Finite Group Databasebeta

← C43×#24512 #24944529

Subgroups — C43×#24512 #24944529

Order 11008.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#447C211yesmaximal, characteristic
2C2×C43×#433C211yesmaximal, characteristic, complemented
3C43×#2624C211yesmaximal, characteristic, complemented
4C43×#2309C211yesmaximal, characteristic, complemented
5C43×#2067C211yesmaximal, characteristic, complemented
6C43×#2065C211yesmaximal, characteristic, complemented
7C43×#2054C211yesmaximal, characteristic, complemented
8C43×#2054C211yesmaximal, characteristic, complemented
9C43×#1972C211yesmaximal, characteristic, complemented
10C43×#1970C211yesmaximal, characteristic, complemented
11C43×#1936C211yesmaximal, characteristic, complemented
12C43×#1934C211yesmaximal, characteristic, complemented
13C43×#1875C211yesmaximal, characteristic, complemented
14C43×#1854C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×#117×C43C2211yescharacteristic
21C2×#117×C43C2211yescharacteristic
22C43×#447—24no—
23C43×#433—24no—
24C2×#107×C43C2211yescharacteristic, complemented
25C2×#106×C43C2211yescharacteristic, complemented
26C2×C4⋊C8×C43C2211yescharacteristic, complemented
27C2×C4⋊C8×C43C2211yescharacteristic, complemented
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic, complemented
35C2×#102×C43C2211yescharacteristic, complemented
36C2×C22⋊C8×C43C2211yescharacteristic
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×#97×C43C2211yescharacteristic, complemented
39C2×C4×C8×C43C2211yescharacteristic, complemented
40C43×#399—21no—
41C43×#397—21no—
42C43×#394—21no—
43C43×#394—21no—
44C43×#390—21no—
45C43×#390—21no—
46C43×#390C2211yescharacteristic
47C43×#390C2211yescharacteristic
48C43×#390C2211yescharacteristic
49C43×#390C2211yescharacteristic
50C43×#390C2211yescharacteristic, complemented
51C43×#390C2211yescharacteristic, complemented
52C43×#389C2211yescharacteristic, complemented
53C43×#389C2211yescharacteristic, complemented
54C43×#380C2211yescharacteristic
55C43×#379—21no—
56C43×#379—21no—
57C43×#340C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C25×C43—21no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—22no—
67C22×D4×C43—22no—
68C22×D4×C43—41no—
69C22×D4×C43—41no—
70C22×D4×C43C2311yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C2×D8×C43—22no—
75C2×D8×C43—22no—
76C2×D8×C43—22no—
77C2×D8×C43—22no—
78C2×D8×C43—41no—
79C2×D8×C43—41no—
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84#121×C43—22no—
85#121×C43—22no—
86#117×C43—22no—
87#117×C43—22no—
88#117×C43—41no—
89#117×C43—41no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43D411yescharacteristic
93C2×C4⋊C4×C43D411yescharacteristic
94C2×C4⋊C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43—21no—
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×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#107×C43—41no—
120#106×C43—41no—
121C4⋊C8×C43—22no—
122C4⋊C8×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—41no—
128#102×C43—41no—
129#102×C43—41no—
130#102×C43—41no—
131C22⋊C8×C43—22no—
132C22⋊C8×C43D414yes—
133#97×C43—22no—
134C4×C8×C43—22no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—24no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C2×D4×C43—24no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
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—21no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43#4112yes—
176C2×D4×C43#4112yes—
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×C43C2×D412yes—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43#4112yes—
193C22×C4×C43C2411yescharacteristic
194D8×C43—44no—
195D8×C43—44no—
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—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43C2×D412yes—
207C2×C8×C43C2×D412yes—
208C4⋊C4×C43—22no—
209C4⋊C4×C43—22no—
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—21no—
220C4⋊C4×C43—81no—
221C4⋊C4×C43—81no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—81no—
227C22⋊C4×C43—81no—
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—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—48no—
253C23×C43—41no—
254C23×C43—41no—
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—84no—
273C23×C43—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43#12112yes—
279C23×C43C22×D411yescharacteristic
280D4×C43—22no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—48no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—84no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
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—41no—
313C2×C4×C43—41no—
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#12112yes—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C8×C43—22no—
335C8×C43—22no—
336C8×C43—41no—
337C8×C43—41no—
338#24512C4311yesmaximal, characteristic, direct product factor, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—816no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
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×C43C2×#12111yescharacteristic
369C22×C43#52511yescharacteristic
370C22×C43#53511yescharacteristic
371C22×C43#57611yescharacteristic
372C22×C43#57611yescharacteristic
373C22×C43#57611yescharacteristic
374C22×C43#57711yescharacteristic
375C4×C43—22no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—81no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43—81no—
385C4×C43#54611yescharacteristic
386C4×C43#54611yescharacteristic
387C4×C43#55111yescharacteristic
388C4×C43#55111yescharacteristic
389C2×#447C2×C4311yescharacteristic
390C2×#433C2×C4311yescharacteristic, complemented
391#2624C2×C4311yescharacteristic, complemented
392#2309C2×C4311yescharacteristic, complemented
393#2067C2×C4311yescharacteristic, complemented
394#2065C2×C4311yescharacteristic, complemented
395#2054C2×C4311yescharacteristic, complemented
396#2054C2×C4311yescharacteristic, complemented
397#1972C2×C4311yescharacteristic, complemented
398#1970C2×C4311yescharacteristic, complemented
399#1936C2×C4311yescharacteristic, complemented
400#1934C2×C4311yescharacteristic, complemented
401#1875C2×C4311yescharacteristic, complemented
402#1854C2×C4311yescharacteristic, complemented
403#1786C2×C4311yescharacteristic, complemented
404C2×C43—42no—
405C2×C43—82no—
406C2×C43—82no—
407C2×C43—161no—
408C2×C43#241111yescharacteristic
409C2×C43#305811yescharacteristic
410C2×C43#306211yescharacteristic
411C2×C43#311811yescharacteristic
412C2×C43#312211yescharacteristic
413C2×C43#322011yescharacteristic
414C2×C43#322411yescharacteristic
415C23×D4C22×C4311yescharacteristic
416C22×D8C22×C4311yescharacteristic
417C22×D8C22×C4311yescharacteristic
418C2×#121C22×C4311yescharacteristic
419C2×#117C22×C4311yescharacteristic
420C2×#117C22×C4311yescharacteristic
421#447—24no—
422#433—24no—
423C2×#107C22×C4311yescharacteristic, complemented
424C2×#106C22×C4311yescharacteristic, complemented
425C2×C4⋊C8C22×C4311yescharacteristic, complemented
426C2×C4⋊C8C22×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#399—21no—
440#397—21no—
441#394—21no—
442#394—21no—
443#390—21no—
444#390—21no—
445#390C22×C4311yescharacteristic
446#390C22×C4311yescharacteristic
447#390C22×C4311yescharacteristic
448#390C22×C4311yescharacteristic
449#390C22×C4311yescharacteristic, complemented
450#390C22×C4311yescharacteristic, complemented
451#389C22×C4311yescharacteristic, complemented
452#389C22×C4311yescharacteristic, complemented
453#380C22×C4311yescharacteristic
454#379—21no—
455#379—21no—
456#340C22×C4311yescharacteristic, complemented
457#340C22×C4311yescharacteristic, complemented
458#340C22×C4311yescharacteristic, complemented
459#340C22×C4311yescharacteristic, complemented
460C43#2451211yescharacteristic, direct product factor, Sylow
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C23×C4311yescharacteristic
471C22×D4C23×C4311yescharacteristic
472C22×D4C23×C4311yescharacteristic
473C23×C4C23×C4311yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—41no—
479C2×D8—41no—
480C22×C8C23×C4311yescharacteristic
481C22×C8C23×C4311yescharacteristic
482C22×C8C23×C4311yescharacteristic
483C22×C8C23×C4311yescharacteristic
484#121—22no—
485#121—22no—
486#117—22no—
487#117—22no—
488#117—41no—
489#117—41no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C4311yescharacteristic
493C2×C4⋊C4D4×C4311yescharacteristic
494C2×C4⋊C4C23×C4311yescharacteristic
495C2×C4⋊C4C23×C4311yescharacteristic
496C2×C4⋊C4C23×C4311yescharacteristic
497C2×C4⋊C4C23×C4311yescharacteristic
498C2×C4⋊C4C23×C4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
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⋊C4D4×C4311yescharacteristic
515C2×C22⋊C4D4×C4311yescharacteristic
516C2×C42—21no—
517C2×C42C23×C4311yescharacteristic
518C2×C42C23×C4311yescharacteristic
519#107—41no—
520#106—41no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102—41no—
531C22⋊C8—22no—
532C22⋊C8D4×C4314yes—
533#97—22no—
534C4×C8—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24C2×D4×C4311yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
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—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#41×C4312yes—
576C2×D4#41×C4312yes—
577C22×C4—21no—
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×C4C2×D4×C4311yescharacteristic
587C22×C4C2×D4×C4311yescharacteristic
588C22×C4C2×D4×C4311yescharacteristic
589C22×C4C2×D4×C4311yescharacteristic
590C22×C4C2×D4×C4311yescharacteristic
591C22×C4C2×D4×C4312yes—
592C22×C4#41×C4312yes—
593C22×C4C24×C4311yescharacteristic
594D8—44no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8C2×D4×C4312yes—
607C2×C8C2×D4×C4312yes—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
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—81no—
621C4⋊C4—81no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
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—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—42no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
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—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#121×C4312yes—
679C23C22×D4×C4311yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
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—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
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#121×C4312yes—
728C2×C4C22×D4×C4311yescharacteristic
729C2×C4C2×#41×C4311yescharacteristic
730C2×C4C2×#41×C4311yescharacteristic
731C2×C4C2×#41×C4311yescharacteristic
732C2×C4H(5,𝔽2)×C4311yescharacteristic
733C2×C4H(5,𝔽2)×C4311yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C4311yescharacteristic
768C22C43×#52511yescharacteristic
769C22C43×#53511yescharacteristic
770C22C43×#57611yescharacteristic
771C22C43×#57611yescharacteristic
772C22C43×#57611yescharacteristic
773C22C43×#57711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4C43×#54611yescharacteristic
785C4C43×#54611yescharacteristic
786C4C43×#55111yescharacteristic
787C4C43×#55111yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C43×#241111yescharacteristic
793C2C43×#305811yescharacteristic
794C2C43×#306211yescharacteristic
795C2C43×#311811yescharacteristic
796C2C43×#312211yescharacteristic
797C2C43×#322011yescharacteristic
798C2C43×#322411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
LCSG ▷ C22×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. C2×C43×#433C2semidirect
3. C43×#2624C2semidirect
4. C43×#2309C2semidirect
5. C43×#2067C2semidirect
6. C43×#2065C2semidirect
7. C43×#2054C2semidirect
8. C43×#2054C2semidirect
9. C43×#1972C2semidirect
10. C43×#1970C2semidirect
11. C43×#1936C2semidirect
12. C43×#1934C2semidirect
13. C43×#1875C2semidirect
14. C43×#1854C2semidirect
15. C43×#1786C2semidirect
24. C2×#107×C43C22semidirect
25. C2×#106×C43C22semidirect
26. C2×C4⋊C8×C43C22semidirect
27. C2×C4⋊C8×C43C22semidirect
34. C2×#102×C43C22semidirect
35. C2×#102×C43C22semidirect
38. C2×#97×C43C22semidirect
39. C2×C4×C8×C43C22semidirect
50. C43×#390C22semidirect
51. C43×#390C22semidirect
52. C43×#389C22semidirect
53. C43×#389C22semidirect
57. C43×#340C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
338. #24512C43direct (N × H)
390. C2×#433C2×C43semidirect
391. #2624C2×C43semidirect
392. #2309C2×C43semidirect
393. #2067C2×C43semidirect
394. #2065C2×C43semidirect
395. #2054C2×C43semidirect
396. #2054C2×C43semidirect
397. #1972C2×C43semidirect
398. #1970C2×C43semidirect
399. #1936C2×C43semidirect
400. #1934C2×C43semidirect
401. #1875C2×C43semidirect
402. #1854C2×C43semidirect
403. #1786C2×C43semidirect
423. C2×#107C22×C43semidirect
424. C2×#106C22×C43semidirect
425. C2×C4⋊C8C22×C43semidirect
426. C2×C4⋊C8C22×C43semidirect
433. C2×#102C22×C43semidirect
434. C2×#102C22×C43semidirect
437. C2×#97C22×C43semidirect
438. C2×C4×C8C22×C43semidirect
449. #390C22×C43semidirect
450. #390C22×C43semidirect
451. #389C22×C43semidirect
452. #389C22×C43semidirect
456. #340C22×C43semidirect
457. #340C22×C43semidirect
458. #340C22×C43semidirect
459. #340C22×C43semidirect
460. C43#24512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4472
C2×C43×#4332
C43×#26242
C43×#23092
C43×#20672
C43×#20652
C43×#20542
C43×#19722
C43×#19702
C43×#19362
C43×#19342
C43×#18752
C43×#18542
C43×#17862
#2451243