—
408D172—44no—
409C4×D43—22no—
410C4×D43—22no—
411C4×D43—22no—
412C4×D43—22no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417Dic86—44no—
418C8×C43—41no—
419C8×C43—41no—
420C8×C43—41no—
421C8×C43—41no—
422C43⋊C8—22no—
423C43⋊C8—22no—
424C43⋊C8—41no—
425C43⋊C8—41no—
426#22400—431nomaximal, Sylow
427C22×C43—22no—
428C22×C43—22no—
429C22×C43—22no—
430C22×C43—22no—
431C22×C43—22no—
432C22×C43—22no—
433C22×C43—22no—
434C22×C43—22no—
435C22×C43—22no—
436C22×C43—416no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—41no—
442C22×C43—41no—
443C22×C43—41no—
444C22×C43—41no—
445C22×C43—41no—
446C22×C43—41no—
447C22×C43—41no—
448C22×C43—41no—
449C22×C43C22×C22⋊C411yescharacteristic
450C22×C43C2×C4×D411yescharacteristic
451C22×C43#51811yescharacteristic
452C22×C43C2×#13111yescharacteristic
453C22×C43#56811yescharacteristic
454C22×C43#56811yescharacteristic
455C22×C43#56811yescharacteristic
456C2×D43—22no—
457C2×D43—22no—
458C2×D43—22no—
459C2×D43—41no—
460C2×D43—41no—
461C2×D43—41no—
462C2×D43—41no—
463C2×D43—41no—
464C2×D43—41no—
465C2×D43—41no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C4×C43—22no—
471C4×C43—22no—
472C4×C43—41no—
473C4×C43D4211yescharacteristic
474C4×C43D4211yescharacteristic
475C4×C43#54611yescharacteristic
476C4×C43#54611yescharacteristic
477Dic43—22no—
478Dic43—22no—
479Dic43—22no—
480Dic43—41no—
481Dic43—41no—
482Dic43—41no—
483C2×#525—431no—
484C2×#436—431no—
485C2×#435—431no—
486C2×#408—431no—
487C2×#407—431no—
488#1955—431no—
489#1954—431no—
490#1870—431no—
491#1870—431no—
492#1870—431no—
493#1869—431no—
494#1798—431no—
495#1780—431no—
496#1779D4311yescharacteristic, complemented
497#1750—431no—
498C2×C43—42no—
499C2×C43—42no—
500C2×C43—42no—
501C2×C43D4×C22⋊C411yescharacteristic
502C2×C43#287911yescharacteristic
503C2×C43#288011yescharacteristic
504C2×C43#293011yescharacteristic
505C2×C43#293311yescharacteristic
506C2×C43#297611yescharacteristic
507C2×C43#297811yescharacteristic
508D43—42no—
509D43—81no—
510C22×#41—431no—
511C24×C4C2×D4311yescharacteristic
512C22×M16—431no—
513C22×M16—431no—
514C22×M16—431no—
515C23×C8—431no—
516#525—864no—
517#525—864no—
518C2×#123—431no—
519C2×#123—431no—
520C2×C22⋊Q8—431no—
521C2×C22⋊Q8—431no—
522C2×#121—431no—
523C2×#121—431no—
524C2×#120—431no—
525C2×#120—431no—
526C2×C4×D4—431no—
527C2×C4×D4—431no—
528C2×C4×D4—431no—
529C2×C4×D4—431no—
530C2×#117—431no—
531#436—864no—
532#435—864no—
533C2×C4⋊C8—431no—
534C2×C4⋊C8—431no—
535#408—864no—
536#407—864no—
537C2×C22⋊C8—431no—
538C2×C22⋊C8—431no—
539C2×C22⋊C8—431no—
540C2×C22⋊C8—431no—
541C2×C22⋊C8—431no—
542C2×C22⋊C8—431no—
543C2×C22⋊C8—431no—
544C2×C22⋊C8—431no—
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×C22⋊C8C2×D4311yescharacteristic
548C2×C22⋊C8C2×D4311yescharacteristic
549C2×C22⋊C8C2×D4311yescharacteristic
550C2×C22⋊C8C2×D4311yescharacteristic
551C2×C22⋊C8C2×D4311yescharacteristic
552C2×C22⋊C8C2×D4311yescharacteristic
553C2×#97—431no—
554C2×C4×C8—431no—
555#336—431no—
556#336—431no—
557#336—431no—
558#336—431no—
559C43#2240011yescharacteristic, complemented, Sylow
560C25C4×D4311yescharacteristic
561C2×#41—862no—
562C2×#41—862no—
563C2×#41—862no—
564C2×#41—862no—
565C2×#41—1721no—
566C2×#41—1721no—
567C22×Q8—431no—
568C22×D4—431no—
569C22×D4—431no—
570C22×D4—431no—
571C22×D4—431no—
572C22×D4—431no—
573C22×D4—431no—
574C22×D4—431no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—41no—
580C23×C4—41no—
581C23×C4—431no—
582C23×C4—431no—
583C23×C4C4×D4311yescharacteristic
584C23×C4C4×D4311yescharacteristic
585C23×C4C4×D4311yescharacteristic
586C23×C4C22×D4311yescharacteristic
587C23×C4C22×D4311yescharacteristic
588C23×C4C22×D4311yescharacteristic
589C2×M16—862no—
590C2×M16—862no—
591C2×M16—862no—
592C2×M16—862no—
593C2×M16—862no—
594C2×M16—862no—
595C2×M16—1721no—
596C2×M16—1721no—
597C2×M16—1721no—
598C22×C8—431no—
599C22×C8—431no—
600C22×C8—431no—
601C22×C8—431no—
602C22×C8—862no—
603C22×C8—862no—
604C22×C8—1721no—
605C22×C8C22×D4311yescharacteristic
606C22×C8C22×D4311yescharacteristic
607C22×C8C22×D4311yescharacteristic
608C22×C8C22×D4311yescharacteristic
609#123—864no—
610#123—864no—
611C22⋊Q8—864no—
612C22⋊Q8—864no—
613#121—864no—
614#121—864no—
615#120—864no—
616#120—864no—
617C4×D4—434no—
618C4×D4—434no—
619C4×D4—862no—
620C4×D4—862no—
621C4×D4—862no—
622C4×D4—862no—
623C4×D4—862no—
624C4×D4—862no—
625#117—862no—
626#117—862no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4—431no—
632C2×C4⋊C4—431no—
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—431no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—431no—
639C2×C22⋊C4—431no—
640C2×C22⋊C4—431no—
641C2×C22⋊C4—431no—
642C2×C22⋊C4—431no—
643C2×C42—431no—
644C2×C42—431no—
645C4⋊C8—862no—
646C4⋊C8—862no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—22no—
650C22⋊C8—22no—
651C22⋊C8—41no—
652C22⋊C8—41no—
653C22⋊C8—434no—
654C22⋊C8—862no—
655C22⋊C8—862no—
656C22⋊C8—862no—
657C22⋊C8—862no—
658C22⋊C8—862no—
659C22⋊C8—862no—
660C22⋊C8—862no—
661C22⋊C8—1721no—
662C22⋊C8—1721no—
663#97—862no—
664C4×C8—862no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—41no—
669C24—41no—
670C24—41no—
671C24—41no—
672C24—431no—
673C24—431no—
674C24C2×C4×D4311yescharacteristic
675C24C2×C4×D4311yescharacteristic
676C24C2×C4×D4311yescharacteristic
677#41—1724no—
678#41—1724no—
679#41—1724no—
680#41—1724no—
681C2×Q8—862no—
682C2×Q8—862no—
683C2×Q8—1721no—
684C2×D4—434no—
685C2×D4—862no—
686C2×D4—862no—
687C2×D4—862no—
688C2×D4—862no—
689C2×D4—862no—
690C2×D4—862no—
691C2×D4—862no—
692C2×D4—862no—
693C2×D4—862no—
694C2×D4—862no—
695C2×D4—862no—
696C2×D4—1721no—
697C2×D4—1721no—
698C2×D4—1721no—
699C2×D4—1721no—
700C2×D4—1721no—
701C2×D4—1721no—
702C2×D4—1721no—
703C2×D4—1721no—
704C2×D4—1721no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—432no—
736C22×C4—432no—
737C22×C4—431no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4C2×C4×D4311yescharacteristic
751C22×C4C2×C4×D4311yescharacteristic
752C22×C4C2×C4×D4311yescharacteristic
753C22×C4D4×D4312yes—
754C22×C4D4×D4312yes—
755C22×C4D4×D4312yes—
756C22×C4#1062190012yes—
757C22×C4C23×D4311yescharacteristic
758M16—1724no—
759M16—1724no—
760M16—1724no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—432no—
774C2×C8—432no—
775C2×C8—861no—
776C2×C8—861no—
777C2×C8—861no—
778C2×C8—861no—
779C2×C8—861no—
780C2×C8—861no—
781C2×C8—861no—
782C2×C8—861no—
783C2×C8—861no—
784C2×C8—861no—
785C2×C8—1724no—
786C4⋊C4—434no—
787C4⋊C4—862no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C22⋊C4—434no—
793C22⋊C4—434no—
794C22⋊C4—862no—
795C22⋊C4—862no—
796C22⋊C4—862no—
797C22⋊C4—862no—
798C22⋊C4—862no—
799C22⋊C4—862no—
800C22⋊C4—862no—
801C22⋊C4—862no—
802C42—432no—
803C42—432no—
804C42—861no—
805C42—861no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—432no—
832C23—861no—
833C23—861no—
834C23—861no—
835C23—861no—
836C23—861no—
837C23—861no—
838C23—861no—
839C23—861no—
840C23—861no—
841C23—861no—
842C23—861no—
843C23—861no—
844C23—861no—
845C23C22⋊C4×D4312yes—
846C23(C22⋊D43)⋊C412yes—
847C23#1306333112yes—
848C23C22×C4×D4311yescharacteristic
849Q8—1724no—
850D4—1724no—
851D4—1724no—
852D4—1724no—
853D4—1724no—
854D4—1724no—
855D4—1724no—
856D4—1724no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—432no—
880C2×C4—432no—
881C2×C4—432no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—861no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—861no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—861no—
893C2×C4—861no—
894C2×C4—861no—
895C2×C4—861no—
896C2×C4—861no—
897C2×C4—861no—
898C2×C4—861no—
899C2×C4—861no—
900C2×C4—861no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4C22⋊C4×D4312yes—
906C2×C4(C22⋊D43)⋊C412yes—
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C2×D4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C2×C4C2×#1062190011yescharacteristic
911C2×C4#1306337011yescharacteristic
912C2×C4#1306337011yescharacteristic
913C8—41no—
914C8—41no—
915C8—41no—
916C8—41no—
917C8—862no—
918C8—862no—
919C8—1721no—
920C8—1721no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—416no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—862no—
944C22—862no—
945C22—862no—
946C22—1721no—
947C22—1721no—
948C22—1721no—
949C22—1721no—
950C22—1721no—
951C22—1721no—
952C22—1721no—
953C22—1721no—
954C22—1721no—
955C22—1721no—
956C22—1721no—
957C22C2×C22⋊C4×D4311yescharacteristic
958C22C2×(C22⋊D43)⋊C411yescharacteristic
959C22#1458337211yescharacteristic
960C22C2×#1306333111yescharacteristic
961C22#1458366511yescharacteristic
962C22#1458366511yescharacteristic
963C22#1458366511yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—862no—
968C4—862no—
969C4—862no—
970C4—1721no—
971C4—1721no—
972C4—1721no—
973C4#1458353111yescharacteristic
974C4#1458353111yescharacteristic
975C4#1458353611yescharacteristic
976C4#1458353611yescharacteristic
977C2—42no—
978C2—42no—
979C2—42no—
980C2—3441no—
981C2—1722no—
982C2#1913741111yescharacteristic
983C2#1914303811yescharacteristic
984C2#1914304111yescharacteristic
985C2#1914329411yescharacteristic
986C2#1914331611yescharacteristic
987C2#1914364011yescharacteristic
988C2#1914365511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1779C2
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenter#1779D43
hypocenterC43#22400
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#14582974C2semidirect
3. C2×#14582973C2semidirect
4. C2×#14582864C2semidirect
5. C2×#14582863C2semidirect
6. #19135391C2semidirect
7. #19135387C2semidirect
8. #19134890C2semidirect
9. #19134890C2semidirect
10. #19134889C2semidirect
11. #19134884C2semidirect
12. #19134577C2semidirect
13. #19134506C2semidirect
14. #19134363C2semidirect
15. C43×#1779C2semidirect
19. C22×#10621872C22semidirect
20. C22×C8×D43C22semidirect
38. C2×Dic43⋊C8C22semidirect
39. C2×Dic43⋊C8C22semidirect
46. C2×(C2×D43)⋊C8C22semidirect
47. C2×(C2×D43)⋊C8C22semidirect
48. C2×(C2×D43)⋊C8C22semidirect
49. C2×(C2×D43)⋊C8C22semidirect
50. C2×(C2×D43)⋊C8C22semidirect
51. C2×(C2×D43)⋊C8C22semidirect
52. C2×#13063235C22semidirect
53. C2×C8×Dic43C22semidirect
54. #14582653C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
57. #14582653C22semidirect
138. C22⋊(C43⋊C8)D4semidirect
496. #1779D43semidirect
559. C43#22400semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145829742
C2×#145829732
C2×#145828642
C2×#145828632
#191353912
#191353872
#191348902
#191348892
#191348842
#191345772
#191345062
#191343632
C43×#17792
#2240043