Finite Group Databasebeta

← #25105844

Subgroups — #25105844

Order 11008.

1442 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583408C211yesmaximal, characteristic
2C2×#14582959C211yesmaximal, characteristic, complemented
3C2×#14582958C211yesmaximal, characteristic, complemented
4#19135394C211yesmaximal, characteristic, complemented
5#19135392C211yesmaximal, characteristic, complemented
6#19135391C211yesmaximal, characteristic, complemented
7#19135391C211yesmaximal, characteristic, complemented
8#19135389C211yesmaximal, characteristic, complemented
9#19135387C211yesmaximal, characteristic, complemented
10#19135387C211yesmaximal, characteristic, complemented
11#19134506C211yesmaximal, characteristic, complemented
12#19134506C211yesmaximal, characteristic, complemented
13#19134504C211yesmaximal, characteristic, complemented
14#19134504C211yesmaximal, characteristic, complemented
15C43×#1954C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18#14583408—24no—
19#14583408—24no—
20C2×#13063310C411yescharacteristic
21C2×#13063307C411yescharacteristic
22C2×#13063303C411yescharacteristic
23C2×#13063302C411yescharacteristic
24C2×#13063298C411yescharacteristic
25C2×#13063297C411yescharacteristic
26C2×#13063295C411yescharacteristic
27C2×#13063293C411yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×#13063282C2211yescharacteristic
32#14582959—24no—
33#14582958—24no—
34C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35C2×Dic43⋊C8C2211yescharacteristic, complemented
36C2×Dic43⋊C8C2211yescharacteristic, complemented
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
50C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
53C2×#13063236C2211yescharacteristic, complemented
54C2×#13063235C2211yescharacteristic, complemented
55C2×C8×Dic43C2211yescharacteristic, complemented
56C2×C4×D4×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic, complemented
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic, complemented
62C2×C4×C8×C43C2211yescharacteristic, complemented
63C24×D43C2×C411yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—41no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898—41no—
70C22×Dic86C2×C411yescharacteristic
71C22×D172C2×C411yescharacteristic
72C22×D172C2×C411yescharacteristic
73C22×C22⋊D43C2×C411yescharacteristic
74C22×C22⋊D43C2×C411yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C23×Dic43C2×C411yescharacteristic
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—41no—
81C22×C4×D43—41no—
82C22×C4×D43—41no—
83C22×C4×D43—41no—
84C22×C4×D43C2×C411yescharacteristic
85C22×C4×D43C2×C411yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063310—24no—
94#13063307—24no—
95#13063303—24no—
96#13063302—24no—
97#13063298—24no—
98#13063297—24no—
99#13063295—24no—
100#13063293—24no—
101C4×D172—22no—
102C4×D172—22no—
103C4×C22⋊D43—22no—
104C4×C22⋊D43—22no—
105C4×C22⋊D43—22no—
106C4×C22⋊D43—22no—
107#13063282D414yes—
108#13063282D414yes—
109C2×C4⋊Dic43C2×C411yescharacteristic
110C2×Dic43⋊C4C2×C411yescharacteristic
111C2×Dic43⋊C4C2×C411yescharacteristic
112C2×Dic43⋊C4C2×C411yescharacteristic
113C2×Dic43⋊C4C2×C411yescharacteristic
114C2×C22⋊Dic43C2×C411yescharacteristic
115C2×C22⋊Dic43C2×C411yescharacteristic
116C2×(C2×D43)⋊C4C2×C411yescharacteristic
117C2×(C2×D43)⋊C4C2×C411yescharacteristic
118C2×(C2×D43)⋊C4C2×C411yescharacteristic
119C2×(C2×D43)⋊C4C2×C411yescharacteristic
120C2×(C2×D43)⋊C4C2×C411yescharacteristic
121C2×(C2×D43)⋊C4C2×C411yescharacteristic
122C2×C4×Dic43C2311yescharacteristic
123C4⋊(C43⋊C8)—22no—
124Dic43⋊C8—22no—
125Dic43⋊C8—22no—
126C22⋊(C43⋊C8)—41no—
127C22⋊(C43⋊C8)—41no—
128C22⋊(C43⋊C8)—41no—
129C22⋊(C43⋊C8)—41no—
130(C2×D43)⋊C8—22no—
131(C2×D43)⋊C8—22no—
132(C2×D43)⋊C8—22no—
133(C2×D43)⋊C8—22no—
134(C2×D43)⋊C8—41no—
135(C2×D43)⋊C8—41no—
136(C2×D43)⋊C8—41no—
137(C2×D43)⋊C8—41no—
138(C2×D43)⋊C8—41no—
139(C2×D43)⋊C8—41no—
140(C2×D43)⋊C8—41no—
141(C2×D43)⋊C8—41no—
142#13063236—22no—
143#13063235—22no—
144C8×Dic43—22no—
145C22×D4×C43C2×C411yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C4×D4×C43—22no—
153C4×D4×C43—22no—
154C2×C4⋊C4×C43C2×C411yescharacteristic
155C2×C22⋊C4×C43C2×C411yescharacteristic
156C2×C22⋊C4×C43C2×C411yescharacteristic
157C2×C42×C43C2311yescharacteristic
158C4⋊C8×C43—22no—
159C22⋊C8×C43—41no—
160C22⋊C8×C43—41no—
161C22⋊C8×C43—41no—
162C22⋊C8×C43—41no—
163C4×C8×C43—22no—
164C24×C43C22×C411yescharacteristic
165C24×C43C22×C411yescharacteristic
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—41no—
170C23×D43—41no—
171C23×D43—41no—
172C23×D43—41no—
173C23×D43C22×C411yescharacteristic
174C23×D43C22×C411yescharacteristic
175C23×D43C22×C411yescharacteristic
176C2×D4×C43—22no—
177C2×D4×C43—22no—
178C2×D4×C43—41no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C22×C411yescharacteristic
194C22×C4×C43C22×C411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—22no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—41no—
203C2×C22⋊D43—41no—
204C2×C22⋊D43—41no—
205C2×C22⋊D43—41no—
206C2×C22⋊D43—41no—
207C2×C22⋊D43—41no—
208C22×Dic43—22no—
209C22×Dic43—41no—
210C22×Dic43—41no—
211C22×Dic43C22×C411yescharacteristic
212C22×Dic43C22×C411yescharacteristic
213C22×Dic43C22×C411yescharacteristic
214C22×Dic43C22×C411yescharacteristic
215C22×Dic43C22×C411yescharacteristic
216#10621898—44no—
217#10621898—44no—
218#10621898—44no—
219#10621898—44no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172—41no—
224C2×D172—41no—
225C2×D172—41no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—41no—
245C2×C4×D43—41no—
246C2×C4×D43—41no—
247C2×C4×D43—41no—
248C2×C4×D43—44no—
249C2×C4×D43—44no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43C2×D412yes—
253C2×C4×D43C2×D412yes—
254C2×Dic86—22no—
255C2×Dic86—41no—
256C2×Dic86—41no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C4⋊C4×C43—22no—
270C22⋊C4×C43—22no—
271C22⋊C4×C43—22no—
272C42×C43C2×D412yes—
273C42×C43C2×D412yes—
274C22⋊Dic43—22no—
275C22⋊Dic43—22no—
276(C2×D43)⋊C4—22no—
277(C2×D43)⋊C4—22no—
278(C2×D43)⋊C4—22no—
279(C2×D43)⋊C4—22no—
280(C2×D43)⋊C4C22⋊C414yes—
281(C2×D43)⋊C4C22⋊C414yes—
282C4⋊Dic43—22no—
283Dic43⋊C4—22no—
284Dic43⋊C4—22no—
285Dic43⋊C4C22⋊C414yes—
286Dic43⋊C4C22⋊C414yes—
287C4×Dic43C2×D412yes—
288C4×Dic43C2×D412yes—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43#13112yes—
315C23×C43C23×C411yescharacteristic
316C22×D43—21no—
317C22×D43—21no—
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—21no—
321C22×D43—21no—
322C22×D43—21no—
323C22×D43—21no—
324C22×D43—21no—
325C22×D43—21no—
326C22×D43—21no—
327C22×D43—21no—
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—21no—
331C22×D43—21no—
332C22×D43—21no—
333C22×D43—21no—
334C22×D43—21no—
335C22×D43—44no—
336C22×D43—44no—
337C22×D43—44no—
338C22×D43—44no—
339C22×D43—44no—
340C22×D43—44no—
341C22×D43—44no—
342C22×D43C2×C22⋊C412yes—
343C22×D43#13112yes—
344D4×C43—44no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43C2×C22⋊C412yes—
364C2×C4×C43C2×C22⋊C412yes—
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43H(5,𝔽2)11yescharacteristic
368C2×C4×C43H(5,𝔽2)11yescharacteristic
369C2×C4×C43H(5,𝔽2)11yescharacteristic
370C2×C4×C43H(5,𝔽2)11yescharacteristic
371C22⋊D43—44no—
372C22⋊D43—44no—
373C22⋊D43—44no—
374C22⋊D43—44no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—21no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—44no—
388C2×Dic43C2×C22⋊C412yes—
389C2×Dic43C2×C22⋊C412yes—
390C2×Dic43C2×C22⋊C412yes—
391D172—44no—
392D172—44no—
393C4×D43—22no—
394C4×D43—22no—
395C4×D43—22no—
396C4×D43—22no—
397C4×D43—44no—
398C4×D43—44no—
399C4×D43—41no—
400C4×D43—41no—
401C4×D43—41no—
402C4×D43—41no—
403C4×D43—41no—
404C4×D43—41no—
405C4×D43—41no—
406C4×D43—41no—
407Dic86—44no—
408C8×C43—41no—
409C8×C43—41no—
410C8×C43—41no—
411C8×C43—41no—
412C43⋊C8—41no—
413C43⋊C8—41no—
414C43⋊C8—41no—
415C43⋊C8—41no—
416#21792—431nomaximal, Sylow
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43C22×C22⋊C411yescharacteristic
432C22×C43#51811yescharacteristic
433C22×C43#51811yescharacteristic
434C22×C43C2×#13111yescharacteristic
435C22×C43C2×#13111yescharacteristic
436C22×C43#56811yescharacteristic
437C22×C43#56811yescharacteristic
438C2×D43—22no—
439C2×D43—22no—
440C2×D43—22no—
441C2×D43—22no—
442C2×D43—22no—
443C2×D43—22no—
444C2×D43—416no—
445C2×D43—41no—
446C2×D43—41no—
447C2×D43—41no—
448C2×D43—41no—
449C2×D43—41no—
450C2×D43—41no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—41no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43—41no—
458C2×D43—41no—
459C2×D43—41no—
460C4×C43—22no—
461C4×C43—22no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43#53511yescharacteristic
465C4×C43#53511yescharacteristic
466C4×C43#53511yescharacteristic
467C4×C43#53511yescharacteristic
468Dic43—22no—
469Dic43—22no—
470Dic43—22no—
471Dic43—41no—
472Dic43—41no—
473C2×#525—431no—
474C2×#433—431no—
475C2×#433—431no—
476#1955—431no—
477#1955—431no—
478#1955—431no—
479#1955—431no—
480#1954—431no—
481#1954—431no—
482#1954—431no—
483#1954D4311yescharacteristic, complemented
484#1780—431no—
485#1780—431no—
486#1779—431no—
487#1779—431no—
488C2×C43—42no—
489C2×C43—81no—
490C2×C43#230911yescharacteristic
491C2×C43#288011yescharacteristic
492C2×C43#288011yescharacteristic
493C2×C43#297611yescharacteristic
494C2×C43#297611yescharacteristic
495C2×C43#297711yescharacteristic
496C2×C43#297811yescharacteristic
497D43—42no—
498D43—42no—
499D43—81no—
500C22×#41—431no—
501C24×C4—431no—
502#525—864no—
503#525—864no—
504C2×#123—431no—
505C2×#123—431no—
506C2×C22⋊Q8—431no—
507C2×C22⋊Q8—431no—
508C2×#121—431no—
509C2×#121—431no—
510C2×#120—431no—
511C2×#120—431no—
512C2×C4×D4—431no—
513C2×C4×D4—431no—
514C2×C4×D4—431no—
515C2×C4×D4C2×D4311yescharacteristic
516C2×#117—431no—
517#433—864no—
518#433—864no—
519C2×C4⋊C8—431no—
520C2×C4⋊C8—431no—
521C2×C4⋊C8—431no—
522C2×C4⋊C8C2×D4311yescharacteristic, complemented
523C2×C22⋊C8—431no—
524C2×C22⋊C8—431no—
525C2×C22⋊C8—431no—
526C2×C22⋊C8—431no—
527C2×C22⋊C8—431no—
528C2×C22⋊C8—431no—
529C2×C22⋊C8—431no—
530C2×C22⋊C8—431no—
531C2×C22⋊C8—431no—
532C2×C22⋊C8—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535C2×C22⋊C8—431no—
536C2×C22⋊C8—431no—
537C2×C22⋊C8—431no—
538C2×C22⋊C8—431no—
539C2×C22⋊C8C2×D4311yescharacteristic
540C2×C22⋊C8C2×D4311yescharacteristic
541C2×C22⋊C8C2×D4311yescharacteristic, complemented
542C2×C22⋊C8C2×D4311yescharacteristic, complemented
543C2×#97—431no—
544C2×#97—431no—
545C2×C4×C8—431no—
546C2×C4×C8C2×D4311yescharacteristic, complemented
547C43#2179211yescharacteristic, complemented, Sylow
548C25—431no—
549C2×#41—862no—
550C2×#41—862no—
551C2×#41—1721no—
552C2×#41—1721no—
553C2×#41—1721no—
554C2×#41—1721no—
555C22×Q8—431no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—431no—
559C22×D4—431no—
560C22×D4—431no—
561C22×D4—431no—
562C22×D4C4×D4311yescharacteristic
563C23×C4—431no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—431no—
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—862no—
570C23×C4—862no—
571C23×C4—1721no—
572C23×C4—1721no—
573C23×C4—1721no—
574C23×C4—1721no—
575C23×C4C22×D4311yescharacteristic
576C23×C4C22×D4311yescharacteristic
577C22×C8—431no—
578C22×C8—431no—
579C22×C8—431no—
580C22×C8—431no—
581C22×C8C22×D4311yescharacteristic
582C22×C8C22×D4311yescharacteristic
583C22×C8C22×D4311yescharacteristic
584C22×C8C22×D4311yescharacteristic
585#123—864no—
586#123—864no—
587C22⋊Q8—864no—
588C22⋊Q8—864no—
589#121—864no—
590#121—864no—
591#120—864no—
592#120—864no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—862no—
596C4×D4—862no—
597C4×D4—862no—
598C4×D4—862no—
599C4×D4—862no—
600C4×D4—862no—
601#117—434no—
602#117—434no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4—431no—
608C2×C4⋊C4C4×D4311yescharacteristic
609C2×C22⋊C4—431no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—431no—
612C2×C22⋊C4—431no—
613C2×C22⋊C4—431no—
614C2×C22⋊C4—431no—
615C2×C22⋊C4—431no—
616C2×C22⋊C4—431no—
617C2×C22⋊C4C4×D4311yescharacteristic
618C2×C22⋊C4C4×D4311yescharacteristic
619C2×C42—431no—
620C2×C42C22×D4311yescharacteristic
621C4⋊C8—22no—
622C4⋊C8—862no—
623C4⋊C8—862no—
624C4⋊C8—862no—
625C22⋊C8—41no—
626C22⋊C8—41no—
627C22⋊C8—41no—
628C22⋊C8—41no—
629C22⋊C8—862no—
630C22⋊C8—862no—
631C22⋊C8—862no—
632C22⋊C8—862no—
633C22⋊C8—1721no—
634C22⋊C8—1721no—
635C22⋊C8—1721no—
636C22⋊C8—1721no—
637C22⋊C8—1721no—
638C22⋊C8—1721no—
639C22⋊C8—1721no—
640C22⋊C8—1721no—
641C22⋊C8—1721no—
642C22⋊C8—1721no—
643C22⋊C8—1721no—
644C22⋊C8—1721no—
645#97—862no—
646#97—862no—
647C4×C8—22no—
648C4×C8—862no—
649C24—431no—
650C24—431no—
651C24—431no—
652C24—862no—
653C24—862no—
654C24—862no—
655C24—1721no—
656C24—1721no—
657C24—1721no—
658C24—1721no—
659C24C2×C4×D4311yescharacteristic
660C24C2×C4×D4311yescharacteristic
661#41—1724no—
662#41—1724no—
663#41—1724no—
664#41—1724no—
665C2×Q8—862no—
666C2×Q8—1721no—
667C2×Q8—1721no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—41no—
671C2×D4—862no—
672C2×D4—862no—
673C2×D4—862no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—862no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—862no—
680C2×D4—1721no—
681C2×D4—1721no—
682C2×D4—1721no—
683C2×D4—1721no—
684C2×D4—1721no—
685C2×D4—1721no—
686C2×D4—1721no—
687C2×D4—1721no—
688C2×D4—1721no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—431no—
702C22×C4—431no—
703C22×C4—431no—
704C22×C4—432no—
705C22×C4—432no—
706C22×C4—431no—
707C22×C4—431no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—1721no—
728C22×C4—1721no—
729C22×C4—1721no—
730C22×C4—1721no—
731C22×C4—1724no—
732C22×C4—1724no—
733C22×C4—1724no—
734C22×C4—1724no—
735C22×C4—1721no—
736C22×C4—1721no—
737C22×C4C2×C4×D4311yescharacteristic
738C22×C4C2×C4×D4311yescharacteristic
739C22×C4C2×C4×D4311yescharacteristic
740C22×C4C2×C4×D4311yescharacteristic
741C22×C4C23×D4311yescharacteristic
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—861no—
755C2×C8—861no—
756C2×C8—861no—
757C2×C8—861no—
758C2×C8—861no—
759C2×C8—861no—
760C2×C8—861no—
761C2×C8—861no—
762C2×C8—861no—
763C2×C8—861no—
764C2×C8—861no—
765C2×C8—861no—
766C4⋊C4—22no—
767C4⋊C4—434no—
768C4⋊C4—434no—
769C4⋊C4—862no—
770C4⋊C4—862no—
771C4⋊C4—862no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—434no—
775C22⋊C4—434no—
776C22⋊C4—862no—
777C22⋊C4—862no—
778C22⋊C4—862no—
779C22⋊C4—862no—
780C22⋊C4—862no—
781C22⋊C4—862no—
782C42—432no—
783C42—432no—
784C42D4×D4312yes—
785C42D4×D4312yes—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—432no—
800C23—432no—
801C23—861no—
802C23—861no—
803C23—861no—
804C23—861no—
805C23—861no—
806C23—861no—
807C23—861no—
808C23—861no—
809C23—861no—
810C23—861no—
811C23—861no—
812C23—861no—
813C23—861no—
814C23—861no—
815C23—861no—
816C23—861no—
817C23—861no—
818C23—861no—
819C23—861no—
820C23—1724no—
821C23—1724no—
822C23—1724no—
823C23—1724no—
824C23—1724no—
825C23—1724no—
826C23—1724no—
827C23#1306333112yes—
828C23C22×C4×D4311yescharacteristic
829Q8—1724no—
830D4—44no—
831D4—1724no—
832D4—1724no—
833D4—1724no—
834D4—1724no—
835D4—1724no—
836D4—1724no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—432no—
856C2×C4—432no—
857C2×C4—432no—
858C2×C4—861no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—861no—
869C2×C4—861no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—861no—
873C2×C4—861no—
874C2×C4—1724no—
875C2×C4—1724no—
876C2×C4—1724no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4C22⋊C4×D4312yes—
886C2×C4C22⋊C4×D4312yes—
887C2×C4C2×D4×D4311yescharacteristic
888C2×C4C2×D4×D4311yescharacteristic
889C2×C4#1306337011yescharacteristic
890C2×C4#1306337011yescharacteristic
891C2×C4#1306337111yescharacteristic
892C2×C4#1306337111yescharacteristic
893C8—41no—
894C8—41no—
895C8—41no—
896C8—41no—
897C8—1721no—
898C8—1721no—
899C8—1721no—
900C8—1721no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—862no—
916C22—862no—
917C22—862no—
918C22—862no—
919C22—862no—
920C22—862no—
921C22—17216no—
922C22—1721no—
923C22—1721no—
924C22—1721no—
925C22—1721no—
926C22—1721no—
927C22—1721no—
928C22—1721no—
929C22—1721no—
930C22—1721no—
931C22—1721no—
932C22—1721no—
933C22—1721no—
934C22—1721no—
935C22—1721no—
936C22—1721no—
937C22C2×C22⋊C4×D4311yescharacteristic
938C22#1458337111yescharacteristic
939C22#1458337111yescharacteristic
940C22#131×D4311yescharacteristic
941C22C2×#1306333111yescharacteristic
942C22#1458366411yescharacteristic
943C22#1458366511yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—41no—
948C4—862no—
949C4—862no—
950C4—862no—
951C4—1721no—
952C4—1721no—
953C4#1458346211yescharacteristic
954C4#1458346511yescharacteristic
955C4#1458346511yescharacteristic
956C4#1458346711yescharacteristic
957C2—42no—
958C2—81no—
959C2—3441no—
960C2—1722no—
961C2—1722no—
962C2#1913717411yescharacteristic
963C2#1914304111yescharacteristic
964C2#1914304311yescharacteristic
965C2#1914363711yescharacteristic
966C2#1914363911yescharacteristic
967C2#1914364811yescharacteristic
968C2#1914365211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1954C2
prime radicalC2×#14583408C2
cosocleC22×C4×C43C24
hypercenter#1954D43
hypocenterC43#21792
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#14582959C2semidirect
3. C2×#14582958C2semidirect
4. #19135394C2semidirect
5. #19135392C2semidirect
6. #19135391C2semidirect
7. #19135391C2semidirect
8. #19135389C2semidirect
9. #19135387C2semidirect
10. #19135387C2semidirect
11. #19134506C2semidirect
12. #19134506C2semidirect
13. #19134504C2semidirect
14. #19134504C2semidirect
15. C43×#1954C2semidirect
34. C2×C4⋊(C43⋊C8)C22semidirect
35. C2×Dic43⋊C8C22semidirect
36. C2×Dic43⋊C8C22semidirect
39. C2×C22⋊(C43⋊C8)C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
49. C2×(C2×D43)⋊C8C22semidirect
50. C2×(C2×D43)⋊C8C22semidirect
51. C2×(C2×D43)⋊C8C22semidirect
52. C2×(C2×D43)⋊C8C22semidirect
53. C2×#13063236C22semidirect
54. C2×#13063235C22semidirect
55. C2×C8×Dic43C22semidirect
57. C2×C4⋊C8×C43C22semidirect
60. C2×C22⋊C8×C43C22semidirect
61. C2×C22⋊C8×C43C22semidirect
62. C2×C4×C8×C43C22semidirect
483. #1954D43semidirect
522. C2×C4⋊C8C2×D43semidirect
541. C2×C22⋊C8C2×D43semidirect
542. C2×C22⋊C8C2×D43semidirect
546. C2×C4×C8C2×D43semidirect
547. C43#21792semidirect

Maximal subgroups

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

subgroupindex
C2×#145834082
C2×#145829592
C2×#145829582
#191353942
#191353922
#191353912
#191353892
#191353872
#191345062
#191345042
C43×#19542
#2179243