Finite Group Databasebeta

← C43×#17766 #24937783

Subgroups — C43×#17766 #24937783

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3508C211yesmaximal, characteristic
2C43×#2989C211yesmaximal, characteristic, complemented
3C43×#2925C211yesmaximal, characteristic, complemented
4C43×#1560C211yesmaximal, characteristic, complemented
5C43×#1559C211yesmaximal, characteristic, complemented
6C43×#1557C211yesmaximal, characteristic, complemented
7C43×#1555C211yesmaximal, characteristic, complemented
8C43×#1554C211yesmaximal, characteristic, complemented
9C43×#1553C211yesmaximal, characteristic, complemented
10C43×#1551C211yesmaximal, characteristic, complemented
11C43×#1551C211yesmaximal, characteristic, complemented
12C43×#1547C211yesmaximal, characteristic, complemented
13C43×#1545C211yesmaximal, characteristic, complemented
14C43×#1543C211yesmaximal, characteristic, complemented
15C43×#1540C211yesmaximal, characteristic, complemented
16C43×#559—21no—
17C43×#559C412yes—
18C43×#550—21no—
19C43×#550C412yes—
20C43×#546—21no—
21C43×#546—21no—
22C43×#546C412yes—
23C43×#546C412yes—
24C43×#540—21no—
25C43×#540—21no—
26C43×#535—21no—
27C43×#533C2211yescharacteristic
28C43×#532C2211yescharacteristic
29C43×#532C2211yescharacteristic
30C43×#532C2211yescharacteristic
31C43×#532C2211yescharacteristic
32C2×#127×C43C2211yescharacteristic
33C43×#518—21no—
34C4×#41×C43C2211yescharacteristic
35C43×#446—21no—
36C43×#436—21no—
37C43×#435—21no—
38C43×#435—21no—
39C43×#433—21no—
40C43×#433—21no—
41C43×#432C2211yescharacteristic
42C43×#432C2211yescharacteristic
43C43×#432C2211yescharacteristic, complemented
44C43×#432C2211yescharacteristic, complemented
45C43×#431C2211yescharacteristic
46C43×#431C2211yescharacteristic, complemented
47C43×#431C2211yescharacteristic, complemented
48C43×#423C2211yescharacteristic
49C43×#423C2211yescharacteristic, complemented
50C43×#423C2211yescharacteristic, complemented
51C2×C4⋊C8×C43C2211yescharacteristic, complemented
52C2×C4⋊C8×C43C2211yescharacteristic, complemented
53C43×#408—21no—
54C43×#405—21no—
55C43×#333C2211yescharacteristic, complemented
56C43×#333C2211yescharacteristic, complemented
57C43×#333C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#332C2211yescharacteristic, complemented
62C43×#332C2211yescharacteristic, complemented
63C43×#331C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C43×#331C2211yescharacteristic
68C43×#331C2211yescharacteristic
69C43×#331C2211yescharacteristic
70C43×#331C2211yescharacteristic
71C2×#41×C43—21no—
72C2×#41×C43—21no—
73C2×#41×C43C2×C412yes—
74C2×#41×C43C2×C412yes—
75C2×#41×C43D411yescharacteristic
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43C2×C412yes—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C22×C8×C43—21no—
83C22×C8×C43—21no—
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43—22no—
87#127×C43—21no—
88#127×C43—21no—
89#127×C43C2×C412yes—
90#127×C43C2311yescharacteristic
91#127×C43C2311yescharacteristic
92#125×C43—21no—
93#124×C43—22no—
94#124×C43—21no—
95#124×C43—21no—
96#124×C43C2×C412yes—
97#124×C43C2×C412yes—
98#123×C43—22no—
99#123×C43—22no—
100#123×C43—22no—
101#123×C43—22no—
102C22⋊Q8×C43—21no—
103C22⋊Q8×C43C2×C412yes—
104#121×C43—21no—
105#121×C43—21no—
106#121×C43—21no—
107#121×C43—21no—
108#121×C43—21no—
109#121×C43—21no—
110#121×C43—22no—
111#121×C43—22no—
112#121×C43—22no—
113#121×C43—22no—
114#121×C43C2×C412yes—
115#121×C43C2×C412yes—
116#120×C43—22no—
117#120×C43—22no—
118C4×Q8×C43—21no—
119C4×Q8×C43C2×C412yes—
120C4×Q8×C43C2×C411yescharacteristic
121C4×Q8×C43D411yescharacteristic
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2×C412yes—
131C4×D4×C43C2×C412yes—
132C4×D4×C43C2×C411yescharacteristic
133C4×D4×C43C2×C411yescharacteristic
134C4×D4×C43C2×C411yescharacteristic
135C4×D4×C43D411yescharacteristic
136C4×D4×C43D411yescharacteristic
137C4×D4×C43D411yescharacteristic
138#117×C43—21no—
139#117×C43D411yescharacteristic
140#117×C43D411yescharacteristic
141#117×C43D411yescharacteristic
142C2×C22⋊C4×C43—22no—
143C2×C22⋊C4×C43—22no—
144C2×C42×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C4⋊C8×C43—21no—
148C4⋊C8×C43—21no—
149C4⋊C8×C43—21no—
150C4⋊C8×C43—21no—
151C4⋊C8×C43—21no—
152C4⋊C8×C43C2311yescharacteristic
153C4⋊C8×C43C2311yescharacteristic
154C4⋊C8×C43C2311yescharacteristic
155C4⋊C8×C43C2311yescharacteristic
156C4⋊C8×C43C2311yescharacteristic
157C4⋊C8×C43C2311yescharacteristic
158C4⋊C8×C43C2311yescharacteristic
159C4⋊C8×C43C2311yescharacteristic
160C22⋊C8×C43—21no—
161C22⋊C8×C43—21no—
162C22⋊C8×C43—21no—
163C22⋊C8×C43—21no—
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167#97×C43—21no—
168#97×C43—21no—
169#97×C43—21no—
170#97×C43—21no—
171C4×C8×C43—21no—
172C4×C8×C43—21no—
173C4×C8×C43—21no—
174C24×C43—22no—
175#41×C43—41no—
176#41×C43—41no—
177#41×C43—81no—
178#41×C43—81no—
179#41×C43—81no—
180#41×C43—81no—
181#41×C43—82no—
182#41×C43—82no—
183C2×Q8×C43—21no—
184C2×Q8×C43C22⋊C411yescharacteristic
185C2×Q8×C43C22×C412yes—
186C2×D4×C43—22no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—42no—
198C2×D4×C43—42no—
199C2×D4×C43—81no—
200C2×D4×C43—81no—
201C2×D4×C43—82no—
202C2×D4×C43C22⋊C411yescharacteristic
203C2×D4×C43C22⋊C411yescharacteristic
204C2×D4×C43C22⋊C411yescharacteristic
205C2×D4×C43C22×C412yes—
206C2×D4×C43C22×C412yes—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220M16×C43—42no—
221M16×C43—81no—
222M16×C43—81no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—42no—
232C2×C8×C43—81no—
233C4⋊C4×C43—22no—
234C4⋊C4×C43—22no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43C22⋊C411yescharacteristic
239C4⋊C4×C43C22⋊C411yescharacteristic
240C4⋊C4×C43C22⋊C411yescharacteristic
241C4⋊C4×C43C22⋊C411yescharacteristic
242C4⋊C4×C43C22⋊C411yescharacteristic
243C4⋊C4×C43C22⋊C411yescharacteristic
244C4⋊C4×C43C22×C412yes—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—22no—
254C22⋊C4×C43C22⋊C411yescharacteristic
255C22⋊C4×C43C22⋊C411yescharacteristic
256C22⋊C4×C43C22⋊C411yescharacteristic
257C22⋊C4×C43C22⋊C411yescharacteristic
258C22⋊C4×C43C22⋊C411yescharacteristic
259C22⋊C4×C43C22⋊C411yescharacteristic
260C42×C43—22no—
261C42×C43C22×C411yescharacteristic
262C42×C43C22×C411yescharacteristic
263C42×C43C22×C411yescharacteristic
264C42×C43C2×D411yescharacteristic
265C42×C43C2×D411yescharacteristic
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2×D411yescharacteristic
269C42×C43C2×D411yescharacteristic
270C42×C43C2411yescharacteristic
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—44no—
274C23×C43—82no—
275C23×C43—82no—
276C23×C43C2×C22⋊C411yescharacteristic
277C23×C43C2×C22⋊C411yescharacteristic
278C23×C43C2×C22⋊C411yescharacteristic
279Q8×C43—41no—
280Q8×C43—42no—
281Q8×C43—41no—
282Q8×C43—41no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43—42no—
287D4×C43—42no—
288D4×C43—44no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—82no—
298D4×C43—82no—
299D4×C43—82no—
300D4×C43—82no—
301D4×C43—82no—
302D4×C43—82no—
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—21no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—82no—
321C2×C4×C43—82no—
322C2×C4×C43—82no—
323C2×C4×C43—82no—
324C2×C4×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43C2×C22⋊C411yescharacteristic
326C2×C4×C43C2×C22⋊C411yescharacteristic
327C2×C4×C43C2×C22⋊C411yescharacteristic
328C2×C4×C43C2×C22⋊C411yescharacteristic
329C2×C4×C43C2×C22⋊C411yescharacteristic
330C2×C4×C43C2×C22⋊C411yescharacteristic
331C2×C4×C43C2×C22⋊C411yescharacteristic
332C2×C4×C43C2×C22⋊C411yescharacteristic
333C2×C4×C43C23×C411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C8×C43—41no—
337C8×C43—41no—
338C8×C43—41no—
339C8×C43—41no—
340C8×C43—41no—
341C8×C43—41no—
342C8×C43—41no—
343C8×C43—41no—
344#17766C4311yesmaximal, characteristic, direct product factor, Sylow
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—21no—
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—164no—
361C22×C43C22×C22⋊C411yescharacteristic
362C4×C43—21no—
363C4×C43—21no—
364C4×C43—21no—
365C4×C43—21no—
366C4×C43—21no—
367C4×C43—21no—
368C4×C43—21no—
369C4×C43—21no—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43#57511yescharacteristic
375C4×C43#57511yescharacteristic
376C4×C43#57611yescharacteristic
377C4×C43#57711yescharacteristic
378#3508C2×C4311yescharacteristic
379#2989C2×C4311yescharacteristic, complemented
380#2925C2×C4311yescharacteristic, complemented
381#1560C2×C4311yescharacteristic, complemented
382#1559C2×C4311yescharacteristic, complemented
383#1557C2×C4311yescharacteristic, complemented
384#1555C2×C4311yescharacteristic, complemented
385#1554C2×C4311yescharacteristic, complemented
386#1553C2×C4311yescharacteristic, complemented
387#1551C2×C4311yescharacteristic, complemented
388#1551C2×C4311yescharacteristic, complemented
389#1547C2×C4311yescharacteristic, complemented
390#1545C2×C4311yescharacteristic, complemented
391#1543C2×C4311yescharacteristic, complemented
392#1540C2×C4311yescharacteristic, complemented
393C2×C43—41no—
394C2×C43—41no—
395C2×C43—41no—
396C2×C43—82no—
397C2×C43—82no—
398C2×C43#288811yescharacteristic
399C2×C43#289611yescharacteristic
400C2×C43#289711yescharacteristic
401#559—21no—
402#559C4×C4312yes—
403#550—21no—
404#550C4×C4312yes—
405#546—21no—
406#546—21no—
407#546C4×C4312yes—
408#546C4×C4312yes—
409#540—21no—
410#540—21no—
411#535—21no—
412#533C22×C4311yescharacteristic
413#532C22×C4311yescharacteristic
414#532C22×C4311yescharacteristic
415#532C22×C4311yescharacteristic
416#532C22×C4311yescharacteristic
417C2×#127C22×C4311yescharacteristic
418#518—21no—
419C4×#41C22×C4311yescharacteristic
420#446—21no—
421#436—21no—
422#435—21no—
423#435—21no—
424#433—21no—
425#433—21no—
426#432C22×C4311yescharacteristic
427#432C22×C4311yescharacteristic
428#432C22×C4311yescharacteristic, complemented
429#432C22×C4311yescharacteristic, complemented
430#431C22×C4311yescharacteristic
431#431C22×C4311yescharacteristic, complemented
432#431C22×C4311yescharacteristic, complemented
433#423C22×C4311yescharacteristic
434#423C22×C4311yescharacteristic, complemented
435#423C22×C4311yescharacteristic, complemented
436C2×C4⋊C8C22×C4311yescharacteristic, complemented
437C2×C4⋊C8C22×C4311yescharacteristic, complemented
438#408—21no—
439#405—21no—
440#333C22×C4311yescharacteristic, complemented
441#333C22×C4311yescharacteristic, complemented
442#333C22×C4311yescharacteristic, complemented
443#333C22×C4311yescharacteristic, complemented
444#332C22×C4311yescharacteristic, complemented
445#332C22×C4311yescharacteristic, complemented
446#332C22×C4311yescharacteristic, complemented
447#332C22×C4311yescharacteristic, complemented
448#331C22×C4311yescharacteristic
449#331C22×C4311yescharacteristic
450#331C22×C4311yescharacteristic
451#331C22×C4311yescharacteristic
452#331C22×C4311yescharacteristic
453#331C22×C4311yescharacteristic
454#331C22×C4311yescharacteristic
455#331C22×C4311yescharacteristic
456C43#1776611yescharacteristic, direct product factor, Sylow
457C2×#41—21no—
458C2×#41—21no—
459C2×#41C2×C4×C4312yes—
460C2×#41C2×C4×C4312yes—
461C2×#41D4×C4311yescharacteristic
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C2×C4×C4312yes—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C22×C8—21no—
469C22×C8—21no—
470C4⋊Q8C23×C4311yescharacteristic
471C4⋊Q8C23×C4311yescharacteristic
472#127—22no—
473#127—21no—
474#127—21no—
475#127C2×C4×C4312yes—
476#127C23×C4311yescharacteristic
477#127C23×C4311yescharacteristic
478#125—21no—
479#124—22no—
480#124—21no—
481#124—21no—
482#124C2×C4×C4312yes—
483#124C2×C4×C4312yes—
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488C22⋊Q8—21no—
489C22⋊Q8C2×C4×C4312yes—
490#121—21no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121C2×C4×C4312yes—
501#121C2×C4×C4312yes—
502#120—22no—
503#120—22no—
504C4×Q8—21no—
505C4×Q8C2×C4×C4312yes—
506C4×Q8C2×C4×C4311yescharacteristic
507C4×Q8D4×C4311yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4C2×C4×C4312yes—
517C4×D4C2×C4×C4312yes—
518C4×D4C2×C4×C4311yescharacteristic
519C4×D4C2×C4×C4311yescharacteristic
520C4×D4C2×C4×C4311yescharacteristic
521C4×D4D4×C4311yescharacteristic
522C4×D4D4×C4311yescharacteristic
523C4×D4D4×C4311yescharacteristic
524#117—21no—
525#117D4×C4311yescharacteristic
526#117D4×C4311yescharacteristic
527#117D4×C4311yescharacteristic
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C42C23×C4311yescharacteristic
531C2×C42C23×C4311yescharacteristic
532C2×C42C23×C4311yescharacteristic
533C4⋊C8—21no—
534C4⋊C8—21no—
535C4⋊C8—21no—
536C4⋊C8—21no—
537C4⋊C8—21no—
538C4⋊C8C23×C4311yescharacteristic
539C4⋊C8C23×C4311yescharacteristic
540C4⋊C8C23×C4311yescharacteristic
541C4⋊C8C23×C4311yescharacteristic
542C4⋊C8C23×C4311yescharacteristic
543C4⋊C8C23×C4311yescharacteristic
544C4⋊C8C23×C4311yescharacteristic
545C4⋊C8C23×C4311yescharacteristic
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550C22⋊C8—21no—
551C22⋊C8—21no—
552C22⋊C8—21no—
553#97—21no—
554#97—21no—
555#97—21no—
556#97—21no—
557C4×C8—21no—
558C4×C8—21no—
559C4×C8—21no—
560C24—22no—
561#41—41no—
562#41—41no—
563#41—81no—
564#41—81no—
565#41—81no—
566#41—81no—
567#41—82no—
568#41—82no—
569C2×Q8—21no—
570C2×Q8C22⋊C4×C4311yescharacteristic
571C2×Q8C22×C4×C4312yes—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—82no—
588C2×D4C22⋊C4×C4311yescharacteristic
589C2×D4C22⋊C4×C4311yescharacteristic
590C2×D4C22⋊C4×C4311yescharacteristic
591C2×D4C22×C4×C4312yes—
592C2×D4C22×C4×C4312yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4C22×C4×C4311yescharacteristic
598C22×C4C22×C4×C4311yescharacteristic
599C22×C4C22×C4×C4311yescharacteristic
600C22×C4C2×D4×C4311yescharacteristic
601C22×C4C2×D4×C4311yescharacteristic
602C22×C4C2×D4×C4311yescharacteristic
603C22×C4C2×D4×C4311yescharacteristic
604C22×C4C2×D4×C4311yescharacteristic
605C22×C4C2×D4×C4311yescharacteristic
606M16—42no—
607M16—81no—
608M16—81no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—42no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4C22⋊C4×C4311yescharacteristic
625C4⋊C4C22⋊C4×C4311yescharacteristic
626C4⋊C4C22⋊C4×C4311yescharacteristic
627C4⋊C4C22⋊C4×C4311yescharacteristic
628C4⋊C4C22⋊C4×C4311yescharacteristic
629C4⋊C4C22⋊C4×C4311yescharacteristic
630C4⋊C4C22×C4×C4312yes—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4C22⋊C4×C4311yescharacteristic
641C22⋊C4C22⋊C4×C4311yescharacteristic
642C22⋊C4C22⋊C4×C4311yescharacteristic
643C22⋊C4C22⋊C4×C4311yescharacteristic
644C22⋊C4C22⋊C4×C4311yescharacteristic
645C22⋊C4C22⋊C4×C4311yescharacteristic
646C42—22no—
647C42C22×C4×C4311yescharacteristic
648C42C22×C4×C4311yescharacteristic
649C42C22×C4×C4311yescharacteristic
650C42C2×D4×C4311yescharacteristic
651C42C2×D4×C4311yescharacteristic
652C42C2×D4×C4311yescharacteristic
653C42C2×D4×C4311yescharacteristic
654C42C2×D4×C4311yescharacteristic
655C42C2×D4×C4311yescharacteristic
656C42C24×C4311yescharacteristic
657C23—22no—
658C23—22no—
659C23—44no—
660C23—82no—
661C23—82no—
662C23C2×C22⋊C4×C4311yescharacteristic
663C23C2×C22⋊C4×C4311yescharacteristic
664C23C2×C22⋊C4×C4311yescharacteristic
665Q8—41no—
666Q8—42no—
667Q8—41no—
668Q8—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—42no—
673D4—42no—
674D4—44no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—82no—
684D4—82no—
685D4—82no—
686D4—82no—
687D4—82no—
688D4—82no—
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—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4C2×C22⋊C4×C4311yescharacteristic
711C2×C4C2×C22⋊C4×C4311yescharacteristic
712C2×C4C2×C22⋊C4×C4311yescharacteristic
713C2×C4C2×C22⋊C4×C4311yescharacteristic
714C2×C4C2×C22⋊C4×C4311yescharacteristic
715C2×C4C2×C22⋊C4×C4311yescharacteristic
716C2×C4C2×C22⋊C4×C4311yescharacteristic
717C2×C4C2×C22⋊C4×C4311yescharacteristic
718C2×C4C2×C22⋊C4×C4311yescharacteristic
719C2×C4C23×C4×C4311yescharacteristic
720C2×C4C22×D4×C4311yescharacteristic
721C2×C4C22×D4×C4311yescharacteristic
722C8—41no—
723C8—41no—
724C8—41no—
725C8—41no—
726C8—41no—
727C8—41no—
728C8—41no—
729C8—41no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—164no—
746C22C22×C22⋊C4×C4311yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—42no—
759C4C43×#57511yescharacteristic
760C4C43×#57511yescharacteristic
761C4C43×#57611yescharacteristic
762C4C43×#57711yescharacteristic
763C2—41no—
764C2—41no—
765C2—41no—
766C2—82no—
767C2—82no—
768C2C43×#288811yescharacteristic
769C2C43×#289611yescharacteristic
770C2C43×#289711yescharacteristic
subgroupG/H
center, socleC22×C43C22×C22⋊C4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC42C24×C43
prime radicalC43×#3508C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C4×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2989C2semidirect
3. C43×#2925C2semidirect
4. C43×#1560C2semidirect
5. C43×#1559C2semidirect
6. C43×#1557C2semidirect
7. C43×#1555C2semidirect
8. C43×#1554C2semidirect
9. C43×#1553C2semidirect
10. C43×#1551C2semidirect
11. C43×#1551C2semidirect
12. C43×#1547C2semidirect
13. C43×#1545C2semidirect
14. C43×#1543C2semidirect
15. C43×#1540C2semidirect
43. C43×#432C22semidirect
44. C43×#432C22semidirect
46. C43×#431C22semidirect
47. C43×#431C22semidirect
49. C43×#423C22semidirect
50. C43×#423C22semidirect
51. C2×C4⋊C8×C43C22semidirect
52. C2×C4⋊C8×C43C22semidirect
55. C43×#333C22semidirect
56. C43×#333C22semidirect
57. C43×#333C22semidirect
58. C43×#333C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
61. C43×#332C22semidirect
62. C43×#332C22semidirect
344. #17766C43direct (N × H)
379. #2989C2×C43semidirect
380. #2925C2×C43semidirect
381. #1560C2×C43semidirect
382. #1559C2×C43semidirect
383. #1557C2×C43semidirect
384. #1555C2×C43semidirect
385. #1554C2×C43semidirect
386. #1553C2×C43semidirect
387. #1551C2×C43semidirect
388. #1551C2×C43semidirect
389. #1547C2×C43semidirect
390. #1545C2×C43semidirect
391. #1543C2×C43semidirect
392. #1540C2×C43semidirect
428. #432C22×C43semidirect
429. #432C22×C43semidirect
431. #431C22×C43semidirect
432. #431C22×C43semidirect
434. #423C22×C43semidirect
435. #423C22×C43semidirect
436. C2×C4⋊C8C22×C43semidirect
437. C2×C4⋊C8C22×C43semidirect
440. #333C22×C43semidirect
441. #333C22×C43semidirect
442. #333C22×C43semidirect
443. #333C22×C43semidirect
444. #332C22×C43semidirect
445. #332C22×C43semidirect
446. #332C22×C43semidirect
447. #332C22×C43semidirect
456. C43#17766direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35082
C43×#29892
C43×#29252
C43×#15602
C43×#15592
C43×#15572
C43×#15552
C43×#15542
C43×#15532
C43×#15512
C43×#15472
C43×#15452
C43×#15432
C43×#15402
#1776643