Finite Group Databasebeta

← C43×#17609 #24937626

Subgroups — C43×#17609 #24937626

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3495C211yesmaximal, characteristic
2C43×#2924C211yesmaximal, characteristic, complemented
3C43×#2343C211yesmaximal, characteristic, complemented
4C43×#1521C211yesmaximal, characteristic, complemented
5C43×#1518C211yesmaximal, characteristic, complemented
6C43×#1516C211yesmaximal, characteristic
7C43×#1515C211yesmaximal, characteristic, complemented
8C43×#1512C211yesmaximal, characteristic, complemented
9C43×#1511C211yesmaximal, characteristic, complemented
10C43×#1509C211yesmaximal, characteristic, complemented
11C43×#1506C211yesmaximal, characteristic, complemented
12C43×#1504C211yesmaximal, characteristic
13C43×#1503C211yesmaximal, characteristic, complemented
14C43×#1500C211yesmaximal, characteristic, complemented
15C2×C43×#328C211yesmaximal, characteristic, complemented
16C43×#556—21no—
17C43×#554—21no—
18C43×#552—21no—
19C43×#552—21no—
20C43×#552—21no—
21C43×#552—21no—
22C43×#551—21no—
23C43×#551—21no—
24C43×#544C411yescharacteristic, complemented
25C43×#542C411yescharacteristic, complemented
26C43×#542C411yescharacteristic, complemented
27C43×#541C411yescharacteristic, complemented
28C43×#541C411yescharacteristic, complemented
29C43×#536C411yescharacteristic, complemented
30C43×#533C2211yescharacteristic
31C43×#533C2211yescharacteristic
32C43×#529C2211yescharacteristic
33C43×#529C2211yescharacteristic
34C43×#525C2211yescharacteristic
35C2×C22⋊Q8×C43C2211yescharacteristic
36C43×#520C411yescharacteristic, complemented
37C43×#519C411yescharacteristic, complemented
38C2×#117×C43C2211yescharacteristic
39C43×#433—21no—
40C43×#433—21no—
41C43×#432C2211yescharacteristic
42C43×#432C2211yescharacteristic
43C43×#431C2211yescharacteristic
44C43×#431C2211yescharacteristic
45C43×#424—21no—
46C43×#407C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#405—21no—
49C43×#387—21no—
50C43×#387—21no—
51C43×#385—21no—
52C43×#383C2211yescharacteristic
53C43×#382C2211yescharacteristic
54C43×#381C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C4×C22⋊C4×C43—21no—
57C43×#376C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C43×#328C2211yescharacteristic
60C43×#328C2211yescharacteristic
61C43×#328C2211yescharacteristic
62C43×#328C2211yescharacteristic
63C43×#328C2211yescharacteristic
64C43×#328C2211yescharacteristic
65C43×#328C2211yescharacteristic
66C43×#328C2211yescharacteristic
67C43×#328C2211yescharacteristic
68C43×#328C2211yescharacteristic
69C43×#328C2211yescharacteristic
70C43×#328C2211yescharacteristic
71C43×#327C2211yescharacteristic
72C43×#327C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#41×C43C2×C411yescharacteristic
76C22×Q8×C43C2×C411yescharacteristic
77C23×C4×C43—21no—
78C23×C4×C43C2311yescharacteristic
79C2×M16×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43C2×C411yescharacteristic, complemented
83C4⋊Q8×C43C2×C411yescharacteristic, complemented
84C4⋊Q8×C43C2×C411yescharacteristic, complemented
85C4⋊Q8×C43C2×C411yescharacteristic, complemented
86#126×C43—21no—
87#126×C43—21no—
88#126×C43—21no—
89#126×C43—21no—
90#126×C43—21no—
91#126×C43—21no—
92#126×C43—21no—
93#126×C43—21no—
94#125×C43—21no—
95#125×C43—21no—
96#125×C43—21no—
97#125×C43—21no—
98#125×C43—21no—
99#125×C43—21no—
100#125×C43—21no—
101#125×C43C2×C411yescharacteristic, complemented
102#125×C43C2×C411yescharacteristic, complemented
103#124×C43—21no—
104#124×C43—21no—
105#124×C43C2×C411yescharacteristic, complemented
106#124×C43C2×C411yescharacteristic, complemented
107#123×C43—21no—
108#123×C43—21no—
109#123×C43—21no—
110#123×C43—21no—
111#123×C43—21no—
112#123×C43—21no—
113#123×C43—21no—
114C22⋊Q8×C43—21no—
115C22⋊Q8×C43—21no—
116C22⋊Q8×C43—21no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43C2×C411yescharacteristic
125C22⋊Q8×C43C2×C411yescharacteristic
126C22⋊Q8×C43C2×C411yescharacteristic
127C22⋊Q8×C43C2311yescharacteristic
128C22⋊Q8×C43C2311yescharacteristic
129C22⋊Q8×C43C2311yescharacteristic
130#121×C43C2×C411yescharacteristic
131#121×C43C2311yescharacteristic
132#120×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135C4×Q8×C43—21no—
136C4×Q8×C43—21no—
137C4×Q8×C43C2×C411yescharacteristic, complemented
138C4×Q8×C43C2×C411yescharacteristic, complemented
139C4×Q8×C43C2×C411yescharacteristic, complemented
140C4×Q8×C43C2×C411yescharacteristic, complemented
141C4×Q8×C43C2×C411yescharacteristic, complemented
142C4×Q8×C43C2×C411yescharacteristic, complemented
143C4×D4×C43—21no—
144C4×D4×C43—21no—
145C4×D4×C43—21no—
146C4×D4×C43—21no—
147C4×D4×C43—21no—
148C4×D4×C43—21no—
149C4×D4×C43C2×C411yescharacteristic, complemented
150C4×D4×C43C2×C411yescharacteristic, complemented
151#117×C43—21no—
152#117×C43—21no—
153#117×C43—21no—
154#117×C43—21no—
155#117×C43—21no—
156#117×C43—21no—
157#117×C43—21no—
158#117×C43C2×C411yescharacteristic
159#117×C43C2×C411yescharacteristic
160#117×C43C2×C411yescharacteristic
161#117×C43C2×C411yescharacteristic
162#117×C43C2×C411yescharacteristic
163#117×C43D411yescharacteristic
164#117×C43D411yescharacteristic
165#117×C43D411yescharacteristic
166#117×C43D411yescharacteristic
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43C2×C411yescharacteristic
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C4⋊C4×C43D411yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43D411yescharacteristic
177C2×C22⋊C4×C43D411yescharacteristic
178C2×C42×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43—21no—
183C4⋊C8×C43—21no—
184C4⋊C8×C43—21no—
185C4⋊C8×C43—21no—
186C22⋊C8×C43—21no—
187C22⋊C8×C43—21no—
188C22⋊C8×C43C2311yescharacteristic
189C22⋊C8×C43C2311yescharacteristic
190C22⋊C8×C43C2311yescharacteristic
191C22⋊C8×C43C2311yescharacteristic
192#97×C43—21no—
193#97×C43—21no—
194C4×C8×C43—21no—
195C4×C8×C43—21no—
196#95×C43—21no—
197#95×C43—21no—
198#95×C43—21no—
199#95×C43—21no—
200#95×C43—21no—
201#95×C43—21no—
202#95×C43C2311yescharacteristic
203#95×C43C2311yescharacteristic
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43C2×D411yescharacteristic
207#41×C43—42no—
208C2×Q8×C43—21no—
209C2×Q8×C43—21no—
210C2×Q8×C43—21no—
211C2×Q8×C43—42no—
212C2×Q8×C43C22×C411yescharacteristic
213C2×Q8×C43C22×C411yescharacteristic
214C2×Q8×C43C22×C411yescharacteristic
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43C22×C411yescharacteristic
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—42no—
229C22×C4×C43—42no—
230C22×C4×C43—42no—
231C22×C4×C43—81no—
232C22×C4×C43C22×C411yescharacteristic
233C22×C4×C43C22×C411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2411yescharacteristic
242M16×C43—42no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—42no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—42no—
272C4⋊C4×C43—81no—
273C4⋊C4×C43C22⋊C411yescharacteristic
274C4⋊C4×C43C22⋊C411yescharacteristic
275C4⋊C4×C43C22⋊C411yescharacteristic
276C4⋊C4×C43C22⋊C411yescharacteristic
277C4⋊C4×C43C22⋊C411yescharacteristic
278C4⋊C4×C43C22⋊C411yescharacteristic
279C4⋊C4×C43C22⋊C411yescharacteristic
280C4⋊C4×C43C22⋊C411yescharacteristic
281C4⋊C4×C43C22×C411yescharacteristic
282C4⋊C4×C43C22×C411yescharacteristic
283C4⋊C4×C43C22×C411yescharacteristic
284C4⋊C4×C43C22×C411yescharacteristic
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—21no—
295C22⋊C4×C43—21no—
296C22⋊C4×C43—21no—
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—42no—
301C22⋊C4×C43C22⋊C411yescharacteristic
302C22⋊C4×C43C22⋊C411yescharacteristic
303C22⋊C4×C43C22⋊C411yescharacteristic
304C22⋊C4×C43C22⋊C411yescharacteristic
305C22⋊C4×C43C22⋊C411yescharacteristic
306C22⋊C4×C43C22⋊C411yescharacteristic
307C22⋊C4×C43C22⋊C411yescharacteristic
308C22⋊C4×C43C22⋊C411yescharacteristic
309C42×C43—21no—
310C42×C43—21no—
311C42×C43—21no—
312C42×C43—21no—
313C42×C43—21no—
314C42×C43—21no—
315C42×C43—21no—
316C42×C43—42no—
317C42×C43—81no—
318C42×C43C22×C411yescharacteristic
319C42×C43C22×C411yescharacteristic
320C42×C43C22×C411yescharacteristic
321C42×C43C22×C411yescharacteristic
322C42×C43C2×D411yescharacteristic
323C42×C43C2×D411yescharacteristic
324C42×C43C2×D411yescharacteristic
325C42×C43C2×D411yescharacteristic
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—22no—
329C23×C43—21no—
330C23×C43—41no—
331C23×C43C2×C22⋊C411yescharacteristic
332C23×C43C2×C22⋊C411yescharacteristic
333C23×C43C22×D411yescharacteristic
334Q8×C43—41no—
335Q8×C43—41no—
336Q8×C43—41no—
337Q8×C43—42no—
338Q8×C43—81no—
339Q8×C43—81no—
340D4×C43—41no—
341D4×C43—41no—
342D4×C43—41no—
343D4×C43—42no—
344D4×C43—81no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
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—42no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—42no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—81no—
379C2×C4×C43—81no—
380C2×C4×C43—81no—
381C2×C4×C43—84no—
382C2×C4×C43C2×C22⋊C411yescharacteristic
383C2×C4×C43C2×C22⋊C411yescharacteristic
384C2×C4×C43C2×C22⋊C411yescharacteristic
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C2×C22⋊C411yescharacteristic
388C2×C4×C43C2×C22⋊C411yescharacteristic
389C2×C4×C43C2×C22⋊C411yescharacteristic
390C2×C4×C43C2×C22⋊C411yescharacteristic
391C2×C4×C43C2×C22⋊C411yescharacteristic
392C2×C4×C43C23×C411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C8×C43—41no—
395C8×C43—41no—
396C8×C43—41no—
397C8×C43—41no—
398#17609C4311yesmaximal, characteristic, direct product factor, Sylow
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43#41012yes—
412C22×C43C22×C22⋊C411yescharacteristic
413C22×C43#57711yescharacteristic
414C22×C43#57811yescharacteristic
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—21no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—42no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43—41no—
431C4×C43—41no—
432C4×C43—41no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43—81no—
436C4×C43—81no—
437C4×C43—81no—
438#3495C2×C4311yescharacteristic
439#2924C2×C4311yescharacteristic, complemented
440#2343C2×C4311yescharacteristic, complemented
441#1521C2×C4311yescharacteristic, complemented
442#1518C2×C4311yescharacteristic, complemented
443#1516C2×C4311yescharacteristic
444#1515C2×C4311yescharacteristic, complemented
445#1512C2×C4311yescharacteristic, complemented
446#1511C2×C4311yescharacteristic, complemented
447#1509C2×C4311yescharacteristic, complemented
448#1506C2×C4311yescharacteristic, complemented
449#1504C2×C4311yescharacteristic
450#1503C2×C4311yescharacteristic, complemented
451#1500C2×C4311yescharacteristic, complemented
452C2×#328C2×C4311yescharacteristic, complemented
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—22no—
456C2×C43—41no—
457C2×C43—81no—
458C2×C43C2×#41011yescharacteristic
459C2×C43#289811yescharacteristic
460C2×C43#290111yescharacteristic
461#556—21no—
462#554—21no—
463#552—21no—
464#552—21no—
465#552—21no—
466#552—21no—
467#551—21no—
468#551—21no—
469#544C4×C4311yescharacteristic, complemented
470#542C4×C4311yescharacteristic, complemented
471#542C4×C4311yescharacteristic, complemented
472#541C4×C4311yescharacteristic, complemented
473#541C4×C4311yescharacteristic, complemented
474#536C4×C4311yescharacteristic, complemented
475#533C22×C4311yescharacteristic
476#533C22×C4311yescharacteristic
477#529C22×C4311yescharacteristic
478#529C22×C4311yescharacteristic
479#525C22×C4311yescharacteristic
480C2×C22⋊Q8C22×C4311yescharacteristic
481#520C4×C4311yescharacteristic, complemented
482#519C4×C4311yescharacteristic, complemented
483C2×#117C22×C4311yescharacteristic
484#433—21no—
485#433—21no—
486#432C22×C4311yescharacteristic
487#432C22×C4311yescharacteristic
488#431C22×C4311yescharacteristic
489#431C22×C4311yescharacteristic
490#424—21no—
491#407C22×C4311yescharacteristic
492C2×C22⋊C8C22×C4311yescharacteristic
493#405—21no—
494#387—21no—
495#387—21no—
496#385—21no—
497#383C22×C4311yescharacteristic
498#382C22×C4311yescharacteristic
499#381C22×C4311yescharacteristic
500C4×C4⋊C4C22×C4311yescharacteristic
501C4×C22⋊C4—21no—
502#376C22×C4311yescharacteristic
503C2×#95C22×C4311yescharacteristic
504#328C22×C4311yescharacteristic
505#328C22×C4311yescharacteristic
506#328C22×C4311yescharacteristic
507#328C22×C4311yescharacteristic
508#328C22×C4311yescharacteristic
509#328C22×C4311yescharacteristic
510#328C22×C4311yescharacteristic
511#328C22×C4311yescharacteristic
512#328C22×C4311yescharacteristic
513#328C22×C4311yescharacteristic
514#328C22×C4311yescharacteristic
515#328C22×C4311yescharacteristic
516#327C22×C4311yescharacteristic
517#327C22×C4311yescharacteristic
518#327C22×C4311yescharacteristic
519#327C22×C4311yescharacteristic
520C43#1760911yescharacteristic, direct product factor, Sylow
521C2×#41C2×C4×C4311yescharacteristic
522C22×Q8C2×C4×C4311yescharacteristic
523C23×C4—21no—
524C23×C4C23×C4311yescharacteristic
525C2×M16—21no—
526C22×C8—21no—
527C4⋊Q8—21no—
528C4⋊Q8C2×C4×C4311yescharacteristic, complemented
529C4⋊Q8C2×C4×C4311yescharacteristic, complemented
530C4⋊Q8C2×C4×C4311yescharacteristic, complemented
531C4⋊Q8C2×C4×C4311yescharacteristic, complemented
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125C2×C4×C4311yescharacteristic, complemented
548#125C2×C4×C4311yescharacteristic, complemented
549#124—21no—
550#124—21no—
551#124C2×C4×C4311yescharacteristic, complemented
552#124C2×C4×C4311yescharacteristic, complemented
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8C2×C4×C4311yescharacteristic
571C22⋊Q8C2×C4×C4311yescharacteristic
572C22⋊Q8C2×C4×C4311yescharacteristic
573C22⋊Q8C23×C4311yescharacteristic
574C22⋊Q8C23×C4311yescharacteristic
575C22⋊Q8C23×C4311yescharacteristic
576#121C2×C4×C4311yescharacteristic
577#121C23×C4311yescharacteristic
578#120—21no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8C2×C4×C4311yescharacteristic, complemented
584C4×Q8C2×C4×C4311yescharacteristic, complemented
585C4×Q8C2×C4×C4311yescharacteristic, complemented
586C4×Q8C2×C4×C4311yescharacteristic, complemented
587C4×Q8C2×C4×C4311yescharacteristic, complemented
588C4×Q8C2×C4×C4311yescharacteristic, complemented
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4C2×C4×C4311yescharacteristic, complemented
596C4×D4C2×C4×C4311yescharacteristic, complemented
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117C2×C4×C4311yescharacteristic
605#117C2×C4×C4311yescharacteristic
606#117C2×C4×C4311yescharacteristic
607#117C2×C4×C4311yescharacteristic
608#117C2×C4×C4311yescharacteristic
609#117D4×C4311yescharacteristic
610#117D4×C4311yescharacteristic
611#117D4×C4311yescharacteristic
612#117D4×C4311yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4C2×C4×C4311yescharacteristic
618C2×C4⋊C4D4×C4311yescharacteristic
619C2×C4⋊C4D4×C4311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C4311yescharacteristic
623C2×C22⋊C4D4×C4311yescharacteristic
624C2×C42—21no—
625C2×C42—21no—
626C2×C42C23×C4311yescharacteristic
627C2×C42C23×C4311yescharacteristic
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C4⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634C22⋊C8C23×C4311yescharacteristic
635C22⋊C8C23×C4311yescharacteristic
636C22⋊C8C23×C4311yescharacteristic
637C22⋊C8C23×C4311yescharacteristic
638#97—21no—
639#97—21no—
640C4×C8—21no—
641C4×C8—21no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646#95—21no—
647#95—21no—
648#95C23×C4311yescharacteristic
649#95C23×C4311yescharacteristic
650#95C23×C4311yescharacteristic
651#95C23×C4311yescharacteristic
652C24C2×D4×C4311yescharacteristic
653#41—42no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—42no—
658C2×Q8C22×C4×C4311yescharacteristic
659C2×Q8C22×C4×C4311yescharacteristic
660C2×Q8C22×C4×C4311yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22×C4×C4311yescharacteristic
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—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4C22×C4×C4311yescharacteristic
679C22×C4C22×C4×C4311yescharacteristic
680C22×C4C2×D4×C4311yescharacteristic
681C22×C4C2×D4×C4311yescharacteristic
682C22×C4C2×D4×C4311yescharacteristic
683C22×C4C2×D4×C4311yescharacteristic
684C22×C4C2×D4×C4311yescharacteristic
685C22×C4C2×D4×C4311yescharacteristic
686C22×C4C2×D4×C4311yescharacteristic
687C22×C4C24×C4311yescharacteristic
688M16—42no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—81no—
719C4⋊C4C22⋊C4×C4311yescharacteristic
720C4⋊C4C22⋊C4×C4311yescharacteristic
721C4⋊C4C22⋊C4×C4311yescharacteristic
722C4⋊C4C22⋊C4×C4311yescharacteristic
723C4⋊C4C22⋊C4×C4311yescharacteristic
724C4⋊C4C22⋊C4×C4311yescharacteristic
725C4⋊C4C22⋊C4×C4311yescharacteristic
726C4⋊C4C22⋊C4×C4311yescharacteristic
727C4⋊C4C22×C4×C4311yescharacteristic
728C4⋊C4C22×C4×C4311yescharacteristic
729C4⋊C4C22×C4×C4311yescharacteristic
730C4⋊C4C22×C4×C4311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—42no—
747C22⋊C4C22⋊C4×C4311yescharacteristic
748C22⋊C4C22⋊C4×C4311yescharacteristic
749C22⋊C4C22⋊C4×C4311yescharacteristic
750C22⋊C4C22⋊C4×C4311yescharacteristic
751C22⋊C4C22⋊C4×C4311yescharacteristic
752C22⋊C4C22⋊C4×C4311yescharacteristic
753C22⋊C4C22⋊C4×C4311yescharacteristic
754C22⋊C4C22⋊C4×C4311yescharacteristic
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—42no—
763C42—81no—
764C42C22×C4×C4311yescharacteristic
765C42C22×C4×C4311yescharacteristic
766C42C22×C4×C4311yescharacteristic
767C42C22×C4×C4311yescharacteristic
768C42C2×D4×C4311yescharacteristic
769C42C2×D4×C4311yescharacteristic
770C42C2×D4×C4311yescharacteristic
771C42C2×D4×C4311yescharacteristic
772C23—21no—
773C23—21no—
774C23—22no—
775C23—21no—
776C23—41no—
777C23C2×C22⋊C4×C4311yescharacteristic
778C23C2×C22⋊C4×C4311yescharacteristic
779C23C22×D4×C4311yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—42no—
784Q8—81no—
785Q8—81no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—42no—
790D4—81no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C4311yescharacteristic
829C2×C4C2×C22⋊C4×C4311yescharacteristic
830C2×C4C2×C22⋊C4×C4311yescharacteristic
831C2×C4C2×C22⋊C4×C4311yescharacteristic
832C2×C4C2×C22⋊C4×C4311yescharacteristic
833C2×C4C2×C22⋊C4×C4311yescharacteristic
834C2×C4C2×C22⋊C4×C4311yescharacteristic
835C2×C4C2×C22⋊C4×C4311yescharacteristic
836C2×C4C2×C22⋊C4×C4311yescharacteristic
837C2×C4C2×C22⋊C4×C4311yescharacteristic
838C2×C4C23×C4×C4311yescharacteristic
839C2×C4C22×D4×C4311yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22C43×#41012yes—
857C22C22×C22⋊C4×C4311yescharacteristic
858C22C43×#57711yescharacteristic
859C22C43×#57811yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—81no—
881C4—81no—
882C4—81no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—81no—
888C2C2×C43×#41011yescharacteristic
889C2C43×#289811yescharacteristic
890C2C43×#290111yescharacteristic
subgroupG/H
center, socleC22×C43C22×C22⋊C4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC43×#525C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2924C2semidirect
3. C43×#2343C2semidirect
4. C43×#1521C2semidirect
5. C43×#1518C2semidirect
7. C43×#1515C2semidirect
8. C43×#1512C2semidirect
9. C43×#1511C2semidirect
10. C43×#1509C2semidirect
11. C43×#1506C2semidirect
13. C43×#1503C2semidirect
14. C43×#1500C2semidirect
15. C2×C43×#328C2semidirect
24. C43×#544C4semidirect
25. C43×#542C4semidirect
26. C43×#542C4semidirect
27. C43×#541C4semidirect
28. C43×#541C4semidirect
29. C43×#536C4semidirect
36. C43×#520C4semidirect
37. C43×#519C4semidirect
82. C4⋊Q8×C43C2×C4semidirect
83. C4⋊Q8×C43C2×C4semidirect
84. C4⋊Q8×C43C2×C4semidirect
85. C4⋊Q8×C43C2×C4semidirect
101. #125×C43C2×C4semidirect
102. #125×C43C2×C4semidirect
105. #124×C43C2×C4semidirect
106. #124×C43C2×C4semidirect
137. C4×Q8×C43C2×C4semidirect
138. C4×Q8×C43C2×C4semidirect
139. C4×Q8×C43C2×C4semidirect
140. C4×Q8×C43C2×C4semidirect
141. C4×Q8×C43C2×C4semidirect
142. C4×Q8×C43C2×C4semidirect
149. C4×D4×C43C2×C4semidirect
150. C4×D4×C43C2×C4semidirect
398. #17609C43direct (N × H)
439. #2924C2×C43semidirect
440. #2343C2×C43semidirect
441. #1521C2×C43semidirect
442. #1518C2×C43semidirect
444. #1515C2×C43semidirect
445. #1512C2×C43semidirect
446. #1511C2×C43semidirect
447. #1509C2×C43semidirect
448. #1506C2×C43semidirect
450. #1503C2×C43semidirect
451. #1500C2×C43semidirect
452. C2×#328C2×C43semidirect
469. #544C4×C43semidirect
470. #542C4×C43semidirect
471. #542C4×C43semidirect
472. #541C4×C43semidirect
473. #541C4×C43semidirect
474. #536C4×C43semidirect
481. #520C4×C43semidirect
482. #519C4×C43semidirect
520. C43#17609direct (N × H)
528. C4⋊Q8C2×C4×C43semidirect
529. C4⋊Q8C2×C4×C43semidirect
530. C4⋊Q8C2×C4×C43semidirect
531. C4⋊Q8C2×C4×C43semidirect
547. #125C2×C4×C43semidirect
548. #125C2×C4×C43semidirect
551. #124C2×C4×C43semidirect
552. #124C2×C4×C43semidirect
583. C4×Q8C2×C4×C43semidirect
584. C4×Q8C2×C4×C43semidirect
585. C4×Q8C2×C4×C43semidirect
586. C4×Q8C2×C4×C43semidirect
587. C4×Q8C2×C4×C43semidirect
588. C4×Q8C2×C4×C43semidirect
595. C4×D4C2×C4×C43semidirect
596. C4×D4C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34952
C43×#29242
C43×#23432
C43×#15212
C43×#15182
C43×#15162
C43×#15152
C43×#15122
C43×#15112
C43×#15092
C43×#15062
C43×#15042
C43×#15032
C43×#15002
C2×C43×#3282
#1760943