Finite Group Databasebeta

← #25116842

Subgroups — #25116842

Order 11008.

1164 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582977C211yesmaximal, characteristic, complemented
2C2×#14582974C211yesmaximal, characteristic, complemented
3C2×#14582865C211yesmaximal, characteristic, complemented
4C2×#14582864C211yesmaximal, characteristic, complemented
5#19137810C211yesmaximal, characteristic
6#19135387C211yesmaximal, characteristic, complemented
7#19135202C211yesmaximal, characteristic, complemented
8#19135199C211yesmaximal, characteristic, complemented
9#19134890C211yesmaximal, characteristic, complemented
10#19134884C211yesmaximal, characteristic, complemented
11#19134779C211yesmaximal, characteristic, complemented
12#19134777C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic43C211yesmaximal, characteristic, complemented
14#19134365C211yesmaximal, characteristic, complemented
15C43×#1869C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23#14582977—24no—
24#14582974—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28#14582865—24no—
29#14582864—24no—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×C4×C43⋊C8C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41#14582819C411yescharacteristic
42#14582816C411yescharacteristic
43#14582814C411yescharacteristic
44#14582814C411yescharacteristic
45#14582811C411yescharacteristic
46#14582808C411yescharacteristic
47#14582807C411yescharacteristic
48#14582807C411yescharacteristic
49C4×(C2×D43)⋊C4C2211yescharacteristic
50C4×(C2×D43)⋊C4C2211yescharacteristic
51C4×C22⋊Dic43C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C23×C8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C22×Dic86C2×C411yescharacteristic
70C22×D172C2×C411yescharacteristic
71C22×C22⋊D43C2×C411yescharacteristic
72C22×C22⋊D43C2×C411yescharacteristic
73C22×C22⋊D43C2×C411yescharacteristic
74C22×C22⋊D43C2×C411yescharacteristic
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621877—22no—
78C2×#10621877—22no—
79C2×#10621877—22no—
80C2×#10621877—22no—
81C2×#10621877—41no—
82C2×#10621877—41no—
83C2×#10621872—22no—
84C2×#10621872—22no—
85C2×#10621872—41no—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C2×C8×D43—22no—
91C2×C8×D43—22no—
92C2×C8×D43—41no—
93C4×C22⋊D43—22no—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—41no—
96C4×C22⋊D43—41no—
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×C22⋊Dic43C2×C411yescharacteristic
100C2×C22⋊Dic43C2×C411yescharacteristic
101C2×C22⋊Dic43C2×C411yescharacteristic
102C2×C22⋊Dic43C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111C4⋊(C43⋊C8)—22no—
112Dic43⋊C8—22no—
113Dic43⋊C8—41no—
114C22⋊(C43⋊C8)—22no—
115C22⋊(C43⋊C8)D414yescomplemented
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8D414yescomplemented
122C4×C43⋊C8—22no—
123C8×Dic43—22no—
124C8×Dic43—41no—
125C43⋊#95C2×C411yescharacteristic
126C43⋊#95C2×C411yescharacteristic
127C43⋊#95C2×C411yescharacteristic
128C43⋊#95C2×C411yescharacteristic
129C43⋊#95C2×C411yescharacteristic
130C43⋊#95C2×C411yescharacteristic
131C22×D4×C43C2×C411yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C22×C8×C43—22no—
135C22×C8×C43—22no—
136C22×C8×C43—41no—
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×D4×C43—22no—
142C4×D4×C43—22no—
143C2×C4⋊C4×C43C2×C411yescharacteristic
144C2×C22⋊C4×C43C2×C411yescharacteristic
145C2×C22⋊C4×C43C2×C411yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C22⋊C8×C43—22no—
148C22⋊C8×C43—22no—
149C22⋊C8×C43—41no—
150C24×C43C22×C411yescharacteristic
151C24×C43C22×C411yescharacteristic
152C23×D43C22×C411yescharacteristic
153C23×D43C22×C411yescharacteristic
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—41no—
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×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43C22×C411yescharacteristic
168C22×C4×C43C22×C411yescharacteristic
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C2×D412yes—
172C22×C4×C43#4112yes—
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—22no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—22no—
180C2×C22⋊D43—22no—
181C2×C22⋊D43—41no—
182C2×C22⋊D43—41no—
183C2×C22⋊D43—41no—
184C2×C22⋊D43—41no—
185C2×C22⋊D43—41no—
186C22×Dic43C22×C411yescharacteristic
187C22×Dic43C22×C411yescharacteristic
188C22×Dic43C22×C411yescharacteristic
189C22×Dic43C22×C411yescharacteristic
190C22×Dic43C22×C411yescharacteristic
191C22×Dic43C22×C411yescharacteristic
192#10621898—44no—
193#10621898—44no—
194#10621898—44no—
195#10621898—44no—
196C2×D172—22no—
197C2×D172—22no—
198C2×D172—41no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
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×C4×D43—21no—
209C2×C4×D43C2×D412yes—
210C2×C4×D43#4112yes—
211C2×Dic86—22no—
212C2×Dic86—22no—
213C2×Dic86—41no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—44no—
226C2×C8×C43C2×D412yes—
227C4⋊C4×C43—22no—
228C22⋊C4×C43—22no—
229C22⋊C4×C43—22no—
230C42×C43—21no—
231C42×C43—21no—
232C22⋊Dic43—22no—
233C22⋊Dic43—22no—
234C22⋊Dic43—22no—
235C22⋊Dic43—41no—
236(C2×D43)⋊C4—22no—
237(C2×D43)⋊C4—22no—
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4—41no—
242Dic43⋊C4—22no—
243Dic43⋊C4—41no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248#10621877—44no—
249#10621877—44no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8C2×D412yes—
260C2×C43⋊C8C2×D412yes—
261C2×C43⋊C8C2×D412yes—
262#10621872—44no—
263C8×D43—44no—
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×C43—21no—
277C23×C43C4×D412yes—
278C23×C43C23×C411yescharacteristic
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43C4×D412yes—
293D4×C43—44no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43C4×D412yes—
313C2×C4×C43#13112yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C22⋊D43—44no—
321C22⋊D43—44no—
322C22⋊D43—44no—
323C22⋊D43—44no—
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—21no—
339C2×Dic43C4×D412yes—
340C2×Dic43#13112yes—
341C2×Dic43#13112yes—
342D172—44no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—41no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351Dic86—44no—
352C8×C43—22no—
353C8×C43—41no—
354C8×C43—41no—
355C8×C43—41no—
356C43⋊C8—22no—
357C43⋊C8—22no—
358C43⋊C8—22no—
359C43⋊C8—41no—
360#22853—431nomaximal, Sylow
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—22no—
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×C43—41no—
375C22×C43C2×C4×D411yescharacteristic
376C22×C43C2×C4×D411yescharacteristic
377C22×C43#51811yescharacteristic
378C22×C43C2×#13111yescharacteristic
379C22×C43C2×#13111yescharacteristic
380C22×C43C2×#13111yescharacteristic
381C22×C43#56811yescharacteristic
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—41no—
389C2×D43—41no—
390C2×D43—41no—
391C2×D43—41no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—41no—
399C4×C43—41no—
400C4×C43D4211yescharacteristic
401C4×C43#54611yescharacteristic
402C4×C43#54611yescharacteristic
403C4×C43#55111yescharacteristic
404Dic43—22no—
405Dic43—22no—
406Dic43—22no—
407Dic43—41no—
408Dic43—41no—
409Dic43—41no—
410C2×#436—431no—
411C2×#436—431no—
412C2×#408—431no—
413C2×#408—431no—
414#2388—431no—
415#1954—431no—
416#1923—431no—
417#1923—431no—
418#1870—431no—
419#1869—431no—
420#1869D4311yescharacteristic, complemented
421#1851—431no—
422#1851—431no—
423C8×C22⋊C4—431no—
424C8×C22⋊C4—431no—
425C2×C43—42no—
426C2×C43—81no—
427C2×C43#235811yescharacteristic
428C2×C43#293111yescharacteristic
429C2×C43#293111yescharacteristic
430C2×C43#293311yescharacteristic
431C2×C43#293311yescharacteristic
432C2×C43#297611yescharacteristic
433C2×C43#297911yescharacteristic
434D43—42no—
435D43—81no—
436C22×#41—431no—
437C22×M16—431no—
438C22×M16—431no—
439C22×M16—431no—
440C23×C8—431no—
441C23×C8C2×D4311yescharacteristic
442C2×C4×D4—431no—
443C2×C4×D4—431no—
444C2×C4×D4C2×D4311yescharacteristic
445#436—864no—
446#436—864no—
447C2×C4⋊C8—431no—
448C2×C4⋊C8—431no—
449C2×C4⋊C8—431no—
450#408—864no—
451#408—864no—
452C2×C22⋊C8—431no—
453C2×C22⋊C8—431no—
454C2×C22⋊C8—431no—
455C2×C22⋊C8—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×C22⋊C8—431no—
459C2×C22⋊C8—431no—
460C2×C22⋊C8C2×D4311yescharacteristic
461C2×C22⋊C8C2×D4311yescharacteristic
462C2×C22⋊C8C2×D4311yescharacteristic
463C2×C4×C8—431no—
464C2×C4×C8—431no—
465C2×C4×C8—431no—
466#395—431no—
467#394—431no—
468#394—431no—
469#394—431no—
470#393—431no—
471#392—431no—
472#392—431no—
473#392—431no—
474C4×C22⋊C4—431no—
475C4×C22⋊C4—431no—
476C4×C22⋊C4—431no—
477#336—431no—
478#336—431no—
479#336—431no—
480#336—431no—
481#336C2×D4311yescharacteristic
482#336C2×D4311yescharacteristic
483C43#2285311yescharacteristic, complemented, Sylow
484C2×#41—862no—
485C2×#41—862no—
486C2×#41—862no—
487C2×#41—862no—
488C2×#41—1721no—
489C2×#41—1721no—
490C22×Q8—431no—
491C22×D4—431no—
492C22×D4—431no—
493C22×D4—431no—
494C22×D4—431no—
495C22×D4—431no—
496C22×D4C4×D4311yescharacteristic
497C23×C4—431no—
498C23×C4—431no—
499C23×C4C22×D4311yescharacteristic
500C23×C4C22×D4311yescharacteristic
501C2×M16—862no—
502C2×M16—862no—
503C2×M16—862no—
504C2×M16—862no—
505C2×M16—862no—
506C2×M16—862no—
507C2×M16—1721no—
508C2×M16—1721no—
509C2×M16—1721no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8—431no—
514C22×C8—431no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—862no—
518C22×C8—862no—
519C22×C8—1721no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522C22×C8C22×D4311yescharacteristic
523C22×C8C22×D4311yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—1721no—
529C4×D4—1721no—
530C2×C4⋊C4—431no—
531C2×C4⋊C4—431no—
532C2×C4⋊C4C4×D4311yescharacteristic
533C2×C22⋊C4—431no—
534C2×C22⋊C4—431no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—431no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—431no—
540C2×C22⋊C4—431no—
541C2×C22⋊C4—431no—
542C2×C22⋊C4—431no—
543C2×C22⋊C4C4×D4311yescharacteristic
544C2×C22⋊C4C4×D4311yescharacteristic
545C2×C42—431no—
546C2×C42—431no—
547C2×C42C22×D4311yescharacteristic
548C4⋊C8—862no—
549C4⋊C8—862no—
550C4⋊C8—1721no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554C22⋊C8—434no—
555C22⋊C8—434no—
556C22⋊C8—862no—
557C22⋊C8—862no—
558C22⋊C8—862no—
559C22⋊C8—862no—
560C22⋊C8—862no—
561C22⋊C8—862no—
562C4×C8—862no—
563C4×C8—862no—
564C4×C8—1721no—
565#95—431no—
566#95—431no—
567#95—431no—
568#95—431no—
569#95—431no—
570#95—431no—
571C24—431no—
572C24—431no—
573C24C2×C4×D4311yescharacteristic
574C24C2×C4×D4311yescharacteristic
575#41—1724no—
576#41—1724no—
577#41—1724no—
578#41—1724no—
579C2×Q8—862no—
580C2×Q8—862no—
581C2×Q8—1721no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—41no—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—862no—
594C2×D4—1721no—
595C2×D4—1721no—
596C2×D4—1721no—
597C2×D4—1721no—
598C2×D4—1721no—
599C2×D4—1721no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—432no—
614C22×C4—432no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4C2×C4×D4311yescharacteristic
629C22×C4C2×C4×D4311yescharacteristic
630C22×C4C2×C4×D4311yescharacteristic
631C22×C4C2×C4×D4311yescharacteristic
632C22×C4D4×D4312yes—
633C22×C4#1062190012yes—
634C22×C4C23×D4311yescharacteristic
635M16—1724no—
636M16—1724no—
637M16—1724no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—44no—
650C2×C8—432no—
651C2×C8—432no—
652C2×C8—432no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8—861no—
657C2×C8—861no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—1724no—
663C2×C8D4×D4312yes—
664C4⋊C4—22no—
665C4⋊C4—862no—
666C4⋊C4—1721no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—862no—
670C22⋊C4—862no—
671C22⋊C4—862no—
672C22⋊C4—862no—
673C22⋊C4—862no—
674C22⋊C4—862no—
675C22⋊C4—862no—
676C22⋊C4—862no—
677C22⋊C4—1721no—
678C22⋊C4—1721no—
679C42—21no—
680C42—21no—
681C42—861no—
682C42—861no—
683C42—861no—
684C42—861no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—432no—
699C23—861no—
700C23—861no—
701C23—861no—
702C23—861no—
703C23—861no—
704C23—861no—
705C23—861no—
706C23—861no—
707C23—861no—
708C23—861no—
709C23—861no—
710C23—861no—
711C23—861no—
712C23(C22⋊D43)⋊C412yes—
713C23C22×C4×D4311yescharacteristic
714Q8—1724no—
715D4—44no—
716D4—1724no—
717D4—1724no—
718D4—1724no—
719D4—1724no—
720D4—1724no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—432no—
740C2×C4—432no—
741C2×C4—432no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—861no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—861no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4(C22⋊D43)⋊C412yes—
766C2×C4#1306333112yes—
767C2×C4C2×D4×D4311yescharacteristic
768C2×C4C2×D4×D4311yescharacteristic
769C2×C4#41×D4311yescharacteristic
770C2×C4C2×#1062190011yescharacteristic
771C2×C4#1306337011yescharacteristic
772C2×C4#1306337111yescharacteristic
773C8—22no—
774C8—41no—
775C8—41no—
776C8—41no—
777C8—862no—
778C8—862no—
779C8—862no—
780C8—1721no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—862no—
796C22—862no—
797C22—862no—
798C22—1721no—
799C22—1721no—
800C22—1721no—
801C22—1721no—
802C22—1721no—
803C22—1721no—
804C22—1721no—
805C22—1721no—
806C22—1721no—
807C22—1721no—
808C22—1721no—
809C22C4×D4×D4311yescharacteristic
810C22C2×(C22⋊D43)⋊C411yescharacteristic
811C22#1458337111yescharacteristic
812C22#131×D4311yescharacteristic
813C22#131×D4311yescharacteristic
814C22C2×#1306333111yescharacteristic
815C22#1458366511yescharacteristic
816C4—22no—
817C4—22no—
818C4—41no—
819C4—41no—
820C4—862no—
821C4—862no—
822C4—862no—
823C4—1721no—
824C4—1721no—
825C4—1721no—
826C4#1458353311yescharacteristic
827C4#1458353611yescharacteristic
828C4#1458353811yescharacteristic
829C4#1458357211yescharacteristic
830C2—42no—
831C2—81no—
832C2—3441no—
833C2—1722no—
834C2#1913757511yescharacteristic
835C2#1914330211yescharacteristic
836C2#1914330311yescharacteristic
837C2#1914331611yescharacteristic
838C2#1914331811yescharacteristic
839C2#1914364211yescharacteristic
840C2#1914365811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1869C2
prime radical#19137810C2
cosocleC22×C4×C43C24
hypercenter#1869D43
hypocenterC43#22853
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#14582977C2semidirect
2. C2×#14582974C2semidirect
3. C2×#14582865C2semidirect
4. C2×#14582864C2semidirect
6. #19135387C2semidirect
7. #19135202C2semidirect
8. #19135199C2semidirect
9. #19134890C2semidirect
10. #19134884C2semidirect
11. #19134779C2semidirect
12. #19134777C2semidirect
13. C8×C22⋊Dic43C2semidirect
14. #19134365C2semidirect
15. C43×#1869C2semidirect
115. C22⋊(C43⋊C8)D4semidirect
121. (C2×D43)⋊C8D4semidirect
420. #1869D43semidirect
483. C43#22853semidirect

Maximal subgroups

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

subgroupindex
C2×#145829772
C2×#145829742
C2×#145828652
C2×#145828642
#191378102
#191353872
#191352022
#191351992
#191348902
#191348842
#191347792
#191347772
C8×C22⋊Dic432
#191343652
C43×#18692
#2285343