Finite Group Databasebeta

← #25115369

Subgroups — #25115369

Order 11008.

796 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#10621877C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic
3#19135370C211yesmaximal, characteristic, complemented
4#19135368C211yesmaximal, characteristic, complemented
5#19134800C211yesmaximal, characteristic, complemented
6#19134800C211yesmaximal, characteristic, complemented
7#19134799C211yesmaximal, characteristic, complemented
8#19134799C211yesmaximal, characteristic, complemented
9#19134735C211yesmaximal, characteristic, complemented
10#19134635C211yesmaximal, characteristic, complemented
11#19134631C211yesmaximal, characteristic, complemented
12#19134502C211yesmaximal, characteristic, complemented
13#19134321C211yesmaximal, characteristic, complemented
14C2×#14582663C211yesmaximal, characteristic, complemented
15D4×M16×C43C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14582977—21no—
21#14582971—21no—
22#14582971—21no—
23#14582971C412yes—
24#14582971C412yes—
25#14582971C412yes—
26#14582971C412yes—
27D4×C43⋊C8—21no—
28C2×#13063260C2211yescharacteristic
29C2×#13063260C2211yescharacteristic
30C2×#13063260C2211yescharacteristic
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33C2×#13063260C2211yescharacteristic
34#14582923C2211yescharacteristic
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36#14582863C2211yescharacteristic
37#14582863C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C4×#10621877C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42#14582663C2211yescharacteristic
43#14582663C2211yescharacteristic
44#14582663C2211yescharacteristic
45#14582663C2211yescharacteristic
46#14582663C2211yescharacteristic
47#14582663C2211yescharacteristic
48#14582663C2211yescharacteristic
49#14582663C2211yescharacteristic
50#14582663C2211yescharacteristic
51#14582663C2211yescharacteristic
52C22×M16×C43C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C43×#436—21no—
56C43×#435—21no—
57C43×#435—21no—
58C8×D4×C43—21no—
59C43×#423C2211yescharacteristic
60C43×#407C2211yescharacteristic
61C43×#407C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C2×#10621877—21no—
64C2×#10621877—21no—
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877—41no—
68C2×#10621877—41no—
69C2×#10621877—41no—
70C2×#10621877—41no—
71C2×#10621877C2×C412yes—
72C2×#10621877C2×C412yes—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C22×C43⋊C8—21no—
78C22×C43⋊C8—21no—
79C22×C43⋊C8—41no—
80C22×C43⋊C8—41no—
81C22×C43⋊C8C2×C412yes—
82C22×C43⋊C8C2×C412yes—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063260—22no—
88#13063260—22no—
89#13063260—41no—
90#13063260—41no—
91#13063260—41no—
92#13063260—41no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2×C412yes—
96C4⋊(C43⋊C8)C2×C412yes—
97C22⋊(C43⋊C8)—21no—
98C22⋊(C43⋊C8)—21no—
99C22⋊(C43⋊C8)—21no—
100C22⋊(C43⋊C8)—21no—
101C22⋊(C43⋊C8)C2×C412yes—
102C22⋊(C43⋊C8)C2×C412yes—
103C22⋊(C43⋊C8)C2×C412yes—
104C22⋊(C43⋊C8)C2×C412yes—
105#13063236—21no—
106#13063236C2×C412yes—
107#13063236C2×C412yes—
108C4×C43⋊C8—21no—
109C22×D4×C43Q811yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112C2×M16×C43—21no—
113C2×M16×C43—21no—
114C2×M16×C43—22no—
115C2×M16×C43—22no—
116C2×M16×C43—41no—
117C2×M16×C43—41no—
118C2×M16×C43C2311yescharacteristic
119C2×M16×C43C2311yescharacteristic
120C2×M16×C43C2311yescharacteristic
121C2×M16×C43C2311yescharacteristic
122C22×C8×C43—21no—
123C22×C8×C43—21no—
124C4×D4×C43C2×C411yescharacteristic
125C4×D4×C43C2×C411yescharacteristic
126C4×D4×C43C2×C411yescharacteristic
127C4×D4×C43C2×C411yescharacteristic
128C4×D4×C43D411yescharacteristic
129C4×D4×C43D411yescharacteristic
130C4×D4×C43D411yescharacteristic
131C4×D4×C43D411yescharacteristic
132C2×C4⋊C4×C43Q811yescharacteristic
133C2×C22⋊C4×C43Q811yescharacteristic
134C2×C22⋊C4×C43Q811yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142#97×C43—21no—
143C4×C8×C43—21no—
144C24×C43C2×Q811yescharacteristic
145C24×C43C2×Q811yescharacteristic
146C2×D4×C43—42no—
147C2×D4×C43C4⋊C411yescharacteristic
148C2×D4×C43C4⋊C411yescharacteristic
149C2×D4×C43C4⋊C411yescharacteristic
150C2×D4×C43C4⋊C411yescharacteristic
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×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×Q811yescharacteristic
168C22×C4×C43C2×Q811yescharacteristic
169C22×C4×C43C2×Q811yescharacteristic
170C22×C4×C43C2×Q811yescharacteristic
171C22×C4×C43C2411yescharacteristic
172M16×C43—21no—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—42no—
180M16×C43—42no—
181M16×C43#4112yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—42no—
187C2×C8×C43—42no—
188C4⋊C4×C43C4⋊C411yescharacteristic
189C4⋊C4×C43C4⋊C411yescharacteristic
190C4⋊C4×C43C4⋊C411yescharacteristic
191C4⋊C4×C43C4⋊C411yescharacteristic
192C22⋊C4×C43C4⋊C411yescharacteristic
193C22⋊C4×C43C4⋊C411yescharacteristic
194C22⋊C4×C43C4⋊C411yescharacteristic
195C22⋊C4×C43C4⋊C411yescharacteristic
196C22⋊C4×C43C4⋊C411yescharacteristic
197C22⋊C4×C43C4⋊C411yescharacteristic
198C22⋊C4×C43C4⋊C411yescharacteristic
199C22⋊C4×C43C4⋊C411yescharacteristic
200C42×C43C22×C411yescharacteristic
201C42×C43C22×C411yescharacteristic
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204#10621877—21no—
205#10621877—21no—
206#10621877—21no—
207#10621877—21no—
208#10621877—21no—
209#10621877—21no—
210#10621877—21no—
211#10621877—42no—
212#10621877—42no—
213#10621877—42no—
214#10621877—42no—
215#10621877#4112yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—42no—
229C2×C43⋊C8—42no—
230C2×C43⋊C8—42no—
231C2×C43⋊C8—42no—
232C2×C43⋊C8C22×C412yes—
233C2×C43⋊C8C22×C412yes—
234C2×C43⋊C8C22×C412yes—
235C2×C43⋊C8C22×C412yes—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—22no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43C2×C4⋊C411yescharacteristic
245C23×C43C2×C4⋊C411yescharacteristic
246C23×C43C2×C4⋊C411yescharacteristic
247C23×C43C2×C4⋊C411yescharacteristic
248C23×C43C22×Q811yescharacteristic
249D4×C43—22no—
250D4×C43—22no—
251D4×C43—41no—
252D4×C43—41no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
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—41no—
274C2×C4×C43—41no—
275C2×C4×C43C2×C4⋊C411yescharacteristic
276C2×C4×C43C2×C4⋊C411yescharacteristic
277C2×C4×C43C2×C4⋊C411yescharacteristic
278C2×C4×C43C2×C4⋊C411yescharacteristic
279C2×C4×C43C2×C4⋊C411yescharacteristic
280C2×C4×C43C2×C4⋊C411yescharacteristic
281C2×C4×C43C2×C4⋊C411yescharacteristic
282C2×C4×C43C2×C4⋊C411yescharacteristic
283C2×C4×C43C23×C411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×C4×C43H(5,𝔽2)11yescharacteristic
289C8×C43—22no—
290C8×C43—41no—
291C8×C43—41no—
292C8×C43—41no—
293C43⋊C8—22no—
294C43⋊C8—22no—
295C43⋊C8—22no—
296C43⋊C8—22no—
297C43⋊C8—22no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300C43⋊C8—41no—
301#22718—431nomaximal, Sylow
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—42no—
316C22×C43—42no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43#43012yes—
320C22×C43C22×C4⋊C411yescharacteristic
321C22×C43#55411yescharacteristic
322C22×C43#55411yescharacteristic
323C4×C43—21no—
324C4×C43—21no—
325C4×C43—21no—
326C4×C43—21no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—21no—
330C4×C43—21no—
331C4×C43C4×#4111yescharacteristic
332C4×C43#51811yescharacteristic
333C4×C43#54611yescharacteristic
334C4×C43#54611yescharacteristic
335D4×M16—431no—
336D4×M16D4311yescharacteristic
337C2×#435—431no—
338#1950—431no—
339#1950—431no—
340#1855—431no—
341#1855—431no—
342#1855—431no—
343#1855—431no—
344#1838—431no—
345#1811—431no—
346#1810—431no—
347#1778—431no—
348#1738—431no—
349C2×#341—431no—
350C2×C43—21no—
351C2×C43—21no—
352C2×C43—22no—
353C2×C43—41no—
354C2×C43—41no—
355C2×C43—41no—
356C2×C43#234911yescharacteristic
357C2×C43C2×#43011yescharacteristic
358C2×C43#291611yescharacteristic
359C22×M16—431no—
360C22×M16—431no—
361C22×M16—431no—
362C22×M16C2×D4311yescharacteristic
363C22×M16C2×D4311yescharacteristic
364C23×C8—431no—
365C2×C4×D4C2×D4311yescharacteristic
366#436—21no—
367#436—861no—
368#435—21no—
369#435—21no—
370#435—432no—
371#435—432no—
372#435—432no—
373#435—432no—
374#435—861no—
375#435—861no—
376C8×D4—21no—
377C8×D4—861no—
378C2×#108—431no—
379C2×#108—431no—
380C2×#108—431no—
381C2×#108—431no—
382C2×#108—431no—
383C2×#108—431no—
384#423—431no—
385#423C2×D4311yescharacteristic
386C2×C4⋊C8—431no—
387#407—431no—
388#407—431no—
389#407C2×D4311yescharacteristic
390#407C2×D4311yescharacteristic
391C2×C22⋊C8—431no—
392C2×C22⋊C8—431no—
393C4×M16—431no—
394C4×M16C2×D4311yescharacteristic
395C2×#97—431no—
396#341—431no—
397#341—431no—
398#341—431no—
399#341—431no—
400#341—431no—
401#341—431no—
402#341—431no—
403#341—431no—
404#341—431no—
405#341—431no—
406C43#2271811yescharacteristic, complemented, Sylow
407C22×D4Dic8611yescharacteristic
408C23×C4C22×D4311yescharacteristic
409C23×C4C22×D4311yescharacteristic
410C2×M16—21no—
411C2×M16—21no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—41no—
415C2×M16—41no—
416C2×M16—432no—
417C2×M16—432no—
418C2×M16—431no—
419C2×M16—431no—
420C2×M16—431no—
421C2×M16—431no—
422C2×M16—861no—
423C2×M16—861no—
424C2×M16—862no—
425C2×M16—862no—
426C2×M16—1721no—
427C2×M16—1721no—
428C2×M16—1721no—
429C2×M16—1721no—
430C2×M16C22×D4311yescharacteristic
431C2×M16C22×D4311yescharacteristic
432C2×M16C22×D4311yescharacteristic
433C2×M16C22×D4311yescharacteristic
434C22×C8—21no—
435C22×C8—21no—
436C22×C8—431no—
437C22×C8—431no—
438C22×C8—431no—
439C22×C8—431no—
440C22×C8—432no—
441C22×C8—432no—
442C22×C8—861no—
443C22×C8—861no—
444C22×C8—1721no—
445C22×C8—1721no—
446C4×D4C4×D4311yescharacteristic
447C4×D4C4×D4311yescharacteristic
448C4×D4C4×D4311yescharacteristic
449C4×D4C4×D4311yescharacteristic
450C4×D4C22⋊D4311yescharacteristic
451C4×D4C22⋊D4311yescharacteristic
452C4×D4C22⋊D4311yescharacteristic
453C4×D4C22⋊D4311yescharacteristic
454C2×C4⋊C4Dic8611yescharacteristic
455C2×C22⋊C4Dic8611yescharacteristic
456C2×C22⋊C4Dic8611yescharacteristic
457C2×C42C22×D4311yescharacteristic
458#108—862no—
459#108—862no—
460#108—1721no—
461#108—1721no—
462#108—1721no—
463#108—1721no—
464C4⋊C8—21no—
465C4⋊C8—21no—
466C4⋊C8—432no—
467C4⋊C8—432no—
468C4⋊C8—861no—
469C4⋊C8—861no—
470C22⋊C8—21no—
471C22⋊C8—21no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—432no—
475C22⋊C8—432no—
476C22⋊C8—432no—
477C22⋊C8—432no—
478C22⋊C8—861no—
479C22⋊C8—861no—
480C22⋊C8—861no—
481C22⋊C8—861no—
482#97—21no—
483#97—432no—
484#97—432no—
485#97—861no—
486C4×C8—21no—
487C4×C8—861no—
488C24C2×Dic8611yescharacteristic
489C24C2×Dic8611yescharacteristic
490C2×D4—42no—
491C2×D4Dic43⋊C411yescharacteristic
492C2×D4Dic43⋊C411yescharacteristic
493C2×D4Dic43⋊C411yescharacteristic
494C2×D4Dic43⋊C411yescharacteristic
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4C2×Dic8611yescharacteristic
504C22×C4C2×Dic8611yescharacteristic
505C22×C4C2×Dic8611yescharacteristic
506C22×C4C2×Dic8611yescharacteristic
507C22×C4C2×C4×D4311yescharacteristic
508C22×C4C2×C4×D4311yescharacteristic
509C22×C4C2×C4×D4311yescharacteristic
510C22×C4C2×C4×D4311yescharacteristic
511C22×C4C2×C22⋊D4311yescharacteristic
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C23×D4311yescharacteristic
516M16—21no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—21no—
523M16—42no—
524M16—42no—
525M16—432no—
526M16—861no—
527M16—861no—
528M16—861no—
529M16—861no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16—1722no—
534M16—1722no—
535M16—1722no—
536M16—1722no—
537M16#1062190012yes—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—432no—
545C2×C8—432no—
546C2×C8—432no—
547C2×C8—432no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—1722no—
561C2×C8—1722no—
562C2×C8—1722no—
563C2×C8—1722no—
564C4⋊C4Dic43⋊C411yescharacteristic
565C4⋊C4Dic43⋊C411yescharacteristic
566C4⋊C4Dic43⋊C411yescharacteristic
567C4⋊C4Dic43⋊C411yescharacteristic
568C22⋊C4Dic43⋊C411yescharacteristic
569C22⋊C4Dic43⋊C411yescharacteristic
570C22⋊C4Dic43⋊C411yescharacteristic
571C22⋊C4Dic43⋊C411yescharacteristic
572C22⋊C4Dic43⋊C411yescharacteristic
573C22⋊C4Dic43⋊C411yescharacteristic
574C22⋊C4Dic43⋊C411yescharacteristic
575C22⋊C4Dic43⋊C411yescharacteristic
576C42C2×C4×D4311yescharacteristic
577C42C2×C4×D4311yescharacteristic
578C42C2×C22⋊D4311yescharacteristic
579C42C2×C22⋊D4311yescharacteristic
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C2×Dic43⋊C411yescharacteristic
589C23C2×Dic43⋊C411yescharacteristic
590C23C2×Dic43⋊C411yescharacteristic
591C23C2×Dic43⋊C411yescharacteristic
592C23C22×Dic8611yescharacteristic
593D4—22no—
594D4—22no—
595D4—41no—
596D4—41no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4C2×Dic43⋊C411yescharacteristic
620C2×C4C2×Dic43⋊C411yescharacteristic
621C2×C4C2×Dic43⋊C411yescharacteristic
622C2×C4C2×Dic43⋊C411yescharacteristic
623C2×C4C2×Dic43⋊C411yescharacteristic
624C2×C4C2×Dic43⋊C411yescharacteristic
625C2×C4C2×Dic43⋊C411yescharacteristic
626C2×C4C2×Dic43⋊C411yescharacteristic
627C2×C4C22×C4×D4311yescharacteristic
628C2×C4C22×C22⋊D4311yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4C2×#1062190011yescharacteristic
631C2×C4#1306337011yescharacteristic
632C2×C4#1306337111yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8—41no—
637C8—862no—
638C8—862no—
639C8—862no—
640C8—862no—
641C8—862no—
642C8—1721no—
643C8—1721no—
644C8—1721no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22#1458294712yes—
663C22C22×Dic43⋊C411yescharacteristic
664C22#1458360611yescharacteristic
665C22#1458360811yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—21no—
671C4—21no—
672C4—21no—
673C4—21no—
674C4C4×#1062190011yescharacteristic
675C4#1458337111yescharacteristic
676C4#1458353711yescharacteristic
677C4#1458354311yescharacteristic
678C2—21no—
679C2—21no—
680C2—22no—
681C2—41no—
682C2—41no—
683C2—41no—
684C2#1913750011yescharacteristic
685C2C2×#1458294711yescharacteristic
686C2#1914320411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×M16×C43C2
socleC22×C43C22×C4⋊C4
prime radicalC22×D4×C43Q8
cosocleC22×C4×C43C24
hypercenterD4×M16D43
hypocenterC43#22718
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
3. #19135370C2semidirect
4. #19135368C2semidirect
5. #19134800C2semidirect
6. #19134800C2semidirect
7. #19134799C2semidirect
8. #19134799C2semidirect
9. #19134735C2semidirect
10. #19134635C2semidirect
11. #19134631C2semidirect
12. #19134502C2semidirect
13. #19134321C2semidirect
14. C2×#14582663C2semidirect
406. C43#22718semidirect

Maximal subgroups

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

subgroupindex
D4×#106218772
C2×#145829712
#191353702
#191353682
#191348002
#191347992
#191347352
#191346352
#191346312
#191345022
#191343212
C2×#145826632
D4×M16×C432
#2271843