Finite Group Databasebeta

← #25107711

Subgroups — #25107711

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582974C211yesmaximal, characteristic, complemented
2C2×#14582866C211yesmaximal, characteristic, complemented
3#19137808C211yesmaximal, characteristic
4#19135391C211yesmaximal, characteristic, complemented
5#19135387C211yesmaximal, characteristic, complemented
6#19135205C211yesmaximal, characteristic, complemented
7#19135204C211yesmaximal, characteristic, complemented
8#19135204C211yesmaximal, characteristic, complemented
9#19135198C211yesmaximal, characteristic, complemented
10#19134889C211yesmaximal, characteristic, complemented
11#19134889C211yesmaximal, characteristic, complemented
12#19134885C211yesmaximal, characteristic, complemented
13#19134772C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C43×#1780C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C2×C4×C22⋊D43C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22#14582974—24no—
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26#14582866—24no—
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582818C411yescharacteristic
38#14582813C411yescharacteristic
39#14582813C411yescharacteristic
40#14582813C411yescharacteristic
41#14582810C411yescharacteristic
42#14582807C411yescharacteristic
43#14582807C411yescharacteristic
44#14582807C411yescharacteristic
45C4×C22⋊Dic43C2211yescharacteristic
46C4×C22⋊Dic43C2211yescharacteristic
47C4×C22⋊Dic43C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×#41×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C22×C22⋊D43C2×C411yescharacteristic
62C22×C22⋊D43C2×C411yescharacteristic
63C22×C22⋊D43C2×C411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621877—41no—
66C2×#10621877—41no—
67C2×#10621877D414yescomplemented
68C2×#10621872—22no—
69C2×#10621872—41no—
70C2×#10621872—41no—
71C22×C43⋊C8—22no—
72C22×C43⋊C8—41no—
73C22×C43⋊C8—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—41no—
81C4×C22⋊D43—41no—
82C4×C22⋊D43—41no—
83C4×C22⋊D43—41no—
84C2×Dic43⋊C4C2×C411yescharacteristic
85C2×Dic43⋊C4C2×C411yescharacteristic
86C2×Dic43⋊C4C2×C411yescharacteristic
87C2×C22⋊Dic43C2×C411yescharacteristic
88C2×C22⋊Dic43C2×C411yescharacteristic
89C2×C22⋊Dic43C2×C411yescharacteristic
90C2×C22⋊Dic43C2×C411yescharacteristic
91C2×C22⋊Dic43C2×C411yescharacteristic
92C2×C22⋊Dic43C2×C411yescharacteristic
93C2×C22⋊Dic43C2×C411yescharacteristic
94C2×C22⋊Dic43C2×C411yescharacteristic
95C2×C22⋊Dic43C2×C411yescharacteristic
96C2×(C2×D43)⋊C4C2×C411yescharacteristic
97C2×(C2×D43)⋊C4C2×C411yescharacteristic
98C2×(C2×D43)⋊C4C2×C411yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102Dic43⋊C8—22no—
103Dic43⋊C8—41no—
104Dic43⋊C8—41no—
105C22⋊(C43⋊C8)—22no—
106C22⋊(C43⋊C8)—22no—
107C22⋊(C43⋊C8)—22no—
108C22⋊(C43⋊C8)—22no—
109(C2×D43)⋊C8—22no—
110(C2×D43)⋊C8—41no—
111(C2×D43)⋊C8—41no—
112#13063235—41no—
113C8×Dic43—22no—
114C8×Dic43—41no—
115C43⋊#95C2×C411yescharacteristic
116C43⋊#95C2×C411yescharacteristic
117C43⋊#95C2×C411yescharacteristic
118C43⋊#95C2×C411yescharacteristic
119C43⋊#95C2×C411yescharacteristic
120C43⋊#95C2×C411yescharacteristic
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—41no—
124C2×#41×C43—41no—
125C2×#41×C43—41no—
126C2×#41×C43—41no—
127C22×Q8×C43C2×C411yescharacteristic
128C22×D4×C43C2×C411yescharacteristic
129C22×D4×C43C2×C411yescharacteristic
130C22×D4×C43C2×C411yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22⋊C8×C43—22no—
139C22⋊C8×C43—22no—
140C22⋊C8×C43—41no—
141C22⋊C8×C43—41no—
142C22⋊C8×C43—41no—
143C22⋊C8×C43—41no—
144C24×C43C22×C411yescharacteristic
145C24×C43C22×C411yescharacteristic
146C24×C43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148#41×C43—44no—
149#41×C43—44no—
150#41×C43—44no—
151#41×C43—44no—
152C2×Q8×C43—22no—
153C2×Q8×C43—41no—
154C2×Q8×C43—41no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43C22×C411yescharacteristic
181C22×C4×C43C22×C411yescharacteristic
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C2×D412yes—
184C22×C4×C43#4112yes—
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—41no—
190C2×C22⋊D43—41no—
191C2×C22⋊D43—41no—
192C2×C22⋊D43—41no—
193C2×C22⋊D43—41no—
194C2×C22⋊D43—41no—
195C22×Dic43C22×C411yescharacteristic
196C22×Dic43C22×C411yescharacteristic
197C22×Dic43C22×C411yescharacteristic
198C22×Dic43C22×C411yescharacteristic
199C22×Dic43C22×C411yescharacteristic
200C22×Dic43C22×C411yescharacteristic
201C22×Dic43C22×C411yescharacteristic
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—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×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C22⋊Dic43—22no—
221C22⋊Dic43—22no—
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225C22⋊Dic43—41no—
226C22⋊Dic43—41no—
227C22⋊Dic43—41no—
228C22⋊Dic43—41no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—41no—
231(C2×D43)⋊C4—41no—
232Dic43⋊C4—22no—
233Dic43⋊C4—41no—
234Dic43⋊C4—41no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241#10621877—44no—
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⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—44no—
253C2×C43⋊C8C2×D412yes—
254C2×C43⋊C8C2×D412yes—
255#10621872—44no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43C4×D412yes—
277C23×C43C23×C411yescharacteristic
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285Q8×C43—44no—
286D4×C43—44no—
287D4×C43—44no—
288D4×C43—44no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43C4×D412yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C2×C4×C43H(5,𝔽2)11yescharacteristic
315C2×C4×C43H(5,𝔽2)11yescharacteristic
316C22⋊D43—44no—
317C22⋊D43—44no—
318C22⋊D43—44no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43#13112yes—
339C2×Dic43#13112yes—
340C4×D43—41no—
341C4×D43—41no—
342C4×D43—41no—
343C4×D43—41no—
344C8×C43—41no—
345C8×C43—41no—
346C8×C43—41no—
347C8×C43—41no—
348C43⋊C8—22no—
349C43⋊C8—22no—
350C43⋊C8—41no—
351C43⋊C8—41no—
352#22039—431nomaximal, Sylow
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43C2×C4×D411yescharacteristic
375C22×C43#51811yescharacteristic
376C22×C43#51811yescharacteristic
377C22×C43C2×#13111yescharacteristic
378C22×C43C2×#13111yescharacteristic
379C22×C43#56811yescharacteristic
380C22×C43#56811yescharacteristic
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C4×C43—22no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43#53411yescharacteristic
392C4×C43#53511yescharacteristic
393C4×C43#53811yescharacteristic
394C4×C43#53811yescharacteristic
395Dic43—22no—
396Dic43—22no—
397Dic43—41no—
398Dic43—41no—
399Dic43—41no—
400Dic43—41no—
401Dic43—41no—
402C2×#436—431no—
403C2×#408—431no—
404#2388—431no—
405#1955—431no—
406#1954—431no—
407#1924—431no—
408#1923—431no—
409#1923—431no—
410#1923—431no—
411#1870—431no—
412#1870—431no—
413#1869—431no—
414#1850—431no—
415#1780D4311yescharacteristic, complemented
416#1753—431no—
417C2×C43—42no—
418C2×C43—81no—
419C2×C43—81no—
420C2×C43#232111yescharacteristic
421C2×C43#293311yescharacteristic
422C2×C43#293511yescharacteristic
423C2×C43#297611yescharacteristic
424C2×C43#297811yescharacteristic
425C2×C43#297911yescharacteristic
426C2×C43#298111yescharacteristic
427D43—81no—
428C22×#41C2×D4311yescharacteristic
429C22×M16—431no—
430C22×M16—431no—
431C23×C8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435#436—864no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8—431no—
438C2×C4⋊C8—431no—
439#408—864no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8C2×D4311yescharacteristic
448C2×C22⋊C8C2×D4311yescharacteristic
449C2×C22⋊C8C2×D4311yescharacteristic
450C2×C22⋊C8C2×D4311yescharacteristic
451C2×C22⋊C8C2×D4311yescharacteristic
452C2×C22⋊C8C2×D4311yescharacteristic
453C2×#97—431no—
454C2×C4×C8—431no—
455C2×C4×C8—431no—
456#395—431no—
457#394—431no—
458#394—431no—
459#394—431no—
460#393—431no—
461#392—431no—
462#392—431no—
463#392—431no—
464C4×C22⋊C4—431no—
465C4×C22⋊C4—431no—
466C4×C22⋊C4—431no—
467#336—431no—
468#336—431no—
469#336—431no—
470#336—431no—
471#336—431no—
472#336—431no—
473C43#2203911yescharacteristic, complemented, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8C4×D4311yescharacteristic
481C22×D4—431no—
482C22×D4—431no—
483C22×D4—431no—
484C22×D4C4×D4311yescharacteristic
485C22×D4C4×D4311yescharacteristic
486C22×D4C4×D4311yescharacteristic
487C23×C4—431no—
488C23×C4C22×D4311yescharacteristic
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4311yescharacteristic
491C2×M16—434no—
492C2×M16—862no—
493C2×M16—1721no—
494C2×M16—1721no—
495C2×M16—1721no—
496C2×M16—1721no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8—431no—
500C22×C8—431no—
501C22×C8—862no—
502C22×C8—1721no—
503C22×C8—1721no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506C22×C8C22×D4311yescharacteristic
507C22×C8C22×D4311yescharacteristic
508C4×D4—862no—
509C4×D4—862no—
510C4×D4—1721no—
511C4×D4—1721no—
512C4×D4—1721no—
513C4×D4—1721no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—431no—
529C2×C42—431no—
530C2×C42—431no—
531C2×C42—431no—
532C4⋊C8—862no—
533C4⋊C8—1721no—
534C4⋊C8—1721no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538C22⋊C8—41no—
539C22⋊C8—41no—
540C22⋊C8—41no—
541C22⋊C8—862no—
542C22⋊C8—862no—
543C22⋊C8—862no—
544C22⋊C8—862no—
545C22⋊C8—862no—
546C22⋊C8—1721no—
547C22⋊C8—1721no—
548#97—1721no—
549C4×C8—862no—
550C4×C8—1721no—
551#95—431no—
552#95—431no—
553#95—431no—
554#95—431no—
555#95—431no—
556#95—431no—
557C24—431no—
558C24C2×C4×D4311yescharacteristic
559C24C2×C4×D4311yescharacteristic
560C24C2×C4×D4311yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—862no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—1721no—
581C2×D4—1721no—
582C2×D4—1721no—
583C2×D4—1721no—
584C2×D4—1721no—
585C2×D4—1721no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4C2×C4×D4311yescharacteristic
616C22×C4C2×C4×D4311yescharacteristic
617C22×C4C2×C4×D4311yescharacteristic
618C22×C4D4×D4312yes—
619C22×C4#1062190012yes—
620C22×C4C23×D4311yescharacteristic
621M16—1724no—
622M16—1724no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—432no—
636C2×C8—432no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—1724no—
648C4⋊C4—862no—
649C4⋊C4—1721no—
650C4⋊C4—1721no—
651C22⋊C4—862no—
652C22⋊C4—862no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—1721no—
658C22⋊C4—1721no—
659C22⋊C4—1721no—
660C22⋊C4—1721no—
661C22⋊C4—1721no—
662C22⋊C4—1721no—
663C42—861no—
664C42—861no—
665C42—861no—
666C42—861no—
667C42—861no—
668C42—861no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—861no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23(C22⋊D43)⋊C412yes—
697C23C22×C4×D4311yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—1724no—
703D4—1724no—
704D4—1724no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—432no—
726C2×C4—432no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—861no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4(C22⋊D43)⋊C412yes—
751C2×C4C2×D4×D4311yescharacteristic
752C2×C4C2×#1062190011yescharacteristic
753C2×C4#1306337011yescharacteristic
754C2×C4#1306337011yescharacteristic
755C2×C4#1306337011yescharacteristic
756C2×C4#1306337011yescharacteristic
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—862no—
762C8—862no—
763C8—1721no—
764C8—1721no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—1721no—
787C22—1721no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22—1721no—
792C22—1721no—
793C22C2×(C22⋊D43)⋊C411yescharacteristic
794C22#1458337211yescharacteristic
795C22#1458337211yescharacteristic
796C22#131×D4311yescharacteristic
797C22#131×D4311yescharacteristic
798C22#1458366411yescharacteristic
799C22#1458366411yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—862no—
804C4—862no—
805C4—1721no—
806C4—1721no—
807C4—1721no—
808C4—1721no—
809C4—1721no—
810C4#1458345911yescharacteristic
811C4#1458346411yescharacteristic
812C4#1458348411yescharacteristic
813C4#1458348411yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—3441no—
818C2#1913725011yescharacteristic
819C2#1914332511yescharacteristic
820C2#1914333511yescharacteristic
821C2#1914363811yescharacteristic
822C2#1914365311yescharacteristic
823C2#1914365911yescharacteristic
824C2#1914366811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1780C2
prime radical#19137808C2
cosocleC22×C4×C43C24
hypercenter#1780D43
hypocenterC43#22039
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. C2×#14582974C2semidirect
2. C2×#14582866C2semidirect
4. #19135391C2semidirect
5. #19135387C2semidirect
6. #19135205C2semidirect
7. #19135204C2semidirect
8. #19135204C2semidirect
9. #19135198C2semidirect
10. #19134889C2semidirect
11. #19134889C2semidirect
12. #19134885C2semidirect
13. #19134772C2semidirect
14. #19134381C2semidirect
15. C43×#1780C2semidirect
67. C2×#10621877D4semidirect
415. #1780D43semidirect
473. C43#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#145829742
C2×#145828662
#191378082
#191353912
#191353872
#191352052
#191352042
#191351982
#191348892
#191348852
#191347722
#191343812
C43×#17802
#2203943