Finite Group Databasebeta

← #25112771

Subgroups — #25112771

Order 11008.

1106 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic
3#19143327C211yesmaximal, characteristic
4#19135582C211yesmaximal, characteristic, complemented
5#19135582C211yesmaximal, characteristic, complemented
6#19135064C211yesmaximal, characteristic, complemented
7#19135060C211yesmaximal, characteristic, complemented
8#19135060C211yesmaximal, characteristic, complemented
9#19134674C211yesmaximal, characteristic, complemented
10#19134673C211yesmaximal, characteristic, complemented
11#19134589C211yesmaximal, characteristic, complemented
12#101×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582667C211yesmaximal, characteristic, complemented
14#343×D43C211yesmaximal, characteristic, complemented
15C43×#1901C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19#14583607—21no—
20#14583607—21no—
21#14583607—21no—
22#14583607—21no—
23#14583607—21no—
24#14583607—21no—
25#14583607—21no—
26#14583607—21no—
27C2×#13063324C2211yescharacteristic
28C2×#13063315C412yes—
29C2×#13063305C412yes—
30C2×#13063302C412yes—
31C2×#13063301C2211yescharacteristic
32C2×Q8×Dic43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C412yes—
35C22×C4⋊Dic43C2211yescharacteristic
36C2×C4⋊C4×D43C2211yescharacteristic
37#14582975—21no—
38#14582974—21no—
39#14582973—21no—
40#14582970—21no—
41#14582968—21no—
42#14582967—21no—
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582922C2211yescharacteristic
46#14582922C2211yescharacteristic
47C2×#13063244C2211yescharacteristic
48C2×#13063244C2211yescharacteristic
49#14582863C2211yescharacteristic
50#14582862C2211yescharacteristic
51#14582862C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582667C2211yescharacteristic
61#14582667C2211yescharacteristic
62#14582667C2211yescharacteristic
63#14582667C2211yescharacteristic
64C22×M16×C43C2211yescharacteristic
65C2×C22⋊Q8×C43C2211yescharacteristic
66C2×#101×C43C2211yescharacteristic
67C2×#101×C43C2211yescharacteristic
68C43×#407C2211yescharacteristic
69C43×#343C2211yescharacteristic
70C43×#343C2211yescharacteristic
71C22×Dic86C2×C412yes—
72C22×C22⋊D43C2×C411yescharacteristic
73C23×Dic43C2×C412yes—
74C22×C4×D43C2×C412yes—
75C22×C4×D43C2311yescharacteristic
76C2×#10621877—21no—
77C2×#10621877—22no—
78C2×#10621877—41no—
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621872—21no—
84C2×#10621872—21no—
85M16×D43—22no—
86M16×D43—22no—
87M16×D43—41no—
88M16×D43—41no—
89C22×C43⋊C8—21no—
90C2×C8×D43—21no—
91C2×C8×D43—21no—
92#13063324—21no—
93#13063324—21no—
94#13063324—21no—
95#13063324—21no—
96#13063315—22no—
97#13063315—22no—
98#13063315—22no—
99#13063315—22no—
100#13063305—22no—
101#13063305—22no—
102#13063305—22no—
103#13063305—22no—
104#13063302—22no—
105#13063302—22no—
106#13063302—22no—
107#13063302—22no—
108#13063301—21no—
109#13063301—21no—
110#13063301—21no—
111#13063301—21no—
112Q8×Dic43—21no—
113Q8×Dic43—21no—
114Q8×Dic43—21no—
115Q8×Dic43—21no—
116C4×C22⋊D43D411yescharacteristic
117C4×C22⋊D43D411yescharacteristic
118C4×C22⋊D43D411yescharacteristic
119C4×C22⋊D43D411yescharacteristic
120C4×C22⋊D43D411yescharacteristic
121C4×C22⋊D43D411yescharacteristic
122C4×C22⋊D43D411yescharacteristic
123C4×C22⋊D43D411yescharacteristic
124(C22⋊D43)⋊C4—22no—
125(C22⋊D43)⋊C4—22no—
126(C22⋊D43)⋊C4—22no—
127(C22⋊D43)⋊C4—22no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2×C412yes—
133C2×C4⋊Dic43C2×C412yes—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4C2×C412yes—
137C2×Dic43⋊C4C2×C412yes—
138C2×Dic43⋊C4C2×C412yes—
139C2×Dic43⋊C4C2×C411yescharacteristic
140C4⋊C4×D43—21no—
141C4⋊C4×D43—21no—
142C4⋊C4×D43—21no—
143C4⋊C4×D43—21no—
144C2×C22⋊Dic43C2×C411yescharacteristic
145C2×(C2×D43)⋊C4C2×C412yes—
146C2×(C2×D43)⋊C4C2×C411yescharacteristic
147C2×C4×Dic43C2×C412yes—
148C2×C4×Dic43C2311yescharacteristic
149Dic43⋊C8—21no—
150Dic43⋊C8—21no—
151Dic43⋊C8—21no—
152Dic43⋊C8—21no—
153#13063244—22no—
154#13063244—41no—
155C22⋊(C43⋊C8)—21no—
156C22⋊(C43⋊C8)—21no—
157(C2×D43)⋊C8—21no—
158(C2×D43)⋊C8—21no—
159(C2×D43)⋊C8—21no—
160(C2×D43)⋊C8—21no—
161#13063235—21no—
162#13063235—21no—
163C8×Dic43—21no—
164C8×Dic43—21no—
165C22×Q8×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C2×M16×C43—21no—
168C2×M16×C43—22no—
169C2×M16×C43—41no—
170C2×M16×C43C2311yescharacteristic
171C2×M16×C43C2311yescharacteristic
172C2×M16×C43C2311yescharacteristic
173C2×M16×C43C2311yescharacteristic
174C22×C8×C43—21no—
175C22⋊Q8×C43—21no—
176C22⋊Q8×C43—21no—
177C22⋊Q8×C43—21no—
178C22⋊Q8×C43—21no—
179C2×C4⋊C4×C43C2×C412yes—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43C2×C412yes—
182#101×C43—22no—
183#101×C43—41no—
184C22⋊C8×C43—21no—
185C22⋊C8×C43—21no—
186C24×C43C22×C411yescharacteristic
187C23×D43C22×C411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C22×C412yes—
199C22×C4×C43C22×C411yescharacteristic
200C22×C4×C43C22×C412yes—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43C22⋊C411yescharacteristic
208C2×C22⋊D43C22⋊C411yescharacteristic
209C2×C22⋊D43C22⋊C411yescharacteristic
210C2×C22⋊D43C22⋊C411yescharacteristic
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—82no—
214C22×Dic43C22×C411yescharacteristic
215C22×Dic43C22×C411yescharacteristic
216C22×Dic43C22×C412yes—
217C22×Dic43C22×C412yes—
218C22×Dic43C22×C411yescharacteristic
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—82no—
226C2×C4×D43C2×D411yescharacteristic
227C2×C4×D43C2×D411yescharacteristic
228C2×C4×D43C2×D411yescharacteristic
229C2×C4×D43C2×D411yescharacteristic
230C2×Dic86—22no—
231C2×Dic86—22no—
232C2×Dic86—82no—
233M16×C43—21no—
234M16×C43—21no—
235M16×C43—21no—
236M16×C43—21no—
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—42no—
241M16×C43#4112yes—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—42no—
247C4⋊C4×C43—22no—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—22no—
253C22⋊Dic43C22⋊C411yescharacteristic
254C22⋊Dic43C22⋊C411yescharacteristic
255C22⋊Dic43C22⋊C411yescharacteristic
256C22⋊Dic43C22⋊C411yescharacteristic
257(C2×D43)⋊C4—22no—
258(C2×D43)⋊C4—22no—
259(C2×D43)⋊C4C22⋊C411yescharacteristic
260(C2×D43)⋊C4C22⋊C411yescharacteristic
261(C2×D43)⋊C4C22⋊C411yescharacteristic
262(C2×D43)⋊C4C22⋊C411yescharacteristic
263C4⋊Dic43—22no—
264C4⋊Dic43—22no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—22no—
270C4⋊Dic43—22no—
271Dic43⋊C4—22no—
272Dic43⋊C4—22no—
273Dic43⋊C4—22no—
274Dic43⋊C4—22no—
275Dic43⋊C4—22no—
276Dic43⋊C4—22no—
277Dic43⋊C4C22⋊C411yescharacteristic
278Dic43⋊C4C22⋊C411yescharacteristic
279Dic43⋊C4C22⋊C411yescharacteristic
280Dic43⋊C4C22⋊C411yescharacteristic
281C4×Dic43—22no—
282C4×Dic43—22no—
283C4×Dic43C2×D411yescharacteristic
284C4×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287#10621877—21no—
288#10621877—21no—
289#10621877—21no—
290#10621877—21no—
291#10621877—21no—
292#10621877—21no—
293#10621877—21no—
294#10621877—42no—
295#10621877#4112yes—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—42no—
301#10621872—42no—
302#10621872—42no—
303C8×D43—42no—
304C8×D43—42no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—22no—
308C23×C43—41no—
309C23×C43C2×C22⋊C411yescharacteristic
310C23×C43C2×C22⋊C411yescharacteristic
311C23×C43C23×C411yescharacteristic
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—22no—
315C22×D43—41no—
316C22×D43C2×C22⋊C411yescharacteristic
317C22×D43C2×C22⋊C411yescharacteristic
318Q8×C43—41no—
319Q8×C43—41no—
320Q8×C43—41no—
321Q8×C43—41no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—42no—
337C2×C4×C43C2×C22⋊C411yescharacteristic
338C2×C4×C43C2×C22⋊C411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C2×C4×C432−1+411yescharacteristic
345C22⋊D43—22no—
346C22⋊D43—22no—
347C22⋊D43—22no—
348C22⋊D43#10114yescomplemented
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—41no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43—82no—
358C2×Dic43—82no—
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363C2×Dic43C2×C22⋊C411yescharacteristic
364C2×Dic43C2×C22⋊C411yescharacteristic
365C4×D43—21no—
366C4×D43—21no—
367C4×D43—21no—
368C4×D43—21no—
369C4×D43—21no—
370C4×D43—21no—
371C4×D43—21no—
372C4×D43—21no—
373C4×D43—82no—
374C4×D43—82no—
375Dic86—82no—
376Dic86—82no—
377C8×C43—22no—
378C8×C43—41no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—22no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385#22481—431nomaximal, Sylow
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43C2×#10112yes—
396C22×C43C22×C22⋊C411yescharacteristic
397C22×C43C4×#4111yescharacteristic
398C22×C43#52011yescharacteristic
399C2×D43—21no—
400C2×D43—21no—
401C2×D43—21no—
402C2×D43—21no—
403C2×D43—21no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43C2×#10112yes—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43—42no—
410C4×C43—42no—
411C4×C43#54611yescharacteristic
412C4×C43#54611yescharacteristic
413C4×C43#54711yescharacteristic
414C4×C43#54711yescharacteristic
415Dic43—21no—
416Dic43—21no—
417Dic43—21no—
418Dic43—21no—
419Dic43—21no—
420Dic43—42no—
421Dic43—42no—
422Dic43C2×#10112yes—
423C2×#554—431no—
424D4×M16—431no—
425D4×M16—431no—
426#1997—431no—
427#1997—431no—
428#1901—431no—
429#1901—431no—
430#1901—431no—
431#1901D4311yescharacteristic, complemented
432#1821—431no—
433#1821—431no—
434#1801—431no—
435C4×#101—431no—
436C2×#343—431no—
437C2×#343—431no—
438C2×C43—21no—
439C2×C43—21no—
440C2×C43—22no—
441C2×C43—41no—
442C2×C43#233911yescharacteristic
443C2×C43C22×#10111yescharacteristic
444C2×C43#288811yescharacteristic
445D43—22no—
446D43—41no—
447C22×M16—431no—
448C22×M16—431no—
449C22×M16—431no—
450C22×M16C2×D4311yescharacteristic
451#554—861no—
452#554—861no—
453#554—861no—
454#554—861no—
455#554—861no—
456#554—861no—
457#554—861no—
458#554—861no—
459C2×C4⋊Q8—431no—
460C2×#125—432no—
461C2×C22⋊Q8—431no—
462C2×C22⋊Q8—432no—
463C2×C22⋊Q8—432no—
464C2×C22⋊Q8C2×D4311yescharacteristic
465C2×C4×Q8—431no—
466C2×C4×D4—431no—
467C2×C4×D4—432no—
468C22×C4⋊C4—431no—
469C22×C4⋊C4—431no—
470#436—861no—
471#436—861no—
472#435—861no—
473#435—861no—
474#435—861no—
475#435—861no—
476C8×D4—861no—
477C8×D4—861no—
478#423—431no—
479#423—431no—
480C2×#101—431no—
481C2×#101—431no—
482C2×#101C2×D4311yescharacteristic
483C2×#101C2×D4311yescharacteristic
484#407—431no—
485#407—431no—
486#407—431no—
487#407C2×D4311yescharacteristic
488C4×M16—431no—
489C4×M16—431no—
490#343—431no—
491#343—431no—
492#343—431no—
493#343—431no—
494#343—431no—
495#343—431no—
496#343—431no—
497#343—431no—
498#343—431no—
499#343—431no—
500#343C2×D4311yescharacteristic
501#343C2×D4311yescharacteristic
502C43#2248111yescharacteristic, complemented, Sylow
503C22×Q8—432no—
504C22×Q8C22×D4311yescharacteristic
505C22×D4—431no—
506C23×C4—431no—
507C23×C4—432no—
508C23×C4—432no—
509C23×C4C22×D4311yescharacteristic
510C2×M16—21no—
511C2×M16—22no—
512C2×M16—41no—
513C2×M16—431no—
514C2×M16—431no—
515C2×M16—431no—
516C2×M16—431no—
517C2×M16—861no—
518C2×M16—861no—
519C2×M16—861no—
520C2×M16—862no—
521C2×M16—862no—
522C2×M16—862no—
523C2×M16—1721no—
524C2×M16—1721no—
525C2×M16—1721no—
526C2×M16C22×D4311yescharacteristic
527C2×M16C22×D4311yescharacteristic
528C2×M16C22×D4311yescharacteristic
529C2×M16C22×D4311yescharacteristic
530C22×C8—21no—
531C22×C8—861no—
532C22×C8—861no—
533C22×C8—861no—
534C4⋊Q8—861no—
535C4⋊Q8—861no—
536C4⋊Q8—861no—
537C4⋊Q8—861no—
538#125—862no—
539#125—862no—
540#125—862no—
541#125—862no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—862no—
547C22⋊Q8—862no—
548C22⋊Q8—862no—
549C22⋊Q8—862no—
550C22⋊Q8—862no—
551C22⋊Q8—862no—
552C22⋊Q8—862no—
553C22⋊Q8—862no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C4×Q8—861no—
559C4×Q8—861no—
560C4×Q8—861no—
561C4×Q8—861no—
562C4×D4—431no—
563C4×D4—431no—
564C4×D4—431no—
565C4×D4—431no—
566C4×D4—431no—
567C4×D4—431no—
568C4×D4—431no—
569C4×D4—431no—
570C4×D4—862no—
571C4×D4—862no—
572C4×D4—862no—
573C4×D4—862no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—432no—
576C2×C4⋊C4—432no—
577C2×C4⋊C4—432no—
578C2×C4⋊C4—432no—
579C2×C4⋊C4—432no—
580C2×C4⋊C4—431no—
581C2×C4⋊C4—431no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4—861no—
584C2×C4⋊C4—861no—
585C2×C4⋊C4—861no—
586C2×C4⋊C4—861no—
587C2×C4⋊C4—861no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4C4×D4312yes—
591C2×C4⋊C4C22×D4311yescharacteristic
592C2×C22⋊C4—431no—
593C2×C22⋊C4—431no—
594C2×C22⋊C4—432no—
595C2×C22⋊C4C4×D4312yes—
596C2×C42—431no—
597C2×C42—432no—
598C4⋊C8—861no—
599C4⋊C8—861no—
600C4⋊C8—861no—
601C4⋊C8—861no—
602#101—22no—
603#101—41no—
604#101—862no—
605#101—1721no—
606C22⋊C8—21no—
607C22⋊C8—21no—
608C22⋊C8—861no—
609C22⋊C8—861no—
610C22⋊C8—861no—
611C22⋊C8—861no—
612C22⋊C8—861no—
613C22⋊C8—861no—
614#97—861no—
615#97—861no—
616C4×C8—861no—
617C4×C8—861no—
618C24—431no—
619C24C2×C4×D4311yescharacteristic
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—862no—
627C2×Q8—862no—
628C2×Q8—3442no—
629C2×D4—431no—
630C2×D4—431no—
631C2×D4—431no—
632C2×D4—431no—
633C2×D4—864no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—431no—
645C22×C4—432no—
646C22×C4—432no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—3442no—
656C22×C4—3442no—
657C22×C4C2×C4×D4312yes—
658C22×C4C2×C4×D4311yescharacteristic
659C22×C4C2×C4×D4312yes—
660C22×C4D4×D4311yescharacteristic
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4D4×D4311yescharacteristic
664C22×C4C23×D4311yescharacteristic
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—42no—
673M16—432no—
674M16—861no—
675M16—861no—
676M16—861no—
677M16—861no—
678M16—861no—
679M16—861no—
680M16—861no—
681M16—1722no—
682M16—1722no—
683M16—1722no—
684M16#1062190012yes—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—1722no—
695C2×C8—1722no—
696C2×C8—1722no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—431no—
702C4⋊C4—431no—
703C4⋊C4—431no—
704C4⋊C4—431no—
705C4⋊C4—862no—
706C4⋊C4—862no—
707C4⋊C4—862no—
708C4⋊C4—862no—
709C4⋊C4—862no—
710C4⋊C4—862no—
711C4⋊C4—862no—
712C4⋊C4—862no—
713C4⋊C4—862no—
714C4⋊C4—862no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—431no—
722C22⋊C4—431no—
723C22⋊C4—431no—
724C22⋊C4—431no—
725C22⋊C4—431no—
726C22⋊C4—431no—
727C22⋊C4—431no—
728C22⋊C4—431no—
729C22⋊C4—862no—
730C22⋊C4—862no—
731C42—431no—
732C42—431no—
733C42—431no—
734C42—431no—
735C42—862no—
736C42—862no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—431no—
742C23—431no—
743C23—862no—
744C23—861no—
745C23—861no—
746C23—1721no—
747C23C22⋊C4×D4311yescharacteristic
748C23C22⋊C4×D4311yescharacteristic
749C23C22×C4×D4311yescharacteristic
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—3442no—
755Q8—3442no—
756D4—434no—
757D4—862no—
758D4—862no—
759D4—862no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—431no—
776C2×C4—431no—
777C2×C4—431no—
778C2×C4—431no—
779C2×C4—431no—
780C2×C4—431no—
781C2×C4—862no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—862no—
793C2×C4—862no—
794C2×C4—3442no—
795C2×C4—3442no—
796C2×C4—3442no—
797C2×C4—3442no—
798C2×C4—1721no—
799C2×C4—1722no—
800C2×C4—1722no—
801C2×C4C22⋊C4×D4311yescharacteristic
802C2×C4C22⋊C4×D4311yescharacteristic
803C2×C4C2×D4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4#41×D4311yescharacteristic
806C2×C4C2×#1062190011yescharacteristic
807C2×C4#1306337011yescharacteristic
808C2×C4#1306337211yescharacteristic
809C8—22no—
810C8—41no—
811C8—41no—
812C8—41no—
813C8—862no—
814C8—1721no—
815C8—1721no—
816C8—1721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—42no—
825C22—42no—
826C22—432no—
827C22—861no—
828C22—861no—
829C22—861no—
830C22—861no—
831C22—861no—
832C22—1722no—
833C22—1722no—
834C22#101×D4312yes—
835C22C2×C22⋊C4×D4311yescharacteristic
836C22C4×#1062190011yescharacteristic
837C22#1458337811yescharacteristic
838C4—21no—
839C4—21no—
840C4—42no—
841C4—42no—
842C4—432no—
843C4—861no—
844C4—861no—
845C4—861no—
846C4—861no—
847C4—861no—
848C4—1722no—
849C4—1722no—
850C4#1458353611yescharacteristic
851C4#1458353811yescharacteristic
852C4#1458354711yescharacteristic
853C4#1458354911yescharacteristic
854C2—21no—
855C2—21no—
856C2—22no—
857C2—41no—
858C2—862no—
859C2—1721no—
860C2#1913742111yescharacteristic
861C2C2×#101×D4311yescharacteristic
862C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1901C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1901D43
hypocenterC43#22481
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
4. #19135582C2semidirect
5. #19135582C2semidirect
6. #19135064C2semidirect
7. #19135060C2semidirect
8. #19135060C2semidirect
9. #19134674C2semidirect
10. #19134673C2semidirect
11. #19134589C2semidirect
12. #101×Dic43C2semidirect
13. C2×#14582667C2semidirect
14. #343×D43C2semidirect
15. C43×#1901C2semidirect
348. C22⋊D43#101semidirect
431. #1901D43semidirect
502. C43#22481semidirect

Maximal subgroups

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

subgroupindex
C2×#145836072
M16×C22⋊D432
#191433272
#191355822
#191350642
#191350602
#191346742
#191346732
#191345892
#101×Dic432
C2×#145826672
#343×D432
C43×#19012
#2248143