Finite Group Databasebeta

← #25106619

Subgroups — #25106619

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊C4×D43C211yesmaximal, characteristic
2#19135204C211yesmaximal, characteristic, complemented
3#19135203C211yesmaximal, characteristic, complemented
4#19135202C211yesmaximal, characteristic, complemented
5#19135201C211yesmaximal, characteristic, complemented
6#19135200C211yesmaximal, characteristic, complemented
7#19135199C211yesmaximal, characteristic, complemented
8#19135198C211yesmaximal, characteristic, complemented
9#19134574C211yesmaximal, characteristic, complemented
10#19134572C211yesmaximal, characteristic, complemented
11#19134504C211yesmaximal, characteristic
12#19134504C211yesmaximal, characteristic
13C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×C22⋊C4×D43C411yescharacteristic
18C2×C22⋊C4×D43C411yescharacteristic
19C2×C42×D43C2211yescharacteristic
20C2×C42×D43C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
22C2×Dic43⋊C8C2211yescharacteristic, complemented
23C2×Dic43⋊C8C2211yescharacteristic, complemented
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic, complemented
35C2×C8×Dic43C2211yescharacteristic, complemented
36C2×C8×Dic43C2211yescharacteristic, complemented
37C22⋊C4×Dic43C411yescharacteristic
38C22⋊C4×Dic43C411yescharacteristic
39C4×(C2×D43)⋊C4C2211yescharacteristic
40C4×(C2×D43)⋊C4C2211yescharacteristic
41C4×C22⋊Dic43C2211yescharacteristic
42#14582746C411yescharacteristic
43#14582746C411yescharacteristic
44#95×D43C411yescharacteristic
45#95×D43C411yescharacteristic
46#14582654C2211yescharacteristic, complemented
47#14582654C2211yescharacteristic, complemented
48#14582653C2211yescharacteristic, complemented
49#14582653C2211yescharacteristic, complemented
50#14582653C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52C2×C4⋊C8×C43C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic, complemented
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic, complemented
58C43×#336C2211yescharacteristic, complemented
59C24×D43C2×C411yescharacteristic
60C23×Dic43C2×C411yescharacteristic
61C22×C4×D43—22no—
62C22×C4×D43—22no—
63C22×C4×D43—41no—
64C22×C4×D43—41no—
65C22×C4×D43—41no—
66C22×C4×D43—41no—
67C22×C4×D43C2×C411yescharacteristic
68C22×C4×D43C2×C411yescharacteristic
69C22×C4×D43C2×C411yescharacteristic
70C22×C4×D43C2×C411yescharacteristic
71C22×C4×D43C2×C411yescharacteristic
72C22×C4×D43C2×C411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C22⋊Dic43C2×C411yescharacteristic
80C2×C22⋊Dic43C2×C411yescharacteristic
81C2×(C2×D43)⋊C4C2×C411yescharacteristic
82C2×(C2×D43)⋊C4C2×C411yescharacteristic
83C2×(C2×D43)⋊C4C2×C411yescharacteristic
84C2×(C2×D43)⋊C4C2×C411yescharacteristic
85C22⋊C4×D43—24no—
86C22⋊C4×D43C818yescomplemented
87C2×C4×Dic43C2×C411yescharacteristic
88C2×C4×Dic43C2×C411yescharacteristic
89C2×C4×Dic43C2×C411yescharacteristic
90C2×C4×Dic43C2×C411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C42×D43—41no—
94C42×D43—41no—
95C42×D43—41no—
96C42×D43—41no—
97C4⋊(C43⋊C8)—41no—
98Dic43⋊C8—41no—
99Dic43⋊C8—41no—
100C22⋊(C43⋊C8)—41no—
101C22⋊(C43⋊C8)—41no—
102(C2×D43)⋊C8—22no—
103(C2×D43)⋊C8—22no—
104(C2×D43)⋊C8—22no—
105(C2×D43)⋊C8—22no—
106(C2×D43)⋊C8—41no—
107(C2×D43)⋊C8—41no—
108(C2×D43)⋊C8—41no—
109(C2×D43)⋊C8—41no—
110C4×C43⋊C8—41no—
111C8×Dic43—41no—
112C8×Dic43—41no—
113C43⋊#95C2×C411yescharacteristic
114C43⋊#95C2×C411yescharacteristic
115C43⋊#95C2×C411yescharacteristic
116C43⋊#95C2×C411yescharacteristic
117C43⋊#95C2×C411yescharacteristic
118C43⋊#95C2×C411yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C2×C22⋊C4×C43C2×C411yescharacteristic
125C2×C22⋊C4×C43C2×C411yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43—41no—
129C22⋊C8×C43—41no—
130C22⋊C8×C43—41no—
131C4×C8×C43—41no—
132#95×C43C2×C411yescharacteristic
133#95×C43C2×C411yescharacteristic
134C24×C43C22×C411yescharacteristic
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—41no—
138C23×D43—41no—
139C23×D43—41no—
140C23×D43—41no—
141C23×D43C2×C814yes—
142C23×D43C22×C411yescharacteristic
143C23×D43C22×C411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—22no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—41no—
179C2×C4×D43—41no—
180C2×C4×D43—41no—
181C2×C4×D43—41no—
182C2×C4×D43—41no—
183C2×C4×D43—41no—
184C2×C4×D43—41no—
185C2×C4×D43—41no—
186C2×C4×D43—41no—
187C2×C4×D43—41no—
188C2×C4×D43—41no—
189C2×C4×D43—41no—
190C2×C4×D43—44no—
191C2×C4×D43—44no—
192C2×C4×D43—44no—
193C2×C4×D43—44no—
194C2×C4×D43C2×C814yes—
195C2×C4×D43C2×C814yes—
196C2×C4×D43M1614yes—
197C2×C4×D43#4112yes—
198C2×C4×D43#4112yes—
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×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43C2×C814yes—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—22no—
218C22⋊Dic43C2×C814yes—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4—22no—
221(C2×D43)⋊C4C2×C814yes—
222(C2×D43)⋊C4C2×C814yes—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—21no—
227C4×Dic43—41no—
228C4×Dic43—41no—
229C4×Dic43—41no—
230C4×Dic43—41no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43C22×C812yes—
250C23×C43C23×C411yescharacteristic
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—28no—
262C22×D43—44no—
263C22×D43—44no—
264C22×D43—44no—
265C22×D43—44no—
266C22×D43—44no—
267C22×D43—44no—
268C22×D43#11712yes—
269C22×D43C22×C812yes—
270C22×D43C22×C812yes—
271C22×D43C2×M1612yes—
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—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43C22×C812yes—
289C2×C4×C43C22×C812yes—
290C2×C4×C43C2×M1612yes—
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—44no—
312C2×Dic43#11712yes—
313C2×Dic43C22×C812yes—
314C2×Dic43C22×C812yes—
315C2×Dic43C2×M1612yes—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—44no—
321C4×D43—44no—
322C4×D43—44no—
323C4×D43—44no—
324C4×D43—44no—
325C4×D43—44no—
326C4×D43—41no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C8×C43—41no—
331C8×C43—41no—
332C8×C43—41no—
333C8×C43—41no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338#21902—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43C2×#11711yescharacteristic
347C22×C43#51811yescharacteristic
348C22×C43#51811yescharacteristic
349C22×C43C23×C811yescharacteristic
350C22×C43C22×M1611yescharacteristic
351C22×C43#56811yescharacteristic
352C22×C43#56811yescharacteristic
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—416no—
363C2×D43—41no—
364C2×D43—41no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43#43114yes—
368C4×C43—22no—
369C4×C43—22no—
370C4×C43—22no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43#53811yescharacteristic
374C4×C43#53811yescharacteristic
375C4×C43#53811yescharacteristic
376C4×C43#53811yescharacteristic
377Dic43—22no—
378Dic43—22no—
379Dic43—22no—
380Dic43—22no—
381Dic43—41no—
382Dic43—41no—
383C2×C4×C22⋊C4—431no—
384#1923—431no—
385#1923—431no—
386#1923—431no—
387#1923—431no—
388#1923—431no—
389#1923—431no—
390#1923—431no—
391#1923D4311yescharacteristic, complemented
392#1797—431no—
393#1797—431no—
394#1779—431no—
395#1779—431no—
396C4×C22⋊C8—431no—
397C4×C22⋊C8—431no—
398C2×C43—42no—
399C2×C43#231211yescharacteristic
400C2×C43C2×#43111yescharacteristic
401C2×C43#292111yescharacteristic
402C2×C43#297211yescharacteristic
403C2×C43#297211yescharacteristic
404C2×C43#297311yescharacteristic
405C2×C43#297511yescharacteristic
406D43—24no—
407D43—42no—
408C24×C4—431no—
409C22×C22⋊C4—431no—
410C22×C22⋊C4—431no—
411C22×C42—431no—
412C22×C42—431no—
413C2×C4⋊C8—431no—
414C2×C4⋊C8—431no—
415C2×C4⋊C8—431no—
416C2×C4⋊C8C2×D4311yescharacteristic, complemented
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419C2×C22⋊C8—431no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×C22⋊C8—431no—
424C2×C22⋊C8—431no—
425C2×C22⋊C8—431no—
426C2×C22⋊C8—431no—
427C2×C22⋊C8C2×D4311yescharacteristic
428C2×C22⋊C8C2×D4311yescharacteristic
429C2×C4×C8—431no—
430C2×C4×C8—431no—
431C2×C4×C8—431no—
432C2×C4×C8C2×D4311yescharacteristic, complemented
433C4×C22⋊C4—431no—
434C4×C22⋊C4—431no—
435C4×C22⋊C4—431no—
436C4×C22⋊C4—431no—
437C4×C22⋊C4—431no—
438C4×C22⋊C4—431no—
439C4×C22⋊C4—431no—
440C4×C22⋊C4C2×D4311yescharacteristic
441C2×#95—431no—
442C2×#95—431no—
443#336—431no—
444#336—431no—
445#336—431no—
446#336—431no—
447#336—431no—
448#336—431no—
449#336C2×D4311yescharacteristic, complemented
450#336C2×D4311yescharacteristic, complemented
451C43#2190211yescharacteristic, complemented, Sylow
452C25—431no—
453C23×C4—431no—
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—862no—
463C23×C4—862no—
464C23×C4—1721no—
465C23×C4—1721no—
466C23×C4—1721no—
467C23×C4—1721no—
468C23×C4C22×D4311yescharacteristic
469C22×C8—431no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4311yescharacteristic
477C2×C22⋊C4—431no—
478C2×C22⋊C4—431no—
479C2×C22⋊C4—431no—
480C2×C22⋊C4—438no—
481C2×C22⋊C4—431no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—864no—
485C2×C22⋊C4C4×D4311yescharacteristic
486C2×C22⋊C4C4×D4311yescharacteristic
487C2×C42—431no—
488C2×C42—431no—
489C2×C42—431no—
490C2×C42—431no—
491C2×C42—431no—
492C2×C42—431no—
493C2×C42—1721no—
494C2×C42—1721no—
495C2×C42—1721no—
496C2×C42—1721no—
497C2×C42C22×D4311yescharacteristic
498C2×C42C22×D4311yescharacteristic
499C4⋊C8—41no—
500C4⋊C8—1721no—
501C4⋊C8—1721no—
502C4⋊C8—1721no—
503C22⋊C8—41no—
504C22⋊C8—41no—
505C22⋊C8—862no—
506C22⋊C8—862no—
507C22⋊C8—862no—
508C22⋊C8—862no—
509C22⋊C8—1721no—
510C22⋊C8—1721no—
511C22⋊C8—1721no—
512C22⋊C8—1721no—
513C22⋊C8—1721no—
514C22⋊C8—1721no—
515C4×C8—41no—
516C4×C8—1721no—
517C4×C8—1721no—
518C4×C8—1721no—
519#95—431no—
520#95—431no—
521#95—431no—
522#95—431no—
523#95—431no—
524#95—431no—
525#95C4×D4311yescharacteristic
526#95C4×D4311yescharacteristic
527C24—431no—
528C24—431no—
529C24—434no—
530C24—862no—
531C24—862no—
532C24—1721no—
533C24—1721no—
534C24—1721no—
535C24—1721no—
536C24C2×C4×D4311yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—431no—
544C22×C4—431no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—434no—
550C22×C4—434no—
551C22×C4—434no—
552C22×C4—431no—
553C22×C4—431no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—1721no—
569C22×C4—1721no—
570C22×C4—1721no—
571C22×C4—1721no—
572C22×C4—1721no—
573C22×C4—1721no—
574C22×C4—1721no—
575C22×C4—1721no—
576C22×C4—1721no—
577C22×C4—1721no—
578C22×C4—1721no—
579C22×C4—1721no—
580C22×C4—1724no—
581C22×C4—1724no—
582C22×C4—1724no—
583C22×C4—1724no—
584C22×C4—1721no—
585C22×C4—1721no—
586C22×C4C2×C4×D4311yescharacteristic
587C22×C4C2×C4×D4311yescharacteristic
588C22×C4C2×C4×D4311yescharacteristic
589C22×C4C2×C4×D4311yescharacteristic
590C22×C4C2×C4×D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
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—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C22⋊C4—22no—
617C22⋊C4—434no—
618C22⋊C4—434no—
619C22⋊C4—434no—
620C22⋊C4—862no—
621C22⋊C4—862no—
622C22⋊C4—862no—
623C22⋊C4C8×D4314yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—861no—
629C42—861no—
630C42—861no—
631C42—861no—
632C42—1721no—
633C42—1721no—
634C42—1721no—
635C42—1721no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—432no—
643C23—432no—
644C23—432no—
645C23—432no—
646C23—868no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23—1724no—
658C23—1724no—
659C23—1724no—
660C23—1724no—
661C23—1724no—
662C23—1724no—
663C23C2×C8×D4312yes—
664C23C22×C4×D4311yescharacteristic
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—432no—
684C2×C4—432no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—1724no—
704C2×C4—1724no—
705C2×C4—1724no—
706C2×C4—1724no—
707C2×C4—1724no—
708C2×C4—1724no—
709C2×C4—1724no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4C2×C8×D4312yes—
715C2×C4C2×C8×D4312yes—
716C2×C4M16×D4312yes—
717C2×C4#41×D4311yescharacteristic
718C2×C4#41×D4311yescharacteristic
719C2×C4#1306337011yescharacteristic
720C2×C4#1306337011yescharacteristic
721C2×C4#1306337111yescharacteristic
722C2×C4#1306337111yescharacteristic
723C8—41no—
724C8—41no—
725C8—41no—
726C8—41no—
727C8—1721no—
728C8—1721no—
729C8—1721no—
730C8—1721no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—434no—
739C22—862no—
740C22—862no—
741C22—862no—
742C22—862no—
743C22—862no—
744C22—862no—
745C22—862no—
746C22—862no—
747C22—862no—
748C22—17216no—
749C22—1721no—
750C22—1721no—
751C22—1721no—
752C22—1721no—
753C22#117×D4311yescharacteristic
754C22#1458337111yescharacteristic
755C22#1458337111yescharacteristic
756C22C22×C8×D4311yescharacteristic
757C22C2×M16×D4311yescharacteristic
758C22#1458366411yescharacteristic
759C22#1458366411yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—41no—
764C4—41no—
765C4—862no—
766C4—862no—
767C4—862no—
768C4—862no—
769C4—1721no—
770C4—1721no—
771C4#1458348111yescharacteristic
772C4#1458348311yescharacteristic
773C4#1458348511yescharacteristic
774C4#1458348811yescharacteristic
775C2—42no—
776C2—864no—
777C2—1722no—
778C2#1913718911yescharacteristic
779C2#431×D4311yescharacteristic
780C2#1914322911yescharacteristic
781C2#1914361611yescharacteristic
782C2#1914361611yescharacteristic
783C2#1914362011yescharacteristic
784C2#1914363311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C23×C8
FittingC43×#1923C2
socleC23×C43C23×C4
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1923D43
hypocenterC43#21902
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #19135204C2semidirect
3. #19135203C2semidirect
4. #19135202C2semidirect
5. #19135201C2semidirect
6. #19135200C2semidirect
7. #19135199C2semidirect
8. #19135198C2semidirect
9. #19134574C2semidirect
10. #19134572C2semidirect
13. C4×(C2×D43)⋊C8C2semidirect
14. #19134352C2semidirect
15. C43×#1923C2semidirect
21. C2×C4⋊(C43⋊C8)C22semidirect
22. C2×Dic43⋊C8C22semidirect
23. C2×Dic43⋊C8C22semidirect
34. C2×C4×C43⋊C8C22semidirect
35. C2×C8×Dic43C22semidirect
36. C2×C8×Dic43C22semidirect
46. #14582654C22semidirect
47. #14582654C22semidirect
48. #14582653C22semidirect
49. #14582653C22semidirect
50. #14582653C22semidirect
51. #14582653C22semidirect
52. C2×C4⋊C8×C43C22semidirect
55. C2×C4×C8×C43C22semidirect
57. C43×#336C22semidirect
58. C43×#336C22semidirect
86. C22⋊C4×D43C8semidirect
391. #1923D43semidirect
416. C2×C4⋊C8C2×D43semidirect
432. C2×C4×C8C2×D43semidirect
449. #336C2×D43semidirect
450. #336C2×D43semidirect
451. C43#21902semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊C4×D432
#191352042
#191352032
#191352022
#191352012
#191352002
#191351992
#191351982
#191345742
#191345722
#191345042
C4×(C2×D43)⋊C82
#191343522
C43×#19232
#2190243