Finite Group Databasebeta

← #25062828

Subgroups — #25062828

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583582C211yesmaximal, characteristic
2#19143253C211yesmaximal, characteristic, complemented
3#19132965C211yesmaximal, characteristic, complemented
4#19132962C211yesmaximal, characteristic, complemented
5#19132952C211yesmaximal, characteristic, complemented
6#19132950C211yesmaximal, characteristic, complemented
7#19132944C211yesmaximal, characteristic
8#19132941C211yesmaximal, characteristic
9#19132938C211yesmaximal, characteristic, complemented
10#19132927C211yesmaximal, characteristic, complemented
11#19132924C211yesmaximal, characteristic, complemented
12#19132918C211yesmaximal, characteristic, complemented
13#19132907C211yesmaximal, characteristic, complemented
14C2×#14582624C211yesmaximal, characteristic, complemented
15C43×#2924C211yesmaximal, characteristic, complemented
16#14583582—21no—
17#14583582—21no—
18#14583582—21no—
19#14583582—21no—
20#14583582—21no—
21#14583582—21no—
22#14583582—21no—
23#14583582—21no—
24C2×#13063320C411yescharacteristic
25C2×#13063319C2211yescharacteristic
26C2×#13063317C2211yescharacteristic
27C2×#13063315C411yescharacteristic
28C2×#13063315C411yescharacteristic
29C2×#13063309C411yescharacteristic
30C2×#13063308C2211yescharacteristic
31C2×#13063303C411yescharacteristic
32C2×#13063302C411yescharacteristic
33C2×C4×Dic86C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C411yescharacteristic
35C2×#13063282C2211yescharacteristic
36C2×#13063281C411yescharacteristic
37C22×Dic43⋊C4C2211yescharacteristic
38#14582960—21no—
39#14582960—21no—
40#14582956C2211yescharacteristic
41#14582956C2211yescharacteristic
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582926—21no—
45#14582863C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47#14582855—21no—
48#14582624C2211yescharacteristic
49#14582624C2211yescharacteristic
50#14582624C2211yescharacteristic
51#14582624C2211yescharacteristic
52#14582624C2211yescharacteristic
53#14582624C2211yescharacteristic
54#14582624C2211yescharacteristic
55#14582624C2211yescharacteristic
56#14582624C2211yescharacteristic
57#14582624C2211yescharacteristic
58#14582624C2211yescharacteristic
59#14582624C2211yescharacteristic
60#14582622C2211yescharacteristic
61#14582622C2211yescharacteristic
62#14582622C2211yescharacteristic
63#14582622C2211yescharacteristic
64C2×#117×C43C2211yescharacteristic
65C43×#433—21no—
66C43×#433—21no—
67C43×#432C2211yescharacteristic
68C43×#432C2211yescharacteristic
69C43×#431C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×#424—21no—
72C43×#407C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C43×#405—21no—
75C22×Dic86C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C23×Dic43C2×C411yescharacteristic
78C23×Dic43C2×C411yescharacteristic
79C22×C4×D43C2×C411yescharacteristic
80C2×#10621877—21no—
81C22×C43⋊C8—21no—
82#13063320—21no—
83#13063320—21no—
84#13063320—21no—
85#13063320—21no—
86#13063319—21no—
87#13063319—21no—
88#13063319—21no—
89#13063319—21no—
90#13063317—21no—
91#13063317—21no—
92#13063317—21no—
93#13063317—21no—
94#13063315—21no—
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063315—21no—
101#13063315—21no—
102#13063309—21no—
103#13063309—21no—
104#13063309—21no—
105#13063309—21no—
106#13063308—21no—
107#13063308—21no—
108#13063308—21no—
109#13063308—21no—
110#13063303—21no—
111#13063303—21no—
112#13063303—21no—
113#13063303—21no—
114#13063302—21no—
115#13063302—21no—
116#13063302—21no—
117#13063302—21no—
118C4×Dic86—21no—
119C4×Dic86—21no—
120C4×Dic86—21no—
121C4×Dic86—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126#13063282—21no—
127#13063282—21no—
128#13063282—21no—
129#13063282—21no—
130#13063281—21no—
131#13063281—21no—
132#13063281—21no—
133#13063281—21no—
134C2×C4⋊Dic43C2×C411yescharacteristic
135C2×C4⋊Dic43C2×C411yescharacteristic
136C2×C4⋊Dic43C2×C411yescharacteristic
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4C2×C411yescharacteristic
142C2×Dic43⋊C4C2×C411yescharacteristic
143C2×Dic43⋊C4C2×C411yescharacteristic
144C2×Dic43⋊C4C2×C411yescharacteristic
145C2×Dic43⋊C4C2×C411yescharacteristic
146C2×Dic43⋊C4C2×C411yescharacteristic
147C2×Dic43⋊C4C2×C411yescharacteristic
148C2×Dic43⋊C4C2×C411yescharacteristic
149C2×Dic43⋊C4C2311yescharacteristic
150C2×Dic43⋊C4C2311yescharacteristic
151C2×Dic43⋊C4C2311yescharacteristic
152C2×C22⋊Dic43C2×C411yescharacteristic
153C2×(C2×D43)⋊C4C2×C411yescharacteristic
154C2×(C2×D43)⋊C4C2×C411yescharacteristic
155C2×(C2×D43)⋊C4C2×C411yescharacteristic
156C2×(C2×D43)⋊C4C2×C411yescharacteristic
157C2×(C2×D43)⋊C4C2311yescharacteristic
158C2×C4×Dic43C2×C411yescharacteristic
159C2×C4×Dic43C2×C411yescharacteristic
160C2×C4×Dic43C2×C411yescharacteristic
161C4⋊(C43⋊C8)—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)C2311yescharacteristic
168C22⋊(C43⋊C8)C2311yescharacteristic
169C22⋊(C43⋊C8)C2311yescharacteristic
170C22⋊(C43⋊C8)C2311yescharacteristic
171#13063236—21no—
172#13063236—21no—
173C4×C43⋊C8—21no—
174C4×C43⋊C8—21no—
175C23×C4×C43C2311yescharacteristic
176C2×M16×C43—21no—
177C22×C8×C43—21no—
178#117×C43D411yescharacteristic
179#117×C43D411yescharacteristic
180#117×C43D411yescharacteristic
181#117×C43D411yescharacteristic
182#117×C43D411yescharacteristic
183#117×C43D411yescharacteristic
184#117×C43D411yescharacteristic
185#117×C43D411yescharacteristic
186C2×C4⋊C4×C43C2×C411yescharacteristic
187C2×C4⋊C4×C43C2×C411yescharacteristic
188C2×C22⋊C4×C43C2×C411yescharacteristic
189C2×C22⋊C4×C43C2×C411yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C4⋊C8×C43—21no—
193C4⋊C8×C43—21no—
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43C2311yescharacteristic
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202#97×C43—21no—
203#97×C43—21no—
204C4×C8×C43—21no—
205C4×C8×C43—21no—
206C24×C43C22×C411yescharacteristic
207C23×D43C22×C411yescharacteristic
208C22×C4×C43—42no—
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—42no—
222C22×Dic43—22no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—41no—
228C22×Dic43—42no—
229C22×Dic43C22×C411yescharacteristic
230C22×Dic43C22×C411yescharacteristic
231C22×Dic43C22×C411yescharacteristic
232C22×Dic43C22×C411yescharacteristic
233C22×Dic43C22×C411yescharacteristic
234C22×Dic43C22×C411yescharacteristic
235C22×Dic43C22×C411yescharacteristic
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—22no—
239C2×C4×D43—41no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—22no—
243C2×Dic86—41no—
244M16×C43—42no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—42no—
250C4⋊C4×C43C22⋊C411yescharacteristic
251C4⋊C4×C43C22⋊C411yescharacteristic
252C4⋊C4×C43C22⋊C411yescharacteristic
253C4⋊C4×C43C22⋊C411yescharacteristic
254C4⋊C4×C43C22⋊C411yescharacteristic
255C4⋊C4×C43C22⋊C411yescharacteristic
256C4⋊C4×C43C22⋊C411yescharacteristic
257C4⋊C4×C43C22⋊C411yescharacteristic
258C22⋊C4×C43C22⋊C411yescharacteristic
259C22⋊C4×C43C22⋊C411yescharacteristic
260C22⋊C4×C43C22⋊C411yescharacteristic
261C22⋊C4×C43C22⋊C411yescharacteristic
262C22⋊C4×C43C22⋊C411yescharacteristic
263C22⋊C4×C43C22⋊C411yescharacteristic
264C22⋊C4×C43C22⋊C411yescharacteristic
265C22⋊C4×C43C22⋊C411yescharacteristic
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2×D411yescharacteristic
269C42×C43C2×D411yescharacteristic
270C42×C43C2×D411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—21no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320#10621877—42no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—42no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—22no—
329C23×C43—41no—
330C23×C43C2×C22⋊C411yescharacteristic
331C23×C43C2×C22⋊C411yescharacteristic
332C23×C43C23×C411yescharacteristic
333C22×D43—21no—
334C22×D43—21no—
335C22×D43—21no—
336C22×D43—41no—
337C22×D43—41no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C2×C22⋊C411yescharacteristic
357C2×C4×C43C2×C22⋊C411yescharacteristic
358C2×C4×C43C2×C22⋊C411yescharacteristic
359C2×C4×C43C2×C22⋊C411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C22⋊D43—42no—
363C22⋊D43—42no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—21no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—42no—
377C2×Dic43—42no—
378C2×Dic43—42no—
379C2×Dic43—42no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43#13112yes—
385C4×D43—42no—
386C4×D43—42no—
387Dic86—42no—
388Dic86—42no—
389C8×C43—41no—
390C8×C43—41no—
391C8×C43—41no—
392C8×C43—41no—
393C43⋊C8—41no—
394C43⋊C8—41no—
395C43⋊C8—41no—
396C43⋊C8—41no—
397#17417—431nomaximal, Sylow
398C22×C43—21no—
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43#41012yes—
408C22×C43C22×C22⋊C411yescharacteristic
409C22×C43C2×#13111yescharacteristic
410C22×C43#56811yescharacteristic
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—41no—
414C2×D43—81no—
415C2×D43—81no—
416C4×C43—21no—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—21no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428Dic43—22no—
429Dic43—41no—
430Dic43—41no—
431Dic43—41no—
432Dic43—41no—
433Dic43—41no—
434Dic43—41no—
435C2×#552—431no—
436#2924—431no—
437#2924D4311yescharacteristic, complemented
438#1473—431no—
439#1473—431no—
440#1470—431no—
441#1470—431no—
442#1468—431no—
443#1468—431no—
444#1467—431no—
445#1464—431no—
446#1463—431no—
447#1461—431no—
448#1458—431no—
449C2×#324—431no—
450C2×C43—21no—
451C2×C43—21no—
452C2×C43—22no—
453C2×C43—41no—
454C2×C43#288011yescharacteristic
455C2×C43C2×#41011yescharacteristic
456C2×C43#288911yescharacteristic
457D43—81no—
458#552—861no—
459#552—861no—
460#552—861no—
461#552—861no—
462#552—861no—
463#552—861no—
464#552—861no—
465#552—861no—
466C2×#126—431no—
467C2×#126—431no—
468C2×#125—431no—
469C2×#125—431no—
470C2×#125—431no—
471C2×#123—431no—
472C2×#123—431no—
473C2×C22⋊Q8—431no—
474C2×C22⋊Q8—431no—
475C2×C4×Q8—431no—
476C2×C4×D4—431no—
477C2×#117—431no—
478C2×#117—431no—
479C2×#117C2×D4311yescharacteristic
480C22×C4⋊C4—431no—
481#433—21no—
482#433—21no—
483#433—861no—
484#433—861no—
485#432—431no—
486#432—431no—
487#432C2×D4311yescharacteristic
488#432C2×D4311yescharacteristic
489#431—431no—
490#431—431no—
491#431C2×D4311yescharacteristic
492#431C2×D4311yescharacteristic
493#424—21no—
494#424—861no—
495#407—431no—
496#407C2×D4311yescharacteristic
497C2×C22⋊C8—431no—
498C2×C22⋊C8C2×D4311yescharacteristic
499#405—21no—
500#405—861no—
501#324—431no—
502#324—431no—
503#324—431no—
504#324—431no—
505#324—431no—
506#324—431no—
507#324—431no—
508#324—431no—
509#324—431no—
510#324—431no—
511#324—431no—
512#324—431no—
513#323—431no—
514#323—431no—
515#323—431no—
516#323—431no—
517C43#1741711yescharacteristic, complemented, Sylow
518C22×Q8—431no—
519C22×D4—431no—
520C23×C4—431no—
521C23×C4—431no—
522C23×C4—431no—
523C23×C4C22×D4311yescharacteristic
524C2×M16—21no—
525C2×M16—861no—
526C22×C8—21no—
527C22×C8—861no—
528#126—861no—
529#126—861no—
530#126—861no—
531#126—861no—
532#126—861no—
533#126—861no—
534#126—861no—
535#126—861no—
536#125—861no—
537#125—861no—
538#125—861no—
539#125—861no—
540#125—861no—
541#125—861no—
542#125—861no—
543#125—861no—
544#125—861no—
545#125—861no—
546#125—861no—
547#125—861no—
548#123—861no—
549#123—861no—
550#123—861no—
551#123—861no—
552#123—861no—
553#123—861no—
554#123—861no—
555#123—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561C22⋊Q8—861no—
562C22⋊Q8—861no—
563C22⋊Q8—861no—
564C4×Q8—861no—
565C4×Q8—861no—
566C4×Q8—861no—
567C4×Q8—861no—
568C4×D4—861no—
569C4×D4—861no—
570C4×D4—861no—
571C4×D4—861no—
572#117—861no—
573#117—861no—
574#117—861no—
575#117—861no—
576#117—861no—
577#117—861no—
578#117—861no—
579#117—861no—
580#117D17211yescharacteristic
581#117D17211yescharacteristic
582#117D17211yescharacteristic
583#117D17211yescharacteristic
584#117C22⋊D4311yescharacteristic
585#117C22⋊D4311yescharacteristic
586#117C22⋊D4311yescharacteristic
587#117C22⋊D4311yescharacteristic
588C2×C4⋊C4—431no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—431no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—431no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4C4×D4311yescharacteristic
607C2×C4⋊C4C4×D4311yescharacteristic
608C2×C22⋊C4—431no—
609C2×C22⋊C4—431no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—431no—
612C2×C22⋊C4—431no—
613C2×C22⋊C4—431no—
614C2×C22⋊C4C4×D4311yescharacteristic
615C2×C22⋊C4C4×D4311yescharacteristic
616C2×C42—431no—
617C2×C42—431no—
618C2×C42—431no—
619C2×C42C22×D4311yescharacteristic
620C2×C42C22×D4311yescharacteristic
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—21no—
624C4⋊C8—21no—
625C4⋊C8—861no—
626C4⋊C8—861no—
627C4⋊C8—861no—
628C4⋊C8—861no—
629C22⋊C8—21no—
630C22⋊C8—21no—
631C22⋊C8—431no—
632C22⋊C8—431no—
633C22⋊C8—431no—
634C22⋊C8—431no—
635C22⋊C8—861no—
636C22⋊C8—861no—
637C22⋊C8C22×D4311yescharacteristic
638C22⋊C8C22×D4311yescharacteristic
639C22⋊C8C22×D4311yescharacteristic
640C22⋊C8C22×D4311yescharacteristic
641#97—21no—
642#97—21no—
643#97—861no—
644#97—861no—
645C4×C8—21no—
646C4×C8—21no—
647C4×C8—861no—
648C4×C8—861no—
649C24—431no—
650C24C2×C4×D4311yescharacteristic
651C2×Q8—862no—
652C2×Q8—861no—
653C2×Q8—861no—
654C2×Q8—1721no—
655C2×D4—861no—
656C2×D4—861no—
657C2×D4—1722no—
658C22×C4—42no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—862no—
667C22×C4—862no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—1721no—
675C22×C4—1721no—
676C22×C4—1722no—
677C22×C4C2×C4×D4311yescharacteristic
678C22×C4C2×C4×D4311yescharacteristic
679C22×C4C2×C4×D4311yescharacteristic
680C22×C4C2×C4×D4311yescharacteristic
681C22×C4C2×C4×D4311yescharacteristic
682C22×C4C2×D17211yescharacteristic
683C22×C4C2×D17211yescharacteristic
684C22×C4C2×C22⋊D4311yescharacteristic
685C22×C4C2×C22⋊D4311yescharacteristic
686C22×C4C23×D4311yescharacteristic
687M16—42no—
688M16—1722no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—1722no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4(C2×D43)⋊C411yescharacteristic
728C4⋊C4(C2×D43)⋊C411yescharacteristic
729C4⋊C4(C2×D43)⋊C411yescharacteristic
730C4⋊C4(C2×D43)⋊C411yescharacteristic
731C4⋊C4(C2×D43)⋊C411yescharacteristic
732C4⋊C4(C2×D43)⋊C411yescharacteristic
733C4⋊C4(C2×D43)⋊C411yescharacteristic
734C4⋊C4(C2×D43)⋊C411yescharacteristic
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C22⋊C4—861no—
741C22⋊C4—861no—
742C22⋊C4—861no—
743C22⋊C4—861no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4(C2×D43)⋊C411yescharacteristic
748C22⋊C4(C2×D43)⋊C411yescharacteristic
749C22⋊C4(C2×D43)⋊C411yescharacteristic
750C22⋊C4(C2×D43)⋊C411yescharacteristic
751C22⋊C4(C2×D43)⋊C411yescharacteristic
752C22⋊C4(C2×D43)⋊C411yescharacteristic
753C22⋊C4(C2×D43)⋊C411yescharacteristic
754C22⋊C4(C2×D43)⋊C411yescharacteristic
755C42—861no—
756C42—861no—
757C42—861no—
758C42—861no—
759C42—861no—
760C42—861no—
761C42C2×D17211yescharacteristic
762C42C2×D17211yescharacteristic
763C42C2×D17211yescharacteristic
764C42C2×D17211yescharacteristic
765C42C2×C22⋊D4311yescharacteristic
766C42C2×C22⋊D4311yescharacteristic
767C42C2×C22⋊D4311yescharacteristic
768C42C2×C22⋊D4311yescharacteristic
769C23—22no—
770C23—21no—
771C23—21no—
772C23—41no—
773C23—861no—
774C23—861no—
775C23—861no—
776C23—1721no—
777C23—1721no—
778C23C2×(C2×D43)⋊C411yescharacteristic
779C23C2×(C2×D43)⋊C411yescharacteristic
780C23C22×C4×D4311yescharacteristic
781Q8—1722no—
782Q8—1722no—
783D4—1722no—
784D4—1722no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—432no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4—1722no—
813C2×C4—1722no—
814C2×C4—1722no—
815C2×C4—1722no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4C2×(C2×D43)⋊C411yescharacteristic
821C2×C4C2×(C2×D43)⋊C411yescharacteristic
822C2×C4C2×(C2×D43)⋊C411yescharacteristic
823C2×C4C2×(C2×D43)⋊C411yescharacteristic
824C2×C4C2×(C2×D43)⋊C411yescharacteristic
825C2×C4C2×(C2×D43)⋊C411yescharacteristic
826C2×C4C2×(C2×D43)⋊C411yescharacteristic
827C2×C4C2×(C2×D43)⋊C411yescharacteristic
828C2×C4C2×(C2×D43)⋊C411yescharacteristic
829C2×C4C2×(C2×D43)⋊C411yescharacteristic
830C2×C4C22×C22⋊D4311yescharacteristic
831C2×C4C22×D17211yescharacteristic
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—1721no—
837C8—1721no—
838C8—1721no—
839C8—1721no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—42no—
848C22—42no—
849C22—3441no—
850C22—3441no—
851C22—1721no—
852C22—1721no—
853C22—1721no—
854C22#1458287212yes—
855C22C22×(C2×D43)⋊C411yescharacteristic
856C22#131×D4311yescharacteristic
857C22#1458366411yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—862no—
871C4—1721no—
872C4—1721no—
873C4—1721no—
874C4—1721no—
875C4—1721no—
876C4—1721no—
877C2—21no—
878C2—21no—
879C2—22no—
880C2—41no—
881C2—3441no—
882C2#1914304211yescharacteristic
883C2C2×#1458287211yescharacteristic
884C2#1914307711yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2924C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#2924D43
hypocenterC43#17417
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #19143253C2semidirect
3. #19132965C2semidirect
4. #19132962C2semidirect
5. #19132952C2semidirect
6. #19132950C2semidirect
9. #19132938C2semidirect
10. #19132927C2semidirect
11. #19132924C2semidirect
12. #19132918C2semidirect
13. #19132907C2semidirect
14. C2×#14582624C2semidirect
15. C43×#2924C2semidirect
437. #2924D43semidirect
517. C43#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#145835822
#191432532
#191329652
#191329622
#191329522
#191329502
#191329442
#191329412
#191329382
#191329272
#191329242
#191329182
#191329072
C2×#145826242
C43×#29242
#1741743