Finite Group Databasebeta

← C2×#19148185 #26003651

Subgroups — C2×#19148185 #26003651

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#19148185C2132yesmaximal, direct product factor
2C2×#14583631C213yesmaximal, complemented
3C2×#14583625C211yesmaximal, characteristic, complemented
4C2×#14583620C213yesmaximal, complemented
5C2×#14583601C213yesmaximal, complemented
6C2×#14583595C213yesmaximal, complemented
7C2×#14583568C211yesmaximal, characteristic, complemented
8C2×#14583560C211yesmaximal, characteristic, complemented
9C2×#14583444C213yesmaximal, complemented
10C2×#14583435C213yesmaximal, complemented
11C2×#14583428C213yesmaximal, complemented
12C2×#41×Dic43C211yesmaximal, characteristic, complemented
13C2×C4×#10621902C211yesmaximal, characteristic, complemented
14C2×C4×#10621900C213yesmaximal, complemented
15C22×Q8×Dic43C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2213yes—
19#14583631C22148yescomplemented
20#14583625C22116yescomplemented
21#14583620C22148yescomplemented
22#14583601C22148yescomplemented
23#14583595C22148yescomplemented
24#14583568C22116yescomplemented
25#14583560C22116yescomplemented
26#14583444C22148yescomplemented
27C2×#13063324C2213yes—
28C2×#13063321C2213yes—
29#14583435C22148yescomplemented
30#14583428C22148yescomplemented
31C2×#13063320C2216yes—
32C2×#13063318C2216yes—
33C2×#13063317C2213yes—
34C2×#13063316C2213yes—
35C2×#13063314C2213yes—
36C2×#13063311C2216yes—
37C2×#13063309C2216yes—
38C2×#13063307C2216yes—
39C2×#13063301C2213yes—
40C2×#13063299C2213yes—
41C2×#13063299C2213yes—
42C2×#13063297C2216yes—
43C2×#13063296C2213yes—
44#41×Dic43C22116yescomplemented
45C4×#10621902C22116yescomplemented
46C4×#10621900C22148yescomplemented
47C2×Q8×Dic43C2211yescharacteristic
48C2×Q8×Dic43C2211yescharacteristic
49C2×Q8×Dic43C2211yescharacteristic
50C2×Q8×Dic43C2213yes—
51C2×Q8×Dic43C2213yes—
52C2×Q8×Dic43C22116yescomplemented
53C2×C4×Dic86C2213yes—
54C2×#13063290C2213yes—
55C2×C4×D172C2213yes—
56C2×D4×Dic43C2213yes—
57C2×D4×Dic43C2213yes—
58C2×D4×Dic43C2213yes—
59C2×#13063287C2213yes—
60C2×C4×C22⋊D43C2213yes—
61C2×C4×C22⋊D43C2213yes—
62C2×(C22⋊D43)⋊C4C2216yes—
63C2×(C22⋊D43)⋊C4C2213yes—
64C2×(C22⋊D43)⋊C4C2213yes—
65C2×#13063284C2213yes—
66C2×#13063283C2213yes—
67C2×#13063283C2213yes—
68C2×#13063281C2213yes—
69C2×#13063281C2211yescharacteristic
70C22×C4⋊Dic43C2213yes—
71C22×C4×Dic43C2213yes—
72C22×C4×Dic43C2213yes—
73C2×C42×D43C2213yes—
74C22×#41×C43C2211yescharacteristic
75C23×Q8×C43C2211yescharacteristic
76C43×#548C22116yescomplemented
77C2×#124×C43C2213yes—
78C2×C22⋊Q8×C43C2213yes—
79C2×#121×C43C2213yes—
80C2×C4×Q8×C43C2211yescharacteristic
81C2×C4×D4×C43C2213yes—
82C2×#10621902—28no—
83C2×#10621902C2318yes—
84C2×#10621900—224no—
85C2×#10621900C23124yes—
86C22×Dic86C2313yes—
87C22×D172C2313yes—
88C22×C22⋊D43C2313yes—
89C22×C22⋊D43C2313yes—
90C22×C22⋊D43C2316yes—
91C23×Dic43C2313yes—
92C23×Dic43C2313yes—
93C23×Dic43C2313yes—
94C23×Dic43C2311yescharacteristic
95C22×C4×D43C2313yes—
96C22×C4×D43C2313yes—
97C22×C4×D43C2313yes—
98#13063324C23124yes—
99#13063321C23124yes—
100#13063320C23148yes—
101#13063318C23148yes—
102#13063317C23124yes—
103#13063316C23124yes—
104#13063314C23124yes—
105#13063311C23148yes—
106#13063309C23148yes—
107#13063307C23148yes—
108#13063301C23124yes—
109#13063299C23124yes—
110#13063299C23124yes—
111#13063297C23148yes—
112#13063296C23124yes—
113Q8×Dic43C2318yes—
114Q8×Dic43C2318yes—
115Q8×Dic43C23124yes—
116Q8×Dic43C2318yes—
117Q8×Dic43C23124yes—
118C4×Dic86C23124yes—
119#13063290C23124yes—
120C4×D172C23124yes—
121D4×Dic43C23124yes—
122D4×Dic43C23124yes—
123D4×Dic43C23124yes—
124#13063287C23124yes—
125C4×C22⋊D43C23124yes—
126C4×C22⋊D43C23124yes—
127(C22⋊D43)⋊C4C23124yes—
128(C22⋊D43)⋊C4C23124yes—
129(C22⋊D43)⋊C4C23148yes—
130#13063284C23124yes—
131#13063283C23124yes—
132#13063283C23124yes—
133#13063281C2318yes—
134#13063281C23124yes—
135C2×C4⋊Dic43C23124yes—
136C2×C4⋊Dic43C2313yes—
137C2×C4⋊Dic43C2313yes—
138C2×C4⋊Dic43C2316yes—
139C2×C4⋊Dic43C2313yes—
140C2×C4⋊Dic43C2313yes—
141C2×Dic43⋊C4C2311yescharacteristic
142C2×Dic43⋊C4C2313yes—
143C2×Dic43⋊C4C2311yescharacteristic
144C2×Dic43⋊C4C2313yes—
145C2×Dic43⋊C4C2316yes—
146C2×C22⋊Dic43C2311yescharacteristic
147C2×C22⋊Dic43C2313yes—
148C2×C22⋊Dic43C2316yes—
149C2×(C2×D43)⋊C4C2313yes—
150C2×(C2×D43)⋊C4C2313yes—
151C2×(C2×D43)⋊C4C2316yes—
152C2×(C2×D43)⋊C4C2316yes—
153C2×C4×Dic43C2311yescharacteristic
154C2×C4×Dic43C2313yes—
155C2×C4×Dic43C2313yes—
156C2×C4×Dic43C2311yescharacteristic
157C2×C4×Dic43C2313yes—
158C2×C4×Dic43C2313yes—
159C2×C4×Dic43C2313yes—
160C2×C4×Dic43C2313yes—
161C2×C4×Dic43C2313yes—
162C2×C4×Dic43C23124yes—
163C2×C4×Dic43C23124yes—
164C42×D43C23124yes—
165C2×#41×C43—28no—
166C2×#41×C43C2318yes—
167C22×Q8×C43—28no—
168C22×Q8×C43C2318yes—
169C22×Q8×C43C2313yes—
170C22×Q8×C43C2311yescharacteristic
171C22×D4×C43C2313yes—
172C22×D4×C43C2313yes—
173C23×C4×C43C2313yes—
174C23×C4×C43C2313yes—
175#124×C43C23124yes—
176C22⋊Q8×C43C23124yes—
177#121×C43C23124yes—
178C4×Q8×C43C2318yes—
179C4×D4×C43C23124yes—
180C2×C4⋊C4×C43C2313yes—
181C2×C4⋊C4×C43C2313yes—
182C2×C22⋊C4×C43C2311yescharacteristic
183C2×C22⋊C4×C43C2313yes—
184C2×C22⋊C4×C43C2316yes—
185C2×C42×C43C2313yes—
186C24×C43C2413yes—
187C24×C43C2411yescharacteristic
188C23×D43C2413yes—
189#41×C43—232no—
190C2×Q8×C43—232no—
191C2×Q8×C43—212no—
192C2×Q8×C43#4118yescomplemented
193C2×Q8×C43C24112yes—
194C2×Q8×C43C2414yes—
195C2×D4×C43—212no—
196C2×D4×C43—212no—
197C2×D4×C43C24112yes—
198C2×D4×C43C24112yes—
199C22×C4×C43—212no—
200C22×C4×C43—212no—
201C22×C4×C43C2411yescharacteristic
202C22×C4×C43C2413yes—
203C22×C4×C43C2413yes—
204C22×C4×C43C2411yescharacteristic
205C22×C4×C43C24112yes—
206C22×C4×C43C24112yes—
207C22×C4×C43C2413yes—
208C2×C22⋊D43—212no—
209C2×C22⋊D43—212no—
210C2×C22⋊D43—412no—
211C2×C22⋊D43C24112yes—
212C2×C22⋊D43C24112yes—
213C2×C22⋊D43C24124yes—
214C22×Dic43—212no—
215C22×Dic43—46no—
216C22×Dic43—46no—
217C22×Dic43#4118yescomplemented
218C22×Dic43C2411yescharacteristic
219C22×Dic43C2413yes—
220C22×Dic43C2411yescharacteristic
221C22×Dic43C2413yes—
222C22×Dic43C2413yes—
223C22×Dic43C24112yes—
224C22×Dic43C24112yes—
225C22×Dic43C24112yes—
226C22×Dic43C2411yescharacteristic
227C22×Dic43C2411yescharacteristic
228C22×Dic43C2414yes—
229#10621902—232no—
230#10621900—296no—
231C2×D172—212no—
232C2×D172C24112yes—
233C2×C4×D43—212no—
234C2×C4×D43—212no—
235C2×C4×D43—46no—
236C2×C4×D43C24112yes—
237C2×C4×D43C24112yes—
238C2×C4×D43C24112yes—
239C2×Dic86—212no—
240C2×Dic86C24112yes—
241C4⋊C4×C43C24112yes—
242C4⋊C4×C43C24112yes—
243C22⋊C4×C43C2414yes—
244C22⋊C4×C43C24112yes—
245C22⋊C4×C43C24124yes—
246C42×C43C24112yes—
247C22⋊Dic43C2414yes—
248C22⋊Dic43C24112yes—
249C22⋊Dic43C24124yes—
250(C2×D43)⋊C4C24112yes—
251(C2×D43)⋊C4C24112yes—
252(C2×D43)⋊C4C24124yes—
253(C2×D43)⋊C4C24124yes—
254C4⋊Dic43C24112yes—
255C4⋊Dic43C24112yes—
256C4⋊Dic43C24124yes—
257C4⋊Dic43C24112yes—
258C4⋊Dic43C24112yes—
259Dic43⋊C4C2414yes—
260Dic43⋊C4C24112yes—
261Dic43⋊C4C2414yes—
262Dic43⋊C4C24112yes—
263Dic43⋊C4C24124yes—
264C4×Dic43C2414yes—
265C4×Dic43C24112yes—
266C4×Dic43C24112yes—
267C4×Dic43C2414yes—
268C4×Dic43C24112yes—
269C4×Dic43C24112yes—
270C4×Dic43C24112yes—
271C4×Dic43C24112yes—
272C4×Dic43C24112yes—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—26no—
276C23×C43—26no—
277C23×C43—26no—
278C23×C43C2×#4114yes—
279C23×C43C2516yes—
280C23×C43C2512yes—
281C23×C43C2511yescharacteristic
282C22×D43—26no—
283C22×D43—26no—
284C22×D43—26no—
285C22×D43C2516yes—
286Q8×C43—224no—
287Q8×C43C2×#41116yescomplemented
288D4×C43—224no—
289D4×C43—224no—
290C2×C4×C43—26no—
291C2×C4×C43—22no—
292C2×C4×C43—26no—
293C2×C4×C43—22no—
294C2×C4×C43—224no—
295C2×C4×C43—224no—
296C2×C4×C43C2×#41112yes—
297C2×C4×C43C2512yes—
298C2×C4×C43C2516yes—
299C2×C4×C43C2512yes—
300C2×C4×C43C2516yes—
301C2×C4×C43C2516yes—
302C22⋊D43—224no—
303C22⋊D43—224no—
304C22⋊D43—424no—
305C2×Dic43—26no—
306C2×Dic43—22no—
307C2×Dic43—26no—
308C2×Dic43—22no—
309C2×Dic43—26no—
310C2×Dic43—224no—
311C2×Dic43—412no—
312C2×Dic43—412no—
313C2×Dic43C2×#4114yes—
314C2×Dic43C2×#4114yes—
315C2×Dic43C2×#41116yescomplemented
316C2×Dic43C2512yes—
317C2×Dic43C2512yes—
318C2×Dic43C2516yes—
319C2×Dic43C2516yes—
320C2×Dic43C2516yes—
321C2×Dic43C2512yes—
322C2×Dic43C2512yes—
323D172—224no—
324C4×D43—224no—
325C4×D43—224no—
326C4×D43—412no—
327Dic86—224no—
328C2×#3480—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—28no—
332C22×C43—26no—
333C22×C43—26no—
334C22×C43—26no—
335C22×C43—412no—
336C22×C43C22×#4114yes—
337C22×C43C22×#4112yes—
338C22×C43C22×#4112yes—
339C22×C43#58512yes—
340C22×C43C2611yescharacteristic
341C2×D43—26no—
342C2×D43—26no—
343C2×D43—26no—
344C2×D43—412no—
345C4×C43—26no—
346C4×C43—22no—
347C4×C43—26no—
348C4×C43—22no—
349C4×C43C22×#41112yes—
350Dic43—26no—
351Dic43—22no—
352Dic43—26no—
353Dic43—22no—
354Dic43—26no—
355Dic43C22×#4114yes—
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×#548D4311yescharacteristic, complemented
366C2×#532—433no—
367C2×#529—433no—
368C2×#529—433no—
369C2×C4×#41—431no—
370C2×C4×#41—431no—
371C2×C4×#41—433no—
372C22×C4×Q8—431no—
373C2×C43—24no—
374C2×C43—46no—
375C2×C43#348014yescomplemented
376C2×C43C23×#4111yescharacteristic
377C2×C43C23×#4111yescharacteristic
378C2×C43C2×#58511yescharacteristic
379D43—46no—
380C22×#41—431no—
381C22×#41—433no—
382C22×#41C2×D4311yescharacteristic
383C23×Q8C2×D4311yescharacteristic
384#559—4348no—
385#557—4316no—
386#556—4348no—
387#553—4348no—
388#553—4348no—
389#550—4316no—
390#548—4316no—
391#548C2×D43116yescomplemented
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×#124C2×D4313yes—
404C2×#123—436no—
405C2×#123—436no—
406C2×C22⋊Q8—433no—
407C2×C22⋊Q8C2×D4313yes—
408C2×#121—433no—
409C2×#121—436no—
410C2×#121—433no—
411C2×#121—433no—
412C2×#121C2×D4313yes—
413C4×#41—4316no—
414C4×#41—4316no—
415C4×#41—4348no—
416C2×C4×Q8—431no—
417C2×C4×Q8—433no—
418C2×C4×Q8—431no—
419C2×C4×Q8—433no—
420C2×C4×Q8—431no—
421C2×C4×Q8—4316no—
422C2×C4×Q8—433no—
423C2×C4×Q8—433no—
424C2×C4×Q8C2×D4311yescharacteristic
425C2×C4×D4—433no—
426C2×C4×D4—433no—
427C2×C4×D4—433no—
428C2×C4×D4—433no—
429C2×C4×D4—433no—
430C2×C4×D4—433no—
431C2×C4×D4—433no—
432C2×C4×D4—433no—
433C2×C4×D4—436no—
434C2×C4×D4—433no—
435C2×C4×D4C2×D4313yes—
436C2×#117—433no—
437C2×#117—433no—
438C2×#117—433no—
439C2×#117—431no—
440C2×#117—433no—
441C22×C4⋊C4—433no—
442C22×C42—433no—
443C22×C42—433no—
444C22×C42—433no—
445C43C2×#348011yescharacteristic, complemented, Sylow
446C2×#41—28no—
447C2×#41—438no—
448C2×#41—4324no—
449C2×#41—8624no—
450C2×#41—868no—
451C2×#41C22×D4318yes—
452C22×Q8—28no—
453C22×Q8—433no—
454C22×Q8C22×D4313yes—
455C22×Q8C22×D4318yes—
456C22×Q8C22×D4311yescharacteristic
457C22×D4—433no—
458C22×D4—433no—
459C22×D4—436no—
460C22×D4—433no—
461C22×D4C22×D4313yes—
462C22×D4C22×D4313yes—
463C23×C4—431no—
464C23×C4—433no—
465C23×C4—433no—
466C23×C4—433no—
467C23×C4—433no—
468C23×C4—433no—
469C23×C4—433no—
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#124C22×D43124yes—
481#123—4348no—
482#123—4348no—
483C22⋊Q8—4324no—
484C22⋊Q8C22×D43124yes—
485#121—4324no—
486#121—4348no—
487#121—4324no—
488#121—4324no—
489#121C22×D43124yes—
490C4×Q8—438no—
491C4×Q8—4324no—
492C4×Q8—438no—
493C4×Q8—4324no—
494C4×Q8—438no—
495C4×Q8—4324no—
496C4×Q8—4324no—
497C4×Q8C22×D4318yes—
498C4×D4—4324no—
499C4×D4—4324no—
500C4×D4—4324no—
501C4×D4—4324no—
502C4×D4—4324no—
503C4×D4—4324no—
504C4×D4—4324no—
505C4×D4—4324no—
506C4×D4—4348no—
507C4×D4—4324no—
508C4×D4C22×D43124yes—
509#117—4324no—
510#117—4324no—
511#117—4324no—
512#117—438no—
513#117—4324no—
514C2×C4⋊C4—433no—
515C2×C4⋊C4—433no—
516C2×C4⋊C4—436no—
517C2×C4⋊C4—4324no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—433no—
521C2×C4⋊C4—433no—
522C2×C4⋊C4—433no—
523C2×C4⋊C4—433no—
524C2×C4⋊C4—436no—
525C2×C4⋊C4C22×D4313yes—
526C2×C4⋊C4C22×D4313yes—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—433no—
529C2×C22⋊C4—436no—
530C2×C22⋊C4—433no—
531C2×C22⋊C4—436no—
532C2×C22⋊C4—433no—
533C2×C22⋊C4—436no—
534C2×C22⋊C4C22×D4311yescharacteristic
535C2×C22⋊C4C22×D4313yes—
536C2×C22⋊C4C22×D4316yes—
537C2×C42—431no—
538C2×C42—431no—
539C2×C42—433no—
540C2×C42—433no—
541C2×C42—433no—
542C2×C42—433no—
543C2×C42—433no—
544C2×C42—433no—
545C2×C42—433no—
546C2×C42—4324no—
547C2×C42—4324no—
548C2×C42—4324no—
549C2×C42C22×D4313yes—
550C24—433no—
551C24C23×D4313yes—
552C24C23×D4311yescharacteristic
553#41—232no—
554#41—8696no—
555#41—8632no—
556C2×Q8—232no—
557C2×Q8—212no—
558C2×Q8—4312no—
559C2×Q8—8612no—
560C2×Q8#1062190018yescomplemented
561C2×Q8C23×D43112yes—
562C2×Q8C23×D4314yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—4312no—
566C2×D4—4312no—
567C2×D4—4324no—
568C2×D4—4312no—
569C2×D4—8612no—
570C2×D4—8612no—
571C2×D4—8612no—
572C2×D4—17212no—
573C2×D4C23×D43112yes—
574C2×D4C23×D43112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—438no—
578C22×C4—434no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—4312no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—433no—
585C22×C4—433no—
586C22×C4—433no—
587C22×C4—4312no—
588C22×C4—4312no—
589C22×C4—4312no—
590C22×C4—4312no—
591C22×C4—4312no—
592C22×C4—8612no—
593C22×C4—8612no—
594C22×C4—8612no—
595C22×C4—1726no—
596C22×C4—1726no—
597C22×C4—1726no—
598C22×C4C23×D43112yes—
599C22×C4C23×D43112yes—
600C22×C4C23×D4311yescharacteristic
601C22×C4C23×D4313yes—
602C22×C4C23×D4311yescharacteristic
603C22×C4C23×D4313yes—
604C22×C4C23×D4313yes—
605C4⋊C4—4312no—
606C4⋊C4—4312no—
607C4⋊C4—4324no—
608C4⋊C4—434no—
609C4⋊C4—434no—
610C4⋊C4—4312no—
611C4⋊C4—4312no—
612C4⋊C4—4312no—
613C4⋊C4—4312no—
614C4⋊C4—4324no—
615C4⋊C4C23×D43112yes—
616C4⋊C4C23×D43112yes—
617C22⋊C4—434no—
618C22⋊C4—4312no—
619C22⋊C4—4324no—
620C22⋊C4—4312no—
621C22⋊C4—4324no—
622C22⋊C4—4312no—
623C22⋊C4—4324no—
624C22⋊C4C23×D4314yes—
625C22⋊C4C23×D43112yes—
626C22⋊C4C23×D43124yes—
627C42—434no—
628C42—434no—
629C42—4312no—
630C42—4312no—
631C42—4312no—
632C42—4312no—
633C42—4312no—
634C42—4312no—
635C42—4312no—
636C42C23×D43112yes—
637C23—22no—
638C23—22no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—436no—
643C23—866no—
644C23—866no—
645C23—866no—
646C23#41×D4314yes—
647C23C24×D4316yes—
648C23C24×D4312yes—
649C23C24×D4311yescharacteristic
650Q8—224no—
651Q8—8624no—
652Q8C2×#10621900116yescomplemented
653D4—224no—
654D4—224no—
655D4—8624no—
656D4—8624no—
657D4—8624no—
658D4—17224no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—26no—
662C2×C4—22no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—434no—
666C2×C4—434no—
667C2×C4—4316no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—432no—
672C2×C4—436no—
673C2×C4—436no—
674C2×C4—436no—
675C2×C4—8624no—
676C2×C4—8624no—
677C2×C4—866no—
678C2×C4—862no—
679C2×C4—866no—
680C2×C4—862no—
681C2×C4—866no—
682C2×C4—8624no—
683C2×C4—17212no—
684C2×C4—17212no—
685C2×C4—17212no—
686C2×C4C2×#10621900112yes—
687C2×C4C24×D4312yes—
688C2×C4C24×D4316yes—
689C2×C4C24×D4312yes—
690C2×C4C24×D4316yes—
691C2×C4C24×D4316yes—
692C22—22no—
693C22—22no—
694C22—28no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—866no—
700C22—866no—
701C22—866no—
702C22—17212no—
703C22C2×#41×D4314yes—
704C22C2×#41×D4312yes—
705C22C22×#1062190012yes—
706C22#1458373612yes—
707C22C25×D4311yescharacteristic
708C4—26no—
709C4—22no—
710C4—26no—
711C4—22no—
712C4—434no—
713C4—434no—
714C4—866no—
715C4—862no—
716C4—866no—
717C4—862no—
718C4—866no—
719C4C22×#10621900112yes—
720C2—24no—
721C2—46no—
722C2—1726no—
723C2#1914818514yesdirect product factor
724C2C22×#41×D4311yescharacteristic
725C2C23×#1062190011yescharacteristic
726C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C2×#3480
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #19148185C2direct (N × H)
2. C2×#14583631C2semidirect
3. C2×#14583625C2semidirect
4. C2×#14583620C2semidirect
5. C2×#14583601C2semidirect
6. C2×#14583595C2semidirect
7. C2×#14583568C2semidirect
8. C2×#14583560C2semidirect
9. C2×#14583444C2semidirect
10. C2×#14583435C2semidirect
11. C2×#14583428C2semidirect
12. C2×#41×Dic43C2semidirect
13. C2×C4×#10621902C2semidirect
14. C2×C4×#10621900C2semidirect
15. C22×Q8×Dic43C2semidirect
16. C2×C43×#548C2semidirect
19. #14583631C22semidirect
20. #14583625C22semidirect
21. #14583620C22semidirect
22. #14583601C22semidirect
23. #14583595C22semidirect
24. #14583568C22semidirect
25. #14583560C22semidirect
26. #14583444C22semidirect
29. #14583435C22semidirect
30. #14583428C22semidirect
44. #41×Dic43C22semidirect
45. C4×#10621902C22semidirect
46. C4×#10621900C22semidirect
52. C2×Q8×Dic43C22semidirect
76. C43×#548C22semidirect
192. C2×Q8×C43#41semidirect
217. C22×Dic43#41semidirect
287. Q8×C43C2×#41semidirect
315. C2×Dic43C2×#41semidirect
365. C2×#548D43semidirect
375. C2×C43#3480semidirect
391. #548C2×D43semidirect
445. C43C2×#3480semidirect
560. C2×Q8#10621900semidirect
652. Q8C2×#10621900semidirect
723. C2#19148185direct (N × H)

Maximal subgroups

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

subgroupindex
#191481852
C2×#145836312
C2×#145836252
C2×#145836202
C2×#145836012
C2×#145835952
C2×#145835682
C2×#145835602
C2×#145834442
C2×#145834352
C2×#145834282
C2×#41×Dic432
C2×C4×#106219022
C2×C4×#106219002
C22×Q8×Dic432
C2×C43×#5482
C2×#348043