Finite Group Databasebeta

← #25961620

Subgroups — #25961620

Order 11008.

1702 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621898C211yesmaximal, characteristic
2#19143696C213yesmaximal, complemented
3#19143693C213yesmaximal, complemented
4#19143692C213yesmaximal, complemented
5#19143691C213yesmaximal, complemented
6#19143683C211yesmaximal, characteristic, complemented
7#19143676C211yesmaximal, characteristic, complemented
8#19143674C211yesmaximal, characteristic, complemented
9Q8×#10621872C211yesmaximal, characteristic, complemented
10#19143543C213yesmaximal, complemented
11#19143526C213yesmaximal, complemented
12C8×Q8×D43C211yesmaximal, characteristic, complemented
13#19143262C213yesmaximal
14#19143234C213yesmaximal
15C43×#2984C211yesmaximal, characteristic, complemented
16Q8×Dic86C411yescharacteristic
17#14583627C413yes—
18#14583609C413yes—
19#14583604C413yes—
20#14583604C413yes—
21Q8×D172C411yescharacteristic
22Q8×C22⋊D43C411yescharacteristic
23Q8×C22⋊D43C411yescharacteristic
24#14583456C2213yes—
25#14583453C2213yes—
26#14583453C2213yes—
27C4×#10621898C2213yes—
28C4×Q8×D43C2211yescharacteristic
29C4×Q8×D43C2211yescharacteristic
30#14583029C2213yes—
31#14583029C2213yes—
32#14583027C2216yes—
33#14583027C2216yes—
34#14583026C2213yes—
35#14583026C2216yes—
36#14583026C2213yes—
37Q8×C43⋊C8C2211yescharacteristic
38Q8×C43⋊C8C2213yes—
39Q8×C43⋊C8C2213yes—
40Q8×C43⋊C8C2211yescharacteristic
41C8×Dic86C2213yes—
42C8×Dic86C2213yes—
43#14583023C2213yes—
44#14583023C2213yes—
45#14583023C2216yes—
46#14582961C2216yes—
47#14582959C2213yes—
48#14582959C2213yes—
49#14582957C2213yes—
50#14582957C2216yes—
51#14582957C2213yes—
52#14582955C2213yes—
53#14582952C2213yes—
54#14582952C2213yes—
55#14582951C2213yes—
56#14582950C2213yes—
57#14582950C2213yes—
58#14582924C2213yes—
59#14582924C2213yes—
60#14582921C2213yes—
61C4⋊C8×D43C2213yes—
62#14582864C2211yescharacteristic
63#14582864C2213yes—
64#14582856C2216yes—
65C4×#10621872C2213yes—
66C4×C8×D43C2213yes—
67C2×C4×Q8×C43C2211yescharacteristic
68C43×#446C2213yes—
69C43×#446C2213yes—
70C8×Q8×C43C2211yescharacteristic
71C8×Q8×C43C2211yescharacteristic
72C43×#432C2213yes—
73C43×#431C2213yes—
74C2×#10621898C2311yescharacteristic
75C2×Q8×D43C2×C411yescharacteristic
76C2×Q8×D43C2×C411yescharacteristic
77C2×#10621872C2311yescharacteristic
78C2×#10621872C2313yes—
79C2×C8×D43C2311yescharacteristic
80C2×C8×D43C2313yes—
81#13063325C2×C413yes—
82#13063325C2×C413yes—
83#13063324C2×C413yes—
84#13063324C2×C413yes—
85#13063323C2×C413yes—
86#13063323C2×C413yes—
87#13063317C2×C416yes—
88#13063315C2×C416yes—
89#13063315C2×C416yes—
90#13063305C2×C413yes—
91#13063305C2×C413yes—
92#13063304C2×C413yes—
93#13063304C2×C413yes—
94#13063304C2×C416yes—
95#13063303C2×C416yes—
96#13063303C2×C416yes—
97#13063301C2×C413yes—
98#13063301C2×C413yes—
99Q8×Dic43C2×C411yescharacteristic
100Q8×Dic43C2×C411yescharacteristic
101C4×Dic86C2×C413yes—
102C4×Dic86C2×C413yes—
103C4×Dic86C2313yes—
104C4×Dic86C2313yes—
105C4×Dic86C2316yes—
106#13063290C2×C413yes—
107#13063290C2×C413yes—
108C4×D172C2×C413yes—
109C4×D172C2×C413yes—
110C4×C22⋊D43C2×C413yes—
111C4×C22⋊D43C2×C413yes—
112C4×C22⋊D43C2×C413yes—
113C4×C22⋊D43C2×C413yes—
114#13063284C2313yes—
115#13063282C2313yes—
116#13063282C2313yes—
117C4⋊C4×D43C2×C413yes—
118C4⋊C4×D43C2×C413yes—
119C42×D43C2313yes—
120C42×D43C2313yes—
121C4⋊(C43⋊C8)C2313yes—
122C4⋊(C43⋊C8)C2313yes—
123C4⋊(C43⋊C8)C2313yes—
124C4⋊(C43⋊C8)C2313yes—
125Dic43⋊C8C2316yes—
126Dic43⋊C8C2316yes—
127Dic43⋊C8C2313yes—
128Dic43⋊C8C2313yes—
129Dic43⋊C8C2313yes—
130Dic43⋊C8C2313yes—
131C22⋊(C43⋊C8)C2311yescharacteristic
132C22⋊(C43⋊C8)C2313yes—
133(C2×D43)⋊C8C2311yescharacteristic
134(C2×D43)⋊C8C2311yescharacteristic
135(C2×D43)⋊C8C2313yes—
136(C2×D43)⋊C8C2313yes—
137#13063235C2313yes—
138#13063235C2313yes—
139#13063235C2316yes—
140C4×C43⋊C8C2313yes—
141C4×C43⋊C8C2313yes—
142C4×C43⋊C8C2316yes—
143C8×Dic43C2313yes—
144C8×Dic43C2313yes—
145C8×Dic43C2316yes—
146C22×Q8×C43C2×C411yescharacteristic
147C4×Q8×C43C2×C411yescharacteristic
148C4×Q8×C43C2×C413yes—
149C4×Q8×C43C2311yescharacteristic
150C4×Q8×C43C2313yes—
151C2×C4⋊C4×C43C2×C413yes—
152C2×C42×C43C2313yes—
153C4⋊C8×C43C2313yes—
154C4⋊C8×C43C2313yes—
155C4⋊C8×C43C2313yes—
156C4⋊C8×C43C2313yes—
157C22⋊C8×C43C2311yescharacteristic
158C22⋊C8×C43C2313yes—
159#97×C43C2316yes—
160C4×C8×C43C2313yes—
161C4×C8×C43C2313yes—
162C2×Q8×C43—24no—
163C2×Q8×C43C22×C413yes—
164C2×Q8×C43C22×C411yescharacteristic
165C22×C4×C43C22×C413yes—
166C22×C4×C43C22×C413yes—
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43C22×C411yescharacteristic
169C2×C22⋊D43C22×C411yescharacteristic
170Q8×D43—24no—
171Q8×D43—24no—
172#10621898—22no—
173#10621898—22no—
174C2×D172C22×C411yescharacteristic
175C2×C4×D43C22×C413yes—
176C2×C4×D43C22×C413yes—
177C2×C4×D43C22×C413yes—
178C2×C4×D43C22×C413yes—
179C2×C4×D43C2411yescharacteristic
180C2×C4×D43C2411yescharacteristic
181C2×Dic86C22×C413yes—
182C2×Dic86C22×C413yes—
183C2×Dic86C22×C411yescharacteristic
184C2×Dic86C22×C416yes—
185C2×C8×C43C2411yescharacteristic
186C2×C8×C43C2411yescharacteristic
187C2×C8×C43C2413yes—
188C2×C8×C43C2413yes—
189C4⋊C4×C43C22×C413yes—
190C4⋊C4×C43C22×C416yes—
191C4⋊C4×C43C22×C413yes—
192C42×C43C22×C413yes—
193C42×C43C22×C413yes—
194C42×C43C2413yes—
195C42×C43C2413yes—
196C22⋊Dic43C22×C413yes—
197C22⋊Dic43C22×C413yes—
198(C2×D43)⋊C4C22×C413yes—
199(C2×D43)⋊C4C22×C413yes—
200(C2×D43)⋊C4C22×C413yes—
201(C2×D43)⋊C4C22×C413yes—
202C4⋊Dic43C22×C413yes—
203C4⋊Dic43C22×C413yes—
204C4⋊Dic43C22×C413yes—
205C4⋊Dic43C22×C413yes—
206C4⋊Dic43C22×C416yes—
207Dic43⋊C4C22×C416yes—
208Dic43⋊C4C22×C416yes—
209Dic43⋊C4C22×C413yes—
210Dic43⋊C4C22×C413yes—
211Dic43⋊C4C22×C413yes—
212Dic43⋊C4C22×C413yes—
213Dic43⋊C4C22×C416yes—
214Dic43⋊C4C22×C416yes—
215C4×Dic43C22×C413yes—
216C4×Dic43C22×C413yes—
217C4×Dic43C22×C413yes—
218C4×Dic43C22×C413yes—
219C4×Dic43C2413yes—
220C4×Dic43C2413yes—
221C2×C43⋊C8C2413yes—
222C2×C43⋊C8C2411yescharacteristic
223C2×C43⋊C8C2411yescharacteristic
224C2×C43⋊C8C2413yes—
225#10621872—22no—
226#10621872—26no—
227C8×D43—26no—
228C8×D43—22no—
229C23×C43C23×C411yescharacteristic
230C22×D43C23×C411yescharacteristic
231C22×D43C23×C411yescharacteristic
232Q8×C43—26no—
233Q8×C43#13114yes—
234C2×C4×C43—26no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—43no—
238C2×C4×C43C23×C413yes—
239C2×C4×C43C23×C413yes—
240C2×C4×C43C23×C413yes—
241C2×C4×C43C23×C411yescharacteristic
242C2×C4×C43C23×C413yes—
243C2×C4×C43C2511yescharacteristic
244C22⋊D43—22no—
245C22⋊D43—22no—
246C2×Dic43C23×C411yescharacteristic
247C2×Dic43C23×C413yes—
248C2×Dic43C23×C413yes—
249C2×Dic43C23×C413yes—
250C2×Dic43C23×C413yes—
251C2×Dic43C23×C411yescharacteristic
252D172—22no—
253C4×D43—26no—
254C4×D43—26no—
255C4×D43—21no—
256C4×D43—21no—
257C4×D43—43no—
258C4×D43—43no—
259C4×D432−1+412yes—
260C4×D432−1+412yes—
261Dic86—26no—
262Dic86—26no—
263Dic86—22no—
264Dic86—46no—
265C8×C43—21no—
266C8×C43—23no—
267C8×C43—21no—
268C8×C43—23no—
269C43⋊C8—23no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—23no—
273#60253—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43C24×C411yescharacteristic
278C2×D43—21no—
279C2×D43—21no—
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—21no—
283C2×D43#51912yes—
284C4×C43—21no—
285C4×C43—23no—
286C4×C43—23no—
287C4×C43—23no—
288C4×C43C2×#13116yes—
289C4×C43C2×2−1+411yescharacteristic
290C4×C43C2×2−1+411yescharacteristic
291Dic43—21no—
292Dic43—23no—
293Dic43—23no—
294Dic43—23no—
295Dic43—23no—
296Dic43#51912yes—
297Q8×#41—431no—
298#2986—433no—
299#2986—433no—
300#2985—433no—
301#2985—433no—
302#2984—431no—
303#2984D4311yescharacteristic, complemented
304#2982—431no—
305#2982—431no—
306Q8×M16—431no—
307#2962—433no—
308#2960—433no—
309C2×C8×Q8—431no—
310#2925—433no—
311#2922—433no—
312C2×C43—41no—
313C2×C43C2×#51911yescharacteristic
314C2×C43C22×#13111yescharacteristic
315C2×C43#357311yescharacteristic
316D43—22no—
317D43—41no—
318Q82—431no—
319#557—433no—
320#554—433no—
321#554—433no—
322#554—433no—
323D4×Q8—431no—
324D4×Q8—431no—
325D4×Q8—431no—
326#533—433no—
327#533—433no—
328#533—433no—
329C4×#41—433no—
330C2×C4×Q8—431no—
331C2×C4×Q8—431no—
332C2×C4×Q8C2×D4311yescharacteristic
333#446—433no—
334#446—436no—
335#446—433no—
336#446—436no—
337#446—436no—
338#446—433no—
339#446—433no—
340#446C2×D4313yes—
341#446C2×D4313yes—
342C8×Q8—431no—
343C8×Q8—433no—
344C8×Q8—433no—
345C8×Q8—431no—
346C8×Q8—433no—
347C8×Q8—433no—
348C8×Q8—436no—
349C8×Q8—433no—
350C8×Q8—433no—
351C8×Q8C2×D4311yescharacteristic
352C8×Q8C2×D4311yescharacteristic
353#433—433no—
354#433—433no—
355#433—433no—
356#433—433no—
357#433—436no—
358#433—436no—
359#432—433no—
360#432C2×D4313yes—
361#431—433no—
362#431—433no—
363#431—433no—
364#431—433no—
365#431—433no—
366#431C2×D4313yes—
367#424—433no—
368#424—433no—
369#423—433no—
370C2×C4⋊C8—433no—
371#408—431no—
372#408—433no—
373#405—436no—
374C4×M16—433no—
375C2×C4×C8—433no—
376C43#6025311yescharacteristic, complemented, Sylow
377C2×#41—431no—
378C22×Q8—431no—
379C22×Q8—431no—
380C22×Q8C4×D4311yescharacteristic
381C2×M16—431no—
382C2×M16—433no—
383C22×C8—431no—
384C22×C8—433no—
385C4⋊Q8—433no—
386C4⋊Q8—433no—
387C4⋊Q8—433no—
388C4⋊Q8—433no—
389C4⋊Q8—433no—
390C4⋊Q8—433no—
391#125—436no—
392#125—436no—
393#125—436no—
394C22⋊Q8—433no—
395C22⋊Q8—433no—
396C22⋊Q8—433no—
397C22⋊Q8—433no—
398C22⋊Q8—436no—
399C22⋊Q8—433no—
400C22⋊Q8—433no—
401C22⋊Q8—436no—
402C22⋊Q8—436no—
403C4×Q8—431no—
404C4×Q8—431no—
405C4×Q8—433no—
406C4×Q8—433no—
407C4×Q8—433no—
408C4×Q8—433no—
409C4×Q8—433no—
410C4×Q8—433no—
411C4×Q8—436no—
412C4×Q8C4×D4311yescharacteristic
413C4×Q8C4×D4313yes—
414C4×Q8C22×D4311yescharacteristic
415C4×Q8C22×D4313yes—
416C4×D4—433no—
417C4×D4—433no—
418C4×D4—433no—
419C4×D4—433no—
420C4×D4—433no—
421C4×D4—433no—
422#117—433no—
423#117—433no—
424#117—433no—
425C2×C4⋊C4—433no—
426C2×C4⋊C4—433no—
427C2×C4⋊C4C4×D4313yes—
428C2×C42—433no—
429C2×C42—433no—
430C2×C42C22×D4313yes—
431C4⋊C8—436no—
432C4⋊C8—436no—
433C4⋊C8—433no—
434C4⋊C8—433no—
435C4⋊C8—433no—
436C4⋊C8—433no—
437C4⋊C8—433no—
438C4⋊C8—433no—
439C4⋊C8—433no—
440C4⋊C8—433no—
441C4⋊C8C22×D4313yes—
442C4⋊C8C22×D4313yes—
443C4⋊C8C22×D4313yes—
444C4⋊C8C22×D4313yes—
445C22⋊C8—431no—
446C22⋊C8—433no—
447C22⋊C8—433no—
448C22⋊C8—431no—
449C22⋊C8—431no—
450C22⋊C8—433no—
451C22⋊C8C22×D4311yescharacteristic
452C22⋊C8C22×D4313yes—
453#97—433no—
454#97—433no—
455#97—436no—
456#97C22×D4316yes—
457C4×C8—433no—
458C4×C8—433no—
459C4×C8—436no—
460C4×C8—433no—
461C4×C8—433no—
462C4×C8—436no—
463C4×C8C22×D4313yes—
464C4×C8C22×D4313yes—
465#41—862no—
466#41—862no—
467C2×Q8—24no—
468C2×Q8—431no—
469C2×Q8—433no—
470C2×Q8—433no—
471C2×Q8—436no—
472C2×Q8—864no—
473C2×Q8—864no—
474C2×Q8C2×C4×D4313yes—
475C2×Q8C2×C4×D4311yescharacteristic
476C2×D4—431no—
477C2×D4—431no—
478C2×D4—431no—
479C22×C4—431no—
480C22×C4—433no—
481C22×C4—433no—
482C22×C4—431no—
483C22×C4—433no—
484C22×C4—433no—
485C22×C4C2×C4×D4313yes—
486C22×C4C2×C4×D4313yes—
487C22×C4C23×D4311yescharacteristic
488M16—862no—
489M16—866no—
490C2×C8—433no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—433no—
494C2×C8—866no—
495C2×C8—862no—
496C2×C8C23×D4311yescharacteristic
497C2×C8C23×D4313yes—
498C2×C8C23×D4313yes—
499C2×C8C23×D4311yescharacteristic
500C4⋊C4—436no—
501C4⋊C4—436no—
502C4⋊C4—433no—
503C4⋊C4—433no—
504C4⋊C4—433no—
505C4⋊C4—433no—
506C4⋊C4—433no—
507C4⋊C4—433no—
508C4⋊C4—433no—
509C4⋊C4—433no—
510C4⋊C4—436no—
511C4⋊C4—436no—
512C4⋊C4—436no—
513C4⋊C4C2×C4×D4313yes—
514C4⋊C4C2×C4×D4316yes—
515C4⋊C4C2×C4×D4313yes—
516C22⋊C4—433no—
517C22⋊C4—433no—
518C22⋊C4—433no—
519C22⋊C4—433no—
520C22⋊C4—433no—
521C22⋊C4—433no—
522C42—433no—
523C42—433no—
524C42—433no—
525C42—433no—
526C42—433no—
527C42—433no—
528C42C2×C4×D4313yes—
529C42C2×C4×D4313yes—
530C42C23×D4313yes—
531C42C23×D4313yes—
532C23—431no—
533C23—431no—
534C23C22×C4×D4311yescharacteristic
535Q8—26no—
536Q8—862no—
537Q8—866no—
538Q8—866no—
539Q8—1726no—
540Q8#1306333314yes—
541D4—862no—
542D4—862no—
543D4—862no—
544C2×C4—26no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—43no—
548C2×C4—431no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—431no—
552C2×C4—433no—
553C2×C4—433no—
554C2×C4—433no—
555C2×C4—433no—
556C2×C4—866no—
557C2×C4—866no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—1723no—
561C2×C4—1723no—
562C2×C4C22×C4×D4313yes—
563C2×C4C22×C4×D4311yescharacteristic
564C2×C4C22×C4×D4313yes—
565C2×C4C22×C4×D4313yes—
566C2×C4C22×C4×D4313yes—
567C2×C4C24×D4311yescharacteristic
568C8—21no—
569C8—23no—
570C8—23no—
571C8—21no—
572C8—863no—
573C8—861no—
574C8—861no—
575C8—863no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—432no—
580C22—861no—
581C22—861no—
582C22—861no—
583C22—861no—
584C22—861no—
585C22C23×C4×D4311yescharacteristic
586C4—21no—
587C4—23no—
588C4—23no—
589C4—23no—
590C4—432no—
591C4—861no—
592C4—863no—
593C4—863no—
594C4—863no—
595C4—863no—
596C4C2×#1306333316yes—
597C42−1+4×D4311yescharacteristic
598C42−1+4×D4311yescharacteristic
599C2—41no—
600C2—862no—
601C2—1721no—
602C2#519×D4311yescharacteristic
603C2C22×#1306333311yescharacteristic
604C2#1914930611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2984C2
prime radicalC2×#10621898C23
cosocleC2×C4×C43C25
hypercenter#2984D43
hypocenterC43#60253
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2984

Complements

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

NH ≅ G/Ntype
2. #19143696C2semidirect
3. #19143693C2semidirect
4. #19143692C2semidirect
5. #19143691C2semidirect
6. #19143683C2semidirect
7. #19143676C2semidirect
8. #19143674C2semidirect
9. Q8×#10621872C2semidirect
10. #19143543C2semidirect
11. #19143526C2semidirect
12. C8×Q8×D43C2semidirect
15. C43×#2984C2semidirect
303. #2984D43semidirect
376. C43#60253semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218982
#191436962
#191436932
#191436922
#191436912
#191436832
#191436762
#191436742
Q8×#106218722
#191435432
#191435262
C8×Q8×D432
#191432622
#191432342
C43×#29842
#6025343