Finite Group Databasebeta

← #25116844

Subgroups — #25116844

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×#14582978C211yesmaximal, characteristic, complemented
2C2×#14582974C211yesmaximal, characteristic, complemented
3C2×#14582865C211yesmaximal, characteristic, complemented
4C2×#14582864C211yesmaximal, characteristic, complemented
5#19137811C211yesmaximal, characteristic
6#19135389C211yesmaximal, characteristic, complemented
7#19135202C211yesmaximal, characteristic, complemented
8#19135201C211yesmaximal, characteristic, complemented
9#19134891C211yesmaximal, characteristic, complemented
10#19134887C211yesmaximal, characteristic, complemented
11#19134886C211yesmaximal, characteristic, complemented
12#19134780C211yesmaximal, characteristic, complemented
13#19134779C211yesmaximal, characteristic, complemented
14C8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24#14582978—24no—
25#14582974—24no—
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29#14582865—24no—
30#14582864—24no—
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×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582820C411yescharacteristic
43#14582817C411yescharacteristic
44#14582815C411yescharacteristic
45#14582815C411yescharacteristic
46#14582812C411yescharacteristic
47#14582809C411yescharacteristic
48#14582808C411yescharacteristic
49#14582808C411yescharacteristic
50C4×(C2×D43)⋊C4C2211yescharacteristic
51C4×(C2×D43)⋊C4C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C23×C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C2×C4×C8×C43C2211yescharacteristic
60C4×C22⋊C4×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×D172C2×C411yescharacteristic
72C22×D172C2×C411yescharacteristic
73C22×C22⋊D43C2×C411yescharacteristic
74C22×C22⋊D43C2×C411yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C22×C4×D43C2311yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×#10621877—22no—
80C2×#10621877—22no—
81C2×#10621877—41no—
82C2×#10621872—22no—
83C2×#10621872—22no—
84C2×#10621872—22no—
85C2×#10621872—22no—
86C2×#10621872—41no—
87C2×#10621872—41no—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C2×C8×D43—22no—
93C2×C8×D43—22no—
94C2×C8×D43—41no—
95C4×D172—22no—
96C4×D172—22no—
97C4×D172—41no—
98C4×D172—41no—
99C4×C22⋊D43—22no—
100C4×C22⋊D43—22no—
101C2×C4⋊Dic43C2×C411yescharacteristic
102C2×C4⋊Dic43C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×C22⋊Dic43C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C4⋊(C43⋊C8)—22no—
116C4⋊(C43⋊C8)—41no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—41no—
127(C2×D43)⋊C8D414yescomplemented
128C8×Dic43—22no—
129C43⋊#95C2×C411yescharacteristic
130C43⋊#95C2×C411yescharacteristic
131C43⋊#95C2×C411yescharacteristic
132C43⋊#95C2×C411yescharacteristic
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
141C2×C22⋊C4×C43C2×C411yescharacteristic
142C2×C22⋊C4×C43C2×C411yescharacteristic
143C2×C42×C43C2311yescharacteristic
144C2×C42×C43C2311yescharacteristic
145C22⋊C8×C43D414yescomplemented
146C4×C8×C43—22no—
147C4×C8×C43—41no—
148#95×C43C2×C411yescharacteristic
149#95×C43C2×C411yescharacteristic
150C24×C43C22×C411yescharacteristic
151C23×D43C22×C411yescharacteristic
152C23×D43C22×C411yescharacteristic
153C23×D43C22×C411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C2×D412yes—
164C22×C4×C43#4112yes—
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43—41no—
174C2×C22⋊D43—41no—
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C22×Dic43C22×C411yescharacteristic
180#10621898—44no—
181#10621898—44no—
182#10621898—44no—
183#10621898—44no—
184C2×D172—22no—
185C2×D172—22no—
186C2×D172—22no—
187C2×D172—22no—
188C2×D172—22no—
189C2×D172—41no—
190C2×D172—41no—
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×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—44no—
224C2×C8×C43C2×D412yes—
225C2×C8×C43C2×D412yes—
226C2×C8×C43C2×D412yes—
227C22⋊C4×C43—22no—
228C22⋊C4×C43—22no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—21no—
232C42×C43—21no—
233C22⋊Dic43—22no—
234(C2×D43)⋊C4—22no—
235(C2×D43)⋊C4—22no—
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—
242(C2×D43)⋊C4—41no—
243C4⋊Dic43—22no—
244C4⋊Dic43—41no—
245Dic43⋊C4—22no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248#10621877—44no—
249C2×C43⋊C8—21no—
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⋊C8—21no—
260C2×C43⋊C8C2×D412yes—
261#10621872—44no—
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×C43C4×D412yes—
271C23×C43C23×C411yescharacteristic
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—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43C4×D412yes—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43C4×D412yes—
310C2×C4×C43#13112yes—
311C2×C4×C43#13112yes—
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C22⋊D43—44no—
319C22⋊D43—44no—
320C22⋊D43—44no—
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×Dic43C4×D412yes—
335C2×Dic43#13112yes—
336D172—44no—
337D172—44no—
338D172—44no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—41no—
344C4×D43—41no—
345C4×D43—41no—
346C4×D43—41no—
347C4×D43—41no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351Dic86—44no—
352C8×C43—22no—
353C8×C43—22no—
354C8×C43—22no—
355C8×C43—41no—
356C43⋊C8—22no—
357C43⋊C8—41no—
358C43⋊C8—41no—
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×C43C2×C4×D411yescharacteristic
369C22×C43C2×C4×D411yescharacteristic
370C22×C43#51811yescharacteristic
371C22×C43C2×#13111yescharacteristic
372C22×C43C2×#13111yescharacteristic
373C22×C43C2×#13111yescharacteristic
374C22×C43#56811yescharacteristic
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
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—
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—22no—
399C4×C43—41no—
400C4×C43—41no—
401C4×C43D4211yescharacteristic
402C4×C43#54611yescharacteristic
403C4×C43#54611yescharacteristic
404C4×C43#55111yescharacteristic
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#1869—431no—
421#1851—431no—
422#1851—431no—
423C8×C22⋊C4—431no—
424C8×C22⋊C4D4311yescharacteristic, complemented
425C2×C43—42no—
426C2×C43#235811yescharacteristic
427C2×C43#293111yescharacteristic
428C2×C43#293111yescharacteristic
429C2×C43#293311yescharacteristic
430C2×C43#293311yescharacteristic
431C2×C43#297611yescharacteristic
432C2×C43#297911yescharacteristic
433D43—42no—
434D43—81no—
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×D4—431no—
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⋊C8—431no—
461C2×C22⋊C8—431no—
462C2×C22⋊C8C2×D4311yescharacteristic
463C2×C4×C8—431no—
464C2×C4×C8C2×D4311yescharacteristic
465C2×C4×C8C2×D4311yescharacteristic
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⋊C4C2×D4311yescharacteristic
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×D4—431no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—431no—
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—862no—
525C4×D4—862no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—1721no—
529C4×D4—1721no—
530C2×C4⋊C4—431no—
531C2×C4⋊C4—431no—
532C2×C4⋊C4—431no—
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×C42C22×D4311yescharacteristic
547C2×C42C22×D4311yescharacteristic
548C4⋊C8—862no—
549C4⋊C8—862no—
550C4⋊C8—1721no—
551C22⋊C8—434no—
552C22⋊C8—862no—
553C22⋊C8—862no—
554C22⋊C8—862no—
555C22⋊C8—862no—
556C22⋊C8—862no—
557C22⋊C8—862no—
558C22⋊C8—862no—
559C22⋊C8—862no—
560C22⋊C8—1721no—
561C22⋊C8D17214yescomplemented
562C4×C8—22no—
563C4×C8—41no—
564C4×C8—862no—
565#95—431no—
566#95—431no—
567#95—431no—
568#95—431no—
569#95C4×D4311yescharacteristic
570#95C4×D4311yescharacteristic
571C24—431no—
572C24—431no—
573C24—431no—
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—862no—
583C2×D4—862no—
584C2×D4—862no—
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—1721no—
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—431no—
605C22×C4—431no—
606C22×C4—432no—
607C22×C4—432no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
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×C4C2×C4×D4311yescharacteristic
628C22×C4C2×C4×D4311yescharacteristic
629C22×C4C2×C4×D4311yescharacteristic
630C22×C4C2×C4×D4311yescharacteristic
631C22×C4C2×C4×D4311yescharacteristic
632C22×C4C2×D17212yes—
633C22×C4#1062189812yes—
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—44no—
648C2×C8—432no—
649C2×C8—861no—
650C2×C8—861no—
651C2×C8—861no—
652C2×C8—861no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8—861no—
657C2×C8—861no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—1724no—
661C2×C8C2×D17212yes—
662C2×C8C2×D17212yes—
663C2×C8D4×D4312yes—
664C4⋊C4—862no—
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—21no—
682C42—21no—
683C42—861no—
684C42—861no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—432no—
692C23—861no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—861no—
698C23—861no—
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—
712C23C4×D17212yes—
713C23C22×C4×D4311yescharacteristic
714Q8—1724no—
715D4—1724no—
716D4—1724no—
717D4—1724no—
718D4—1724no—
719D4—1724no—
720D4—1724no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4C4×D17212yes—
765C2×C4#1306333112yes—
766C2×C4#1306333112yes—
767C2×C4C2×D4×D4311yescharacteristic
768C2×C4C22×D17211yescharacteristic
769C2×C4#41×D4311yescharacteristic
770C2×C4C2×#1062189811yescharacteristic
771C2×C4#1306337011yescharacteristic
772C2×C4#1306337111yescharacteristic
773C8—22no—
774C8—22no—
775C8—22no—
776C8—41no—
777C8—862no—
778C8—1721no—
779C8—1721no—
780C8—1721no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—862no—
789C22—862no—
790C22—862no—
791C22—1721no—
792C22—1721no—
793C22—1721no—
794C22—1721no—
795C22—1721no—
796C22—1721no—
797C22—1721no—
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×C4×D17211yescharacteristic
811C22#1458337111yescharacteristic
812C22#131×D4311yescharacteristic
813C22C2×#1306333111yescharacteristic
814C22C2×#1306333111yescharacteristic
815C22#1458366411yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—41no—
820C4—41no—
821C4—862no—
822C4—862no—
823C4—1721no—
824C4—1721no—
825C4—1721no—
826C4D4×D17211yescharacteristic
827C4#1458353911yescharacteristic
828C4#1458354411yescharacteristic
829C4#1458357311yescharacteristic
830C2—42no—
831C2—3441no—
832C2—3441no—
833C2—1722no—
834C2#1913757711yescharacteristic
835C2#1914330211yescharacteristic
836C2#1914330811yescharacteristic
837C2#1914331511yescharacteristic
838C2#1914332311yescharacteristic
839C2#1914363711yescharacteristic
840C2#1914365811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC8×C22⋊C4×C43C2
prime radical#19137811C2
cosocleC22×C4×C43C24
hypercenterC8×C22⋊C4D43
hypocenterC43#22853
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14582978C2semidirect
2. C2×#14582974C2semidirect
3. C2×#14582865C2semidirect
4. C2×#14582864C2semidirect
6. #19135389C2semidirect
7. #19135202C2semidirect
8. #19135201C2semidirect
9. #19134891C2semidirect
10. #19134887C2semidirect
11. #19134886C2semidirect
12. #19134780C2semidirect
13. #19134779C2semidirect
14. C8×(C2×D43)⋊C4C2semidirect
15. C8×C22⋊C4×C43C2semidirect
127. (C2×D43)⋊C8D4semidirect
145. C22⋊C8×C43D4semidirect
424. C8×C22⋊C4D43semidirect
483. C43#22853semidirect
561. C22⋊C8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145829782
C2×#145829742
C2×#145828652
C2×#145828642
#191378112
#191353892
#191352022
#191352012
#191348912
#191348872
#191348862
#191347802
#191347792
C8×(C2×D43)⋊C42
C8×C22⋊C4×C432
#2285343