Finite Group Databasebeta

← #25062591

Subgroups — #25062591

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583429C211yesmaximal, characteristic
2C2×#14582953C211yesmaximal, characteristic, complemented
3C2×#14582949C211yesmaximal, characteristic, complemented
4#19132963C212yesmaximal, complemented
5#19132961C212yesmaximal, complemented
6#19132949C212yesmaximal, complemented
7#19132945C212yesmaximal, complemented
8#19132913C211yesmaximal, characteristic, complemented
9#19132911C211yesmaximal, characteristic, complemented
10#19132911C211yesmaximal, characteristic, complemented
11C43×#1459C211yesmaximal, characteristic, complemented
12#14583429—21no—
13#14583429—21no—
14#14583429—21no—
15#14583429—21no—
16#14583429—21no—
17#14583429—21no—
18#14583429—21no—
19#14583429—21no—
20C2×#13063320C2211yescharacteristic
21C2×#13063318C2211yescharacteristic
22C2×#13063315C2211yescharacteristic
23C2×#13063311C2211yescharacteristic
24C2×#13063309C411yescharacteristic
25C2×#13063306C411yescharacteristic
26C2×#13063302C411yescharacteristic
27C2×#13063297C411yescharacteristic
28C2×C4×Dic86C411yescharacteristic
29C2×C4×C22⋊D43C411yescharacteristic
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×#13063284C411yescharacteristic
32C2×#13063282C411yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582953—21no—
35#14582953—21no—
36#14582953C2212yes—
37#14582953C2212yes—
38#14582949—21no—
39#14582949—21no—
40#14582949C2212yes—
41#14582949C2212yes—
42C2×Dic43⋊C8—21no—
43C2×Dic43⋊C8—21no—
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×#13063235—21no—
47C2×C8×Dic43—21no—
48#14582625C2212yes—
49#14582624C2212yes—
50#14582624C2212yes—
51#14582623C2212yes—
52#14582622C2212yes—
53#14582622C2212yes—
54C2×C4×D4×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#324C2212yes—
58C43×#323C2212yes—
59C22×Dic86C2×C411yescharacteristic
60C22×C22⋊D43C2×C411yescharacteristic
61C22×C22⋊D43C2×C411yescharacteristic
62C23×Dic43C2×C411yescharacteristic
63C23×Dic43C2×C411yescharacteristic
64C22×C4×D43C2×C411yescharacteristic
65C22×C43⋊C8—21no—
66C22×C43⋊C8—21no—
67#13063320—21no—
68#13063320—21no—
69#13063320—21no—
70#13063320—21no—
71#13063318—21no—
72#13063318—21no—
73#13063318—21no—
74#13063318—21no—
75#13063315—21no—
76#13063315—21no—
77#13063315—21no—
78#13063315—21no—
79#13063311—21no—
80#13063311—21no—
81#13063311—21no—
82#13063311—21no—
83#13063309—21no—
84#13063309—21no—
85#13063309—21no—
86#13063309—21no—
87#13063306—21no—
88#13063306—21no—
89#13063306—21no—
90#13063306—21no—
91#13063302—21no—
92#13063302—21no—
93#13063302—21no—
94#13063302—21no—
95#13063297—21no—
96#13063297—21no—
97#13063297—21no—
98#13063297—21no—
99C4×Dic86—21no—
100C4×Dic86—21no—
101C4×Dic86—21no—
102C4×Dic86—21no—
103C4×C22⋊D43—21no—
104C4×C22⋊D43—21no—
105C4×C22⋊D43—21no—
106C4×C22⋊D43—21no—
107C4×C22⋊D43—21no—
108C4×C22⋊D43—21no—
109C4×C22⋊D43—21no—
110C4×C22⋊D43—21no—
111#13063284—21no—
112#13063284—21no—
113#13063284—21no—
114#13063284—21no—
115#13063282—21no—
116#13063282—21no—
117#13063282—21no—
118#13063282—21no—
119C2×C4⋊Dic43C2×C411yescharacteristic
120C2×C4⋊Dic43C2×C411yescharacteristic
121C2×C4⋊Dic43C2×C411yescharacteristic
122C2×Dic43⋊C4C2×C411yescharacteristic
123C2×Dic43⋊C4C2×C411yescharacteristic
124C2×Dic43⋊C4C2×C411yescharacteristic
125C2×Dic43⋊C4C2×C411yescharacteristic
126C2×Dic43⋊C4C2×C411yescharacteristic
127C2×Dic43⋊C4C2311yescharacteristic
128C2×C22⋊Dic43C2×C411yescharacteristic
129C2×C22⋊Dic43C2×C411yescharacteristic
130C2×C22⋊Dic43C2×C411yescharacteristic
131C2×C22⋊Dic43C2×C411yescharacteristic
132C2×(C2×D43)⋊C4C2×C411yescharacteristic
133C2×(C2×D43)⋊C4C2×C411yescharacteristic
134C2×(C2×D43)⋊C4C2×C411yescharacteristic
135C2×(C2×D43)⋊C4C2311yescharacteristic
136C2×C4×Dic43C2×C411yescharacteristic
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43C2×C411yescharacteristic
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43C2311yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149Dic43⋊C8—22no—
150Dic43⋊C8—22no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)—21no—
154C22⋊(C43⋊C8)—21no—
155C22⋊(C43⋊C8)C2312yes—
156C22⋊(C43⋊C8)C2312yes—
157#13063235—22no—
158#13063235—22no—
159C8×Dic43—22no—
160C8×Dic43—22no—
161C22×D4×C43C2×C411yescharacteristic
162C23×C4×C43C2×C411yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C22×C8×C43—21no—
165C22×C8×C43—21no—
166C4×D4×C43—21no—
167C4×D4×C43—21no—
168C4×D4×C43—21no—
169C4×D4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43C2×C411yescharacteristic
172C2×C22⋊C4×C43C2311yescharacteristic
173C2×C42×C43C2×C411yescharacteristic
174C22⋊C8×C43—21no—
175C22⋊C8×C43—21no—
176C22⋊C8×C43C2312yes—
177C22⋊C8×C43C2312yes—
178C24×C43C22×C411yescharacteristic
179C24×C43C22×C411yescharacteristic
180C23×D43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—42no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—42no—
208C22×Dic43C22⋊C411yescharacteristic
209C22×Dic43C22⋊C411yescharacteristic
210C22×Dic43C22⋊C411yescharacteristic
211C22×Dic43C22⋊C411yescharacteristic
212C22×Dic43C22⋊C411yescharacteristic
213C22×Dic43C22⋊C411yescharacteristic
214C22×Dic43C22⋊C411yescharacteristic
215C22×Dic43C22⋊C411yescharacteristic
216C22×Dic43C22×C411yescharacteristic
217C22×Dic43C22×C411yescharacteristic
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C411yescharacteristic
220C22×Dic43C22×C411yescharacteristic
221C22×Dic43C22×C411yescharacteristic
222C22×Dic43C22×C411yescharacteristic
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—42no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—42no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43—42no—
232C2×C8×C43—42no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C22⋊Dic43—21no—
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C4×Dic43C2×D411yescharacteristic
291C4×Dic43C2×D411yescharacteristic
292C4×Dic43C2×D411yescharacteristic
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8—42no—
296C2×C43⋊C8—42no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43C2×C22⋊C411yescharacteristic
305C23×C43C2×C22⋊C411yescharacteristic
306C23×C43#13112yes—
307C23×C43#13112yes—
308C23×C43C23×C411yescharacteristic
309C22×D43—21no—
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—41no—
313C22×D43—41no—
314D4×C43—42no—
315D4×C43—42no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43C2×C22⋊C411yescharacteristic
332C2×C4×C43C2×C22⋊C411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C22⋊D43—42no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363C2×Dic43C2×C22⋊C411yescharacteristic
364C2×Dic43C2×C22⋊C411yescharacteristic
365C2×Dic43C2×C22⋊C411yescharacteristic
366C2×Dic43C2×C22⋊C411yescharacteristic
367C2×Dic43C2×C22⋊C411yescharacteristic
368C4×D43—42no—
369C4×D43—42no—
370Dic86—42no—
371Dic86—42no—
372C8×C43—42no—
373C8×C43—42no—
374C43⋊C8—42no—
375C43⋊C8—42no—
376#17382—431nomaximal, Sylow
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43#40812yes—
391C22×C43#40812yes—
392C22×C43C22×C22⋊C411yescharacteristic
393C22×C43C2×#13111yescharacteristic
394C22×C43C2×#13111yescharacteristic
395C2×D43—41no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—81no—
399C2×D43—81no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43#41012yes—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—21no—
414Dic43—41no—
415Dic43—41no—
416Dic43—41no—
417Dic43#41312yes—
418C2×#529—431no—
419C2×#432—431no—
420C2×#431—431no—
421#1473—432no—
422#1473—432no—
423#1470—432no—
424#1469—432no—
425#1459—431no—
426#1459—431no—
427#1459—431no—
428#1459D4311yescharacteristic, complemented
429C2×C43—21no—
430C2×C43—21no—
431C2×C43—22no—
432C2×C43—22no—
433C2×C43—81no—
434C2×C43C2×#40811yescharacteristic
435C2×C43C2×#41011yescharacteristic
436C2×C43C2×#41311yescharacteristic
437D43—81no—
438#529—861no—
439#529—861no—
440#529—861no—
441#529—861no—
442#529—861no—
443#529—861no—
444#529—861no—
445#529—861no—
446C2×#126—431no—
447C2×#126—431no—
448C2×#125—431no—
449C2×#124—431no—
450C2×#123—431no—
451C2×#123—431no—
452C2×C22⋊Q8—431no—
453C2×#121—431no—
454C2×C4×Q8—431no—
455C2×C4×D4—431no—
456C2×C4×D4—431no—
457C2×C4×D4C2×D4311yescharacteristic
458C2×#117—431no—
459C2×#117—431no—
460C22×C42—431no—
461#432—432no—
462#432—432no—
463#432—861no—
464#432—861no—
465#431—432no—
466#431—432no—
467#431—861no—
468#431—861no—
469C2×C4⋊C8—861no—
470C2×C4⋊C8—861no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×C22⋊C8C2×D4311yescharacteristic
474C2×C22⋊C8C2×D4311yescharacteristic
475C2×#97—861no—
476C2×C4×C8—861no—
477#324—432no—
478#324—432no—
479#324—432no—
480#324C2×D4312yes—
481#323—432no—
482#323—432no—
483#323—432no—
484#323C2×D4312yes—
485C43#1738211yescharacteristic, complemented, Sylow
486C22×Q8—431no—
487C22×D4—431no—
488C22×D4—431no—
489C22×D4C4×D4311yescharacteristic
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—431no—
493C23×C4C4×D4311yescharacteristic
494C23×C4C22×D4311yescharacteristic
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—861no—
498C22×C8—861no—
499#126—861no—
500#126—861no—
501#126—861no—
502#126—861no—
503#126—861no—
504#126—861no—
505#126—861no—
506#126—861no—
507#125—861no—
508#125—861no—
509#125—861no—
510#125—861no—
511#124—861no—
512#124—861no—
513#124—861no—
514#124—861no—
515#123—861no—
516#123—861no—
517#123—861no—
518#123—861no—
519#123—861no—
520#123—861no—
521#123—861no—
522#123—861no—
523C22⋊Q8—861no—
524C22⋊Q8—861no—
525C22⋊Q8—861no—
526C22⋊Q8—861no—
527#121—861no—
528#121—861no—
529#121—861no—
530#121—861no—
531C4×Q8—861no—
532C4×Q8—861no—
533C4×Q8—861no—
534C4×Q8—861no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4—861no—
547#117—861no—
548#117—861no—
549#117—861no—
550#117—861no—
551#117—861no—
552#117—861no—
553#117—861no—
554#117—861no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4C22×D4311yescharacteristic
565C2×C22⋊C4—431no—
566C2×C22⋊C4—431no—
567C2×C22⋊C4—431no—
568C2×C22⋊C4—431no—
569C2×C22⋊C4—431no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4C4×D4311yescharacteristic
574C2×C22⋊C4C22×D4311yescharacteristic
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—431no—
587C2×C42—431no—
588C2×C42C4×D4311yescharacteristic
589C4⋊C8—862no—
590C4⋊C8—862no—
591C4⋊C8—862no—
592C4⋊C8—862no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—432no—
596C22⋊C8—432no—
597C22⋊C8—861no—
598C22⋊C8—861no—
599C22⋊C8C22×D4312yes—
600C22⋊C8C22×D4312yes—
601#97—862no—
602#97—862no—
603C4×C8—862no—
604C4×C8—862no—
605C24—431no—
606C24C2×C4×D4311yescharacteristic
607C24C2×C4×D4311yescharacteristic
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—1722no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—1722no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—1722no—
646C22×C4—1722no—
647C22×C4C2×C4×D4311yescharacteristic
648C22×C4C2×C4×D4311yescharacteristic
649C22×C4C2×C4×D4311yescharacteristic
650C22×C4C2×C4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—862no—
661C2×C8—862no—
662C2×C8—1722no—
663C2×C8—1722no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—861no—
689C22⋊C4—861no—
690C22⋊C4—861no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—861no—
697C22⋊C4—861no—
698C22⋊C4—861no—
699C22⋊C4—861no—
700C22⋊C4—861no—
701C22⋊C4—861no—
702C22⋊C4—861no—
703C22⋊C4—861no—
704C42—21no—
705C42—21no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—431no—
715C42—431no—
716C42—431no—
717C42—431no—
718C42—431no—
719C42—431no—
720C42—431no—
721C42—431no—
722C42—861no—
723C42—861no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—861no—
732C23—861no—
733C23—861no—
734C23—1721no—
735C23—1721no—
736C23C22⋊C4×D4311yescharacteristic
737C23C22⋊C4×D4311yescharacteristic
738C23#1306333112yes—
739C23#1306333312yes—
740C23C22×C4×D4311yescharacteristic
741Q8—1722no—
742Q8—1722no—
743D4—42no—
744D4—42no—
745D4—1722no—
746D4—1722no—
747D4—1722no—
748D4—1722no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—431no—
765C2×C4—431no—
766C2×C4—431no—
767C2×C4—431no—
768C2×C4—431no—
769C2×C4—431no—
770C2×C4—431no—
771C2×C4—431no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—861no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—1722no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1722no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4C22⋊C4×D4311yescharacteristic
796C2×C4C22⋊C4×D4311yescharacteristic
797C2×C4C2×D4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C8—42no—
800C8—42no—
801C8—1722no—
802C8—1722no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—42no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—81no—
815C22—81no—
816C22—3441no—
817C22—3441no—
818C22—1721no—
819C22—1721no—
820C22—1721no—
821C22#1458286412yes—
822C22#1458286412yes—
823C22C2×C22⋊C4×D4311yescharacteristic
824C22C2×#1306333111yescharacteristic
825C22C2×#1306333311yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—432no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—861no—
837C4—861no—
838C4—861no—
839C4—861no—
840C4—1721no—
841C4—1721no—
842C4—1721no—
843C4#1458287112yes—
844C2—21no—
845C2—21no—
846C2—22no—
847C2—22no—
848C2—81no—
849C2—3441no—
850C2C2×#1458286411yescharacteristic
851C2C2×#1458287111yescharacteristic
852C2#413×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1459C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063297C4
cosocleC22×C4×C43C24
hypercenter#1459D43
hypocenterC43#17382
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. C2×#14582953C2semidirect
3. C2×#14582949C2semidirect
4. #19132963C2semidirect
5. #19132961C2semidirect
6. #19132949C2semidirect
7. #19132945C2semidirect
8. #19132913C2semidirect
9. #19132911C2semidirect
10. #19132911C2semidirect
11. C43×#1459C2semidirect
428. #1459D43semidirect
485. C43#17382semidirect

Maximal subgroups

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

subgroupindex
C2×#145834292
C2×#145829532
C2×#145829492
#191329632
#191329612
#191329492
#191329452
#191329132
#191329112
C43×#14592
#1738243