Finite Group Databasebeta

← C43×#22056 #24942073

Subgroups — C43×#22056 #24942073

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#447C211yesmaximal, characteristic
2C43×#2324C211yesmaximal, characteristic, complemented
3C43×#2309C211yesmaximal, characteristic, complemented
4C43×#1972C211yesmaximal, characteristic, complemented
5C43×#1970C211yesmaximal, characteristic, complemented
6C43×#1936C211yesmaximal, characteristic, complemented
7C43×#1934C211yesmaximal, characteristic, complemented
8C43×#1926C211yesmaximal, characteristic, complemented
9C43×#1925C211yesmaximal, characteristic, complemented
10C43×#1879C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1875C211yesmaximal, characteristic, complemented
13C43×#1854C211yesmaximal, characteristic, complemented
14C43×#1786C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic, complemented
21C2×#117×C43C2211yescharacteristic
22C2×#117×C43C2211yescharacteristic
23C43×#447C418yescomplemented
24C2×#107×C43C2211yescharacteristic, complemented
25C2×#106×C43C2211yescharacteristic, complemented
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic, complemented
33C2×#102×C43C2211yescharacteristic, complemented
34C2×C22⋊C8×C43C2211yescharacteristic
35C2×C22⋊C8×C43C2211yescharacteristic
36C2×#97×C43C2211yescharacteristic, complemented
37C2×C4×C8×C43C2211yescharacteristic, complemented
38C43×#390—21no—
39C43×#390—21no—
40C43×#390—21no—
41C43×#390C2211yescharacteristic
42C43×#390C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic, complemented
46C43×#389C2211yescharacteristic, complemented
47C43×#388—21no—
48C43×#386—21no—
49C43×#385—21no—
50C43×#380C2211yescharacteristic
51C43×#379—21no—
52C43×#379—21no—
53C4×C4⋊C4×C43C2211yescharacteristic, complemented
54C43×#340C2211yescharacteristic, complemented
55C43×#340C2211yescharacteristic, complemented
56C43×#340C2211yescharacteristic, complemented
57C43×#340C2211yescharacteristic, complemented
58C43×#336C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C25×C43—21no—
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—22no—
64C22×D4×C43—41no—
65C22×D4×C43—41no—
66C22×D4×C43—41no—
67C22×D4×C43—41no—
68C22×D4×C43C2×C414yescomplemented
69C22×D4×C43C2311yescharacteristic
70C22×D4×C43C2311yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C2×D8×C43—41no—
75C2×D8×C43—41no—
76C2×D8×C43—41no—
77C2×D8×C43—41no—
78C2×D8×C43C2×C414yes—
79C2×D8×C43C2×C414yes—
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84#121×C43—22no—
85#121×C43C2×C414yes—
86C4×D4×C43—41no—
87C4×D4×C43—41no—
88#117×C43—41no—
89#117×C43—41no—
90#117×C43—41no—
91#117×C43—41no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43D411yescharacteristic
94C2×C4⋊C4×C43D411yescharacteristic
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#107×C43—41no—
121#106×C43—41no—
122#102×C43—41no—
123#102×C43—41no—
124#102×C43—41no—
125#102×C43—41no—
126#102×C43—41no—
127#102×C43—41no—
128#102×C43C2×C414yescomplemented
129#102×C43C2×C414yescomplemented
130C22⋊C8×C43—22no—
131C22⋊C8×C43C2×C414yescomplemented
132#97×C43—41no—
133C4×C8×C43—41no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—81no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43—81no—
147C24×C43C2×D411yescharacteristic
148C2×D4×C43—24no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—24no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—44no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—81no—
172C2×D4×C43—81no—
173C2×D4×C43C22×C412yes—
174C2×D4×C43C22×C412yes—
175C2×D4×C43C22×C412yes—
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—42no—
186C22×C4×C43—81no—
187C22×C4×C43—81no—
188C22×C4×C43C22×C412yes—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4112yes—
195C22×C4×C43C2411yescharacteristic
196D8×C43—44no—
197D8×C43—44no—
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—
208C2×C8×C43C22×C412yes—
209C2×C8×C43C22×C412yes—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—41no—
220C4⋊C4×C43—41no—
221C4⋊C4×C43—81no—
222C4⋊C4×C43C22×C412yes—
223C22⋊C4×C43—24no—
224C22⋊C4×C43—41no—
225C22⋊C4×C43—41no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—81no—
229C22⋊C4×C43—81no—
230C22⋊C4×C43—81no—
231C22⋊C4×C43—81no—
232C22⋊C4×C43—81no—
233C22⋊C4×C43—81no—
234C22⋊C4×C43—81no—
235C22⋊C4×C43—81no—
236C22⋊C4×C43—81no—
237C22⋊C4×C43—81no—
238C22⋊C4×C43—81no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—21no—
243C42×C43—42no—
244C42×C43—81no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43—48no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43C4×D412yes—
280C23×C43C22×D411yescharacteristic
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—48no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—84no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—84no—
329C2×C4×C43C4×D412yes—
330C2×C4×C43C23×C411yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C8×C43—22no—
337C8×C43—22no—
338C8×C43—41no—
339C8×C43—41no—
340#22056C4311yesmaximal, characteristic, direct product factor, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—816no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43C2×C4×D411yescharacteristic
371C22×C43#53411yescharacteristic
372C22×C43#53511yescharacteristic
373C22×C43#57611yescharacteristic
374C22×C43#57611yescharacteristic
375C22×C43#57611yescharacteristic
376C22×C43#57711yescharacteristic
377C4×C43—22no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43—42no—
383C4×C43—81no—
384C4×C43—81no—
385C4×C43—81no—
386C4×C43—81no—
387C4×C43#51811yescharacteristic
388C4×C43#51811yescharacteristic
389C4×C43#53811yescharacteristic
390C4×C43#53811yescharacteristic
391C2×#447C2×C4311yescharacteristic
392#2324C2×C4311yescharacteristic, complemented
393#2309C2×C4311yescharacteristic, complemented
394#1972C2×C4311yescharacteristic, complemented
395#1970C2×C4311yescharacteristic, complemented
396#1936C2×C4311yescharacteristic, complemented
397#1934C2×C4311yescharacteristic, complemented
398#1926C2×C4311yescharacteristic, complemented
399#1925C2×C4311yescharacteristic, complemented
400#1879C2×C4311yescharacteristic, complemented
401#1879C2×C4311yescharacteristic, complemented
402#1875C2×C4311yescharacteristic, complemented
403#1854C2×C4311yescharacteristic, complemented
404#1786C2×C4311yescharacteristic, complemented
405#1750C2×C4311yescharacteristic, complemented
406C2×C43—42no—
407C2×C43—82no—
408C2×C43—82no—
409C2×C43—82no—
410C2×C43#232111yescharacteristic
411C2×C43#294611yescharacteristic
412C2×C43#294811yescharacteristic
413C2×C43#319811yescharacteristic
414C2×C43#319911yescharacteristic
415C2×C43#322011yescharacteristic
416C2×C43#322411yescharacteristic
417C23×D4C22×C4311yescharacteristic
418C22×D8C22×C4311yescharacteristic
419C22×D8C22×C4311yescharacteristic
420C2×#121C22×C4311yescharacteristic
421C2×C4×D4C22×C4311yescharacteristic, complemented
422C2×#117C22×C4311yescharacteristic
423C2×#117C22×C4311yescharacteristic
424#447C4×C4318yescomplemented
425C2×#107C22×C4311yescharacteristic, complemented
426C2×#106C22×C4311yescharacteristic, complemented
427C2×#102C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431C2×#102C22×C4311yescharacteristic
432C2×#102C22×C4311yescharacteristic
433C2×#102C22×C4311yescharacteristic, complemented
434C2×#102C22×C4311yescharacteristic, complemented
435C2×C22⋊C8C22×C4311yescharacteristic
436C2×C22⋊C8C22×C4311yescharacteristic
437C2×#97C22×C4311yescharacteristic, complemented
438C2×C4×C8C22×C4311yescharacteristic, complemented
439#390—21no—
440#390—21no—
441#390—21no—
442#390C22×C4311yescharacteristic
443#390C22×C4311yescharacteristic
444#390C22×C4311yescharacteristic
445#390C22×C4311yescharacteristic
446#390C22×C4311yescharacteristic, complemented
447#389C22×C4311yescharacteristic, complemented
448#388—21no—
449#386—21no—
450#385—21no—
451#380C22×C4311yescharacteristic
452#379—21no—
453#379—21no—
454C4×C4⋊C4C22×C4311yescharacteristic, complemented
455#340C22×C4311yescharacteristic, complemented
456#340C22×C4311yescharacteristic, complemented
457#340C22×C4311yescharacteristic, complemented
458#340C22×C4311yescharacteristic, complemented
459#336C22×C4311yescharacteristic, complemented
460#336C22×C4311yescharacteristic, complemented
461C43#2205611yescharacteristic, direct product factor, Sylow
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×C4×C4314yescomplemented
471C22×D4C23×C4311yescharacteristic
472C22×D4C23×C4311yescharacteristic
473C22×D4C23×C4311yescharacteristic
474C23×C4—21no—
475C23×C4C23×C4311yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×C4×C4314yes—
481C2×D8C2×C4×C4314yes—
482C22×C8C23×C4311yescharacteristic
483C22×C8C23×C4311yescharacteristic
484C22×C8C23×C4311yescharacteristic
485C22×C8C23×C4311yescharacteristic
486#121—22no—
487#121C2×C4×C4314yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4D4×C4311yescharacteristic
496C2×C4⋊C4D4×C4311yescharacteristic
497C2×C4⋊C4C23×C4311yescharacteristic
498C2×C4⋊C4C23×C4311yescharacteristic
499C2×C4⋊C4C23×C4311yescharacteristic
500C2×C4⋊C4C23×C4311yescharacteristic
501C2×C4⋊C4C23×C4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C4311yescharacteristic
517C2×C22⋊C4D4×C4311yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C4311yescharacteristic
521C2×C42C23×C4311yescharacteristic
522#107—41no—
523#106—41no—
524#102—41no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102C2×C4×C4314yescomplemented
531#102C2×C4×C4314yescomplemented
532C22⋊C8—22no—
533C22⋊C8C2×C4×C4314yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24C2×D4×C4311yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×C4×C4312yes—
576C2×D4C22×C4×C4312yes—
577C2×D4C22×C4×C4312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×C4×C4312yes—
591C22×C4C2×D4×C4311yescharacteristic
592C22×C4C2×D4×C4311yescharacteristic
593C22×C4C2×D4×C4311yescharacteristic
594C22×C4C2×D4×C4311yescharacteristic
595C22×C4C2×D4×C4311yescharacteristic
596C22×C4#41×C4312yes—
597C22×C4C24×C4311yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
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×C8C22×C4×C4312yes—
611C2×C8C22×C4×C4312yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—81no—
624C4⋊C4C22×C4×C4312yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C4×D4×C4312yes—
682C23C22×D4×C4311yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4C4×D4×C4312yes—
732C2×C4C23×C4×C4311yescharacteristic
733C2×C4C2×#41×C4311yescharacteristic
734C2×C4H(5,𝔽2)×C4311yescharacteristic
735C2×C4H(5,𝔽2)×C4311yescharacteristic
736C2×C4H(5,𝔽2)×C4311yescharacteristic
737C2×C4H(5,𝔽2)×C4311yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C4×D4×C4311yescharacteristic
772C22C43×#53411yescharacteristic
773C22C43×#53511yescharacteristic
774C22C43×#57611yescharacteristic
775C22C43×#57611yescharacteristic
776C22C43×#57611yescharacteristic
777C22C43×#57711yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4C43×#51811yescharacteristic
789C4C43×#51811yescharacteristic
790C4C43×#53811yescharacteristic
791C4C43×#53811yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2C43×#232111yescharacteristic
797C2C43×#294611yescharacteristic
798C2C43×#294811yescharacteristic
799C2C43×#319811yescharacteristic
800C2C43×#319911yescharacteristic
801C2C43×#322011yescharacteristic
802C2C43×#322411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2324C2semidirect
3. C43×#2309C2semidirect
4. C43×#1972C2semidirect
5. C43×#1970C2semidirect
6. C43×#1936C2semidirect
7. C43×#1934C2semidirect
8. C43×#1926C2semidirect
9. C43×#1925C2semidirect
10. C43×#1879C2semidirect
11. C43×#1879C2semidirect
12. C43×#1875C2semidirect
13. C43×#1854C2semidirect
14. C43×#1786C2semidirect
15. C43×#1750C2semidirect
20. C2×C4×D4×C43C22semidirect
23. C43×#447C4semidirect
24. C2×#107×C43C22semidirect
25. C2×#106×C43C22semidirect
32. C2×#102×C43C22semidirect
33. C2×#102×C43C22semidirect
36. C2×#97×C43C22semidirect
37. C2×C4×C8×C43C22semidirect
45. C43×#390C22semidirect
46. C43×#389C22semidirect
53. C4×C4⋊C4×C43C22semidirect
54. C43×#340C22semidirect
55. C43×#340C22semidirect
56. C43×#340C22semidirect
57. C43×#340C22semidirect
58. C43×#336C22semidirect
59. C43×#336C22semidirect
68. C22×D4×C43C2×C4semidirect
128. #102×C43C2×C4semidirect
129. #102×C43C2×C4semidirect
131. C22⋊C8×C43C2×C4semidirect
340. #22056C43direct (N × H)
392. #2324C2×C43semidirect
393. #2309C2×C43semidirect
394. #1972C2×C43semidirect
395. #1970C2×C43semidirect
396. #1936C2×C43semidirect
397. #1934C2×C43semidirect
398. #1926C2×C43semidirect
399. #1925C2×C43semidirect
400. #1879C2×C43semidirect
401. #1879C2×C43semidirect
402. #1875C2×C43semidirect
403. #1854C2×C43semidirect
404. #1786C2×C43semidirect
405. #1750C2×C43semidirect
421. C2×C4×D4C22×C43semidirect
424. #447C4×C43semidirect
425. C2×#107C22×C43semidirect
426. C2×#106C22×C43semidirect
433. C2×#102C22×C43semidirect
434. C2×#102C22×C43semidirect
437. C2×#97C22×C43semidirect
438. C2×C4×C8C22×C43semidirect
446. #390C22×C43semidirect
447. #389C22×C43semidirect
454. C4×C4⋊C4C22×C43semidirect
455. #340C22×C43semidirect
456. #340C22×C43semidirect
457. #340C22×C43semidirect
458. #340C22×C43semidirect
459. #336C22×C43semidirect
460. #336C22×C43semidirect
461. C43#22056direct (N × H)
470. C22×D4C2×C4×C43semidirect
530. #102C2×C4×C43semidirect
531. #102C2×C4×C43semidirect
533. C22⋊C8C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4472
C43×#23242
C43×#23092
C43×#19722
C43×#19702
C43×#19362
C43×#19342
C43×#19262
C43×#19252
C43×#18792
C43×#18752
C43×#18542
C43×#17862
C43×#17502
#2205643