Finite Group Databasebeta

← #25106624

Subgroups — #25106624

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137081C211yesmaximal, characteristic
2#19135204C211yesmaximal, characteristic, complemented
3#19135203C211yesmaximal, characteristic, complemented
4#19135202C211yesmaximal, characteristic, complemented
5#19135201C211yesmaximal, characteristic, complemented
6#19135200C211yesmaximal, characteristic, complemented
7#19135199C211yesmaximal, characteristic, complemented
8#19135198C211yesmaximal, characteristic, complemented
9#19134578C211yesmaximal, characteristic, complemented
10#19134576C211yesmaximal, characteristic, complemented
11#19134506C211yesmaximal, characteristic
12#19134506C211yesmaximal, characteristic
13C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063282C2211yescharacteristic
18C2×C42×D43C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×(C2×D43)⋊C8C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582803C411yescharacteristic
36#14582803C411yescharacteristic
37#14582799C411yescharacteristic
38#14582799C411yescharacteristic
39#14582777C411yescharacteristic
40#14582777C411yescharacteristic
41#14582775C411yescharacteristic
42#14582775C411yescharacteristic
43C4×(C2×D43)⋊C4C2211yescharacteristic
44C4×(C2×D43)⋊C4C2211yescharacteristic
45C4×C22⋊Dic43C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C2×#10621898—22no—
60C2×#10621898—22no—
61C2×#10621898—41no—
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C22×Dic86C2×C411yescharacteristic
66C22×D172C2×C411yescharacteristic
67C22×C22⋊D43C2×C411yescharacteristic
68C22×C22⋊D43C2×C411yescharacteristic
69C22×C4×D43C2×C411yescharacteristic
70C22×C4×D43C2×C411yescharacteristic
71C22×C4×D43C2311yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063282—41no—
78#13063282—41no—
79C2×Dic43⋊C4C2×C411yescharacteristic
80C2×Dic43⋊C4C2×C411yescharacteristic
81C2×C22⋊Dic43C2×C411yescharacteristic
82C2×C22⋊Dic43C2×C411yescharacteristic
83C2×(C2×D43)⋊C4C2×C411yescharacteristic
84C2×(C2×D43)⋊C4C2×C411yescharacteristic
85C2×(C2×D43)⋊C4C2×C411yescharacteristic
86C2×(C2×D43)⋊C4C2×C411yescharacteristic
87C2×(C2×D43)⋊C4C2×C411yescharacteristic
88C2×(C2×D43)⋊C4C2×C411yescharacteristic
89C2×C4×Dic43C2×C411yescharacteristic
90C2×C4×Dic43C2×C411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C42×D43—41no—
94C42×D43—41no—
95C4⋊(C43⋊C8)—41no—
96Dic43⋊C8—41no—
97Dic43⋊C8—41no—
98C22⋊(C43⋊C8)—41no—
99C22⋊(C43⋊C8)—41no—
100(C2×D43)⋊C8—22no—
101(C2×D43)⋊C8—22no—
102(C2×D43)⋊C8—22no—
103(C2×D43)⋊C8—22no—
104(C2×D43)⋊C8—41no—
105(C2×D43)⋊C8—41no—
106(C2×D43)⋊C8—41no—
107(C2×D43)⋊C8—41no—
108C4×C43⋊C8—41no—
109C8×Dic43—41no—
110C8×Dic43—41no—
111C43⋊#95C2×C411yescharacteristic
112C43⋊#95C2×C411yescharacteristic
113C43⋊#95C2×C411yescharacteristic
114C43⋊#95C2×C411yescharacteristic
115C43⋊#95C2×C411yescharacteristic
116C43⋊#95C2×C411yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C22⋊C4×C43C2×C411yescharacteristic
123C2×C22⋊C4×C43C2×C411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—41no—
127C22⋊C8×C43—41no—
128C22⋊C8×C43—41no—
129C4×C8×C43—41no—
130#95×C43C2×C411yescharacteristic
131#95×C43C2×C411yescharacteristic
132C24×C43C22×C411yescharacteristic
133C23×D43C22×C411yescharacteristic
134C23×D43C22×C411yescharacteristic
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C22×C411yescharacteristic
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C2×C22⋊D43—22no—
148C2×C22⋊D43—22no—
149C2×C22⋊D43—41no—
150C2×C22⋊D43—41no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C22×Dic43C22×C411yescharacteristic
154C22×Dic43C22×C411yescharacteristic
155C22×Dic43C22×C411yescharacteristic
156C22×Dic43C22×C411yescharacteristic
157C22×Dic43C22×C411yescharacteristic
158C22×Dic43C22×C411yescharacteristic
159#10621898—44no—
160#10621898—44no—
161#10621898—44no—
162#10621898—44no—
163C2×D172—22no—
164C2×D172—41no—
165C2×D172—41no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—22no—
179C2×C4×D43—22no—
180C2×C4×D43—41no—
181C2×C4×D43—41no—
182C2×C4×D43#4112yes—
183C2×C4×D43#4112yes—
184C2×Dic86—22no—
185C2×Dic86—41no—
186C2×Dic86—41no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—41no—
212(C2×D43)⋊C4—41no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—41no—
220C4×Dic43—41no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43C23×C411yescharacteristic
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43#11712yes—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43#13112yes—
273C2×C4×C43#13112yes—
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C2×C4×C43H(5,𝔽2)11yescharacteristic
278C2×C4×C43H(5,𝔽2)11yescharacteristic
279C2×C4×C43H(5,𝔽2)11yescharacteristic
280C22⋊D43—44no—
281C22⋊D43—44no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43#11712yes—
298C2×Dic43#13112yes—
299C2×Dic43#13112yes—
300D172—44no—
301C4×D43—22no—
302C4×D43—22no—
303C4×D43—22no—
304C4×D43—22no—
305C4×D43—44no—
306C4×D43—44no—
307C4×D43—41no—
308C4×D43—41no—
309C4×D43—41no—
310C4×D43—41no—
311Dic86—44no—
312C8×C43—41no—
313C8×C43—41no—
314C8×C43—41no—
315C8×C43—41no—
316C43⋊C8—41no—
317C43⋊C8—41no—
318C43⋊C8—41no—
319C43⋊C8—41no—
320#21903—431nomaximal, Sylow
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43C2×#11711yescharacteristic
329C22×C43#51811yescharacteristic
330C22×C43#51811yescharacteristic
331C22×C43C2×#13111yescharacteristic
332C22×C43C2×#13111yescharacteristic
333C22×C43C2×#13111yescharacteristic
334C22×C43C2×#13111yescharacteristic
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—41no—
339C2×D43—41no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—41no—
354C4×C43#53811yescharacteristic
355C4×C43#53811yescharacteristic
356C4×C43#53811yescharacteristic
357C4×C43#53811yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—22no—
361Dic43—41no—
362Dic43—41no—
363Dic43—41no—
364#2297—431no—
365#1923—431no—
366#1923—431no—
367#1923—431no—
368#1923—431no—
369#1923—431no—
370#1923—431no—
371#1923—431no—
372#1923D4311yescharacteristic, complemented
373#1798—431no—
374#1798—431no—
375#1780—431no—
376#1780—431no—
377C4×C22⋊C8—431no—
378C4×C22⋊C8—431no—
379C2×C43—81no—
380C2×C43#231211yescharacteristic
381C2×C43#292211yescharacteristic
382C2×C43#292211yescharacteristic
383C2×C43#297711yescharacteristic
384C2×C43#297711yescharacteristic
385C2×C43#297911yescharacteristic
386C2×C43#297911yescharacteristic
387D43—42no—
388D43—81no—
389C22×#41—431no—
390C2×#117—431no—
391C22×C42—431no—
392C2×C4⋊C8—431no—
393C2×C4⋊C8—431no—
394C2×C4⋊C8—431no—
395C2×C4⋊C8C2×D4311yescharacteristic
396C2×C22⋊C8—431no—
397C2×C22⋊C8—431no—
398C2×C22⋊C8—431no—
399C2×C22⋊C8—431no—
400C2×C22⋊C8—431no—
401C2×C22⋊C8—431no—
402C2×C22⋊C8—431no—
403C2×C22⋊C8—431no—
404C2×C22⋊C8—431no—
405C2×C22⋊C8—431no—
406C2×C22⋊C8C2×D4311yescharacteristic
407C2×C22⋊C8C2×D4311yescharacteristic
408C2×C4×C8—431no—
409C2×C4×C8—431no—
410C2×C4×C8—431no—
411C2×C4×C8C2×D4311yescharacteristic
412#391—431no—
413#391—431no—
414#390—431no—
415#390—431no—
416#386—431no—
417#386—431no—
418#386—431no—
419#386—431no—
420C4×C22⋊C4—431no—
421C4×C22⋊C4—431no—
422C4×C22⋊C4—431no—
423C4×C22⋊C4C2×D4311yescharacteristic
424#336—431no—
425#336—431no—
426#336—431no—
427#336—431no—
428#336—431no—
429#336—431no—
430#336C2×D4311yescharacteristic
431#336C2×D4311yescharacteristic
432C43#2190311yescharacteristic, complemented, Sylow
433C2×#41—862no—
434C2×#41—862no—
435C2×#41—1721no—
436C2×#41—1721no—
437C2×#41—1721no—
438C2×#41—1721no—
439C22×Q8—431no—
440C22×D4—431no—
441C22×D4—431no—
442C22×D4—431no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—431no—
447C23×C4C22×D4311yescharacteristic
448C22×C8—431no—
449C22×C8—431no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8C22×D4311yescharacteristic
453C22×C8C22×D4311yescharacteristic
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456#117—1721no—
457#117—1721no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—431no—
460C2×C22⋊C4—431no—
461C2×C22⋊C4—431no—
462C2×C22⋊C4—431no—
463C2×C22⋊C4—431no—
464C2×C22⋊C4—431no—
465C2×C22⋊C4—431no—
466C2×C22⋊C4—431no—
467C2×C22⋊C4—431no—
468C2×C22⋊C4C4×D4311yescharacteristic
469C2×C22⋊C4C4×D4311yescharacteristic
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—431no—
473C2×C42—431no—
474C2×C42—1721no—
475C2×C42—1721no—
476C2×C42C22×D4311yescharacteristic
477C2×C42C22×D4311yescharacteristic
478C4⋊C8—41no—
479C4⋊C8—1721no—
480C4⋊C8—1721no—
481C4⋊C8—1721no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—862no—
485C22⋊C8—862no—
486C22⋊C8—862no—
487C22⋊C8—862no—
488C22⋊C8—1721no—
489C22⋊C8—1721no—
490C22⋊C8—1721no—
491C22⋊C8—1721no—
492C22⋊C8—1721no—
493C22⋊C8—1721no—
494C4×C8—41no—
495C4×C8—1721no—
496C4×C8—1721no—
497C4×C8—1721no—
498#95—431no—
499#95—431no—
500#95—431no—
501#95—431no—
502#95—431no—
503#95—431no—
504#95C4×D4311yescharacteristic
505#95C4×D4311yescharacteristic
506C24—431no—
507C24—431no—
508C24C2×C4×D4311yescharacteristic
509#41—1724no—
510#41—1724no—
511#41—1724no—
512#41—1724no—
513C2×Q8—862no—
514C2×Q8—1721no—
515C2×Q8—1721no—
516C2×D4—862no—
517C2×D4—862no—
518C2×D4—862no—
519C2×D4—1721no—
520C2×D4—1721no—
521C2×D4—1721no—
522C2×D4—1721no—
523C2×D4—1721no—
524C2×D4—1721no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—431no—
532C22×C4—431no—
533C22×C4—431no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—431no—
537C22×C4—431no—
538C22×C4—431no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—861no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—1721no—
554C22×C4—1721no—
555C22×C4C2×C4×D4311yescharacteristic
556C22×C4C2×C4×D4311yescharacteristic
557C22×C4C2×C4×D4311yescharacteristic
558C22×C4C2×C4×D4311yescharacteristic
559C22×C4C2×C4×D4311yescharacteristic
560C22×C4C23×D4311yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C4⋊C4—1721no—
586C4⋊C4—1721no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—862no—
590C22⋊C4—862no—
591C22⋊C4—862no—
592C22⋊C4—862no—
593C22⋊C4—862no—
594C22⋊C4—862no—
595C22⋊C4—1721no—
596C22⋊C4—1721no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—861no—
602C42—861no—
603C42—861no—
604C42—861no—
605C42—1721no—
606C42—1721no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—432no—
615C23—861no—
616C23—861no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23C22×C4×D4311yescharacteristic
629Q8—1724no—
630D4—1724no—
631D4—1724no—
632D4—1724no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—432no—
651C2×C4—432no—
652C2×C4—432no—
653C2×C4—861no—
654C2×C4—861no—
655C2×C4—861no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—1724no—
673C2×C4—1724no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4#1306333112yes—
679C2×C4#1306333312yes—
680C2×C4#41×D4311yescharacteristic
681C2×C4#41×D4311yescharacteristic
682C2×C4#1306337011yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337111yescharacteristic
685C2×C4#1306337111yescharacteristic
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—1721no—
691C8—1721no—
692C8—1721no—
693C8—1721no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—862no—
702C22—862no—
703C22—862no—
704C22—1721no—
705C22—1721no—
706C22—1721no—
707C22—1721no—
708C22—1721no—
709C22—1721no—
710C22—1721no—
711C22—1721no—
712C22—1721no—
713C22—1721no—
714C22—1721no—
715C22#117×D4311yescharacteristic
716C22#1458337111yescharacteristic
717C22#1458337111yescharacteristic
718C22#131×D4311yescharacteristic
719C22#131×D4311yescharacteristic
720C22C2×#1306333111yescharacteristic
721C22C2×#1306333311yescharacteristic
722C4—22no—
723C4—22no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—862no—
728C4—862no—
729C4—862no—
730C4—1721no—
731C4—1721no—
732C4—1721no—
733C4#1458348111yescharacteristic
734C4#1458348311yescharacteristic
735C4#1458348511yescharacteristic
736C4#1458348811yescharacteristic
737C2—81no—
738C2—3441no—
739C2—1722no—
740C2#1913718911yescharacteristic
741C2#1914323411yescharacteristic
742C2#1914323611yescharacteristic
743C2#1914364611yescharacteristic
744C2#1914364811yescharacteristic
745C2#1914365811yescharacteristic
746C2#1914366011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1923C2
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1923D43
hypocenterC43#21903
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #19135204C2semidirect
3. #19135203C2semidirect
4. #19135202C2semidirect
5. #19135201C2semidirect
6. #19135200C2semidirect
7. #19135199C2semidirect
8. #19135198C2semidirect
9. #19134578C2semidirect
10. #19134576C2semidirect
13. C4×(C2×D43)⋊C8C2semidirect
14. #19134352C2semidirect
15. C43×#1923C2semidirect
372. #1923D43semidirect
432. C43#21903semidirect

Maximal subgroups

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

subgroupindex
#191370812
#191352042
#191352032
#191352022
#191352012
#191352002
#191351992
#191351982
#191345782
#191345762
#191345062
C4×(C2×D43)⋊C82
#191343522
C43×#19232
#2190343