Finite Group Databasebeta

← C2×#19148193 #26003655

Subgroups — C2×#19148193 #26003655

Order 11008.

7802 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148193C2132yesmaximal, direct product factor
2C2×#14583632C213yesmaximal, complemented
3C2×#14583625C211yesmaximal, characteristic, complemented
4C2×#14583617C213yesmaximal, complemented
5C2×#14583599C213yesmaximal, complemented
6C2×#14583593C213yesmaximal, complemented
7C2×#14583568C211yesmaximal, characteristic, complemented
8C2×#14583561C211yesmaximal, characteristic, complemented
9C2×#14583556C211yesmaximal, characteristic, complemented
10C2×#14583446C213yesmaximal, complemented
11C2×#14583433C213yesmaximal, complemented
12C2×#14583431C213yesmaximal, complemented
13C2×C4×#10621902C211yesmaximal, characteristic, complemented
14C2×C4×#10621898C213yesmaximal, complemented
15C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
16C2×C4×#41×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898C2213yes—
19C22×Q8×D43C2211yescharacteristic
20#14583632C22148yescomplemented
21#14583625C22116yescomplemented
22#14583617C22148yescomplemented
23#14583599C22148yescomplemented
24#14583593C22148yescomplemented
25#14583568C22116yescomplemented
26#14583561C22116yescomplemented
27#14583556C22116yescomplemented
28#14583446C22148yescomplemented
29C2×#13063324C2213yes—
30C2×#13063321C2213yes—
31#14583433C22148yescomplemented
32#14583431C22148yescomplemented
33C2×#13063319C2216yes—
34C2×#13063318C2216yes—
35C2×#13063317C2213yes—
36C2×#13063316C2213yes—
37C2×#13063313C2213yes—
38C2×#13063312C2213yes—
39C2×#13063311C2216yes—
40C2×#13063308C2216yes—
41C2×#13063307C2216yes—
42C2×#13063305C2213yes—
43C2×#13063304C2213yes—
44C2×#13063300C2213yes—
45C2×#13063299C2213yes—
46C2×#13063298C2216yes—
47C2×#13063296C2213yes—
48C2×#13063296C2213yes—
49C4×#10621902C22116yescomplemented
50C4×#10621898C22148yescomplemented
51C2×Q8×Dic43C2211yescharacteristic
52C2×Q8×Dic43C2211yescharacteristic
53C2×C4×Dic86C2213yes—
54C2×C4×Dic86C2213yes—
55C2×C4×Dic86C2213yes—
56C2×#13063290C2213yes—
57C4×Q8×D43C22116yescomplemented
58C2×C4×D172C2213yes—
59C2×C4×D172C2213yes—
60C2×C4×D172C2213yes—
61C2×#13063287C2213yes—
62C2×C4×C22⋊D43C2213yes—
63C2×C4×C22⋊D43C2213yes—
64C2×C4×C22⋊D43C2216yes—
65C2×C4×C22⋊D43C2213yes—
66C2×C4×C22⋊D43C2213yes—
67C2×#13063284C2213yes—
68C2×#13063283C2213yes—
69C2×#13063282C2213yes—
70C2×#13063282C2211yescharacteristic
71C2×C4⋊C4×D43C2213yes—
72C2×C42×D43C2213yes—
73C2×C42×D43C2213yes—
74C22×#41×C43C2211yescharacteristic
75C4×#41×C43C22116yescomplemented
76C2×C4×Q8×C43C2211yescharacteristic
77C2×C4×Q8×C43C2211yescharacteristic
78C2×C4×D4×C43C2213yes—
79C2×C4×D4×C43C2213yes—
80C2×#117×C43C2213yes—
81C22×C42×C43C2213yes—
82C2×#10621902—28no—
83C2×#10621902C2318yes—
84C2×#10621898—224no—
85C2×#10621898C23124yes—
86C22×Dic86C2313yes—
87C22×Dic86C2313yes—
88C2×Q8×D43—28no—
89C2×Q8×D43C2318yes—
90C22×D172C2313yes—
91C22×D172C2313yes—
92C22×C22⋊D43C2313yes—
93C22×C22⋊D43C2313yes—
94C22×C22⋊D43C2316yes—
95C22×C4×D43C2313yes—
96C22×C4×D43C2313yes—
97C22×C4×D43C2313yes—
98C22×C4×D43C2313yes—
99C22×C4×D43C2313yes—
100C22×C4×D43C2311yescharacteristic
101#13063324C23124yes—
102#13063321C23124yes—
103#13063319C23148yes—
104#13063318C23148yes—
105#13063317C23124yes—
106#13063316C23124yes—
107#13063313C23124yes—
108#13063312C23124yes—
109#13063311C23148yes—
110#13063308C23148yes—
111#13063307C23148yes—
112#13063305C23124yes—
113#13063304C23124yes—
114#13063300C23124yes—
115#13063299C23124yes—
116#13063298C23148yes—
117#13063296C23124yes—
118#13063296C23124yes—
119Q8×Dic43C2318yes—
120Q8×Dic43C2318yes—
121C4×Dic86C23124yes—
122C4×Dic86C23124yes—
123C4×Dic86C23124yes—
124#13063290C23124yes—
125C4×D172C23124yes—
126C4×D172C23124yes—
127C4×D172C23124yes—
128#13063287C23124yes—
129C4×C22⋊D43C23124yes—
130C4×C22⋊D43C23124yes—
131C4×C22⋊D43C23124yes—
132C4×C22⋊D43C23124yes—
133C4×C22⋊D43C23148yes—
134#13063284C23124yes—
135#13063283C23124yes—
136#13063282C2318yes—
137#13063282C23124yes—
138C2×C4⋊Dic43C2313yes—
139C2×C4⋊Dic43C2313yes—
140C2×C4⋊Dic43C2313yes—
141C2×C4⋊Dic43C2313yes—
142C2×Dic43⋊C4C2316yes—
143C2×Dic43⋊C4C2311yescharacteristic
144C2×Dic43⋊C4C2311yescharacteristic
145C2×Dic43⋊C4C2313yes—
146C2×Dic43⋊C4C2313yes—
147C2×Dic43⋊C4C2316yes—
148C4⋊C4×D43C23124yes—
149C2×C22⋊Dic43C2313yes—
150C2×C22⋊Dic43C2313yes—
151C2×C22⋊Dic43C2316yes—
152C2×(C2×D43)⋊C4C2311yescharacteristic
153C2×(C2×D43)⋊C4C2311yescharacteristic
154C2×(C2×D43)⋊C4C2313yes—
155C2×(C2×D43)⋊C4C2313yes—
156C2×(C2×D43)⋊C4C2316yes—
157C2×(C2×D43)⋊C4C2316yes—
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2313yes—
160C2×C4×Dic43C2313yes—
161C2×C4×Dic43C2313yes—
162C2×C4×Dic43C2313yes—
163C2×C4×Dic43C2313yes—
164C42×D43C23124yes—
165C42×D43C23124yes—
166C2×#41×C43—28no—
167C2×#41×C43C2318yes—
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43C2313yes—
170C23×C4×C43C2313yes—
171C23×C4×C43C2313yes—
172C23×C4×C43C2313yes—
173C4×Q8×C43C2318yes—
174C4×Q8×C43C2318yes—
175C4×D4×C43C23124yes—
176C4×D4×C43C23124yes—
177#117×C43C23124yes—
178C2×C4⋊C4×C43C2313yes—
179C2×C4⋊C4×C43C2313yes—
180C2×C22⋊C4×C43C2316yes—
181C2×C42×C43C2311yescharacteristic
182C2×C42×C43C2313yes—
183C2×C42×C43C2313yes—
184C2×C42×C43C2313yes—
185C2×C42×C43C23124yes—
186C24×C43C2413yes—
187C23×D43C2413yes—
188C23×D43C2411yescharacteristic
189#41×C43—232no—
190C2×Q8×C43#4118yescomplemented
191C2×Q8×C43C2414yes—
192C2×D4×C43—212no—
193C2×D4×C43C24112yes—
194C22×C4×C43—212no—
195C22×C4×C43—212no—
196C22×C4×C43—46no—
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C22×C4×C43C2413yes—
200C22×C4×C43C2413yes—
201C22×C4×C43C24112yes—
202C22×C4×C43C24112yes—
203C22×C4×C43C24112yes—
204C22×C4×C43C2413yes—
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—212no—
207C2×C22⋊D43—212no—
208C2×C22⋊D43—412no—
209C2×C22⋊D43C24112yes—
210C2×C22⋊D43C24112yes—
211C2×C22⋊D43C24124yes—
212C22×Dic43C2411yescharacteristic
213C22×Dic43C2411yescharacteristic
214C22×Dic43C2413yes—
215C22×Dic43C2413yes—
216C22×Dic43C2413yes—
217C22×Dic43C2411yescharacteristic
218#10621902—232no—
219Q8×D43—232no—
220#10621898—296no—
221C2×D172—212no—
222C2×D172—212no—
223C2×D172C24112yes—
224C2×D172C24112yes—
225C2×C4×D43—212no—
226C2×C4×D43—212no—
227C2×C4×D43—212no—
228C2×C4×D43—46no—
229C2×C4×D43—46no—
230C2×C4×D43#4118yescomplemented
231C2×C4×D43C24112yes—
232C2×C4×D43C24112yes—
233C2×C4×D43C24112yes—
234C2×C4×D43C24112yes—
235C2×C4×D43C24112yes—
236C2×C4×D43C2414yes—
237C2×Dic86—212no—
238C2×Dic86—212no—
239C2×Dic86C24112yes—
240C2×Dic86C24112yes—
241C4⋊C4×C43C24112yes—
242C4⋊C4×C43C24112yes—
243C22⋊C4×C43C24124yes—
244C42×C43C2414yes—
245C42×C43C24112yes—
246C42×C43C24112yes—
247C42×C43C24112yes—
248C22⋊Dic43C24112yes—
249C22⋊Dic43C24112yes—
250C22⋊Dic43C24124yes—
251(C2×D43)⋊C4C2414yes—
252(C2×D43)⋊C4C2414yes—
253(C2×D43)⋊C4C24112yes—
254(C2×D43)⋊C4C24112yes—
255(C2×D43)⋊C4C24124yes—
256(C2×D43)⋊C4C24124yes—
257C4⋊Dic43C24112yes—
258C4⋊Dic43C24112yes—
259C4⋊Dic43C24112yes—
260C4⋊Dic43C24112yes—
261Dic43⋊C4C24124yes—
262Dic43⋊C4C2414yes—
263Dic43⋊C4C2414yes—
264Dic43⋊C4C24112yes—
265Dic43⋊C4C24112yes—
266Dic43⋊C4C24124yes—
267C4×Dic43C2414yes—
268C4×Dic43C24112yes—
269C4×Dic43C24112yes—
270C4×Dic43C24112yes—
271C4×Dic43C24112yes—
272C4×Dic43C24112yes—
273C23×C43—26no—
274C23×C43—26no—
275C23×C43—26no—
276C23×C43C2516yes—
277C23×C43C2511yescharacteristic
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—26no—
281C22×D43—26no—
282C22×D43—26no—
283C22×D43C2×#4114yes—
284C22×D43C2516yes—
285C22×D43C2512yes—
286Q8×C43C2×#41116yescomplemented
287D4×C43—224no—
288C2×C4×C43—26no—
289C2×C4×C43—22no—
290C2×C4×C43—26no—
291C2×C4×C43—22no—
292C2×C4×C43—224no—
293C2×C4×C43—224no—
294C2×C4×C43—412no—
295C2×C4×C43C2×#4114yes—
296C2×C4×C43C2×#41112yes—
297C2×C4×C43C2516yes—
298C2×C4×C43C2512yes—
299C2×C4×C43C2512yes—
300C2×C4×C43C2516yes—
301C2×C4×C43C2512yes—
302C2×C4×C43C2516yes—
303C22⋊D43—224no—
304C22⋊D43—224no—
305C22⋊D43—424no—
306C2×Dic43—26no—
307C2×Dic43—26no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—26no—
311C2×Dic43C2×#4114yes—
312C2×Dic43C2512yes—
313C2×Dic43C2512yes—
314C2×Dic43C2516yes—
315C2×Dic43C2516yes—
316C2×Dic43C2516yes—
317C2×Dic43C2512yes—
318D172—224no—
319D172—224no—
320C4×D43—224no—
321C4×D43—224no—
322C4×D43—224no—
323C4×D43—412no—
324C4×D43—412no—
325C4×D43C2×#41116yescomplemented
326Dic86—224no—
327Dic86—224no—
328C2×#3480—431nomaximal, Sylow
329C22×C43—26no—
330C22×C43—26no—
331C22×C43—26no—
332C22×C43—412no—
333C22×C43C22×#4112yes—
334C22×C43C22×#4112yes—
335C22×C43#58512yes—
336C22×C43C2611yescharacteristic
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—28no—
340C2×D43—26no—
341C2×D43—26no—
342C2×D43—26no—
343C2×D43—412no—
344C2×D43C22×#4114yes—
345C4×C43—26no—
346C4×C43—22no—
347C4×C43—26no—
348C4×C43—22no—
349C4×C43C22×#4114yes—
350C4×C43C22×#41112yes—
351Dic43—26no—
352Dic43—26no—
353Dic43—22no—
354Dic43—22no—
355Dic43—26no—
356Dic43C22×#4114yes—
357#3480—4332no—
358C2×#559—433no—
359C2×#557—431no—
360C2×#556—433no—
361C2×#553—433no—
362C2×#553—433no—
363C2×#550—431no—
364C2×#548—431no—
365C2×#548—431no—
366C2×#532—433no—
367C2×#529—433no—
368C2×#529—433no—
369C2×C4×#41—433no—
370C2×C4×#41—431no—
371C2×C4×#41D4311yescharacteristic, complemented
372C22×C4×Q8—431no—
373C2×C43—46no—
374C2×C43#348014yescomplemented
375C2×C43C23×#4111yescharacteristic
376C2×C43C23×#4111yescharacteristic
377C2×C43C2×#58511yescharacteristic
378D43—24no—
379D43—46no—
380C22×#41—431no—
381C22×#41—433no—
382C22×#41C2×D4311yescharacteristic
383C23×Q8—431no—
384#559—4348no—
385#557—4316no—
386#556—4348no—
387#553—4348no—
388#553—4348no—
389#550—4316no—
390#548—4316no—
391#548—4316no—
392#532—4348no—
393C2×C4⋊Q8—433no—
394C2×#127—433no—
395#529—4348no—
396#529—4348no—
397C2×#126—436no—
398C2×#126—436no—
399C2×#125—433no—
400C2×#125—433no—
401C2×#124—433no—
402C2×#124—436no—
403C2×#124—433no—
404C2×#123—436no—
405C2×#123—436no—
406C2×C22⋊Q8—433no—
407C2×C22⋊Q8—433no—
408C2×#121—433no—
409C2×#121—433no—
410C2×#121—433no—
411C2×#121—433no—
412C2×#121—436no—
413C4×#41—4316no—
414C4×#41—4348no—
415C4×#41C2×D43116yescomplemented
416C2×C4×Q8—431no—
417C2×C4×Q8—431no—
418C2×C4×Q8—4316no—
419C2×C4×Q8—433no—
420C2×C4×Q8—433no—
421C2×C4×Q8—433no—
422C2×C4×Q8—433no—
423C2×C4×Q8C2×D4311yescharacteristic
424C2×C4×Q8C2×D4311yescharacteristic
425C2×C4×D4—433no—
426C2×C4×D4—433no—
427C2×C4×D4—433no—
428C2×C4×D4—433no—
429C2×C4×D4—436no—
430C2×C4×D4—433no—
431C2×C4×D4—433no—
432C2×C4×D4—433no—
433C2×C4×D4—433no—
434C2×C4×D4C2×D4313yes—
435C2×C4×D4C2×D4313yes—
436C2×#117—433no—
437C2×#117—433no—
438C2×#117—431no—
439C2×#117—433no—
440C2×#117C2×D4313yes—
441C22×C4⋊C4—433no—
442C22×C42—433no—
443C22×C42—433no—
444C22×C42C2×D4313yes—
445C43C2×#348011yescharacteristic, complemented, Sylow
446C2×#41—28no—
447C2×#41—438no—
448C2×#41—4324no—
449C2×#41—8624no—
450C2×#41—868no—
451C2×#41C22×D4318yes—
452C22×Q8—438no—
453C22×Q8—433no—
454C22×Q8—433no—
455C22×Q8—868no—
456C22×Q8C22×D4311yescharacteristic
457C22×D4—433no—
458C22×D4—433no—
459C22×D4—436no—
460C22×D4—433no—
461C22×D4—433no—
462C22×D4C22×D4313yes—
463C23×C4—431no—
464C23×C4—433no—
465C23×C4—433no—
466C23×C4—433no—
467C23×C4—433no—
468C23×C4—433no—
469C23×C4C22×D4313yes—
470C23×C4C22×D4313yes—
471C23×C4C22×D4313yes—
472C4⋊Q8—4324no—
473#127—4324no—
474#126—4348no—
475#126—4348no—
476#125—4324no—
477#125—4324no—
478#124—4324no—
479#124—4348no—
480#124—4324no—
481#123—4348no—
482#123—4348no—
483C22⋊Q8—4324no—
484C22⋊Q8—4324no—
485#121—4324no—
486#121—4324no—
487#121—4324no—
488#121—4324no—
489#121—4348no—
490C4×Q8—438no—
491C4×Q8—438no—
492C4×Q8—4324no—
493C4×Q8—4324no—
494C4×Q8—4324no—
495C4×Q8—4324no—
496C4×Q8C22×D4318yes—
497C4×Q8C22×D4318yes—
498C4×D4—4324no—
499C4×D4—4324no—
500C4×D4—4324no—
501C4×D4—4324no—
502C4×D4—4348no—
503C4×D4—4324no—
504C4×D4—4324no—
505C4×D4—4324no—
506C4×D4—4324no—
507C4×D4C22×D43124yes—
508C4×D4C22×D43124yes—
509#117—4324no—
510#117—4324no—
511#117—438no—
512#117—4324no—
513#117C22×D43124yes—
514C2×C4⋊C4—433no—
515C2×C4⋊C4—436no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—433no—
519C2×C4⋊C4—433no—
520C2×C4⋊C4—433no—
521C2×C4⋊C4—433no—
522C2×C4⋊C4—433no—
523C2×C4⋊C4—436no—
524C2×C4⋊C4—4324no—
525C2×C4⋊C4C22×D4313yes—
526C2×C4⋊C4C22×D4313yes—
527C2×C22⋊C4—433no—
528C2×C22⋊C4—433no—
529C2×C22⋊C4—436no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—433no—
533C2×C22⋊C4—436no—
534C2×C22⋊C4—433no—
535C2×C22⋊C4—436no—
536C2×C22⋊C4C22×D4316yes—
537C2×C42—433no—
538C2×C42—433no—
539C2×C42—433no—
540C2×C42—433no—
541C2×C42—431no—
542C2×C42—433no—
543C2×C42—4324no—
544C2×C42—4324no—
545C2×C42C22×D4313yes—
546C2×C42C22×D4313yes—
547C2×C42C22×D43124yes—
548C2×C42C22×D4311yescharacteristic
549C2×C42C22×D4313yes—
550C24—431no—
551C24—433no—
552C24C23×D4313yes—
553#41—232no—
554#41—8696no—
555#41—8632no—
556C2×Q8—4312no—
557C2×Q8—4312no—
558C2×Q8—8612no—
559C2×Q8—8632no—
560C2×Q8—8612no—
561C2×Q8#1062189818yescomplemented
562C2×Q8C23×D4314yes—
563C2×D4—212no—
564C2×D4—4312no—
565C2×D4—4312no—
566C2×D4—4324no—
567C2×D4—4312no—
568C2×D4—4312no—
569C2×D4—8612no—
570C2×D4—8612no—
571C2×D4—8612no—
572C2×D4—8612no—
573C2×D4—17212no—
574C2×D4C23×D43112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—46no—
578C22×C4—431no—
579C22×C4—438no—
580C22×C4—434no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—433no—
584C22×C4—433no—
585C22×C4—433no—
586C22×C4—4312no—
587C22×C4—4312no—
588C22×C4—4312no—
589C22×C4—4312no—
590C22×C4—4312no—
591C22×C4—8612no—
592C22×C4—8612no—
593C22×C4—8612no—
594C22×C4—1726no—
595C22×C4—1726no—
596C22×C4C23×D4313yes—
597C22×C4C23×D4311yescharacteristic
598C22×C4C23×D4311yescharacteristic
599C22×C4C23×D4313yes—
600C22×C4C23×D43112yes—
601C22×C4C23×D43112yes—
602C22×C4C23×D43112yes—
603C22×C4C23×D4313yes—
604C22×C4C23×D4311yescharacteristic
605C4⋊C4—4312no—
606C4⋊C4—4324no—
607C4⋊C4—434no—
608C4⋊C4—434no—
609C4⋊C4—4312no—
610C4⋊C4—4312no—
611C4⋊C4—4312no—
612C4⋊C4—4312no—
613C4⋊C4—4312no—
614C4⋊C4—4324no—
615C4⋊C4C23×D43112yes—
616C4⋊C4C23×D43112yes—
617C22⋊C4—4312no—
618C22⋊C4—4312no—
619C22⋊C4—4324no—
620C22⋊C4—434no—
621C22⋊C4—434no—
622C22⋊C4—4312no—
623C22⋊C4—4324no—
624C22⋊C4—4312no—
625C22⋊C4—4324no—
626C22⋊C4C23×D43124yes—
627C42—434no—
628C42—4312no—
629C42—4312no—
630C42—4312no—
631C42—4312no—
632C42—4312no—
633C42C23×D43112yes—
634C42C23×D4314yes—
635C42C23×D43112yes—
636C42C23×D43112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—434no—
641C23—432no—
642C23—436no—
643C23—862no—
644C23—862no—
645C23—866no—
646C23—866no—
647C23—866no—
648C23C24×D4316yes—
649C23C24×D4311yescharacteristic
650Q8—8624no—
651Q8—8624no—
652Q8C2×#10621898116yescomplemented
653D4—224no—
654D4—8624no—
655D4—8624no—
656D4—8624no—
657D4—8624no—
658D4—17224no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—412no—
666C2×C4—434no—
667C2×C4—432no—
668C2×C4—4316no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—436no—
672C2×C4—436no—
673C2×C4—436no—
674C2×C4—866no—
675C2×C4—862no—
676C2×C4—866no—
677C2×C4—862no—
678C2×C4—866no—
679C2×C4—8624no—
680C2×C4—8624no—
681C2×C4—8624no—
682C2×C4—17212no—
683C2×C4—17212no—
684C2×C4#41×D4314yes—
685C2×C4C2×#10621898112yes—
686C2×C4C24×D4316yes—
687C2×C4C24×D4312yes—
688C2×C4C24×D4312yes—
689C2×C4C24×D4316yes—
690C2×C4C24×D4312yes—
691C2×C4C24×D4316yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—434no—
697C22—862no—
698C22—862no—
699C22—868no—
700C22—866no—
701C22—866no—
702C22—866no—
703C22—17212no—
704C22C2×#41×D4312yes—
705C22C22×#1062189812yes—
706C22#1458373512yes—
707C22C25×D4311yescharacteristic
708C4—26no—
709C4—22no—
710C4—22no—
711C4—26no—
712C4—434no—
713C4—866no—
714C4—862no—
715C4—866no—
716C4—862no—
717C4—866no—
718C4C2×#41×D4314yes—
719C4C22×#10621898112yes—
720C2—46no—
721C2—864no—
722C2—1726no—
723C2#1914819314yesdirect product factor
724C2C22×#41×D4311yescharacteristic
725C2C23×#1062189811yescharacteristic
726C2C2×#1458373511yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C4×#41×C43C2
socleC23×C43C25
hypercenterC2×C4×#41D43
hypocenterC43C2×#3480
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #19148193C2direct (N × H)
2. C2×#14583632C2semidirect
3. C2×#14583625C2semidirect
4. C2×#14583617C2semidirect
5. C2×#14583599C2semidirect
6. C2×#14583593C2semidirect
7. C2×#14583568C2semidirect
8. C2×#14583561C2semidirect
9. C2×#14583556C2semidirect
10. C2×#14583446C2semidirect
11. C2×#14583433C2semidirect
12. C2×#14583431C2semidirect
13. C2×C4×#10621902C2semidirect
14. C2×C4×#10621898C2semidirect
15. C2×C4×Q8×D43C2semidirect
16. C2×C4×#41×C43C2semidirect
20. #14583632C22semidirect
21. #14583625C22semidirect
22. #14583617C22semidirect
23. #14583599C22semidirect
24. #14583593C22semidirect
25. #14583568C22semidirect
26. #14583561C22semidirect
27. #14583556C22semidirect
28. #14583446C22semidirect
31. #14583433C22semidirect
32. #14583431C22semidirect
49. C4×#10621902C22semidirect
50. C4×#10621898C22semidirect
57. C4×Q8×D43C22semidirect
75. C4×#41×C43C22semidirect
190. C2×Q8×C43#41semidirect
230. C2×C4×D43#41semidirect
286. Q8×C43C2×#41semidirect
325. C4×D43C2×#41semidirect
371. C2×C4×#41D43semidirect
374. C2×C43#3480semidirect
415. C4×#41C2×D43semidirect
445. C43C2×#3480semidirect
561. C2×Q8#10621898semidirect
652. Q8C2×#10621898semidirect
723. C2#19148193direct (N × H)

Maximal subgroups

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

subgroupindex
#191481932
C2×#145836322
C2×#145836252
C2×#145836172
C2×#145835992
C2×#145835932
C2×#145835682
C2×#145835612
C2×#145835562
C2×#145834462
C2×#145834332
C2×#145834312
C2×C4×#106219022
C2×C4×#106218982
C2×C4×Q8×D432
C2×C4×#41×C432
C2×#348043