Finite Group Databasebeta

← #25101619

Subgroups — #25101619

Order 11008.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583429C211yesmaximal, characteristic
2C2×#14582959C211yesmaximal, characteristic, complemented
3C2×#14582856C211yesmaximal, characteristic, complemented
4#19135535C211yesmaximal, characteristic, complemented
5#19135530C211yesmaximal, characteristic, complemented
6#19135390C211yesmaximal, characteristic, complemented
7#19134889C211yesmaximal, characteristic, complemented
8#19134889C211yesmaximal, characteristic, complemented
9#19134884C211yesmaximal, characteristic, complemented
10#19134884C211yesmaximal, characteristic, complemented
11#19134363C211yesmaximal, characteristic, complemented
12#19134363C211yesmaximal, characteristic, complemented
13#19134359C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#1955C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583429—24no—
19#14583429—24no—
20C2×#13063320C411yescharacteristic
21C2×#13063318C411yescharacteristic
22C2×#13063315C411yescharacteristic
23C2×#13063311C411yescharacteristic
24C2×#13063309C411yescharacteristic
25C2×#13063306C411yescharacteristic
26C2×#13063302C411yescharacteristic
27C2×#13063297C411yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×#13063284C2211yescharacteristic
32C2×#13063282C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582959—24no—
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42#14582856—24no—
43C2×#13063235C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46C2×C8×Dic43C2211yescharacteristic
47C2×C8×Dic43C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C22×Dic86C2×C411yescharacteristic
64C22×C22⋊D43C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C23×Dic43C2×C411yescharacteristic
67C23×Dic43C2×C411yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621872—22no—
70C2×#10621872—22no—
71C2×#10621872—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C2×C8×D43—22no—
77C2×C8×D43—22no—
78C2×C8×D43—22no—
79#13063320—24no—
80#13063318—24no—
81#13063315—24no—
82#13063311—24no—
83#13063309—24no—
84#13063306—24no—
85#13063302—24no—
86#13063297—24no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93#13063284—22no—
94#13063284—22no—
95#13063282D414yes—
96#13063282D414yes—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×C4⋊Dic43C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2×C411yescharacteristic
105C2×Dic43⋊C4C2×C411yescharacteristic
106C2×C22⋊Dic43C2×C411yescharacteristic
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×C22⋊Dic43C2×C411yescharacteristic
109C2×C22⋊Dic43C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43C2×C411yescharacteristic
117C2×C4×Dic43C2×C411yescharacteristic
118C2×C4×Dic43C2311yescharacteristic
119C2×C4×Dic43C2311yescharacteristic
120C2×C4×Dic43C2311yescharacteristic
121C4⋊(C43⋊C8)—22no—
122C22⋊(C43⋊C8)—22no—
123C22⋊(C43⋊C8)—22no—
124C22⋊(C43⋊C8)—22no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128#13063235—22no—
129#13063235—22no—
130C4×C43⋊C8—22no—
131C8×Dic43—22no—
132C8×Dic43—22no—
133C22×D4×C43C2×C411yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C4×D4×C43—22no—
141C4×D4×C43—22no—
142C2×C4⋊C4×C43C2×C411yescharacteristic
143C2×C22⋊C4×C43C2×C411yescharacteristic
144C2×C22⋊C4×C43C2×C411yescharacteristic
145C2×C42×C43C2311yescharacteristic
146C4⋊C8×C43—22no—
147C22⋊C8×C43—22no—
148C22⋊C8×C43—22no—
149C22⋊C8×C43—22no—
150C22⋊C8×C43—22no—
151#97×C43—22no—
152C24×C43C22×C411yescharacteristic
153C24×C43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—41no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—22no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43—41no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—41no—
186C22×Dic43—41no—
187C22×Dic43C22×C411yescharacteristic
188C22×Dic43C22×C411yescharacteristic
189C22×Dic43C22×C411yescharacteristic
190C22×Dic43C22×C411yescharacteristic
191C22×Dic43C22×C411yescharacteristic
192C22×Dic43C22×C411yescharacteristic
193C22×Dic43C22×C411yescharacteristic
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43C2×D412yes—
199C2×C4×D43C2×D412yes—
200C2×Dic86—22no—
201C2×Dic86—22no—
202C2×Dic86—41no—
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—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C42×C43C2×D412yes—
219C42×C43C2×D412yes—
220C22⋊Dic43—22no—
221C22⋊Dic43—22no—
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4C22⋊C414yes—
227(C2×D43)⋊C4C22⋊C414yes—
228C4⋊Dic43—22no—
229C4⋊Dic43—22no—
230C4⋊Dic43—22no—
231Dic43⋊C4—22no—
232Dic43⋊C4—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4C22⋊C414yes—
236Dic43⋊C4C22⋊C414yes—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—22no—
242C4×Dic43—22no—
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#4112yes—
256C2×C43⋊C8#4112yes—
257#10621872—28no—
258C8×D43—28no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43#13112yes—
273C23×C43C23×C411yescharacteristic
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43C2×C22⋊C412yes—
281D4×C43—44no—
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×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43C2×C22⋊C412yes—
301C2×C4×C43C2×C22⋊C412yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C22⋊D43—44no—
309C22⋊D43—44no—
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—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—44no—
328C2×Dic43—44no—
329C2×Dic43C2×C22⋊C412yes—
330C2×Dic43C2×C22⋊C412yes—
331C2×Dic43C2×C22⋊C412yes—
332C2×Dic43#13112yes—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—22no—
337Dic86—44no—
338C8×C43—22no—
339C8×C43—22no—
340C8×C43—41no—
341C8×C43—41no—
342C43⋊C8—22no—
343C43⋊C8—22no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346#21381—431nomaximal, Sylow
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43C22×C22⋊C411yescharacteristic
362C22×C43C4×#4111yescharacteristic
363C22×C43C4×#4111yescharacteristic
364C22×C43C2×#13111yescharacteristic
365C22×C43C2×#13111yescharacteristic
366C22×C43#56811yescharacteristic
367C22×C43#56811yescharacteristic
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C4×C43—22no—
376C4×C43—22no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43#52511yescharacteristic
380C4×C43#52511yescharacteristic
381C4×C43#53211yescharacteristic
382C4×C43#53211yescharacteristic
383Dic43—22no—
384Dic43—22no—
385Dic43—22no—
386Dic43—22no—
387Dic43—41no—
388Dic43—41no—
389Dic43—41no—
390C2×#529—431no—
391C2×#433—431no—
392C2×#405—431no—
393#1985—431no—
394#1984—431no—
395#1955D4311yescharacteristic, complemented
396#1954—431no—
397#1870—431no—
398#1870—431no—
399#1869—431no—
400#1869—431no—
401#1750—431no—
402#1750—431no—
403#1749—431no—
404C4×C22⋊C8—431no—
405C2×C43—42no—
406C2×C43—81no—
407C2×C43#229711yescharacteristic
408C2×C43#288011yescharacteristic
409C2×C43#288011yescharacteristic
410C2×C43#296611yescharacteristic
411C2×C43#296711yescharacteristic
412C2×C43#296811yescharacteristic
413C2×C43#296911yescharacteristic
414D43—42no—
415C22×M16—431no—
416C23×C8—431no—
417#529—864no—
418#529—864no—
419C2×#126—431no—
420C2×#126—431no—
421C2×#125—431no—
422C2×#124—431no—
423C2×#123—431no—
424C2×#123—431no—
425C2×C22⋊Q8—431no—
426C2×#121—431no—
427C2×C4×Q8—431no—
428C2×C4×D4—431no—
429C2×C4×D4—431no—
430C2×C4×D4C2×D4311yescharacteristic
431C2×#117—431no—
432C2×#117—431no—
433C22×C42—431no—
434#433—864no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8C2×D4311yescharacteristic
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8C2×D4311yescharacteristic
444C2×C22⋊C8C2×D4311yescharacteristic
445C2×C22⋊C8C2×D4311yescharacteristic
446C2×C22⋊C8C2×D4311yescharacteristic
447#405—864no—
448C2×#97—431no—
449C2×#97—431no—
450C2×#97C2×D4311yescharacteristic
451C2×C4×C8—431no—
452C2×C4×C8—431no—
453C2×C4×C8—431no—
454#336—431no—
455#336—431no—
456#336—431no—
457#336—431no—
458#336—431no—
459#336—431no—
460#336—431no—
461#336—431no—
462C43#2138111yescharacteristic, complemented, Sylow
463C22×Q8—431no—
464C22×D4—431no—
465C22×D4—431no—
466C22×D4C4×D4311yescharacteristic
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4C22×D4311yescharacteristic
471C23×C4C22×D4311yescharacteristic
472C2×M16—862no—
473C2×M16—862no—
474C2×M16—862no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—862no—
480C22×C8—862no—
481C22×C8—862no—
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#126—864no—
487#126—864no—
488#125—864no—
489#124—864no—
490#123—864no—
491#123—864no—
492C22⋊Q8—864no—
493#121—864no—
494C4×Q8—862no—
495C4×Q8—862no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—862no—
499C4×D4—862no—
500C4×D4—862no—
501C4×D4—862no—
502#117—434no—
503#117—434no—
504#117—862no—
505#117—862no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4C4×D4311yescharacteristic
516C2×C22⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4C4×D4311yescharacteristic
525C2×C22⋊C4C4×D4311yescharacteristic
526C2×C42—431no—
527C2×C42—431no—
528C2×C42—431no—
529C2×C42—431no—
530C2×C42—431no—
531C2×C42—862no—
532C2×C42—862no—
533C2×C42C22×D4311yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—862no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—862no—
541C22⋊C8—862no—
542C22⋊C8—862no—
543C22⋊C8—862no—
544C22⋊C8—862no—
545C22⋊C8—862no—
546#97—22no—
547#97—862no—
548#97—862no—
549C4×C8—862no—
550C4×C8—862no—
551C4×C8—862no—
552C24—431no—
553C24C2×C4×D4311yescharacteristic
554C24C2×C4×D4311yescharacteristic
555C2×Q8—862no—
556C2×Q8—862no—
557C2×Q8—1721no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—41no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—862no—
565C2×D4—1721no—
566C2×D4—1721no—
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—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—862no—
596C22×C4—1721no—
597C22×C4—1721no—
598C22×C4C2×C4×D4311yescharacteristic
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C2×C4×D4311yescharacteristic
601C22×C4C2×C4×D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603M16—868no—
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—21no—
614C2×C8—432no—
615C2×C8—432no—
616C2×C8—868no—
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—861no—
626C2×C8—861no—
627C2×C8#1062190012yes—
628C2×C8#1062190012yes—
629C4⋊C4—22no—
630C4⋊C4—434no—
631C4⋊C4—434no—
632C4⋊C4—862no—
633C4⋊C4—862no—
634C4⋊C4—862no—
635C4⋊C4—862no—
636C4⋊C4—862no—
637C4⋊C4—862no—
638C4⋊C4—862no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—434no—
642C22⋊C4—434no—
643C22⋊C4—862no—
644C22⋊C4—862no—
645C22⋊C4—862no—
646C22⋊C4—862no—
647C22⋊C4—862no—
648C22⋊C4—862no—
649C42—432no—
650C42—432no—
651C42—862no—
652C42—862no—
653C42—861no—
654C42—861no—
655C42—861no—
656C42—861no—
657C42D4×D4312yes—
658C42D4×D4312yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—432no—
673C23—861no—
674C23—861no—
675C23—861no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23#1306333312yes—
680C23C22×C4×D4311yescharacteristic
681Q8—1724no—
682D4—44no—
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—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—432no—
704C2×C4—432no—
705C2×C4—432no—
706C2×C4—432no—
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—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—1724no—
729C2×C4—1724no—
730C2×C4C22⋊C4×D4312yes—
731C2×C4C22⋊C4×D4312yes—
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4C2×D4×D4311yescharacteristic
734C2×C4#41×D4311yescharacteristic
735C2×C4#41×D4311yescharacteristic
736C2×C4C2×#1062190011yescharacteristic
737C2×C4C2×#1062190011yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—862no—
743C8—862no—
744C8—1721no—
745C8—1721no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—862no—
761C22—862no—
762C22—862no—
763C22—1721no—
764C22—1721no—
765C22—1721no—
766C22—1721no—
767C22C2×C22⋊C4×D4311yescharacteristic
768C22C4×#1062190011yescharacteristic
769C22C4×#1062190011yescharacteristic
770C22#131×D4311yescharacteristic
771C22C2×#1306333311yescharacteristic
772C22#1458366411yescharacteristic
773C22#1458366511yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—862no—
779C4—862no—
780C4—862no—
781C4—862no—
782C4—1721no—
783C4—1721no—
784C4—1721no—
785C4#1458340911yescharacteristic
786C4#1458340911yescharacteristic
787C4#1458344711yescharacteristic
788C4#1458344811yescharacteristic
789C2—42no—
790C2—81no—
791C2—1722no—
792C2#1913708211yescharacteristic
793C2#1914304311yescharacteristic
794C2#1914304511yescharacteristic
795C2#1914356511yescharacteristic
796C2#1914357411yescharacteristic
797C2#1914359011yescharacteristic
798C2#1914359211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1955C2
prime radicalC2×#13063297C4
cosocleC22×C4×C43C24
hypercenter#1955D43
hypocenterC43#21381
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#14582959C2semidirect
3. C2×#14582856C2semidirect
4. #19135535C2semidirect
5. #19135530C2semidirect
6. #19135390C2semidirect
7. #19134889C2semidirect
8. #19134889C2semidirect
9. #19134884C2semidirect
10. #19134884C2semidirect
11. #19134363C2semidirect
12. #19134363C2semidirect
13. #19134359C2semidirect
14. C22⋊C8×Dic43C2semidirect
15. C43×#1955C2semidirect
395. #1955D43semidirect
462. C43#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#145834292
C2×#145829592
C2×#145828562
#191355352
#191355302
#191353902
#191348892
#191348842
#191343632
#191343592
C22⋊C8×Dic432
C43×#19552
#2138143