Finite Group Databasebeta

← #25113340

Subgroups — #25113340

Order 11008.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583427C211yesmaximal, characteristic
2C2×#14583029C211yesmaximal, characteristic, complemented
3C2×#14583027C211yesmaximal, characteristic, complemented
4#19135393C211yesmaximal, characteristic, complemented
5#19135391C211yesmaximal, characteristic, complemented
6#19135391C211yesmaximal, characteristic, complemented
7#19135391C211yesmaximal, characteristic, complemented
8#19135389C211yesmaximal, characteristic, complemented
9#19135387C211yesmaximal, characteristic, complemented
10#19134579C211yesmaximal, characteristic, complemented
11#19134578C211yesmaximal, characteristic, complemented
12#19134574C211yesmaximal, characteristic, complemented
13#19134360C211yesmaximal, characteristic, complemented
14#19134356C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16#14583427—24no—
17#14583427—24no—
18C2×#13063320C411yescharacteristic
19C2×#13063318C411yescharacteristic
20C2×#13063315C411yescharacteristic
21C2×#13063311C411yescharacteristic
22C2×#13063310C411yescharacteristic
23C2×#13063307C411yescharacteristic
24C2×#13063303C411yescharacteristic
25C2×#13063298C411yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31C2×C42×D43C2211yescharacteristic
32#14583029—24no—
33#14583027—24no—
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×Dic43⋊C8C2211yescharacteristic
38C2×Dic43⋊C8C2211yescharacteristic
39C2×Dic43⋊C8C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
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
50C2×#13063235C2211yescharacteristic
51C2×#13063235C2211yescharacteristic
52C2×#13063235C2211yescharacteristic
53C2×C8×Dic43C2211yescharacteristic
54#14582654C2211yescharacteristic
55#14582654C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86C2×C411yescharacteristic
64C22×D172C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C22×C22⋊D43C2×C411yescharacteristic
67C22×C4×D43C2×C411yescharacteristic
68C22×C4×D43C2×C411yescharacteristic
69C22×C4×D43C2311yescharacteristic
70C22×C4×D43C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063320—24no—
76#13063318—24no—
77#13063315—24no—
78#13063311—24no—
79#13063310—24no—
80#13063307—24no—
81#13063303—24no—
82#13063298—24no—
83C4×Dic86D414yes—
84C4×Dic86D414yes—
85C4×D172—22no—
86C4×D172—22no—
87C4×C22⋊D43—22no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063282—22no—
92#13063282—22no—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×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×Dic43C2×C411yescharacteristic
110C2×C4×Dic43C2×C411yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113C42×D43—22no—
114C42×D43—22no—
115C4⋊(C43⋊C8)—22no—
116C4⋊(C43⋊C8)—22no—
117Dic43⋊C8—22no—
118Dic43⋊C8—22no—
119Dic43⋊C8—22no—
120Dic43⋊C8—22no—
121C22⋊(C43⋊C8)—41no—
122C22⋊(C43⋊C8)—41no—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—41no—
128(C2×D43)⋊C8—41no—
129(C2×D43)⋊C8—41no—
130(C2×D43)⋊C8—41no—
131#13063235—22no—
132#13063235—22no—
133#13063235—22no—
134C8×Dic43—22no—
135C23×C4×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140#117×C43—22no—
141#117×C43—22no—
142C2×C4⋊C4×C43C2×C411yescharacteristic
143C2×C4⋊C4×C43C2×C411yescharacteristic
144C2×C22⋊C4×C43C2×C411yescharacteristic
145C2×C22⋊C4×C43C2×C411yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C22⋊C8×C43—22no—
149C22⋊C8×C43—22no—
150#97×C43—22no—
151C4×C8×C43—22no—
152C24×C43C22×C411yescharacteristic
153C23×D43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
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×C43C22×C411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—41no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C2×D172—22no—
180C2×D172—22no—
181C2×D172—41no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—22no—
195C2×C4×D43—22no—
196C2×C4×D43—22no—
197C2×C4×D43—41no—
198C2×C4×D43—41no—
199C2×C4×D43—41no—
200C2×Dic86—41no—
201C2×Dic86—41no—
202C2×Dic86C22⋊C414yes—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43#4112yes—
214C2×C8×C43#4112yes—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43C2×D412yes—
222C42×C43C2×D412yes—
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231C4⋊Dic43—22no—
232C4⋊Dic43C22⋊C414yes—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4C22⋊C414yes—
238Dic43⋊C4C22⋊C414yes—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C4×Dic43C2×D412yes—
242C4×Dic43C2×D412yes—
243C4×Dic43C2×D412yes—
244C4×Dic43C2×D412yes—
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⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43C23×C411yescharacteristic
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43#13112yes—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
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—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43C2×C22⋊C412yes—
297C2×C4×C43C2×C22⋊C412yes—
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C432−1+411yescharacteristic
304C22⋊D43—44no—
305C22⋊D43—44no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43C2×C22⋊C412yes—
321C2×Dic43C2×C22⋊C412yes—
322C2×Dic43C2×C22⋊C412yes—
323C2×Dic43C2×C22⋊C412yes—
324D172—44no—
325C4×D43—44no—
326C4×D43—44no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—41no—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—41no—
335Dic86—44no—
336C8×C43—22no—
337C8×C43—22no—
338C8×C43—41no—
339C8×C43—41no—
340C43⋊C8—41no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344#22533—431nomaximal, Sylow
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43C22×C22⋊C411yescharacteristic
353C22×C43C4×#4111yescharacteristic
354C22×C43#52011yescharacteristic
355C22×C43C2×#13111yescharacteristic
356C22×C43#56811yescharacteristic
357C22×C43#56811yescharacteristic
358C22×C43#56811yescharacteristic
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—41no—
363C2×D43—41no—
364C2×D43—41no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43—41no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43#54811yescharacteristic
379C4×C43#54811yescharacteristic
380C4×C43#55011yescharacteristic
381C4×C43#55011yescharacteristic
382Dic43—22no—
383Dic43—22no—
384Dic43—22no—
385Dic43—22no—
386Dic43—41no—
387Dic43—41no—
388C2×#529—431no—
389C2×#446—431no—
390C2×#446—431no—
391#1955—431no—
392#1955—431no—
393#1955—431no—
394#1955—431no—
395#1954—431no—
396#1954—431no—
397#1798—431no—
398#1798—431no—
399#1797—431no—
400#1750—431no—
401#1750D4311yescharacteristic, complemented
402#1749—431no—
403C2×C43—81no—
404C2×C43#234111yescharacteristic
405C2×C43#287911yescharacteristic
406C2×C43#288011yescharacteristic
407C2×C43#296711yescharacteristic
408C2×C43#296811yescharacteristic
409C2×C43#299211yescharacteristic
410C2×C43#299511yescharacteristic
411D43—42no—
412D43—81no—
413#529—864no—
414#529—864no—
415C2×#126—431no—
416C2×#126—431no—
417C2×#125—431no—
418C2×#124—431no—
419C2×#123—431no—
420C2×#123—431no—
421C2×C22⋊Q8—431no—
422C2×#121—431no—
423C2×C4×Q8—431no—
424C2×C4×D4—431no—
425C2×C4×D4—431no—
426C2×C4×D4—431no—
427C2×#117—431no—
428C2×#117C2×D4311yescharacteristic
429C22×C42—431no—
430#446—864no—
431#446—864no—
432C2×C4⋊C8—431no—
433C2×C4⋊C8—431no—
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
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⋊C8C2×D4311yescharacteristic
449C2×C22⋊C8C2×D4311yescharacteristic
450C2×#97—431no—
451C2×#97—431no—
452C2×#97—431no—
453C2×#97C2×D4311yescharacteristic
454C2×C4×C8—431no—
455C2×C4×C8C2×D4311yescharacteristic
456#336—431no—
457#336—431no—
458#336C2×D4311yescharacteristic
459#336C2×D4311yescharacteristic
460C43#2253311yescharacteristic, complemented, Sylow
461C22×Q8—431no—
462C22×D4—431no—
463C22×D4—431no—
464C22×D4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4C22×D4311yescharacteristic
470C22×C8—431no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8C22×D4311yescharacteristic
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4311yescharacteristic
477C22×C8C22×D4311yescharacteristic
478#126—864no—
479#126—864no—
480#125—864no—
481#124—864no—
482#123—864no—
483#123—864no—
484C22⋊Q8—864no—
485#121—864no—
486C4×Q8—434no—
487C4×Q8—434no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—862no—
491C4×D4—862no—
492C4×D4—862no—
493C4×D4—862no—
494#117—22no—
495#117—22no—
496#117—862no—
497#117—862no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4C4×D4311yescharacteristic
507C2×C4⋊C4C4×D4311yescharacteristic
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—431no—
513C2×C22⋊C4—431no—
514C2×C22⋊C4—431no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4C4×D4311yescharacteristic
517C2×C22⋊C4C4×D4311yescharacteristic
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—431no—
521C2×C42—431no—
522C2×C42—862no—
523C2×C42—862no—
524C2×C42C22×D4311yescharacteristic
525C2×C42C22×D4311yescharacteristic
526C4⋊C8—862no—
527C4⋊C8—862no—
528C4⋊C8—862no—
529C4⋊C8—862no—
530C4⋊C8—862no—
531C4⋊C8—862no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—862no—
535C22⋊C8—862no—
536C22⋊C8—862no—
537C22⋊C8—862no—
538C22⋊C8—1721no—
539C22⋊C8—1721no—
540C22⋊C8—1721no—
541C22⋊C8—1721no—
542C22⋊C8—1721no—
543C22⋊C8—1721no—
544#97—22no—
545#97—862no—
546#97—862no—
547#97—862no—
548C4×C8—22no—
549C4×C8—862no—
550C24—431no—
551C24—431no—
552C24C2×C4×D4311yescharacteristic
553C2×Q8—434no—
554C2×Q8—1721no—
555C2×Q8—1721no—
556C2×D4—862no—
557C2×D4—862no—
558C2×D4—862no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—1721no—
562C2×D4—1721no—
563C2×D4—1721no—
564C2×D4—1721no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—1721no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4C2×C4×D4311yescharacteristic
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×C4×D4311yescharacteristic
598C22×C4C2×C4×D4311yescharacteristic
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C23×D4311yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8#1062189812yes—
624C2×C8#1062189812yes—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—434no—
628C4⋊C4—434no—
629C4⋊C4—434no—
630C4⋊C4—862no—
631C4⋊C4—862no—
632C4⋊C4—862no—
633C4⋊C4—862no—
634C4⋊C4—862no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—862no—
638C22⋊C4—862no—
639C22⋊C4—862no—
640C22⋊C4—862no—
641C22⋊C4—862no—
642C22⋊C4—862no—
643C22⋊C4—862no—
644C22⋊C4—862no—
645C42—21no—
646C42—21no—
647C42—432no—
648C42—432no—
649C42—432no—
650C42—432no—
651C42—862no—
652C42—862no—
653C42D4×D4312yes—
654C42D4×D4312yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—432no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—861no—
674C23—861no—
675C23—861no—
676C23C22×C4×D4311yescharacteristic
677Q8—1724no—
678D4—1724no—
679D4—1724no—
680D4—1724no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—432no—
699C2×C4—432no—
700C2×C4—432no—
701C2×C4—432no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—1724no—
717C2×C4—1724no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4C22⋊C4×D4312yes—
727C2×C4C22⋊C4×D4312yes—
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4C2×#1062189811yescharacteristic
731C2×C4C2×#1062189811yescharacteristic
732C2×C4#1306337111yescharacteristic
733C2×C4#1306337211yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C8—1721no—
739C8—1721no—
740C8—1721no—
741C8—1721no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—862no—
750C22—862no—
751C22—862no—
752C22—1721no—
753C22—1721no—
754C22—1721no—
755C22—1721no—
756C22—1721no—
757C22—1721no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22C2×C22⋊C4×D4311yescharacteristic
764C22C4×#1062189811yescharacteristic
765C22#1458337911yescharacteristic
766C22#131×D4311yescharacteristic
767C22#1458366411yescharacteristic
768C22#1458366411yescharacteristic
769C22#1458366411yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—862no—
776C4—862no—
777C4—862no—
778C4—862no—
779C4—1721no—
780C4—1721no—
781C4#1458355811yescharacteristic
782C4#1458355811yescharacteristic
783C4#1458357011yescharacteristic
784C4#1458357011yescharacteristic
785C2—81no—
786C2—3441no—
787C2—1722no—
788C2#1913743511yescharacteristic
789C2#1914303711yescharacteristic
790C2#1914304311yescharacteristic
791C2#1914357611yescharacteristic
792C2#1914358511yescharacteristic
793C2#1914372911yescharacteristic
794C2#1914376011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1750C2
prime radicalC2×#13063298C4
cosocleC22×C4×C43C24
hypercenter#1750D43
hypocenterC43#22533
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#14583029C2semidirect
3. C2×#14583027C2semidirect
4. #19135393C2semidirect
5. #19135391C2semidirect
6. #19135391C2semidirect
7. #19135391C2semidirect
8. #19135389C2semidirect
9. #19135387C2semidirect
10. #19134579C2semidirect
11. #19134578C2semidirect
12. #19134574C2semidirect
13. #19134360C2semidirect
14. #19134356C2semidirect
15. C43×#1750C2semidirect
401. #1750D43semidirect
460. C43#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#145834272
C2×#145830292
C2×#145830272
#191353932
#191353912
#191353892
#191353872
#191345792
#191345782
#191345742
#191343602
#191343562
C43×#17502
#2253343