Finite Group Databasebeta

← #25107721

Subgroups — #25107721

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×#14582977C211yesmaximal, characteristic, complemented
2C2×#14582865C211yesmaximal, characteristic, complemented
3#19137810C211yesmaximal, characteristic
4#19135391C211yesmaximal, characteristic, complemented
5#19135387C211yesmaximal, characteristic, complemented
6#19135209C211yesmaximal, characteristic, complemented
7#19135202C211yesmaximal, characteristic, complemented
8#19135199C211yesmaximal, characteristic, complemented
9#19135199C211yesmaximal, characteristic, complemented
10#19134890C211yesmaximal, characteristic, complemented
11#19134890C211yesmaximal, characteristic, complemented
12#19134773C211yesmaximal, characteristic, complemented
13#19134506C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C43×#1869C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×C4×C22⋊D43C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21#14582977—24no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25#14582865—24no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
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×(C2×D43)⋊C8C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39#14582819C411yescharacteristic
40#14582816C411yescharacteristic
41#14582814C411yescharacteristic
42#14582814C411yescharacteristic
43#14582811C411yescharacteristic
44#14582808C411yescharacteristic
45#14582807C411yescharacteristic
46#14582807C411yescharacteristic
47C4×(C2×D43)⋊C4C2211yescharacteristic
48C4×(C2×D43)⋊C4C2211yescharacteristic
49C4×C22⋊Dic43C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
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×#10621877—41no—
79C2×#10621877—41no—
80C2×#10621877D414yescomplemented
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C4×C22⋊D43—41no—
86C4×C22⋊D43—41no—
87C4×C22⋊D43—41no—
88C4×C22⋊D43—41no—
89C2×Dic43⋊C4C2×C411yescharacteristic
90C2×Dic43⋊C4C2×C411yescharacteristic
91C2×C22⋊Dic43C2×C411yescharacteristic
92C2×C22⋊Dic43C2×C411yescharacteristic
93C2×C22⋊Dic43C2×C411yescharacteristic
94C2×C22⋊Dic43C2×C411yescharacteristic
95C2×(C2×D43)⋊C4C2×C411yescharacteristic
96C2×(C2×D43)⋊C4C2×C411yescharacteristic
97C2×(C2×D43)⋊C4C2×C411yescharacteristic
98C2×(C2×D43)⋊C4C2×C411yescharacteristic
99C2×(C2×D43)⋊C4C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C4⋊(C43⋊C8)—22no—
104Dic43⋊C8—41no—
105Dic43⋊C8—41no—
106C22⋊(C43⋊C8)—22no—
107C22⋊(C43⋊C8)—22no—
108(C2×D43)⋊C8—22no—
109(C2×D43)⋊C8—22no—
110(C2×D43)⋊C8—22no—
111(C2×D43)⋊C8—22no—
112(C2×D43)⋊C8—41no—
113(C2×D43)⋊C8—41no—
114(C2×D43)⋊C8—41no—
115(C2×D43)⋊C8—41no—
116#13063235—41no—
117C4×C43⋊C8—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×C43—22no—
129C22×C8×C43—41no—
130C22×C8×C43—41no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C4×D4×C43—22no—
136C4×D4×C43—22no—
137C2×C4⋊C4×C43C2×C411yescharacteristic
138C2×C22⋊C4×C43C2×C411yescharacteristic
139C2×C22⋊C4×C43C2×C411yescharacteristic
140C2×C42×C43C2311yescharacteristic
141C22⋊C8×C43—22no—
142C22⋊C8×C43—41no—
143C22⋊C8×C43—41no—
144C24×C43C22×C411yescharacteristic
145C24×C43C22×C411yescharacteristic
146C23×D43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148C2×D4×C43—22no—
149C2×D4×C43—22no—
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×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C2×D412yes—
166C22×C4×C43#4112yes—
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
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×D43—21no—
204C2×C4×D43—21no—
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×C43—21no—
220C2×C8×C43—44no—
221C4⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C42×C43—21no—
225C42×C43—21no—
226C22⋊Dic43—22no—
227C22⋊Dic43—41no—
228C22⋊Dic43—41no—
229C22⋊Dic43—41no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—22no—
233(C2×D43)⋊C4—41no—
234(C2×D43)⋊C4—41no—
235(C2×D43)⋊C4—41no—
236Dic43⋊C4—41no—
237Dic43⋊C4—41no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—21no—
242#10621877—44no—
243#10621877—44no—
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⋊C8—21no—
254C2×C43⋊C8C2×D412yes—
255C2×C43⋊C8C2×D412yes—
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×C43C4×D412yes—
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×D43—21no—
285D4×C43—44no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43C4×D412yes—
305C2×C4×C43#13112yes—
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×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43#13112yes—
334D172—44no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—41no—
340C4×D43—41no—
341C4×D43—41no—
342C4×D43—41no—
343Dic86—44no—
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×C43C2×C4×D411yescharacteristic
368C22×C43#51811yescharacteristic
369C22×C43#51811yescharacteristic
370C22×C43C2×#13111yescharacteristic
371C22×C43C2×#13111yescharacteristic
372C22×C43#56811yescharacteristic
373C22×C43#56811yescharacteristic
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
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—22no—
389C4×C43—22no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43#53411yescharacteristic
393C4×C43#53511yescharacteristic
394C4×C43#53811yescharacteristic
395C4×C43#53811yescharacteristic
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#1869D4311yescharacteristic, complemented
414#1850—431no—
415#1780—431no—
416#1753—431no—
417C2×C43—42no—
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—81no—
427D43—81no—
428C22×#41—431no—
429C22×M16—431no—
430C22×M16—431no—
431C23×C8C2×D4311yescharacteristic
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⋊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⋊C8—431no—
448C2×C22⋊C8—431no—
449C2×C22⋊C8—431no—
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#336C2×D4311yescharacteristic
472#336C2×D4311yescharacteristic
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—22no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8—431no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506C22×C8C22×D4311yescharacteristic
507C22×C8C22×D4311yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—1721no—
511C4×D4—1721no—
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—862no—
533C4⋊C8—1721no—
534C4⋊C8—1721no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537C22⋊C8—41no—
538C22⋊C8—862no—
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—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—
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—22no—
569C2×D4—22no—
570C2×D4—41no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—1721no—
576C2×D4—1721no—
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—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
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×C4C2×C4×D4311yescharacteristic
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—44no—
636C2×C8—432no—
637C2×C8—432no—
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—861no—
648C4⋊C4—22no—
649C4⋊C4—1721no—
650C4⋊C4—1721no—
651C22⋊C4—22no—
652C22⋊C4—22no—
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—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—861no—
683C23—861no—
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(C22⋊D43)⋊C412yes—
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—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—432no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
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—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4(C22⋊D43)⋊C412yes—
750C2×C4#1306333112yes—
751C2×C4C2×D4×D4311yescharacteristic
752C2×C4C2×#1062190011yescharacteristic
753C2×C4#1306337011yescharacteristic
754C2×C4#1306337011yescharacteristic
755C2×C4#1306337111yescharacteristic
756C2×C4#1306337111yescharacteristic
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—1721no—
780C22—1721no—
781C22—1721no—
782C22—1721no—
783C22—1721no—
784C22—1721no—
785C22—1721no—
786C22—1721no—
787C22—1721no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22—1721no—
792C22—1721no—
793C22C2×(C22⋊D43)⋊C411yescharacteristic
794C22#1458337111yescharacteristic
795C22#1458337111yescharacteristic
796C22#131×D4311yescharacteristic
797C22C2×#1306333111yescharacteristic
798C22#1458366411yescharacteristic
799C22#1458366511yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—862no—
805C4—1721no—
806C4—1721no—
807C4—1721no—
808C4—1721no—
809C4—1721no—
810C4#1458346011yescharacteristic
811C4#1458346411yescharacteristic
812C4#1458348611yescharacteristic
813C4#1458348611yescharacteristic
814C2—42no—
815C2—81no—
816C2—3441no—
817C2—3441no—
818C2#1913725811yescharacteristic
819C2#1914331611yescharacteristic
820C2#1914333511yescharacteristic
821C2#1914364211yescharacteristic
822C2#1914365411yescharacteristic
823C2#1914365811yescharacteristic
824C2#1914366911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1869C2
prime radical#19137810C2
cosocleC22×C4×C43C24
hypercenter#1869D43
hypocenterC43#22039
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×#14582865C2semidirect
4. #19135391C2semidirect
5. #19135387C2semidirect
6. #19135209C2semidirect
7. #19135202C2semidirect
8. #19135199C2semidirect
9. #19135199C2semidirect
10. #19134890C2semidirect
11. #19134890C2semidirect
12. #19134773C2semidirect
13. #19134506C2semidirect
14. #19134381C2semidirect
15. C43×#1869C2semidirect
80. C2×#10621877D4semidirect
413. #1869D43semidirect
473. C43#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#145829772
C2×#145828652
#191378102
#191353912
#191353872
#191352092
#191352022
#191351992
#191348902
#191347732
#191345062
#191343812
C43×#18692
#2203943