Finite Group Databasebeta

← #25063532

Subgroups — #25063532

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621898C211yesmaximal, characteristic
2#19143557C211yesmaximal, characteristic
3#19143262C211yesmaximal, characteristic
4#19133067C211yesmaximal, characteristic, complemented
5#19133066C211yesmaximal, characteristic, complemented
6#19133048C211yesmaximal, characteristic, complemented
7#19133040C211yesmaximal, characteristic, complemented
8#19133022C211yesmaximal, characteristic, complemented
9#19133017C211yesmaximal, characteristic, complemented
10#19133014C211yesmaximal, characteristic, complemented
11#19132996C211yesmaximal, characteristic, complemented
12#19132990C211yesmaximal, characteristic, complemented
13#19132988C211yesmaximal, characteristic, complemented
14Q8⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1491C211yesmaximal, characteristic, complemented
16Q8×Dic86C411yescharacteristic
17#14583627—21no—
18#14583627C411yescharacteristic
19#14583609—21no—
20#14583609C411yescharacteristic
21#14583604—21no—
22#14583604—21no—
23#14583604C411yescharacteristic
24#14583604C411yescharacteristic
25Q8×D172C411yescharacteristic
26Q8×C22⋊D43C411yescharacteristic
27Q8×C22⋊D43C411yescharacteristic
28#14583456—21no—
29#14583456C2211yescharacteristic
30#14583453—21no—
31#14583453—21no—
32#14583453C2211yescharacteristic
33#14583453C2211yescharacteristic
34C4×#10621898—21no—
35C4×#10621898C2211yescharacteristic
36C4×Q8×D43C2211yescharacteristic
37C4×Q8×D43C2211yescharacteristic
38#14583027—21no—
39#14582975—21no—
40#14582972—21no—
41#14582968—21no—
42#14582961—21no—
43#14582957—21no—
44#14582955C2211yescharacteristic
45#14582952C2211yescharacteristic
46#14582952C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582950C2211yescharacteristic
49#14582950C2211yescharacteristic
50#14582921C2211yescharacteristic
51C4⋊C8×D43C2211yescharacteristic
52#14582864—21no—
53#14582856—21no—
54C4×#10621872C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582631C2211yescharacteristic
60Q8⋊(C43⋊C8)C2211yescharacteristic
61Q8⋊(C43⋊C8)C2211yescharacteristic
62Q8⋊(C43⋊C8)C2211yescharacteristic
63Q8⋊(C43⋊C8)C2211yescharacteristic
64#14582629C2211yescharacteristic
65#14582629C2211yescharacteristic
66#14582629C2211yescharacteristic
67#14582629C2211yescharacteristic
68C2×C4×Q8×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C4×M16×C43C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×Q8⋊C8C2211yescharacteristic
74C43×Q8⋊C8C2211yescharacteristic
75C2×#10621898D411yescharacteristic
76C2×Q8×D43C2×C411yescharacteristic
77C2×Q8×D43C2×C411yescharacteristic
78C2×#10621872—21no—
79C2×#10621872—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82#13063325—21no—
83#13063325—21no—
84#13063325C2×C411yescharacteristic
85#13063325C2×C411yescharacteristic
86#13063324—21no—
87#13063324—21no—
88#13063324C2×C411yescharacteristic
89#13063324C2×C411yescharacteristic
90#13063323—21no—
91#13063323—21no—
92#13063323C2×C411yescharacteristic
93#13063323C2×C411yescharacteristic
94#13063317—21no—
95#13063317—21no—
96#13063317—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063315—21no—
101#13063315—21no—
102#13063315—21no—
103#13063305—21no—
104#13063305—21no—
105#13063305C2×C411yescharacteristic
106#13063305C2×C411yescharacteristic
107#13063304—21no—
108#13063304—21no—
109#13063304—21no—
110#13063304—21no—
111#13063304—21no—
112#13063304C2×C411yescharacteristic
113#13063304C2×C411yescharacteristic
114#13063303—21no—
115#13063303—21no—
116#13063303—21no—
117#13063303—21no—
118#13063303—21no—
119#13063303—21no—
120#13063301—21no—
121#13063301—21no—
122#13063301C2×C411yescharacteristic
123#13063301C2×C411yescharacteristic
124Q8×Dic43C2×C411yescharacteristic
125Q8×Dic43C2×C411yescharacteristic
126C4×Dic86—21no—
127C4×Dic86—21no—
128C4×Dic86—21no—
129C4×Dic86—21no—
130C4×Dic86—21no—
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86C2×C411yescharacteristic
134C4×Dic86D411yescharacteristic
135C4×Dic86C2311yescharacteristic
136C4×Dic86C2311yescharacteristic
137#13063290—21no—
138#13063290—21no—
139#13063290C2×C411yescharacteristic
140#13063290C2×C411yescharacteristic
141C4×D172—21no—
142C4×D172—21no—
143C4×D172C2×C411yescharacteristic
144C4×D172D411yescharacteristic
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43C2×C411yescharacteristic
150C4×C22⋊D43C2×C411yescharacteristic
151C4×C22⋊D43D411yescharacteristic
152C4×C22⋊D43D411yescharacteristic
153#13063284—21no—
154#13063284D411yescharacteristic
155#13063282—21no—
156#13063282—21no—
157#13063282D411yescharacteristic
158#13063282D411yescharacteristic
159C4⋊C4×D43—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43C2×C411yescharacteristic
162C4⋊C4×D43C2×C411yescharacteristic
163C42×D43—21no—
164C42×D43—21no—
165C42×D43C2311yescharacteristic
166C42×D43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168C4⋊(C43⋊C8)C2311yescharacteristic
169C4⋊(C43⋊C8)C2311yescharacteristic
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174C22⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180#13063235—21no—
181#13063235—21no—
182C4×C43⋊C8—21no—
183C4×C43⋊C8C2311yescharacteristic
184C4×C43⋊C8C2311yescharacteristic
185C8×Dic43—21no—
186C8×Dic43—21no—
187C22×Q8×C43C2×C411yescharacteristic
188C2×M16×C43—21no—
189C4×Q8×C43—21no—
190C4×Q8×C43—21no—
191C4×Q8×C43C2×C411yescharacteristic
192C4×Q8×C43C2×C411yescharacteristic
193C4×Q8×C43C2311yescharacteristic
194C4×Q8×C43C2311yescharacteristic
195C2×C4⋊C4×C43—21no—
196C2×C4⋊C4×C43C2×C411yescharacteristic
197C2×C42×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43C2311yescharacteristic
200C4⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43—21no—
202#97×C43—21no—
203#97×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206C2×Q8×C43—21no—
207C2×Q8×C43—22no—
208C2×Q8×C43—41no—
209C2×Q8×C43C22×C411yescharacteristic
210C2×Q8×C43C22×C411yescharacteristic
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C2×C22⋊D43C22⋊C411yescharacteristic
217C2×C22⋊D43C22⋊C411yescharacteristic
218Q8×D43—22no—
219Q8×D43—22no—
220Q8×D43—41no—
221Q8×D43—41no—
222#10621898—22no—
223#10621898—22no—
224C2×D172C22⋊C411yescharacteristic
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43C22×C411yescharacteristic
230C2×C4×D43C22×C411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×C4×D43C2×D411yescharacteristic
234C2×C4×D43C2×D411yescharacteristic
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86C22⋊C411yescharacteristic
241C2×Dic86C22×C411yescharacteristic
242C2×Dic86C22×C411yescharacteristic
243M16×C43—42no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C22×C411yescharacteristic
254C4⋊C4×C43C22×C411yescharacteristic
255C42×C43—21no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43—21no—
259C42×C43C22×C411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C42×C43C2411yescharacteristic
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265C22⋊Dic43C22⋊C411yescharacteristic
266C22⋊Dic43C22⋊C411yescharacteristic
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4C22⋊C411yescharacteristic
272(C2×D43)⋊C4C22⋊C411yescharacteristic
273(C2×D43)⋊C4C22⋊C411yescharacteristic
274(C2×D43)⋊C4C22⋊C411yescharacteristic
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43C22⋊C411yescharacteristic
283C4⋊Dic43C22⋊C411yescharacteristic
284C4⋊Dic43C22×C411yescharacteristic
285C4⋊Dic43C22×C411yescharacteristic
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—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⋊C4C22⋊C411yescharacteristic
303Dic43⋊C4C22⋊C411yescharacteristic
304Dic43⋊C4C22⋊C411yescharacteristic
305Dic43⋊C4C22⋊C411yescharacteristic
306C4×Dic43—21no—
307C4×Dic43—21no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43C22×C411yescharacteristic
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C2×D411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322#10621872—42no—
323#10621872—42no—
324C8×D43—42no—
325C8×D43—42no—
326C23×C43C2×C22⋊C411yescharacteristic
327C22×D43C2×C22⋊C411yescharacteristic
328C22×D43C2×C22⋊C411yescharacteristic
329Q8×C43—21no—
330Q8×C43—21no—
331Q8×C43—21no—
332Q8×C43—42no—
333Q8×C43#13112yes—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—41no—
343C2×C4×C43—42no—
344C2×C4×C43—81no—
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C2×C22⋊C411yescharacteristic
348C2×C4×C43C23×C411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C22⋊D43—22no—
352C22⋊D43—22no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363D172—22no—
364C4×D43—21no—
365C4×D43—21no—
366C4×D43—21no—
367C4×D43—21no—
368C4×D43—21no—
369C4×D43—21no—
370C4×D43—41no—
371C4×D43—41no—
372C4×D43—42no—
373C4×D43—42no—
374C4×D43—81no—
375C4×D43—81no—
376C4×D43#13712yes—
377C4×D43#13712yes—
378Dic86—22no—
379Dic86—21no—
380Dic86—21no—
381Dic86—21no—
382Dic86—21no—
383Dic86—42no—
384Dic86—42no—
385Dic86—81no—
386Dic86—81no—
387Dic86—81no—
388C8×C43—22no—
389C8×C43—41no—
390C8×C43—41no—
391C8×C43—41no—
392C43⋊C8—41no—
393C43⋊C8—41no—
394C43⋊C8—41no—
395C43⋊C8—41no—
396#17514—431nomaximal, Sylow
397C22×C43—21no—
398C22×C43—21no—
399C22×C43—21no—
400C22×C43C22×C22⋊C411yescharacteristic
401C2×D43—21no—
402C2×D43—21no—
403C2×D43—21no—
404C2×D43—21no—
405C2×D43—21no—
406C2×D43#41912yes—
407C4×C43—22no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43—41no—
415C4×C43C2×#13111yescharacteristic
416C4×C43#56811yescharacteristic
417C4×C43C2×#13711yescharacteristic
418C4×C43C2×#13711yescharacteristic
419Dic43—21no—
420Dic43—21no—
421Dic43—21no—
422Dic43—21no—
423Dic43—21no—
424Dic43—41no—
425Dic43—41no—
426Dic43—41no—
427Dic43—41no—
428Dic43#41912yes—
429Q8×#41—431no—
430#2965—431no—
431#2925—431no—
432#1497—431no—
433#1497—431no—
434#1493—431no—
435#1491—431no—
436#1491D4311yescharacteristic, complemented
437#1487—431no—
438#1485—431no—
439#1485—431no—
440#1481—431no—
441#1479—431no—
442#1479—431no—
443C2×Q8⋊C8—431no—
444C2×C43—41no—
445C2×C43#288011yescharacteristic
446C2×C43C2×#41911yescharacteristic
447C2×C43#290111yescharacteristic
448D43—22no—
449D43—41no—
450Q82—431no—
451#557—431no—
452#557—861no—
453#554—431no—
454#554—431no—
455#554—431no—
456#554—861no—
457#554—861no—
458#554—861no—
459D4×Q8—431no—
460D4×Q8—431no—
461D4×Q8—431no—
462#533—431no—
463#533—431no—
464#533—431no—
465#533—861no—
466#533—861no—
467#533—861no—
468C4×#41—431no—
469C4×#41—861no—
470C2×C4×Q8—431no—
471C2×C4×Q8—431no—
472C2×C4×Q8C2×D4311yescharacteristic
473#446—861no—
474#436—861no—
475#435—861no—
476#435—861no—
477#433—861no—
478#433—861no—
479#432—431no—
480#432C2×D4311yescharacteristic
481#431—431no—
482#431—431no—
483#431—431no—
484#431—431no—
485#431—431no—
486#423—431no—
487C2×C4⋊C8—431no—
488#408—861no—
489#405—861no—
490C4×M16—431no—
491C4×M16C2×D4311yescharacteristic
492C2×C4×C8—431no—
493Q8⋊C8—431no—
494Q8⋊C8—431no—
495Q8⋊C8—431no—
496Q8⋊C8—431no—
497Q8⋊C8—431no—
498Q8⋊C8—431no—
499Q8⋊C8—431no—
500Q8⋊C8—431no—
501Q8⋊C8—431no—
502Q8⋊C8—431no—
503Q8⋊C8—431no—
504Q8⋊C8—431no—
505Q8⋊C8C2×D4311yescharacteristic
506Q8⋊C8C2×D4311yescharacteristic
507Q8⋊C8C2×D4311yescharacteristic
508Q8⋊C8C2×D4311yescharacteristic
509C43#1751411yescharacteristic, complemented, Sylow
510C2×#41—431no—
511C22×Q8—431no—
512C22×Q8—431no—
513C22×Q8C4×D4311yescharacteristic
514C2×M16—21no—
515C2×M16—861no—
516C2×M16—861no—
517C22×C8—861no—
518C22×C8—861no—
519C4⋊Q8—431no—
520C4⋊Q8—431no—
521C4⋊Q8—431no—
522C4⋊Q8—431no—
523C4⋊Q8—431no—
524C4⋊Q8—431no—
525C4⋊Q8—861no—
526C4⋊Q8—861no—
527C4⋊Q8—861no—
528C4⋊Q8—861no—
529C4⋊Q8—861no—
530C4⋊Q8—861no—
531#125—861no—
532#125—861no—
533#125—861no—
534#125—861no—
535#125—861no—
536#125—861no—
537#125—861no—
538#125—861no—
539#125—861no—
540C22⋊Q8—431no—
541C22⋊Q8—431no—
542C22⋊Q8—431no—
543C22⋊Q8—431no—
544C22⋊Q8—431no—
545C22⋊Q8—431no—
546C22⋊Q8—861no—
547C22⋊Q8—861no—
548C22⋊Q8—861no—
549C22⋊Q8—861no—
550C22⋊Q8—861no—
551C22⋊Q8—861no—
552C22⋊Q8—861no—
553C22⋊Q8—861no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—431no—
564C4×Q8—431no—
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—431no—
571C4×Q8—861no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×Q8—861no—
577C4×Q8—861no—
578C4×Q8—861no—
579C4×Q8—861no—
580C4×Q8C4×D4311yescharacteristic
581C4×Q8C4×D4311yescharacteristic
582C4×Q8C22×D4311yescharacteristic
583C4×Q8C22×D4311yescharacteristic
584C4×D4—431no—
585C4×D4—431no—
586C4×D4—431no—
587C4×D4—431no—
588C4×D4—431no—
589C4×D4—431no—
590C4×D4—861no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596#117—431no—
597#117—431no—
598#117—431no—
599#117—861no—
600#117—861no—
601#117—861no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4C4×D4311yescharacteristic
608C2×C42—21no—
609C2×C42—431no—
610C2×C42—431no—
611C2×C42—861no—
612C2×C42—861no—
613C2×C42C22×D4311yescharacteristic
614C4⋊C8—431no—
615C4⋊C8—431no—
616C4⋊C8—861no—
617C4⋊C8—861no—
618C4⋊C8—861no—
619C4⋊C8—861no—
620C4⋊C8—861no—
621C4⋊C8C22×D4311yescharacteristic
622C4⋊C8C22×D4311yescharacteristic
623C22⋊C8—21no—
624C22⋊C8—861no—
625C22⋊C8—861no—
626C22⋊C8—861no—
627C22⋊C8—861no—
628C22⋊C8—861no—
629C22⋊C8—861no—
630#97—21no—
631#97—21no—
632#97—861no—
633#97—861no—
634C4×C8—431no—
635C4×C8—431no—
636C4×C8—861no—
637C4×C8—861no—
638C4×C8—861no—
639C4×C8C22×D4311yescharacteristic
640C4×C8C22×D4311yescharacteristic
641#41—862no—
642#41—862no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—41no—
646C2×Q8—431no—
647C2×Q8—431no—
648C2×Q8—431no—
649C2×Q8—861no—
650C2×Q8—861no—
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8—861no—
654C2×Q8—862no—
655C2×Q8—862no—
656C2×Q8—1721no—
657C2×Q8—1721no—
658C2×Q8C2×C4×D4311yescharacteristic
659C2×Q8C2×C4×D4311yescharacteristic
660C2×D4—431no—
661C2×D4—431no—
662C2×D4—431no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4C2×C4×D4311yescharacteristic
676C22×C4D4×D4311yescharacteristic
677C22×C4D4×D4311yescharacteristic
678M16—42no—
679M16—1722no—
680M16—1722no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—1722no—
690C2×C8—1722no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—431no—
697C4⋊C4—431no—
698C4⋊C4—431no—
699C4⋊C4—431no—
700C4⋊C4—431no—
701C4⋊C4—431no—
702C4⋊C4—431no—
703C4⋊C4—431no—
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⋊C4C2×C4×D4311yescharacteristic
728C4⋊C4C2×C4×D4311yescharacteristic
729C22⋊C4—431no—
730C22⋊C4—431no—
731C22⋊C4—431no—
732C22⋊C4—431no—
733C22⋊C4—431no—
734C22⋊C4—431no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C22⋊C4—861no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—431no—
746C42—431no—
747C42—431no—
748C42—431no—
749C42—431no—
750C42—431no—
751C42—861no—
752C42—861no—
753C42—861no—
754C42—861no—
755C42—861no—
756C42—861no—
757C42C2×C4×D4311yescharacteristic
758C42D4×D4311yescharacteristic
759C42D4×D4311yescharacteristic
760C42C23×D4311yescharacteristic
761C23—431no—
762C23—431no—
763C23C22⋊C4×D4311yescharacteristic
764Q8—21no—
765Q8—21no—
766Q8—21no—
767Q8—42no—
768Q8—862no—
769Q8—861no—
770Q8—861no—
771Q8—861no—
772Q8—861no—
773Q8—3441no—
774Q8—3441no—
775Q8—3441no—
776Q8—1722no—
777Q8—1722no—
778Q8#1306333312yes—
779D4—862no—
780D4—862no—
781D4—862no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—81no—
793C2×C4—431no—
794C2×C4—432no—
795C2×C4—432no—
796C2×C4—431no—
797C2×C4—431no—
798C2×C4—431no—
799C2×C4—431no—
800C2×C4—431no—
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—861no—
811C2×C4—3441no—
812C2×C4—3441no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1722no—
816C2×C4—1722no—
817C2×C4C22⋊C4×D4311yescharacteristic
818C2×C4C22⋊C4×D4311yescharacteristic
819C2×C4C22⋊C4×D4311yescharacteristic
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C8—22no—
824C8—41no—
825C8—41no—
826C8—41no—
827C8—1721no—
828C8—1721no—
829C8—1721no—
830C8—1721no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—432no—
835C22—861no—
836C22—861no—
837C22—861no—
838C22—861no—
839C22—861no—
840C22C2×C22⋊C4×D4311yescharacteristic
841C4—21no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—432no—
850C4—861no—
851C4—861no—
852C4—861no—
853C4—861no—
854C4—861no—
855C4—1721no—
856C4—1721no—
857C4—1721no—
858C4—1721no—
859C4C2×#1306333311yescharacteristic
860C4#1458366511yescharacteristic
861C4#137×D4311yescharacteristic
862C4#137×D4311yescharacteristic
863C2—41no—
864C2—862no—
865C2—1721no—
866C2#1914304511yescharacteristic
867C2#419×D4311yescharacteristic
868C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1491C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#10621898D4
cosocleC42×C43C24
hypercenter#1491D43
hypocenterC43#17514
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
4. #19133067C2semidirect
5. #19133066C2semidirect
6. #19133048C2semidirect
7. #19133040C2semidirect
8. #19133022C2semidirect
9. #19133017C2semidirect
10. #19133014C2semidirect
11. #19132996C2semidirect
12. #19132990C2semidirect
13. #19132988C2semidirect
14. Q8⋊C8×D43C2semidirect
15. C43×#1491C2semidirect
436. #1491D43semidirect
509. C43#17514semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218982
#191435572
#191432622
#191330672
#191330662
#191330482
#191330402
#191330222
#191330172
#191330142
#191329962
#191329902
#191329882
Q8⋊C8×D432
C43×#14912
#1751443