Finite Group Databasebeta

← C2×#19148577 #26004783

Subgroups — C2×#19148577 #26004783

Order 11008.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148577C2132yesmaximal, direct product factor
2C2×#14583628C211yesmaximal, characteristic, complemented
3C2×#14583618C213yesmaximal, complemented
4C2×#14583606C213yesmaximal, complemented
5C2×#14583601C213yesmaximal, complemented
6C2×#14583591C213yesmaximal, complemented
7C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
8C2×#14583556C211yesmaximal, characteristic, complemented
9C2×#14583518C213yesmaximal, complemented
10C2×#14583509C213yesmaximal, complemented
11C2×#14583430C213yesmaximal, complemented
12C2×#14583429C213yesmaximal, complemented
13C2×#14583382C211yesmaximal, characteristic, complemented
14C2×#14583375C211yesmaximal, characteristic, complemented
15C22×Q8×Dic43C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18#14583628C22116yescomplemented
19#14583618C22148yescomplemented
20#14583606C22148yescomplemented
21#14583601C22148yescomplemented
22#14583591C22148yescomplemented
23Q8×C22⋊D43C22116yescomplemented
24#14583556C22116yescomplemented
25#14583518C22148yescomplemented
26#14583509C22148yescomplemented
27C2×#13063325C2213yes—
28C2×#13063323C2213yes—
29#14583430C22148yescomplemented
30#14583429C22148yescomplemented
31C2×#13063320C2213yes—
32C2×#13063318C2213yes—
33C2×#13063318C2216yes—
34C2×#13063318C2216yes—
35C2×#13063316C2213yes—
36C2×#13063316C2216yes—
37C2×#13063316C2213yes—
38C2×#13063315C2213yes—
39C2×#13063312C2213yes—
40C2×#13063311C2213yes—
41C2×#13063309C2216yes—
42C2×#13063309C2211yescharacteristic
43C2×#13063306C2213yes—
44C2×#13063304C2213yes—
45C2×#13063304C2213yes—
46C2×#13063302C2213yes—
47C2×#13063302C2216yes—
48C2×#13063301C2213yes—
49C2×#13063297C2213yes—
50C2×#13063296C2213yes—
51#14583382C22116yescomplemented
52#14583375C22116yescomplemented
53C2×Q8×Dic43C2211yescharacteristic
54C2×Q8×Dic43C2211yescharacteristic
55C2×Q8×Dic43C2211yescharacteristic
56C2×Q8×Dic43C2213yes—
57C2×Q8×Dic43C2213yes—
58C2×Q8×Dic43C22116yescomplemented
59C2×C4×Dic86C2213yes—
60C2×C4×Dic86C2213yes—
61C2×#13063290C2213yes—
62C2×D4×Dic43C2213yes—
63C2×D4×Dic43C2213yes—
64C2×D4×Dic43C2216yes—
65C2×C4×C22⋊D43C2213yes—
66C2×C4×C22⋊D43C2213yes—
67C2×#13063284C2213yes—
68C2×#13063283C2213yes—
69C2×#13063282C2213yes—
70C2×#13063281C2216yes—
71C22×C4⋊Dic43C2213yes—
72C22×C4⋊Dic43C2213yes—
73C22×C4×Dic43C2213yes—
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—
82C22×Dic86C2313yes—
83C22×Dic86C2313yes—
84C2×Q8×D43—28no—
85C2×Q8×D43C2318yes—
86C22×C22⋊D43C2311yescharacteristic
87C22×C22⋊D43C2313yes—
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2313yes—
90C23×Dic43C2316yes—
91C22×C4×D43C2313yes—
92#13063325C23124yes—
93#13063323C23124yes—
94#13063320C23124yes—
95#13063318C23148yes—
96#13063318C23124yes—
97#13063318C23148yes—
98#13063316C23148yes—
99#13063316C23124yes—
100#13063316C23124yes—
101#13063315C23124yes—
102#13063312C23124yes—
103#13063311C23124yes—
104#13063309C23148yes—
105#13063309C2318yes—
106#13063306C23124yes—
107#13063304C23124yes—
108#13063304C23124yes—
109#13063302C23124yes—
110#13063302C23148yes—
111#13063301C23124yes—
112#13063297C23124yes—
113#13063296C23124yes—
114Q8×Dic43C2318yes—
115Q8×Dic43C2318yes—
116Q8×Dic43C23124yes—
117Q8×Dic43C2318yes—
118Q8×Dic43C23124yes—
119C4×Dic86C23124yes—
120C4×Dic86C23124yes—
121#13063290C23124yes—
122D4×Dic43C23148yes—
123D4×Dic43C23124yes—
124D4×Dic43C23124yes—
125C4×C22⋊D43C23124yes—
126C4×C22⋊D43C23124yes—
127#13063284C23124yes—
128#13063283C23124yes—
129#13063282C23124yes—
130#13063281C23148yes—
131C2×C4⋊Dic43C23124yes—
132C2×C4⋊Dic43C23124yes—
133C2×C4⋊Dic43C2313yes—
134C2×C4⋊Dic43C2313yes—
135C2×C4⋊Dic43C2313yes—
136C2×C4⋊Dic43C2313yes—
137C2×C4⋊Dic43C2316yes—
138C2×C4⋊Dic43C2311yescharacteristic
139C2×C4⋊Dic43C2316yes—
140C2×C4⋊Dic43C2311yescharacteristic
141C2×Dic43⋊C4C2313yes—
142C2×Dic43⋊C4C2316yes—
143C2×Dic43⋊C4C2313yes—
144C2×Dic43⋊C4C2313yes—
145C2×Dic43⋊C4C2313yes—
146C2×Dic43⋊C4C2313yes—
147C2×Dic43⋊C4C2313yes—
148C2×C22⋊Dic43C2313yes—
149C2×C22⋊Dic43C2313yes—
150C2×C22⋊Dic43C2313yes—
151C2×C22⋊Dic43C2313yes—
152C2×C22⋊Dic43C2316yes—
153C2×(C2×D43)⋊C4C2311yescharacteristic
154C2×(C2×D43)⋊C4C2313yes—
155C2×(C2×D43)⋊C4C2311yescharacteristic
156C2×(C2×D43)⋊C4C2313yes—
157C2×C4×Dic43C2313yes—
158C2×C4×Dic43C2313yes—
159C2×C4×Dic43C2313yes—
160C2×C4×Dic43C2313yes—
161C2×C4×Dic43C23124yes—
162C2×C4×Dic43C2316yes—
163C2×C4×Dic43C2313yes—
164C2×#41×C43—28no—
165C2×#41×C43C2318yes—
166C22×Q8×C43—28no—
167C22×Q8×C43C2318yes—
168C22×Q8×C43C2313yes—
169C22×Q8×C43C2311yescharacteristic
170C22×D4×C43C2313yes—
171C22×D4×C43C2313yes—
172C23×C4×C43C2313yes—
173C23×C4×C43C2313yes—
174#124×C43C23124yes—
175C22⋊Q8×C43C23124yes—
176#121×C43C23124yes—
177C4×Q8×C43C2318yes—
178C4×D4×C43C23124yes—
179C2×C4⋊C4×C43C2313yes—
180C2×C4⋊C4×C43C2313yes—
181C2×C22⋊C4×C43C2311yescharacteristic
182C2×C22⋊C4×C43C2313yes—
183C2×C22⋊C4×C43C2316yes—
184C2×C42×C43C2313yes—
185C24×C43C2413yes—
186C24×C43C2411yescharacteristic
187C23×D43C2411yescharacteristic
188#41×C43—232no—
189C2×Q8×C43—232no—
190C2×Q8×C43—212no—
191C2×Q8×C43#4118yes—
192C2×Q8×C43C24112yes—
193C2×Q8×C43C2414yes—
194C2×D4×C43—212no—
195C2×D4×C43—212no—
196C2×D4×C43C24112yes—
197C2×D4×C43C24112yes—
198C22×C4×C43—212no—
199C22×C4×C43—212no—
200C22×C4×C43C2411yescharacteristic
201C22×C4×C43C2413yes—
202C22×C4×C43C2413yes—
203C22×C4×C43C2411yescharacteristic
204C22×C4×C43C24112yes—
205C22×C4×C43C24112yes—
206C22×C4×C43C2413yes—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—46no—
209C2×C22⋊D43C2414yes—
210C2×C22⋊D43C24112yes—
211C22×Dic43—24no—
212C22×Dic43—46no—
213C22×Dic43—412no—
214C22×Dic43C2411yescharacteristic
215C22×Dic43C2411yescharacteristic
216C22×Dic43C2414yes—
217C22×Dic43C2413yes—
218C22×Dic43C2411yescharacteristic
219C22×Dic43C2413yes—
220C22×Dic43C2413yes—
221C22×Dic43C2413yes—
222C22×Dic43C24112yes—
223C22×Dic43C24124yes—
224Q8×D43—232no—
225C2×C4×D43—212no—
226C2×C4×D43C24112yes—
227C2×Dic86—212no—
228C2×Dic86—46no—
229C2×Dic86C24112yes—
230C2×Dic86C24112yes—
231C4⋊C4×C43C24112yes—
232C4⋊C4×C43C24112yes—
233C22⋊C4×C43C2414yes—
234C22⋊C4×C43C24112yes—
235C22⋊C4×C43C24124yes—
236C42×C43C24112yes—
237C22⋊Dic43C24112yes—
238C22⋊Dic43C24112yes—
239C22⋊Dic43C24112yes—
240C22⋊Dic43C24112yes—
241C22⋊Dic43C24124yes—
242(C2×D43)⋊C4C2414yes—
243(C2×D43)⋊C4C24112yes—
244(C2×D43)⋊C4C2414yes—
245(C2×D43)⋊C4C24112yes—
246C4⋊Dic43C24112yes—
247C4⋊Dic43C24112yes—
248C4⋊Dic43C24112yes—
249C4⋊Dic43C24112yes—
250C4⋊Dic43C24124yes—
251C4⋊Dic43C2414yes—
252C4⋊Dic43C24124yes—
253C4⋊Dic43C2414yes—
254Dic43⋊C4C24112yes—
255Dic43⋊C4C24124yes—
256Dic43⋊C4C24112yes—
257Dic43⋊C4C24112yes—
258Dic43⋊C4C24112yes—
259Dic43⋊C4C24112yes—
260Dic43⋊C4C24112yes—
261C4×Dic43C24112yes—
262C4×Dic43C24112yes—
263C4×Dic43C24112yes—
264C4×Dic43C24112yes—
265C4×Dic43C24124yes—
266C4×Dic43C24112yes—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—26no—
270C23×C43—26no—
271C23×C43—26no—
272C23×C432−1+414yes—
273C23×C43C2516yes—
274C23×C43C2512yes—
275C23×C43C2511yescharacteristic
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43C2512yes—
280Q8×C43—224no—
281Q8×C43C2×#41116yes—
282D4×C43—224no—
283D4×C43—224no—
284C2×C4×C43—22no—
285C2×C4×C43—26no—
286C2×C4×C43—26no—
287C2×C4×C43—22no—
288C2×C4×C43—224no—
289C2×C4×C43—224no—
290C2×C4×C43C2×#41112yes—
291C2×C4×C43C2516yes—
292C2×C4×C43C2516yes—
293C2×C4×C43C2512yes—
294C2×C4×C43C2512yes—
295C2×C4×C43C2516yes—
296C22⋊D43—28no—
297C22⋊D43—412no—
298C2×Dic43—26no—
299C2×Dic43—28no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—26no—
304C2×Dic43—26no—
305C2×Dic43—26no—
306C2×Dic43—424no—
307C2×Dic43—412no—
308C2×Dic43C2512yes—
309C2×Dic43C2512yes—
310C2×Dic43C2516yes—
311C2×Dic43C2512yes—
312C2×Dic43C2516yes—
313C2×Dic43C2516yes—
314C2×Dic43C2516yes—
315C4×D43—224no—
316Dic86—224no—
317Dic86—412no—
318C2×#3516—431nomaximal, Sylow
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—28no—
322C22×C43—26no—
323C22×C43—26no—
324C22×C43—26no—
325C22×C43—412no—
326C22×C43C22×#4112yes—
327C22×C43C2×2−1+414yes—
328C22×C43C2×2−1+412yes—
329C22×C43#58512yes—
330C22×C43C2611yescharacteristic
331C2×D43—22no—
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—44no—
335C4×C43—22no—
336C4×C43—26no—
337C4×C43—26no—
338C4×C43—22no—
339C4×C43C22×#41112yes—
340Dic43—26no—
341Dic43—22no—
342Dic43—22no—
343Dic43—22no—
344Dic43—26no—
345Dic43—26no—
346Dic43—26no—
347#3516—4332no—
348C2×#557—431no—
349C2×#556—433no—
350C2×#554—433no—
351C2×#553—433no—
352C2×#552—433no—
353C2×D4×Q8—431no—
354C2×#548—431no—
355C2×#548D4311yescharacteristic, complemented
356C2×#542—433no—
357C2×#541—433no—
358C2×#529—433no—
359C2×#529—433no—
360C2×#520—431no—
361C2×#519—431no—
362C22×C4×Q8—431no—
363C2×C43—24no—
364C2×C43—46no—
365C2×C43#351614yescomplemented
366C2×C43C23×#4111yescharacteristic
367C2×C43C22×2−1+411yescharacteristic
368C2×C43C2×#58511yescharacteristic
369D43—42no—
370C22×#41C2×D4311yescharacteristic
371C23×Q8—431no—
372C23×Q8C2×D4311yescharacteristic
373#557—4316no—
374#556—4348no—
375#554—4348no—
376#553—4348no—
377#552—4348no—
378D4×Q8—4316no—
379#548—4316no—
380#548C2×D43116yescomplemented
381#542—4348no—
382#541—4348no—
383C2×C4⋊Q8—433no—
384C2×C4⋊Q8—433no—
385#529—4348no—
386#529—4348no—
387C2×#126—433no—
388C2×#126—436no—
389C2×#126—433no—
390C2×#126—436no—
391C2×#125—433no—
392C2×#125—433no—
393C2×#125—436no—
394C2×#125—433no—
395C2×#124—433no—
396C2×#124—433no—
397C2×#124C2×D4313yes—
398C2×#123—433no—
399C2×#123—431no—
400C2×#123—436no—
401C2×C22⋊Q8—433no—
402C2×C22⋊Q8—433no—
403C2×C22⋊Q8—433no—
404C2×C22⋊Q8—433no—
405C2×C22⋊Q8—436no—
406C2×C22⋊Q8C2×D4313yes—
407C2×#121—433no—
408C2×#121—433no—
409C2×#121C2×D4313yes—
410#520—4316no—
411#519—4316no—
412C2×C4×Q8—431no—
413C2×C4×Q8—433no—
414C2×C4×Q8—431no—
415C2×C4×Q8—433no—
416C2×C4×Q8—431no—
417C2×C4×Q8—4316no—
418C2×C4×Q8—433no—
419C2×C4×Q8—433no—
420C2×C4×Q8—433no—
421C2×C4×Q8C2×D4311yescharacteristic
422C2×C4×D4—433no—
423C2×C4×D4—433no—
424C2×C4×D4—436no—
425C2×C4×D4—433no—
426C2×C4×D4—433no—
427C2×C4×D4C2×D4313yes—
428C2×#117—433no—
429C2×#117—433no—
430C2×#117—436no—
431C2×#117—433no—
432C22×C4⋊C4—433no—
433C22×C4⋊C4—433no—
434C22×C42—433no—
435C43C2×#351611yescharacteristic, complemented, Sylow
436C2×#41—28no—
437C2×#41C22×D4318yes—
438C22×Q8—28no—
439C22×Q8—438no—
440C22×Q8—433no—
441C22×Q8—433no—
442C22×Q8—868no—
443C22×Q8C22×D4313yes—
444C22×Q8C22×D4318yes—
445C22×Q8C22×D4311yescharacteristic
446C22×D4—431no—
447C22×D4—433no—
448C22×D4C22×D4313yes—
449C22×D4C22×D4313yes—
450C23×C4—431no—
451C23×C4—433no—
452C23×C4—436no—
453C23×C4—433no—
454C23×C4C22×D4313yes—
455C23×C4C22×D4313yes—
456C4⋊Q8—4324no—
457C4⋊Q8—4324no—
458#126—4324no—
459#126—4348no—
460#126—4324no—
461#126—4348no—
462#125—4324no—
463#125—4324no—
464#125—4348no—
465#125—4324no—
466#124—4324no—
467#124—4324no—
468#124C22×D43124yes—
469#123—4324no—
470#123—438no—
471#123—4348no—
472C22⋊Q8—4324no—
473C22⋊Q8—4324no—
474C22⋊Q8—4324no—
475C22⋊Q8—4324no—
476C22⋊Q8—4348no—
477C22⋊Q8C22×D43124yes—
478#121—4324no—
479#121—4324no—
480#121C22×D43124yes—
481C4×Q8—438no—
482C4×Q8—4324no—
483C4×Q8—438no—
484C4×Q8—4324no—
485C4×Q8—438no—
486C4×Q8—4324no—
487C4×Q8—4324no—
488C4×Q8—4324no—
489C4×Q8C22×D4318yes—
490C4×D4—4324no—
491C4×D4—4324no—
492C4×D4—4348no—
493C4×D4—4324no—
494C4×D4—4324no—
495C4×D4C22×D43124yes—
496#117—4324no—
497#117—4324no—
498#117—4348no—
499#117—4324no—
500C2×C4⋊C4—433no—
501C2×C4⋊C4—433no—
502C2×C4⋊C4—433no—
503C2×C4⋊C4—433no—
504C2×C4⋊C4—436no—
505C2×C4⋊C4—4324no—
506C2×C4⋊C4—4324no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—433no—
509C2×C4⋊C4—433no—
510C2×C4⋊C4—433no—
511C2×C4⋊C4—436no—
512C2×C4⋊C4—433no—
513C2×C4⋊C4—436no—
514C2×C4⋊C4—433no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—433no—
517C2×C4⋊C4C22×D4313yes—
518C2×C4⋊C4C22×D4313yes—
519C2×C22⋊C4—433no—
520C2×C22⋊C4—433no—
521C2×C22⋊C4—433no—
522C2×C22⋊C4—433no—
523C2×C22⋊C4—436no—
524C2×C22⋊C4—433no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—433no—
528C2×C22⋊C4C22×D4316yes—
529C2×C22⋊C4C22×D4311yescharacteristic
530C2×C22⋊C4C22×D4313yes—
531C2×C42—433no—
532C2×C42—436no—
533C2×C42—433no—
534C2×C42—433no—
535C2×C42—433no—
536C2×C42—433no—
537C2×C42—4324no—
538C2×C42C22×D4313yes—
539C24—431no—
540C24C23×D4313yes—
541C24C23×D4311yescharacteristic
542#41—232no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—4312no—
546C2×Q8—4312no—
547C2×Q8—8632no—
548C2×Q8—8612no—
549C2×Q8—1726no—
550C2×Q8#1062190018yes—
551C2×Q8C23×D43112yes—
552C2×Q8C23×D4314yes—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—434no—
556C2×D4—4312no—
557C2×D4—864no—
558C2×D4—1726no—
559C2×D4C23×D43112yes—
560C2×D4C23×D43112yes—
561C22×C4—212no—
562C22×C4—212no—
563C22×C4—434no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—433no—
567C22×C4—431no—
568C22×C4—433no—
569C22×C4—433no—
570C22×C4—433no—
571C22×C4—4312no—
572C22×C4—4324no—
573C22×C4—4312no—
574C22×C4—864no—
575C22×C4—8612no—
576C22×C4—17212no—
577C22×C4—1726no—
578C22×C4C23×D43112yes—
579C22×C4C23×D43112yes—
580C22×C4C23×D4313yes—
581C22×C4C23×D4313yes—
582C22×C4C23×D4311yescharacteristic
583C22×C4C23×D4311yescharacteristic
584C22×C4C23×D4313yes—
585C4⋊C4—4312no—
586C4⋊C4—4312no—
587C4⋊C4—4312no—
588C4⋊C4—4312no—
589C4⋊C4—4324no—
590C4⋊C4—434no—
591C4⋊C4—4312no—
592C4⋊C4—4312no—
593C4⋊C4—4312no—
594C4⋊C4—4324no—
595C4⋊C4—4312no—
596C4⋊C4—4324no—
597C4⋊C4—4312no—
598C4⋊C4—434no—
599C4⋊C4—4312no—
600C4⋊C4C23×D43112yes—
601C4⋊C4C23×D43112yes—
602C22⋊C4—4312no—
603C22⋊C4—4312no—
604C22⋊C4—4312no—
605C22⋊C4—4312no—
606C22⋊C4—4324no—
607C22⋊C4—4312no—
608C22⋊C4—434no—
609C22⋊C4—434no—
610C22⋊C4—4312no—
611C22⋊C4C23×D43124yes—
612C22⋊C4C23×D4314yes—
613C22⋊C4C23×D43112yes—
614C42—4312no—
615C42—4312no—
616C42—4312no—
617C42—4312no—
618C42—4324no—
619C42—4312no—
620C42C23×D43112yes—
621C23—22no—
622C23—22no—
623C23—26no—
624C23—26no—
625C23—26no—
626C23—432no—
627C23—862no—
628C23—862no—
629C23—862no—
630C23#1306337214yes—
631C23C24×D4316yes—
632C23C24×D4312yes—
633C23C24×D4311yescharacteristic
634Q8—224no—
635Q8—8624no—
636Q8—17212no—
637Q8C2×#10621900116yes—
638D4—224no—
639D4—224no—
640D4—868no—
641D4—17212no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—26no—
645C2×C4—22no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—432no—
649C2×C4—432no—
650C2×C4—436no—
651C2×C4—432no—
652C2×C4—436no—
653C2×C4—436no—
654C2×C4—436no—
655C2×C4—866no—
656C2×C4—868no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—866no—
661C2×C4—866no—
662C2×C4—866no—
663C2×C4—8624no—
664C2×C4—17224no—
665C2×C4—17212no—
666C2×C4C2×#10621900112yes—
667C2×C4C24×D4316yes—
668C2×C4C24×D4316yes—
669C2×C4C24×D4312yes—
670C2×C4C24×D4312yes—
671C2×C4C24×D4316yes—
672C22—28no—
673C22—22no—
674C22—22no—
675C22—26no—
676C22—26no—
677C22—26no—
678C22—412no—
679C22—862no—
680C22—862no—
681C22—862no—
682C22—1724no—
683C22C22×#1062190012yes—
684C22C2×#1306337214yes—
685C22C2×#1306337212yes—
686C22#1458373612yes—
687C22C25×D4311yescharacteristic
688C4—22no—
689C4—26no—
690C4—26no—
691C4—22no—
692C4—866no—
693C4—862no—
694C4—862no—
695C4—862no—
696C4—866no—
697C4—866no—
698C4—866no—
699C4C22×#10621900112yes—
700C2—24no—
701C2—46no—
702C2—1722no—
703C2#1914857714yesdirect product factor
704C2C23×#1062190011yescharacteristic
705C2C22×#1306337211yescharacteristic
706C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C2×#3516
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #19148577C2direct (N × H)
2. C2×#14583628C2semidirect
3. C2×#14583618C2semidirect
4. C2×#14583606C2semidirect
5. C2×#14583601C2semidirect
6. C2×#14583591C2semidirect
7. C2×Q8×C22⋊D43C2semidirect
8. C2×#14583556C2semidirect
9. C2×#14583518C2semidirect
10. C2×#14583509C2semidirect
11. C2×#14583430C2semidirect
12. C2×#14583429C2semidirect
13. C2×#14583382C2semidirect
14. C2×#14583375C2semidirect
15. C22×Q8×Dic43C2semidirect
16. C2×C43×#548C2semidirect
18. #14583628C22semidirect
19. #14583618C22semidirect
20. #14583606C22semidirect
21. #14583601C22semidirect
22. #14583591C22semidirect
23. Q8×C22⋊D43C22semidirect
24. #14583556C22semidirect
25. #14583518C22semidirect
26. #14583509C22semidirect
29. #14583430C22semidirect
30. #14583429C22semidirect
51. #14583382C22semidirect
52. #14583375C22semidirect
58. C2×Q8×Dic43C22semidirect
76. C43×#548C22semidirect
355. C2×#548D43semidirect
365. C2×C43#3516semidirect
380. #548C2×D43semidirect
435. C43C2×#3516semidirect
703. C2#19148577direct (N × H)

Maximal subgroups

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

subgroupindex
#191485772
C2×#145836282
C2×#145836182
C2×#145836062
C2×#145836012
C2×#145835912
C2×Q8×C22⋊D432
C2×#145835562
C2×#145835182
C2×#145835092
C2×#145834302
C2×#145834292
C2×#145833822
C2×#145833752
C22×Q8×Dic432
C2×C43×#5482
C2×#351643