Finite Group Databasebeta

← #25123161

Subgroups — #25123161

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137874C211yesmaximal, characteristic
2#19134893C211yesmaximal, characteristic, complemented
3#19134892C211yesmaximal, characteristic, complemented
4#19134892C211yesmaximal, characteristic, complemented
5#19134891C211yesmaximal, characteristic, complemented
6#19134890C211yesmaximal, characteristic, complemented
7#19134890C211yesmaximal, characteristic, complemented
8#19134889C211yesmaximal, characteristic, complemented
9#19134889C211yesmaximal, characteristic, complemented
10#19134886C211yesmaximal, characteristic, complemented
11#19134884C211yesmaximal, characteristic, complemented
12#19134884C211yesmaximal, characteristic, complemented
13#19134739C211yesmaximal, characteristic, complemented
14#19134739C211yesmaximal, characteristic, complemented
15C43×#1870C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33#14582835C411yescharacteristic
34#14582835C411yescharacteristic
35#14582834C411yescharacteristic
36#14582834C411yescharacteristic
37#14582808C411yescharacteristic
38#14582808C411yescharacteristic
39#14582807C411yescharacteristic
40#14582807C411yescharacteristic
41#14582745C2211yescharacteristic
42#14582654C2211yescharacteristic
43#14582654C2211yescharacteristic
44#14582653C2211yescharacteristic
45#14582653C2211yescharacteristic
46#14582653C2211yescharacteristic
47#14582653C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×M16×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2×C411yescharacteristic
60C22×C22⋊D43C2×C411yescharacteristic
61C22×C22⋊D43C2×C411yescharacteristic
62C22×C22⋊D43C2×C411yescharacteristic
63C22×C22⋊D43C2×C411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621877—41no—
67C2×#10621877—41no—
68C2×#10621877—41no—
69C2×#10621872—41no—
70C2×#10621872—41no—
71C2×#10621872—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C2×C8×D43—41no—
77C2×C8×D43—41no—
78C2×C8×D43—41no—
79C4×D172—41no—
80C4×D172—41no—
81C4×C22⋊D43—41no—
82C4×C22⋊D43—41no—
83C4×C22⋊D43—41no—
84C4×C22⋊D43—41no—
85C4×C22⋊D43—41no—
86C4×C22⋊D43—41no—
87C4×C22⋊D43—41no—
88C4×C22⋊D43—41no—
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×Dic43⋊C4C2×C411yescharacteristic
91C2×Dic43⋊C4C2×C411yescharacteristic
92C2×Dic43⋊C4C2×C411yescharacteristic
93C2×Dic43⋊C4C2×C411yescharacteristic
94C2×C22⋊Dic43C2×C411yescharacteristic
95C2×C22⋊Dic43C2×C411yescharacteristic
96C2×C22⋊Dic43C2×C411yescharacteristic
97C2×C22⋊Dic43C2×C411yescharacteristic
98C2×(C2×D43)⋊C4C2×C411yescharacteristic
99C2×(C2×D43)⋊C4C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106C22⋊(C43⋊C8)—41no—
107C22⋊(C43⋊C8)—41no—
108C22⋊(C43⋊C8)—41no—
109(C2×D43)⋊C8—41no—
110(C2×D43)⋊C8—41no—
111(C2×D43)⋊C8—41no—
112(C2×D43)⋊C8—41no—
113(C2×D43)⋊C8—41no—
114(C2×D43)⋊C8—41no—
115C43⋊#95C2×C411yescharacteristic
116C43⋊#95C2×C411yescharacteristic
117C43⋊#95C2×C411yescharacteristic
118C43⋊#95C2×C411yescharacteristic
119C22×D4×C43C2×C411yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C2×M16×C43—41no—
123C2×M16×C43—41no—
124C2×M16×C43—41no—
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4×D4×C43—41no—
130C4×D4×C43—41no—
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C22⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43C2×C411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C22⋊C8×C43—41no—
136C22⋊C8×C43—41no—
137C22⋊C8×C43—41no—
138C24×C43C22×C411yescharacteristic
139C24×C43C22×C411yescharacteristic
140C23×D43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C2×D4×C43—41no—
143C2×D4×C43—41no—
144C2×D4×C43—41no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
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×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—41no—
165C2×C22⋊D43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—41no—
168C2×C22⋊D43—41no—
169C2×C22⋊D43—41no—
170C2×C22⋊D43—41no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43—41no—
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C22×Dic43C22×C411yescharacteristic
180C2×D172—22no—
181C2×D172—41no—
182C2×D172—41no—
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—21no—
195M16×C43—44no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C4⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C42×C43—21no—
212C42×C43—21no—
213C22⋊Dic43—41no—
214C22⋊Dic43—41no—
215C22⋊Dic43—41no—
216C22⋊Dic43—41no—
217(C2×D43)⋊C4—41no—
218(C2×D43)⋊C4—41no—
219(C2×D43)⋊C4—41no—
220(C2×D43)⋊C4—41no—
221(C2×D43)⋊C4—41no—
222(C2×D43)⋊C4—41no—
223C4⋊Dic43—41no—
224Dic43⋊C4—41no—
225Dic43⋊C4—41no—
226Dic43⋊C4—41no—
227Dic43⋊C4—41no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232#10621877—44no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245#10621872—44no—
246C8×D43—44no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43C23×C411yescharacteristic
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
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#13112yes—
276D4×C43—44no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
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—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C22⋊D43—44no—
304C22⋊D43—44no—
305C22⋊D43—44no—
306C22⋊D43—44no—
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×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325D172—44no—
326C4×D43—41no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—41no—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C8×C43—41no—
335C8×C43—41no—
336C8×C43—41no—
337C8×C43—41no—
338C43⋊C8—41no—
339C43⋊C8—41no—
340C43⋊C8—41no—
341C43⋊C8—41no—
342#23359—431nomaximal, Sylow
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43#51811yescharacteristic
358C22×C43#51811yescharacteristic
359C22×C43#51811yescharacteristic
360C22×C43C2×#13111yescharacteristic
361C22×C43#56811yescharacteristic
362C22×C43#56811yescharacteristic
363C22×C43#56811yescharacteristic
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—41no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C2×D43—41no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43#56011yescharacteristic
383C4×C43#56011yescharacteristic
384C4×C43#56011yescharacteristic
385C4×C43#56011yescharacteristic
386Dic43—41no—
387Dic43—41no—
388Dic43—41no—
389Dic43—41no—
390Dic43—41no—
391Dic43—41no—
392#2397—431no—
393#1870—431no—
394#1870—431no—
395#1870—431no—
396#1870—431no—
397#1870—431no—
398#1870—431no—
399#1870—431no—
400#1870—431no—
401#1870D4311yescharacteristic, complemented
402#1869—431no—
403#1869—431no—
404#1869—431no—
405#1840—431no—
406#1840—431no—
407C2×C43—81no—
408C2×C43—81no—
409C2×C43#238011yescharacteristic
410C2×C43#297611yescharacteristic
411C2×C43#297611yescharacteristic
412C2×C43#297611yescharacteristic
413C2×C43#297811yescharacteristic
414C2×C43#297811yescharacteristic
415C2×C43#297811yescharacteristic
416D43—42no—
417D43—81no—
418C22×M16—431no—
419C22×M16—431no—
420C22×M16C2×D4311yescharacteristic
421C23×C8—431no—
422C2×C4×D4—431no—
423C2×C4×D4—431no—
424C2×C4×D4—431no—
425C2×C4×D4—431no—
426C2×C4×D4—431no—
427C2×C4×D4C2×D4311yescharacteristic
428C2×C22⋊C8—431no—
429C2×C22⋊C8—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8—431no—
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×C22⋊C8C2×D4311yescharacteristic
438C2×C22⋊C8C2×D4311yescharacteristic
439C2×C22⋊C8C2×D4311yescharacteristic
440#399—431no—
441#399—431no—
442#399—431no—
443#399—431no—
444#392—431no—
445#392—431no—
446#392—431no—
447#392—431no—
448#376—431no—
449#336—431no—
450#336—431no—
451#336—431no—
452#336—431no—
453#336—431no—
454#336—431no—
455#336—431no—
456#336—431no—
457#336—431no—
458#336—431no—
459#336C2×D4311yescharacteristic
460#336C2×D4311yescharacteristic
461C43#2335911yescharacteristic, complemented, Sylow
462C22×D4—431no—
463C22×D4—431no—
464C22×D4—431no—
465C22×D4—431no—
466C22×D4—431no—
467C22×D4C4×D4311yescharacteristic
468C23×C4—431no—
469C23×C4—431no—
470C23×C4C22×D4311yescharacteristic
471C23×C4C22×D4311yescharacteristic
472C2×M16—41no—
473C2×M16—41no—
474C2×M16—41no—
475C2×M16—1721no—
476C2×M16—1721no—
477C2×M16—1721no—
478C2×M16—1721no—
479C2×M16—1721no—
480C2×M16—1721no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8—431no—
485C22×C8—1721no—
486C22×C8—1721no—
487C22×C8—1721no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C22×C8C22×D4311yescharacteristic
491C22×C8C22×D4311yescharacteristic
492C4×D4—41no—
493C4×D4—41no—
494C4×D4—1721no—
495C4×D4—1721no—
496C4×D4—1721no—
497C4×D4—1721no—
498C4×D4—1721no—
499C4×D4—1721no—
500C4×D4—1721no—
501C4×D4—1721no—
502C4×D4—1721no—
503C4×D4—1721no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4C4×D4311yescharacteristic
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⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4C4×D4311yescharacteristic
521C2×C22⋊C4C4×D4311yescharacteristic
522C2×C42—431no—
523C2×C42—431no—
524C2×C42C22×D4311yescharacteristic
525C22⋊C8—41no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528C22⋊C8—1721no—
529C22⋊C8—1721no—
530C22⋊C8—1721no—
531C22⋊C8—1721no—
532C22⋊C8—1721no—
533C22⋊C8—1721no—
534C22⋊C8—1721no—
535C22⋊C8—1721no—
536C22⋊C8—1721no—
537#95—431no—
538#95—431no—
539#95—431no—
540#95—431no—
541C24—431no—
542C24—431no—
543C24C2×C4×D4311yescharacteristic
544C24C2×C4×D4311yescharacteristic
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—862no—
549C2×D4—862no—
550C2×D4—862no—
551C2×D4—1721no—
552C2×D4—1721no—
553C2×D4—1721no—
554C2×D4—1721no—
555C2×D4—1721no—
556C2×D4—1721no—
557C2×D4—1721no—
558C2×D4—1721no—
559C2×D4—1721no—
560C2×D4—1721no—
561C2×D4—1721no—
562C2×D4—1721no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
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—861no—
593C22×C4C2×C4×D4311yescharacteristic
594C22×C4C2×C4×D4311yescharacteristic
595C22×C4C2×C4×D4311yescharacteristic
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598M16—44no—
599M16—1724no—
600M16—1724no—
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—21no—
612C2×C8—21no—
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—861no—
624C2×C8—861no—
625C2×C8—1724no—
626C4⋊C4—41no—
627C4⋊C4—1721no—
628C4⋊C4—1721no—
629C4⋊C4—1721no—
630C4⋊C4—1721no—
631C4⋊C4—1721no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—1721no—
635C22⋊C4—1721no—
636C22⋊C4—1721no—
637C22⋊C4—1721no—
638C22⋊C4—1721no—
639C22⋊C4—1721no—
640C22⋊C4—1721no—
641C22⋊C4—1721no—
642C22⋊C4—1721no—
643C22⋊C4—1721no—
644C42—21no—
645C42—21no—
646C42—861no—
647C42—861no—
648C42—861no—
649C42—861no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—432no—
665C23—861no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—861no—
674C23—861no—
675C23—861no—
676C23—861no—
677C23—861no—
678C23C22×C4×D4311yescharacteristic
679D4—44no—
680D4—1724no—
681D4—1724no—
682D4—1724no—
683D4—1724no—
684D4—1724no—
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—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
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—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4#1306337011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337011yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337111yescharacteristic
736C2×C4#1306337111yescharacteristic
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—1721no—
742C8—1721no—
743C8—1721no—
744C8—1721no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—862no—
760C22—862no—
761C22—862no—
762C22—1721no—
763C22—1721no—
764C22—1721no—
765C22—1721no—
766C22—1721no—
767C22—1721no—
768C22—1721no—
769C22—1721no—
770C22—1721no—
771C22—1721no—
772C22—1721no—
773C22#1458337111yescharacteristic
774C22#1458337111yescharacteristic
775C22#1458337211yescharacteristic
776C22#131×D4311yescharacteristic
777C22#1458366411yescharacteristic
778C22#1458366511yescharacteristic
779C22#1458366511yescharacteristic
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—1721no—
785C4—1721no—
786C4—1721no—
787C4—1721no—
788C4—1721no—
789C4—1721no—
790C4#1458363711yescharacteristic
791C4#1458363711yescharacteristic
792C4#1458363811yescharacteristic
793C4#1458363911yescharacteristic
794C2—81no—
795C2—81no—
796C2—3441no—
797C2—1722no—
798C2#1913777011yescharacteristic
799C2#1914363811yescharacteristic
800C2#1914363911yescharacteristic
801C2#1914364211yescharacteristic
802C2#1914365211yescharacteristic
803C2#1914365411yescharacteristic
804C2#1914365511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1870C2
prime radical#19137874C2
cosocleC22×C4×C43C24
hypercenter#1870D43
hypocenterC43#23359
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #19134893C2semidirect
3. #19134892C2semidirect
4. #19134892C2semidirect
5. #19134891C2semidirect
6. #19134890C2semidirect
7. #19134890C2semidirect
8. #19134889C2semidirect
9. #19134889C2semidirect
10. #19134886C2semidirect
11. #19134884C2semidirect
12. #19134884C2semidirect
13. #19134739C2semidirect
14. #19134739C2semidirect
15. C43×#1870C2semidirect
401. #1870D43semidirect
461. C43#23359semidirect

Maximal subgroups

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

subgroupindex
#191378742
#191348932
#191348922
#191348912
#191348902
#191348892
#191348862
#191348842
#191347392
C43×#18702
#2335943