Finite Group Databasebeta

← C43×#22144 #24942161

Subgroups — C43×#22144 #24942161

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#435C211yesmaximal, characteristic, complemented
2C2×C43×#433C211yesmaximal, characteristic, complemented
3C43×#2392C211yesmaximal, characteristic
4C43×#1955C211yesmaximal, characteristic, complemented
5C43×#1954C211yesmaximal, characteristic, complemented
6C43×#1954C211yesmaximal, characteristic, complemented
7C43×#1939C211yesmaximal, characteristic, complemented
8C43×#1924C211yesmaximal, characteristic, complemented
9C43×#1923C211yesmaximal, characteristic, complemented
10C43×#1870C211yesmaximal, characteristic, complemented
11C43×#1869C211yesmaximal, characteristic, complemented
12C43×#1851C211yesmaximal, characteristic, complemented
13C43×#1850C211yesmaximal, characteristic, complemented
14C43×#1798C211yesmaximal, characteristic, complemented
15C43×#1771C211yesmaximal, characteristic, complemented
16C22×M16×C43C2211yescharacteristic
17C23×C8×C43C2211yescharacteristic
18C2×C4×D4×C43C2211yescharacteristic
19C2×C4×D4×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C2×#117×C43C2211yescharacteristic
22C43×#435—24no—
23C43×#433—24no—
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C22⋊C8×C43C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×C22⋊C8×C43C2211yescharacteristic
34C2×C22⋊C8×C43C2211yescharacteristic
35C2×C22⋊C8×C43C2211yescharacteristic
36C2×C22⋊C8×C43C2211yescharacteristic
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×#97×C43C2211yescharacteristic
41C2×#97×C43C2211yescharacteristic
42C2×C4×C8×C43C2211yescharacteristic
43C2×C4×C8×C43C2211yescharacteristic
44C43×#398C411yescharacteristic
45C43×#397C411yescharacteristic
46C43×#396C411yescharacteristic
47C43×#396C411yescharacteristic
48C43×#394C411yescharacteristic
49C43×#394C411yescharacteristic
50C43×#394C411yescharacteristic
51C43×#392C411yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C4×C22⋊C4×C43C2211yescharacteristic
54C4×C22⋊C4×C43C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D4×C43C2×C411yescharacteristic
62C22×D4×C43C2×C411yescharacteristic
63C22×D4×C43C2×C411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C23×C4×C43C2311yescharacteristic
67C2×M16×C43—22no—
68C2×M16×C43—41no—
69C2×M16×C43—41no—
70C22×C8×C43—22no—
71C22×C8×C43—41no—
72C22×C8×C43—41no—
73C22×C8×C43C2311yescharacteristic
74C22×C8×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C22×C8×C43C2311yescharacteristic
77C22×C8×C43C2311yescharacteristic
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C4×D4×C43—22no—
82C4×D4×C43—22no—
83C4×D4×C43—41no—
84C4×D4×C43—41no—
85C4×D4×C43—41no—
86C4×D4×C43—41no—
87#117×C43—22no—
88#117×C43—22no—
89C2×C4⋊C4×C43C2×C411yescharacteristic
90C2×C4⋊C4×C43C2×C411yescharacteristic
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C4⋊C4×C43C2×C411yescharacteristic
93C2×C4⋊C4×C43C2×C411yescharacteristic
94C2×C4⋊C4×C43C2×C411yescharacteristic
95C2×C4⋊C4×C43C2×C411yescharacteristic
96C2×C22⋊C4×C43C2×C411yescharacteristic
97C2×C22⋊C4×C43C2×C411yescharacteristic
98C2×C22⋊C4×C43C2×C411yescharacteristic
99C2×C22⋊C4×C43C2×C411yescharacteristic
100C2×C22⋊C4×C43C2×C411yescharacteristic
101C2×C22⋊C4×C43C2×C411yescharacteristic
102C2×C22⋊C4×C43C2×C411yescharacteristic
103C2×C22⋊C4×C43C2×C411yescharacteristic
104C2×C22⋊C4×C43C2×C411yescharacteristic
105C2×C22⋊C4×C43C2×C411yescharacteristic
106C2×C22⋊C4×C43C2×C411yescharacteristic
107C2×C22⋊C4×C43C2×C411yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C4⋊C8×C43—22no—
113C4⋊C8×C43—22no—
114C4⋊C8×C43—22no—
115C4⋊C8×C43—22no—
116C4⋊C8×C43—41no—
117C4⋊C8×C43—41no—
118C22⋊C8×C43—22no—
119C22⋊C8×C43—22no—
120C22⋊C8×C43—22no—
121C22⋊C8×C43—22no—
122C22⋊C8×C43—41no—
123C22⋊C8×C43—41no—
124C22⋊C8×C43—41no—
125C22⋊C8×C43—41no—
126C22⋊C8×C43—41no—
127C22⋊C8×C43—41no—
128#97×C43—41no—
129#97×C43D414yescomplemented
130C4×C8×C43—22no—
131C4×C8×C43—41no—
132#95×C43C2×C411yescharacteristic
133#95×C43C2×C411yescharacteristic
134#95×C43C2×C411yescharacteristic
135#95×C43C2×C411yescharacteristic
136#95×C43C2×C411yescharacteristic
137#95×C43C2×C411yescharacteristic
138C24×C43C22×C411yescharacteristic
139C24×C43C22×C411yescharacteristic
140C24×C43C22×C411yescharacteristic
141C2×D4×C43—22no—
142C2×D4×C43—22no—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—41no—
146C2×D4×C43—41no—
147C2×D4×C43—41no—
148C2×D4×C43—41no—
149C2×D4×C43—41no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
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×C43C22×C411yescharacteristic
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C22×C411yescharacteristic
175C22×C4×C43C22×C411yescharacteristic
176C22×C4×C43C22×C411yescharacteristic
177C22×C4×C43C22×C411yescharacteristic
178C22×C4×C43C22×C411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180M16×C43—44no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—44no—
204C2×C8×C43C2×D412yes—
205C2×C8×C43C2×D412yes—
206C4⋊C4×C43—22no—
207C4⋊C4×C43—22no—
208C4⋊C4×C43—22no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—41no—
211C4⋊C4×C43—41no—
212C4⋊C4×C43—41no—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—41no—
220C22⋊C4×C43—41no—
221C22⋊C4×C43—41no—
222C22⋊C4×C43—41no—
223C22⋊C4×C43—41no—
224C22⋊C4×C43—41no—
225C42×C43—21no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43C2×D412yes—
232C42×C43#4112yes—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43#13112yes—
254C23×C43C23×C411yescharacteristic
255D4×C43—44no—
256D4×C43—44no—
257D4×C43—44no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
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—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
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×C43C4×D412yes—
301C2×C4×C43C4×D412yes—
302C2×C4×C43#13112yes—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C2×C4×C432−1+411yescharacteristic
309C8×C43—22no—
310C8×C43—22no—
311C8×C43—41no—
312C8×C43—41no—
313C8×C43—41no—
314C8×C43—41no—
315C8×C43—41no—
316C8×C43—41no—
317#22144C4311yesmaximal, characteristic, direct product factor, Sylow
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43C2×C4×D411yescharacteristic
340C22×C43#51811yescharacteristic
341C22×C43#52011yescharacteristic
342C22×C43C2×#13111yescharacteristic
343C22×C43C2×#13111yescharacteristic
344C22×C43#56811yescharacteristic
345C22×C43#56811yescharacteristic
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—41no—
350C4×C43—41no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—41no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43#53511yescharacteristic
358C4×C43#53711yescharacteristic
359C4×C43#54011yescharacteristic
360C4×C43#54211yescharacteristic
361C2×#435C2×C4311yescharacteristic, complemented
362C2×#433C2×C4311yescharacteristic, complemented
363#2392C2×C4311yescharacteristic
364#1955C2×C4311yescharacteristic, complemented
365#1954C2×C4311yescharacteristic, complemented
366#1954C2×C4311yescharacteristic, complemented
367#1939C2×C4311yescharacteristic, complemented
368#1924C2×C4311yescharacteristic, complemented
369#1923C2×C4311yescharacteristic, complemented
370#1870C2×C4311yescharacteristic, complemented
371#1869C2×C4311yescharacteristic, complemented
372#1851C2×C4311yescharacteristic, complemented
373#1850C2×C4311yescharacteristic, complemented
374#1798C2×C4311yescharacteristic, complemented
375#1771C2×C4311yescharacteristic, complemented
376C2×C43—42no—
377C2×C43—81no—
378C2×C43—81no—
379C2×C43#232411yescharacteristic
380C2×C43#293311yescharacteristic
381C2×C43#293511yescharacteristic
382C2×C43#297711yescharacteristic
383C2×C43#297811yescharacteristic
384C2×C43#299211yescharacteristic
385C2×C43#299311yescharacteristic
386C22×M16C22×C4311yescharacteristic
387C23×C8C22×C4311yescharacteristic
388C2×C4×D4C22×C4311yescharacteristic
389C2×C4×D4C22×C4311yescharacteristic
390C2×C4×D4C22×C4311yescharacteristic
391C2×#117C22×C4311yescharacteristic
392#435—24no—
393#433—24no—
394C2×C4⋊C8C22×C4311yescharacteristic
395C2×C4⋊C8C22×C4311yescharacteristic
396C2×C4⋊C8C22×C4311yescharacteristic
397C2×C4⋊C8C22×C4311yescharacteristic
398C2×C4⋊C8C22×C4311yescharacteristic
399C2×C4⋊C8C22×C4311yescharacteristic
400C2×C22⋊C8C22×C4311yescharacteristic
401C2×C22⋊C8C22×C4311yescharacteristic
402C2×C22⋊C8C22×C4311yescharacteristic
403C2×C22⋊C8C22×C4311yescharacteristic
404C2×C22⋊C8C22×C4311yescharacteristic
405C2×C22⋊C8C22×C4311yescharacteristic
406C2×C22⋊C8C22×C4311yescharacteristic
407C2×C22⋊C8C22×C4311yescharacteristic
408C2×C22⋊C8C22×C4311yescharacteristic
409C2×C22⋊C8C22×C4311yescharacteristic
410C2×#97C22×C4311yescharacteristic
411C2×#97C22×C4311yescharacteristic
412C2×C4×C8C22×C4311yescharacteristic
413C2×C4×C8C22×C4311yescharacteristic
414#398C4×C4311yescharacteristic
415#397C4×C4311yescharacteristic
416#396C4×C4311yescharacteristic
417#396C4×C4311yescharacteristic
418#394C4×C4311yescharacteristic
419#394C4×C4311yescharacteristic
420#394C4×C4311yescharacteristic
421#392C4×C4311yescharacteristic
422C4×C4⋊C4C22×C4311yescharacteristic
423C4×C22⋊C4C22×C4311yescharacteristic
424C4×C22⋊C4C22×C4311yescharacteristic
425#336C22×C4311yescharacteristic
426#336C22×C4311yescharacteristic
427#336C22×C4311yescharacteristic
428#336C22×C4311yescharacteristic
429#336C22×C4311yescharacteristic
430#336C22×C4311yescharacteristic
431C43#2214411yescharacteristic, direct product factor, Sylow
432C22×D4C2×C4×C4311yescharacteristic
433C22×D4C2×C4×C4311yescharacteristic
434C22×D4C2×C4×C4311yescharacteristic
435C23×C4C23×C4311yescharacteristic
436C23×C4C23×C4311yescharacteristic
437C23×C4C23×C4311yescharacteristic
438C2×M16—22no—
439C2×M16—41no—
440C2×M16—41no—
441C22×C8—22no—
442C22×C8—41no—
443C22×C8—41no—
444C22×C8C23×C4311yescharacteristic
445C22×C8C23×C4311yescharacteristic
446C22×C8C23×C4311yescharacteristic
447C22×C8C23×C4311yescharacteristic
448C22×C8C23×C4311yescharacteristic
449C22×C8C23×C4311yescharacteristic
450C22×C8C23×C4311yescharacteristic
451C22×C8C23×C4311yescharacteristic
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458#117—22no—
459#117—22no—
460C2×C4⋊C4C2×C4×C4311yescharacteristic
461C2×C4⋊C4C2×C4×C4311yescharacteristic
462C2×C4⋊C4C2×C4×C4311yescharacteristic
463C2×C4⋊C4C2×C4×C4311yescharacteristic
464C2×C4⋊C4C2×C4×C4311yescharacteristic
465C2×C4⋊C4C2×C4×C4311yescharacteristic
466C2×C4⋊C4C2×C4×C4311yescharacteristic
467C2×C22⋊C4C2×C4×C4311yescharacteristic
468C2×C22⋊C4C2×C4×C4311yescharacteristic
469C2×C22⋊C4C2×C4×C4311yescharacteristic
470C2×C22⋊C4C2×C4×C4311yescharacteristic
471C2×C22⋊C4C2×C4×C4311yescharacteristic
472C2×C22⋊C4C2×C4×C4311yescharacteristic
473C2×C22⋊C4C2×C4×C4311yescharacteristic
474C2×C22⋊C4C2×C4×C4311yescharacteristic
475C2×C22⋊C4C2×C4×C4311yescharacteristic
476C2×C22⋊C4C2×C4×C4311yescharacteristic
477C2×C22⋊C4C2×C4×C4311yescharacteristic
478C2×C22⋊C4C2×C4×C4311yescharacteristic
479C2×C42C23×C4311yescharacteristic
480C2×C42C23×C4311yescharacteristic
481C2×C42C23×C4311yescharacteristic
482C2×C42C23×C4311yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8—41no—
488C4⋊C8—41no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496C22⋊C8—41no—
497C22⋊C8—41no—
498C22⋊C8—41no—
499#97—41no—
500#97D4×C4314yescomplemented
501C4×C8—22no—
502C4×C8—41no—
503#95C2×C4×C4311yescharacteristic
504#95C2×C4×C4311yescharacteristic
505#95C2×C4×C4311yescharacteristic
506#95C2×C4×C4311yescharacteristic
507#95C2×C4×C4311yescharacteristic
508#95C2×C4×C4311yescharacteristic
509C24C22×C4×C4311yescharacteristic
510C24C22×C4×C4311yescharacteristic
511C24C22×C4×C4311yescharacteristic
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C22×C4×C4311yescharacteristic
540C22×C4C22×C4×C4311yescharacteristic
541C22×C4C22×C4×C4311yescharacteristic
542C22×C4C22×C4×C4311yescharacteristic
543C22×C4C22×C4×C4311yescharacteristic
544C22×C4C22×C4×C4311yescharacteristic
545C22×C4C22×C4×C4311yescharacteristic
546C22×C4C22×C4×C4311yescharacteristic
547C22×C4C22×C4×C4311yescharacteristic
548C22×C4C22×C4×C4311yescharacteristic
549C22×C4C22×C4×C4311yescharacteristic
550C22×C4C24×C4311yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—44no—
575C2×C8C2×D4×C4312yes—
576C2×C8C2×D4×C4312yes—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42C2×D4×C4312yes—
603C42#41×C4312yes—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23#131×C4312yes—
625C23C23×C4×C4311yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4C4×D4×C4312yes—
672C2×C4C4×D4×C4312yes—
673C2×C4#131×C4312yes—
674C2×C4C22×D4×C4311yescharacteristic
675C2×C4C2×#41×C4311yescharacteristic
676C2×C4H(5,𝔽2)×C4311yescharacteristic
677C2×C4H(5,𝔽2)×C4311yescharacteristic
678C2×C4H(5,𝔽2)×C4311yescharacteristic
679C2×C42−1+4×C4311yescharacteristic
680C8—22no—
681C8—22no—
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C2×C4×D4×C4311yescharacteristic
710C22C43×#51811yescharacteristic
711C22C43×#52011yescharacteristic
712C22C2×#131×C4311yescharacteristic
713C22C2×#131×C4311yescharacteristic
714C22C43×#56811yescharacteristic
715C22C43×#56811yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4C43×#53511yescharacteristic
728C4C43×#53711yescharacteristic
729C4C43×#54011yescharacteristic
730C4C43×#54211yescharacteristic
731C2—42no—
732C2—81no—
733C2—81no—
734C2C43×#232411yescharacteristic
735C2C43×#293311yescharacteristic
736C2C43×#293511yescharacteristic
737C2C43×#297711yescharacteristic
738C2C43×#297811yescharacteristic
739C2C43×#299211yescharacteristic
740C2C43×#299311yescharacteristic
subgroupG/H
centerC22×C4×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC22×C4C24×C43
socleC23×C43C23×C4
prime radicalC43×#392C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#435C2semidirect
2. C2×C43×#433C2semidirect
4. C43×#1955C2semidirect
5. C43×#1954C2semidirect
6. C43×#1954C2semidirect
7. C43×#1939C2semidirect
8. C43×#1924C2semidirect
9. C43×#1923C2semidirect
10. C43×#1870C2semidirect
11. C43×#1869C2semidirect
12. C43×#1851C2semidirect
13. C43×#1850C2semidirect
14. C43×#1798C2semidirect
15. C43×#1771C2semidirect
129. #97×C43D4semidirect
317. #22144C43direct (N × H)
361. C2×#435C2×C43semidirect
362. C2×#433C2×C43semidirect
364. #1955C2×C43semidirect
365. #1954C2×C43semidirect
366. #1954C2×C43semidirect
367. #1939C2×C43semidirect
368. #1924C2×C43semidirect
369. #1923C2×C43semidirect
370. #1870C2×C43semidirect
371. #1869C2×C43semidirect
372. #1851C2×C43semidirect
373. #1850C2×C43semidirect
374. #1798C2×C43semidirect
375. #1771C2×C43semidirect
431. C43#22144direct (N × H)
500. #97D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4352
C2×C43×#4332
C43×#23922
C43×#19552
C43×#19542
C43×#19392
C43×#19242
C43×#19232
C43×#18702
C43×#18692
C43×#18512
C43×#18502
C43×#17982
C43×#17712
#2214443