Finite Group Databasebeta

← #25107716

Subgroups — #25107716

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×#14582864C211yesmaximal, characteristic, complemented
3#19137810C211yesmaximal, characteristic
4#19135387C211yesmaximal, characteristic, complemented
5#19135208C211yesmaximal, characteristic, complemented
6#19135204C211yesmaximal, characteristic, complemented
7#19135204C211yesmaximal, characteristic, complemented
8#19135200C211yesmaximal, characteristic, complemented
9#19134893C211yesmaximal, characteristic, complemented
10#19134890C211yesmaximal, characteristic, complemented
11#19134884C211yesmaximal, characteristic, complemented
12#19134771C211yesmaximal, characteristic, complemented
13#19134506C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic, complemented
15C43×#1955C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22#14582974—24no—
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25#14582864—24no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582819C411yescharacteristic
38#14582816C411yescharacteristic
39#14582814C411yescharacteristic
40#14582814C411yescharacteristic
41#14582811C411yescharacteristic
42#14582808C411yescharacteristic
43#14582807C411yescharacteristic
44#14582807C411yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46C4×(C2×D43)⋊C4C2211yescharacteristic
47C4×C22⋊Dic43C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C22×Dic86C2×C411yescharacteristic
68C22×D172C2×C411yescharacteristic
69C22×C22⋊D43C2×C411yescharacteristic
70C22×C22⋊D43C2×C411yescharacteristic
71C22×C22⋊D43C2×C411yescharacteristic
72C22×C22⋊D43C2×C411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C2×#10621877—22no—
76C2×#10621877—41no—
77C2×#10621877—41no—
78C2×#10621872—41no—
79C2×#10621872—41no—
80C2×#10621872D414yescomplemented
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C2×C8×D43—22no—
86C2×C8×D43—41no—
87C2×C8×D43—41no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—41no—
91C4×C22⋊D43—41no—
92C2×Dic43⋊C4C2×C411yescharacteristic
93C2×Dic43⋊C4C2×C411yescharacteristic
94C2×C22⋊Dic43C2×C411yescharacteristic
95C2×C22⋊Dic43C2×C411yescharacteristic
96C2×C22⋊Dic43C2×C411yescharacteristic
97C2×C22⋊Dic43C2×C411yescharacteristic
98C2×(C2×D43)⋊C4C2×C411yescharacteristic
99C2×(C2×D43)⋊C4C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106Dic43⋊C8—22no—
107Dic43⋊C8—41no—
108C22⋊(C43⋊C8)—22no—
109C22⋊(C43⋊C8)—41no—
110C22⋊(C43⋊C8)—41no—
111(C2×D43)⋊C8—22no—
112(C2×D43)⋊C8—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115(C2×D43)⋊C8—41no—
116(C2×D43)⋊C8—41no—
117C8×Dic43—22no—
118C8×Dic43—41no—
119C43⋊#95C2×C411yescharacteristic
120C43⋊#95C2×C411yescharacteristic
121C43⋊#95C2×C411yescharacteristic
122C43⋊#95C2×C411yescharacteristic
123C43⋊#95C2×C411yescharacteristic
124C43⋊#95C2×C411yescharacteristic
125C22×D4×C43C2×C411yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4×D4×C43—41no—
133C4×D4×C43—41no—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43C2×C411yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—41no—
139C22⋊C8×C43—22no—
140C22⋊C8×C43—22no—
141C22⋊C8×C43—41no—
142C22⋊C8×C43—41no—
143#97×C43—41no—
144C24×C43C22×C411yescharacteristic
145C24×C43C22×C411yescharacteristic
146C23×D43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148C2×D4×C43—41no—
149C2×D4×C43—41no—
150C2×D4×C43—41no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C22×C411yescharacteristic
166C22×C4×C43C22×C411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—41no—
174C2×C22⋊D43—41no—
175C2×C22⋊D43—41no—
176C2×C22⋊D43—41no—
177C2×C22⋊D43—41no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C22×Dic43C22×C411yescharacteristic
181C22×Dic43C22×C411yescharacteristic
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186#10621898—44no—
187#10621898—44no—
188#10621898—44no—
189#10621898—44no—
190C2×D172—22no—
191C2×D172—41no—
192C2×D172—41no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43C2×D412yes—
204C2×C4×D43#4112yes—
205C2×Dic86—22no—
206C2×Dic86—41no—
207C2×Dic86—41no—
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×C43C2×D412yes—
220C4⋊C4×C43—41no—
221C22⋊C4×C43—41no—
222C22⋊C4×C43—41no—
223C42×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—41no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—41no—
233(C2×D43)⋊C4—41no—
234(C2×D43)⋊C4—41no—
235Dic43⋊C4—22no—
236Dic43⋊C4—41no—
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—21no—
253C2×C43⋊C8C2×D412yes—
254#10621872—44no—
255C8×D43—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×C43C23×C411yescharacteristic
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43C4×D412yes—
285D4×C43—44no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C22⋊D43—44no—
313C22⋊D43—44no—
314C22⋊D43—44no—
315C22⋊D43—44no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
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×Dic43C4×D412yes—
332C2×Dic43#13112yes—
333C2×Dic43#13112yes—
334D172—44no—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—41no—
340C4×D43—41no—
341C4×D43—41no—
342C4×D43—41no—
343Dic86—44no—
344C8×C43—22no—
345C8×C43—41no—
346C8×C43—41no—
347C8×C43—41no—
348C43⋊C8—22no—
349C43⋊C8—41no—
350C43⋊C8—41no—
351C43⋊C8—41no—
352#22039—431nomaximal, Sylow
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
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×C43C2×C4×D411yescharacteristic
368C22×C43#51811yescharacteristic
369C22×C43#51811yescharacteristic
370C22×C43C2×#13111yescharacteristic
371C22×C43C2×#13111yescharacteristic
372C22×C43#56811yescharacteristic
373C22×C43#56811yescharacteristic
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43#53411yescharacteristic
393C4×C43#53511yescharacteristic
394C4×C43#53811yescharacteristic
395C4×C43#53811yescharacteristic
396Dic43—22no—
397Dic43—22no—
398Dic43—22no—
399Dic43—41no—
400Dic43—41no—
401Dic43—41no—
402C2×#436—431no—
403C2×#408—431no—
404#2388—431no—
405#1955D4311yescharacteristic, complemented
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#1780—431no—
416#1753—431no—
417C2×C43—81no—
418C2×C43—81no—
419C2×C43#232111yescharacteristic
420C2×C43#293311yescharacteristic
421C2×C43#293511yescharacteristic
422C2×C43#297611yescharacteristic
423C2×C43#297811yescharacteristic
424C2×C43#297911yescharacteristic
425C2×C43#298111yescharacteristic
426D43—42no—
427D43—81no—
428C22×#41—431no—
429C22×M16—431no—
430C22×M16—431no—
431C23×C8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4C2×D4311yescharacteristic
435#436—864no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8—431no—
438C2×C4⋊C8C2×D4311yescharacteristic
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⋊C8—431no—
448C2×C22⋊C8—431no—
449C2×C22⋊C8C2×D4311yescharacteristic
450C2×C22⋊C8C2×D4311yescharacteristic
451C2×C22⋊C8C2×D4311yescharacteristic
452C2×C22⋊C8C2×D4311yescharacteristic
453C2×#97C2×D4311yescharacteristic
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—862no—
475C2×#41—862no—
476C2×#41—1721no—
477C2×#41—1721no—
478C2×#41—1721no—
479C2×#41—1721no—
480C22×Q8—431no—
481C22×D4—431no—
482C22×D4—431no—
483C22×D4—431no—
484C22×D4—431no—
485C22×D4—431no—
486C22×D4C4×D4311yescharacteristic
487C23×C4—431no—
488C23×C4—431no—
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—41no—
509C4×D4—41no—
510C4×D4—862no—
511C4×D4—862no—
512C4×D4—1721no—
513C4×D4—1721no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4C4×D4311yescharacteristic
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⋊C4C4×D4311yescharacteristic
528C2×C22⋊C4C4×D4311yescharacteristic
529C2×C42—431no—
530C2×C42—431no—
531C2×C42C22×D4311yescharacteristic
532C4⋊C8—41no—
533C4⋊C8—862no—
534C4⋊C8—1721no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538C22⋊C8—41no—
539C22⋊C8—862no—
540C22⋊C8—862no—
541C22⋊C8—862no—
542C22⋊C8—862no—
543C22⋊C8—862no—
544C22⋊C8—1721no—
545C22⋊C8—1721no—
546C22⋊C8—1721no—
547C22⋊C8—1721no—
548#97—41no—
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—
558C24—431no—
559C24C2×C4×D4311yescharacteristic
560C24C2×C4×D4311yescharacteristic
561#41—1724no—
562#41—1724no—
563#41—1724no—
564#41—1724no—
565C2×Q8—862no—
566C2×Q8—1721no—
567C2×Q8—1721no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—1721no—
578C2×D4—1721no—
579C2×D4—1721no—
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—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4C2×C4×D4311yescharacteristic
617C22×C4C2×C4×D4311yescharacteristic
618C22×C4C2×C4×D4311yescharacteristic
619C22×C4C2×C4×D4311yescharacteristic
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—432no—
635C2×C8—861no—
636C2×C8—861no—
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—1724no—
647C2×C8D4×D4312yes—
648C4⋊C4—41no—
649C4⋊C4—862no—
650C4⋊C4—1721no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—862no—
658C22⋊C4—862no—
659C22⋊C4—1721no—
660C22⋊C4—1721no—
661C22⋊C4—1721no—
662C22⋊C4—1721no—
663C42—21no—
664C42—21no—
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—432no—
684C23—861no—
685C23—861no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—861no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23C22×C4×D4311yescharacteristic
698Q8—1724no—
699D4—44no—
700D4—1724no—
701D4—1724no—
702D4—1724no—
703D4—1724no—
704D4—1724no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
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—432no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
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—861no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4C2×D4×D4311yescharacteristic
752C2×C4#41×D4311yescharacteristic
753C2×C4#1306337011yescharacteristic
754C2×C4#1306337011yescharacteristic
755C2×C4#1306337011yescharacteristic
756C2×C4#1306337111yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—862no—
762C8—1721no—
763C8—1721no—
764C8—1721no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—862no—
780C22—862no—
781C22—862no—
782C22—1721no—
783C22—1721no—
784C22—1721no—
785C22—1721no—
786C22—1721no—
787C22—1721no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22—1721no—
792C22—1721no—
793C22C4×D4×D4311yescharacteristic
794C22#1458337111yescharacteristic
795C22#1458337211yescharacteristic
796C22#131×D4311yescharacteristic
797C22#131×D4311yescharacteristic
798C22#1458366511yescharacteristic
799C22#1458366511yescharacteristic
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—862no—
805C4—862no—
806C4—862no—
807C4—1721no—
808C4—1721no—
809C4—1721no—
810C4#1458345711yescharacteristic
811C4#1458346211yescharacteristic
812C4#1458348111yescharacteristic
813C4#1458348311yescharacteristic
814C2—81no—
815C2—81no—
816C2—3441no—
817C2—1722no—
818C2#1913725411yescharacteristic
819C2#1914331811yescharacteristic
820C2#1914333611yescharacteristic
821C2#1914364211yescharacteristic
822C2#1914365511yescharacteristic
823C2#1914365911yescharacteristic
824C2#1914366711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1955C2
prime radical#19137810C2
cosocleC22×C4×C43C24
hypercenter#1955D43
hypocenterC43#22039
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. C2×#14582974C2semidirect
2. C2×#14582864C2semidirect
4. #19135387C2semidirect
5. #19135208C2semidirect
6. #19135204C2semidirect
7. #19135204C2semidirect
8. #19135200C2semidirect
9. #19134893C2semidirect
10. #19134890C2semidirect
11. #19134884C2semidirect
12. #19134771C2semidirect
13. #19134506C2semidirect
14. #19134380C2semidirect
15. C43×#1955C2semidirect
80. C2×#10621872D4semidirect
405. #1955D43semidirect
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×#145828642
#191378102
#191353872
#191352082
#191352042
#191352002
#191348932
#191348902
#191348842
#191347712
#191345062
#191343802
C43×#19552
#2203943