Finite Group Databasebeta

← #25024233

Subgroups — #25024233

Order 11008.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582789C211yesmaximal, characteristic
2C2×#14582770C211yesmaximal, characteristic
3C2×#14582761C211yesmaximal, characteristic
4C2×#14582756C211yesmaximal, characteristic
5#19132861C211yesmaximal, characteristic, complemented
6#19132854C211yesmaximal, characteristic, complemented
7#19132848C211yesmaximal, characteristic, complemented
8#19132845C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic
10#19132837C211yesmaximal, characteristic
11#19132833C211yesmaximal, characteristic
12#19132829C211yesmaximal, characteristic, complemented
13#19132827C211yesmaximal, characteristic, complemented
14#19132822C211yesmaximal, characteristic, complemented
15C2×C43×#389C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26#14582789—24no—
27#14582770C418yescomplemented
28#14582761—24no—
29#14582756—24no—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2211yescharacteristic
37C2×C43⋊#95C2211yescharacteristic
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C22×C4⋊C4×C43C2211yescharacteristic
49C22×C4⋊C4×C43C2211yescharacteristic
50C22×C4⋊C4×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C43×#389—24no—
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—41no—
69C22×C4×D43—41no—
70C22×C4×D43C2×C414yes—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—41no—
74C2×Dic43⋊C4—41no—
75C2×Dic43⋊C4—41no—
76C2×Dic43⋊C4C2×C414yes—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4—41no—
87C2×(C2×D43)⋊C4—41no—
88C2×(C2×D43)⋊C4—41no—
89C2×(C2×D43)⋊C4—41no—
90C2×(C2×D43)⋊C4—41no—
91C2×(C2×D43)⋊C4—41no—
92C2×(C2×D43)⋊C4C2×C414yes—
93C2×(C2×D43)⋊C4C2×C414yes—
94C2×(C2×D43)⋊C4D414yes—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—41no—
97C2×C4×Dic43—41no—
98C43⋊#95—22no—
99C43⋊#95—22no—
100C43⋊#95—22no—
101C43⋊#95—22no—
102C43⋊#95—22no—
103C43⋊#95—22no—
104C43⋊#95—22no—
105C43⋊#95—22no—
106C43⋊#95—22no—
107C43⋊#95—41no—
108C43⋊#95—41no—
109C43⋊#95—41no—
110C43⋊#95—41no—
111C43⋊#95—41no—
112C43⋊#95—41no—
113C43⋊#95—41no—
114C43⋊#95C2×C414yes—
115C43⋊#95C2×C414yes—
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43—22no—
124C2×C4⋊C4×C43—22no—
125C2×C4⋊C4×C43—22no—
126C2×C4⋊C4×C43—22no—
127C2×C4⋊C4×C43—22no—
128C2×C4⋊C4×C43—22no—
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43—41no—
132C2×C4⋊C4×C43—41no—
133C2×C4⋊C4×C43—41no—
134C2×C4⋊C4×C43C2×C414yes—
135C2×C42×C43—22no—
136C2×C42×C43—22no—
137C2×C42×C43—41no—
138#95×C43—22no—
139#95×C43D414yes—
140C24×C43C2411yescharacteristic
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—21no—
145C23×D43—21no—
146C23×D43—21no—
147C23×D43—21no—
148C23×D43—21no—
149C23×D43—21no—
150C23×D43—21no—
151C23×D43—21no—
152C23×D43—21no—
153C23×D43C22×C412yes—
154C23×D43C2×D412yes—
155C23×D43#4112yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
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×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
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×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C22×C412yes—
196C22×C4×C43C22×C412yes—
197C22×C4×C43C22×C412yes—
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D412yes—
202C22×C4×C43#4112yes—
203C22×C4×C43#4112yes—
204C22×C4×C43#4112yes—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43C22×C412yes—
251C22×Dic43C22×C412yes—
252C22×Dic43C22×C412yes—
253C22×Dic43C2×D412yes—
254C2×C4×D43—28no—
255C2×C4×D43—28no—
256C2×C4×D43—44no—
257C2×C4×D43—44no—
258C2×C4×D43—44no—
259C2×C4×D43—44no—
260C2×C4×D43—44no—
261C4⋊C4×C43—28no—
262C4⋊C4×C43—44no—
263C4⋊C4×C43—44no—
264C4⋊C4×C43—44no—
265C42×C43—44no—
266(C2×D43)⋊C4—28no—
267(C2×D43)⋊C4—28no—
268(C2×D43)⋊C4—44no—
269(C2×D43)⋊C4—44no—
270(C2×D43)⋊C4—44no—
271(C2×D43)⋊C4—44no—
272C4⋊Dic43—44no—
273Dic43⋊C4—44no—
274C4×Dic43—44no—
275C23×C43C23×C411yescharacteristic
276C23×C43C22×D411yescharacteristic
277C23×C43C22×D411yescharacteristic
278C23×C43C2×#4111yescharacteristic
279C23×C43C2×#4111yescharacteristic
280C23×C43C2×#4111yescharacteristic
281C23×C43C2×#4111yescharacteristic
282C23×C43H(5,𝔽2)11yescharacteristic
283C23×C43H(5,𝔽2)11yescharacteristic
284C23×C43H(5,𝔽2)11yescharacteristic
285C23×C43H(5,𝔽2)11yescharacteristic
286C23×C432−1+411yescharacteristic
287C23×C432−1+411yescharacteristic
288C23×C432−1+411yescharacteristic
289C23×C432−1+411yescharacteristic
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—41no—
324C22×D43C4×D414yes—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
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×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43#11714yes—
373C2×C4×C43C4×D414yes—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C4×D43—416no—
424#14382—431nomaximal, Sylow
425C22×C43C2×#11711yescharacteristic
426C22×C43C2×C4×D411yescharacteristic
427C22×C43C2×C4×D411yescharacteristic
428C22×C43#51811yescharacteristic
429C22×C43#51911yescharacteristic
430C22×C43#52011yescharacteristic
431C22×C43#52011yescharacteristic
432C22×C43#53411yescharacteristic
433C22×C43#53611yescharacteristic
434C22×C43#53611yescharacteristic
435C22×C43#53711yescharacteristic
436C22×C43#53911yescharacteristic
437C22×C43#53911yescharacteristic
438C22×C43#54011yescharacteristic
439C22×C43#54011yescharacteristic
440C22×C43#54111yescharacteristic
441C22×C43#54211yescharacteristic
442C22×C43#54211yescharacteristic
443C22×C43#54211yescharacteristic
444C22×C43D4211yescharacteristic
445C22×C43#54611yescharacteristic
446C22×C43#54611yescharacteristic
447C22×C43#54611yescharacteristic
448C22×C43#54711yescharacteristic
449C22×C43#54711yescharacteristic
450C22×C43#54811yescharacteristic
451C22×C43#55111yescharacteristic
452C22×C43#55211yescharacteristic
453C22×C43#55211yescharacteristic
454C22×C43#55211yescharacteristic
455C22×C43#55311yescharacteristic
456C22×C43#56211yescharacteristic
457C22×C43#56211yescharacteristic
458C22×C43#56311yescharacteristic
459C22×C43#56311yescharacteristic
460C2×D43—24no—
461C2×D43—24no—
462C2×D43—24no—
463C2×D43—42no—
464C2×D43—42no—
465C2×D43—42no—
466C2×D43—42no—
467C2×D43—42no—
468C2×D43—42no—
469C2×D43—42no—
470C2×D43—42no—
471C2×D43—42no—
472C2×D43—42no—
473C2×D43—42no—
474C2×D43—42no—
475C4×C43—24no—
476C4×C43—24no—
477C4×C43—42no—
478C4×C43—42no—
479C4×C43—42no—
480C4×C43—42no—
481C4×C43—81no—
482Dic43—42no—
483Dic43—42no—
484Dic43—42no—
485Dic43—42no—
486Dic43—81no—
487Dic43—81no—
488Dic43—81no—
489C2×#389D4311yescharacteristic, complemented
490C2×#388—431no—
491C2×#385—431no—
492C2×#381—431no—
493C2×#380—431no—
494#1445—431no—
495#1442—431no—
496#1441—431no—
497#1441—431no—
498#1440—431no—
499#1439—431no—
500#1437—431no—
501#1436—431no—
502#1436—431no—
503#1434—431no—
504C2×C43#231911yescharacteristic
505C2×C43#232211yescharacteristic
506C2×C43#232311yescharacteristic
507C2×C43#234411yescharacteristic
508C2×C43#235211yescharacteristic
509C2×C43#235811yescharacteristic
510C2×C43#237811yescharacteristic
511C2×C43#267111yescharacteristic
512C2×C43#267411yescharacteristic
513C2×C43#268711yescharacteristic
514C2×C43#269811yescharacteristic
515C2×C43#270111yescharacteristic
516C2×C43#270711yescharacteristic
517C2×C43#273811yescharacteristic
518C2×C43#273911yescharacteristic
519D43—44no—
520C24×C4—431no—
521C22×C4⋊C4—431no—
522C22×C4⋊C4—431no—
523C22×C4⋊C4C2×D4311yescharacteristic
524C22×C4⋊C4C2×D4311yescharacteristic
525C22×C4⋊C4C2×D4311yescharacteristic
526C22×C4⋊C4C2×D4311yescharacteristic
527C22×C22⋊C4—431no—
528C22×C22⋊C4—431no—
529C22×C22⋊C4—431no—
530C22×C22⋊C4—431no—
531C22×C22⋊C4—431no—
532C22×C22⋊C4—431no—
533C22×C42—431no—
534C22×C42C2×D4311yescharacteristic
535#389—24no—
536#388—864no—
537#385—438no—
538#381—864no—
539#380—864no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95—431no—
544C2×#95—431no—
545C2×#95—431no—
546C2×#95—431no—
547C2×#95—431no—
548C2×#95—431no—
549C2×#95—431no—
550C2×#95—431no—
551C2×#95—431no—
552C2×#95—431no—
553C2×#95—431no—
554C2×#95—431no—
555C2×#95—431no—
556C2×#95—431no—
557C2×#95—431no—
558C2×#95C2×D4311yescharacteristic
559C2×#95C2×D4311yescharacteristic
560C43#1438211yescharacteristic, complemented, Sylow
561C25—431no—
562C23×C4—431no—
563C23×C4—431no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—434no—
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—862no—
571C23×C4—862no—
572C23×C4—862no—
573C23×C4—862no—
574C23×C4—1721no—
575C23×C4—1721no—
576C23×C4C22×D4311yescharacteristic
577C23×C4C22×D4311yescharacteristic
578C23×C4C22×D4311yescharacteristic
579C23×C4C22×D4311yescharacteristic
580C23×C4C22×D4311yescharacteristic
581C23×C4C22×D4311yescharacteristic
582C23×C4C22×D4311yescharacteristic
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—434no—
595C2×C4⋊C4—862no—
596C2×C4⋊C4—862no—
597C2×C4⋊C4—1721no—
598C2×C4⋊C4—1721no—
599C2×C4⋊C4—1721no—
600C2×C4⋊C4C4×D4314yes—
601C2×C22⋊C4—434no—
602C2×C22⋊C4—434no—
603C2×C22⋊C4—434no—
604C2×C22⋊C4—862no—
605C2×C22⋊C4—862no—
606C2×C22⋊C4—862no—
607C2×C22⋊C4—862no—
608C2×C22⋊C4—862no—
609C2×C22⋊C4—862no—
610C2×C22⋊C4—862no—
611C2×C22⋊C4—862no—
612C2×C22⋊C4—862no—
613C2×C22⋊C4—1721no—
614C2×C22⋊C4—1721no—
615C2×C22⋊C4—1721no—
616C2×C22⋊C4—1721no—
617C2×C22⋊C4—1721no—
618C2×C22⋊C4—1721no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—41no—
622C2×C42—862no—
623C2×C42—1721no—
624C2×C42—1721no—
625#95—22no—
626#95—434no—
627#95—434no—
628#95—862no—
629#95—862no—
630#95—862no—
631#95—862no—
632#95—862no—
633#95—862no—
634#95—862no—
635#95—862no—
636#95—862no—
637#95—1721no—
638#95—1721no—
639#95—1721no—
640#95—1721no—
641#95—1721no—
642#95—1721no—
643#95—1721no—
644#95C22⋊D4314yes—
645C24—432no—
646C24—432no—
647C24—432no—
648C24—861no—
649C24—861no—
650C24—861no—
651C24—861no—
652C24—861no—
653C24—861no—
654C24—861no—
655C24—861no—
656C24—861no—
657C24—861no—
658C24—861no—
659C24—861no—
660C24C23×D4311yescharacteristic
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
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—432no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—868no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
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—861no—
728C22×C4—861no—
729C22×C4—868no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—1724no—
752C22×C4—1724no—
753C22×C4—1724no—
754C22×C4—1724no—
755C22×C4—1724no—
756C22×C4C2×C4×D4312yes—
757C22×C4C2×C4×D4312yes—
758C22×C4C2×C4×D4312yes—
759C22×C4#1062189812yes—
760C22×C4D4×D4312yes—
761C22×C4#1062190012yes—
762C22×C4#1062190212yes—
763C22×C4C2×C22⋊D4312yes—
764C22×C4C2×C22⋊D4312yes—
765C22×C4C2×C22⋊D4312yes—
766C4⋊C4—28no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—1724no—
771C4⋊C4—1724no—
772C22⋊C4—868no—
773C22⋊C4—868no—
774C22⋊C4—1724no—
775C22⋊C4—1724no—
776C22⋊C4—1724no—
777C22⋊C4—1724no—
778C42—44no—
779C42—1724no—
780C23—434no—
781C23—862no—
782C23—862no—
783C23—862no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—862no—
793C23—862no—
794C23—862no—
795C23—862no—
796C23—862no—
797C23—862no—
798C23—862no—
799C23—1721no—
800C23—1721no—
801C23—1721no—
802C23—1721no—
803C23—1721no—
804C23—1721no—
805C23—1721no—
806C23—1721no—
807C23—1721no—
808C23—1721no—
809C23—1721no—
810C23—1721no—
811C23—1721no—
812C23—1721no—
813C23—1721no—
814C23—1721no—
815C23C22×C4×D4311yescharacteristic
816C23C2×D4×D4311yescharacteristic
817C23C22×C22⋊D4311yescharacteristic
818C23#41×D4311yescharacteristic
819C23C2×#1062190011yescharacteristic
820C23C2×#1062189811yescharacteristic
821C23C2×#1062190211yescharacteristic
822C23#1306337011yescharacteristic
823C23#1306337011yescharacteristic
824C23#1306337111yescharacteristic
825C23#1306337111yescharacteristic
826C23#1306337211yescharacteristic
827C23#1306337311yescharacteristic
828C23#1306337311yescharacteristic
829C23#1306337311yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—17216no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4—1721no—
917C2×C4—1721no—
918C2×C4—1721no—
919C2×C4—1721no—
920C2×C4—1721no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4#1306328314yes—
928C2×C4C4×C22⋊D4314yes—
929C22—864no—
930C22—864no—
931C22—864no—
932C22—1722no—
933C22—1722no—
934C22—1722no—
935C22—1722no—
936C22—1722no—
937C22—1722no—
938C22—1722no—
939C22—1722no—
940C22—1722no—
941C22—1722no—
942C22—1722no—
943C22—1722no—
944C22C2×#1306328311yescharacteristic
945C22C4×D4×D4311yescharacteristic
946C22C2×C4×C22⋊D4311yescharacteristic
947C22#1458337111yescharacteristic
948C22#1458337511yescharacteristic
949C22#1458338011yescharacteristic
950C22#1458338111yescharacteristic
951C22#1458345711yescharacteristic
952C22#1458347311yescharacteristic
953C22#1458347411yescharacteristic
954C22#1458347711yescharacteristic
955C22#1458349511yescharacteristic
956C22#1458349711yescharacteristic
957C22#1458350211yescharacteristic
958C22#1458350511yescharacteristic
959C22#1458350711yescharacteristic
960C22#1458352111yescharacteristic
961C22#1458352211yescharacteristic
962C22#1458352311yescharacteristic
963C22D4×C22⋊D4311yescharacteristic
964C22#1458353711yescharacteristic
965C22#1458354311yescharacteristic
966C22#1458354511yescharacteristic
967C22#1458354911yescharacteristic
968C22#1458355211yescharacteristic
969C22#1458356011yescharacteristic
970C22#1458357811yescharacteristic
971C22#1458358311yescharacteristic
972C22#1458358411yescharacteristic
973C22#1458358711yescharacteristic
974C22#1458359711yescharacteristic
975C22#1458364411yescharacteristic
976C22#1458364511yescharacteristic
977C22#1458364811yescharacteristic
978C22#1458365311yescharacteristic
979C4—24no—
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—3441no—
987C4—3441no—
988C4—3441no—
989C4—1722no—
990C4—1722no—
991C4—1722no—
992C4—1722no—
993C2—1724no—
994C2#1913723411yescharacteristic
995C2#1913725911yescharacteristic
996C2#1913727111yescharacteristic
997C2#1913746311yescharacteristic
998C2#1913752011yescharacteristic
999C2#1913757211yescharacteristic
1000C2#1913775711yescharacteristic
1001C2#1914082611yescharacteristic
1002C2#1914087111yescharacteristic
1003C2#1914101211yescharacteristic
1004C2#1914116411yescharacteristic
1005C2#1914120311yescharacteristic
1006C2#1914129211yescharacteristic
1007C2#1914166811yescharacteristic
1008C2#1914168311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#389C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#389D43
hypocenterC43#14382
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
5. #19132861C2semidirect
6. #19132854C2semidirect
7. #19132848C2semidirect
8. #19132845C2semidirect
12. #19132829C2semidirect
13. #19132827C2semidirect
14. #19132822C2semidirect
15. C2×C43×#389C2semidirect
27. #14582770C4semidirect
489. C2×#389D43semidirect
560. C43#14382semidirect

Maximal subgroups

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

subgroupindex
C2×#145827892
C2×#145827702
C2×#145827612
C2×#145827562
#191328612
#191328542
#191328482
#191328452
#191328432
#191328372
#191328332
#191328292
#191328272
#191328222
C2×C43×#3892
#1438243