Finite Group Databasebeta

← C2×#19144312 #25963989

Subgroups — C2×#19144312 #25963989

Order 11008.

2650 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583697C211yesmaximal, characteristic, complemented
2C22×#13063345C211yesmaximal, characteristic, complemented
3C22×#13063332C211yesmaximal, characteristic, complemented
4#19144312C2116yesmaximal, direct product factor
5C2×#14583172C212yesmaximal, complemented
6C2×#14583167C212yesmaximal, complemented
7C2×#14583164C212yesmaximal, complemented
8C2×#14583160C212yesmaximal, complemented
9C22×#13063260C211yesmaximal, characteristic, complemented
10C2×#14582883C211yesmaximal, characteristic, complemented
11C2×#14582881C211yesmaximal, characteristic, complemented
12C2×C43×#575C211yesmaximal, characteristic, complemented
13C22×#10621898C2211yescharacteristic
14#14583697—24no—
15#14583697C2218yescomplemented
16C2×#13063356—21no—
17C2×#13063355C2212yes—
18C2×#13063351—21no—
19C2×#13063350C2212yes—
20C2×#13063345—21no—
21C2×#13063345—21no—
22C2×#13063345—21no—
23C2×#13063345—21no—
24C2×#13063345—24no—
25C2×#13063345—22no—
26C2×#13063345C2218yescomplemented
27C22×#10621885C2211yescharacteristic, complemented
28C22×#10621883C2211yescharacteristic, complemented
29C22×#10621884C2211yescharacteristic, complemented
30C22×#10621882C2211yescharacteristic, complemented
31C2×#13063332—21no—
32C2×#13063332—21no—
33C2×#13063332—24no—
34C2×#13063332C2212yes—
35C2×#13063332C2212yes—
36C2×#13063332C2218yescomplemented
37C22×#10621877—21no—
38C22×#10621877C2211yescharacteristic
39C22×#10621877C2211yescharacteristic
40C23×C43⋊C8—21no—
41C23×C43⋊C8C2211yescharacteristic
42#14583172C22116yescomplemented
43#14583167C22116yescomplemented
44#14583164C22116yescomplemented
45#14583160C22116yescomplemented
46C2×#13063260C2212yescomplemented
47C2×#13063260C2212yescomplemented
48C2×#13063260C2218yescomplemented
49#14582883C2218yescomplemented
50#14582881C2218yescomplemented
51C2×#13063244C2212yescomplemented
52C2×#13063243C2212yescomplemented
53C2×#13063242C2212yescomplemented
54C2×#13063241C2212yescomplemented
55C22×#41×C43C2211yescharacteristic
56C22×#41×C43C2211yescharacteristic
57C43×#575—24no—
58C43×#575C2218yescomplemented
59C2×#137×C43—21no—
60C2×#137×C43C2212yes—
61C2×AGL(1,ℤ/8)×C43—21no—
62C2×AGL(1,ℤ/8)×C43C2212yes—
63C2×#135×C43—22no—
64C22×M16×C43C2211yescharacteristic
65C2×#10621898—22no—
66C2×#10621898—21no—
67C2×#10621898—21no—
68C2×#10621898—22no—
69C2×#10621898—21no—
70C2×#10621898—21no—
71C2×#10621898—22no—
72C2×#10621898C2314yes—
73C22×Dic86C2311yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C4×D43—21no—
77#13063356—28no—
78#13063355—24no—
79#13063355C2318yes—
80#13063351—28no—
81#13063350—24no—
82#13063350C2318yes—
83#13063345—216no—
84#13063345—28no—
85#13063345—28no—
86#13063345—28no—
87#13063345—28no—
88C2×#10621885—22no—
89C2×#10621885—21no—
90C2×#10621885—21no—
91C2×#10621885—22no—
92C2×#10621885C2314yescomplemented
93C2×#10621883—22no—
94C2×#10621883—21no—
95C2×#10621883—21no—
96C2×#10621883—22no—
97C2×#10621883C2314yescomplemented
98C2×#10621884—22no—
99C2×#10621884—21no—
100C2×#10621884—21no—
101C2×#10621884—22no—
102C2×#10621884C2314yescomplemented
103C2×#10621882—22no—
104C2×#10621882—21no—
105C2×#10621882—21no—
106C2×#10621882—22no—
107C2×#10621882C2314yescomplemented
108#13063332—24no—
109#13063332—24no—
110#13063332—28no—
111#13063332—28no—
112#13063332C2318yes—
113#13063332C2318yes—
114C2×#10621877—21no—
115C2×#10621877—22no—
116C2×#10621877—21no—
117C2×#10621877—22no—
118C2×#10621877—22no—
119C2×#10621877—22no—
120C2×#10621877—28no—
121C2×#10621877C2312yes—
122C2×#10621877C2312yes—
123C2×#10621877C2314yes—
124C2×#10621877C2314yes—
125C22×C43⋊C8—21no—
126C22×C43⋊C8—21no—
127C22×C43⋊C8—22no—
128C22×C43⋊C8—22no—
129C22×C43⋊C8—28no—
130C22×C43⋊C8D411yescharacteristic
131C22×C43⋊C8D411yescharacteristic
132C22×C43⋊C8D411yescharacteristic
133C22×C43⋊C8D411yescharacteristic
134C22×C43⋊C8D414yes—
135C22×C43⋊C8C2311yescharacteristic
136C22×C43⋊C8C2311yescharacteristic
137C22×C43⋊C8C2314yes—
138#13063260C2318yescomplemented
139#13063260C2318yescomplemented
140#13063244C2318yescomplemented
141#13063243C2318yescomplemented
142#13063242C2318yescomplemented
143#13063241C2318yescomplemented
144C2×#41×C43—21no—
145C2×#41×C43—22no—
146C2×#41×C43—21no—
147C2×#41×C43—22no—
148C2×#41×C43—22no—
149C2×#41×C43—21no—
150C2×#41×C43—21no—
151C2×#41×C43—22no—
152C2×#41×C43—21no—
153C2×#41×C43—21no—
154C2×#41×C43—22no—
155C2×#41×C43D412yes—
156C2×#41×C43D414yes—
157C2×#41×C43C2312yes—
158C2×#41×C43C2314yes—
159C2×#41×C43C2314yes—
160C22×Q8×C43D411yescharacteristic
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43—21no—
163C22×D4×C43—21no—
164C22×D4×C43D411yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C23×C4×C43—21no—
168C23×C4×C43C2311yescharacteristic
169#137×C43—24no—
170#137×C43—28no—
171#137×C43C2318yes—
172AGL(1,ℤ/8)×C43—24no—
173AGL(1,ℤ/8)×C43—28no—
174AGL(1,ℤ/8)×C43C2318yes—
175#135×C43—216no—
176C2×Q16×C43—22no—
177C2×SD16×C43—22no—
178C2×SD16×C43—22no—
179C2×D8×C43—22no—
180C2×M16×C43—21no—
181C2×M16×C43—22no—
182C2×M16×C43C2312yes—
183C2×M16×C43C2314yes—
184C22×C8×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43#4111yescharacteristic
188C23×D43—21no—
189#41×C43—24no—
190#41×C43—24no—
191#41×C43—24no—
192#41×C43—22no—
193#41×C43—24no—
194#41×C43—22no—
195#41×C43—24no—
196#41×C43—24no—
197#41×C43—24no—
198#41×C43—24no—
199#41×C43—24no—
200#41×C43—42no—
201#41×C43—42no—
202#41×C43—42no—
203#41×C43—42no—
204#41×C43C2×D418yes—
205#41×C43C2×D414yes—
206#41×C43C2414yes—
207C2×Q8×C43—21no—
208C2×Q8×C43—22no—
209C2×Q8×C43—21no—
210C2×Q8×C43—21no—
211C2×Q8×C43—21no—
212C2×Q8×C43—21no—
213C2×Q8×C43—21no—
214C2×Q8×C43C2×D412yes—
215C2×Q8×C43C2×D414yes—
216C2×Q8×C43C2412yes—
217C2×D4×C43—21no—
218C2×D4×C43—22no—
219C2×D4×C43—21no—
220C2×D4×C43—22no—
221C2×D4×C43—24no—
222C2×D4×C43—22no—
223C2×D4×C43—24no—
224C2×D4×C43—24no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—41no—
230C2×D4×C43—41no—
231C2×D4×C43—42no—
232C2×D4×C43C2×D412yes—
233C2×D4×C43C2×D414yes—
234C2×D4×C43C2412yes—
235C22×C4×C43—24no—
236C22×C4×C43—22no—
237C22×C4×C43—22no—
238C22×C4×C43—24no—
239C22×C4×C43—24no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—41no—
243C22×C4×C43—42no—
244C22×C4×C43—41no—
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D412yes—
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D412yes—
251C22×C4×C43#4111yescharacteristic
252C22×C4×C43#4112yes—
253C22×C4×C43C2411yescharacteristic
254C22×C4×C43C2412yes—
255C2×C22⋊D43—24no—
256C2×C22⋊D43—41no—
257C2×C22⋊D43—41no—
258C2×C22⋊D43—42no—
259C22×Dic43—21no—
260#10621898—24no—
261#10621898—24no—
262#10621898—24no—
263#10621898—24no—
264#10621898—42no—
265#10621898—42no—
266#10621898—42no—
267#10621898—42no—
268C2×D172—21no—
269C2×D172—21no—
270C2×D172—21no—
271C2×D172—21no—
272C2×D172—21no—
273C2×D172C2412yes—
274C2×C4×D43—24no—
275C2×C4×D43—41no—
276C2×C4×D43—42no—
277C2×C4×D43—41no—
278C2×Dic86—21no—
279C2×Dic86—21no—
280C2×Dic86—21no—
281C2×Dic86—21no—
282C2×Dic86—21no—
283C2×Dic86C2412yes—
284Q16×C43—28no—
285SD16×C43—28no—
286SD16×C43—28no—
287D8×C43—28no—
288M16×C43—22no—
289M16×C43—24no—
290M16×C43C2414yes—
291C2×C8×C43—22no—
292C2×C8×C43—24no—
293#10621885—28no—
294#10621885—24no—
295#10621885—24no—
296#10621884—28no—
297#10621884—24no—
298#10621884—24no—
299#10621883—28no—
300#10621883—24no—
301#10621883—24no—
302#10621882—28no—
303#10621882—24no—
304#10621882—24no—
305#10621877—22no—
306#10621877—24no—
307#10621877—22no—
308#10621877—24no—
309#10621877—28no—
310#10621877—28no—
311#10621877C2414yes—
312#10621877C2414yes—
313C2×C43⋊C8—22no—
314C2×C43⋊C8—24no—
315C2×C43⋊C8—22no—
316C2×C43⋊C8—24no—
317C2×C43⋊C8—28no—
318C2×C43⋊C8—28no—
319C2×C43⋊C8C2×D411yescharacteristic
320C2×C43⋊C8C2×D411yescharacteristic
321C2×C43⋊C8C2×D414yes—
322C2×C43⋊C8C2×D411yescharacteristic
323C2×C43⋊C8C2×D411yescharacteristic
324C2×C43⋊C8C2×D414yes—
325C2×C43⋊C8C2×D412yes—
326C2×C43⋊C8C2×D412yes—
327C2×C43⋊C8C2×D414yes—
328C2×C43⋊C8C2×D414yes—
329C2×C43⋊C8C2412yes—
330C2×C43⋊C8C2412yes—
331C23×C43—24no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—42no—
335C23×C43—44no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—82no—
339C23×C43#12111yescharacteristic
340C23×C43#12111yescharacteristic
341C23×C43#12112yes—
342C23×C43C2×#4111yescharacteristic
343C23×C43C2×#4112yes—
344C22×D43—22no—
345C22×D43—41no—
346C22×D43—41no—
347C22×D43—82no—
348Q8×C43—22no—
349Q8×C43—24no—
350Q8×C43—22no—
351Q8×C43—22no—
352Q8×C43—41no—
353Q8×C43—41no—
354Q8×C43C22×D414yes—
355D4×C43—24no—
356D4×C43—28no—
357D4×C43—24no—
358D4×C43—22no—
359D4×C43—24no—
360D4×C43—22no—
361D4×C43—22no—
362D4×C43—44no—
363D4×C43—44no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43C22×D414yes—
367C2×C4×C43—24no—
368C2×C4×C43—22no—
369C2×C4×C43—24no—
370C2×C4×C43—28no—
371C2×C4×C43—24no—
372C2×C4×C43—22no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—44no—
376C2×C4×C43—44no—
377C2×C4×C43#12111yescharacteristic
378C2×C4×C43#12112yes—
379C2×C4×C43#12112yes—
380C2×C4×C43#12112yes—
381C2×C4×C43#12112yes—
382C2×C4×C43#12112yes—
383C2×C4×C43#12111yescharacteristic
384C2×C4×C43C22×D411yescharacteristic
385C2×C4×C43C22×D412yes—
386C2×C4×C43C22×D411yescharacteristic
387C2×C4×C43C22×D412yes—
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D412yes—
390C2×C4×C43C22×D411yescharacteristic
391C2×C4×C43C22×D412yes—
392C2×C4×C43C2×#4111yescharacteristic
393C2×C4×C43C2×#4112yes—
394C2×C4×C43C2511yescharacteristic
395C22⋊D43—44no—
396C22⋊D43—44no—
397C2×Dic43—22no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400D172—22no—
401D172—22no—
402D172—41no—
403D172—41no—
404C4×D43—44no—
405C4×D43—44no—
406Dic86—22no—
407Dic86—22no—
408Dic86—41no—
409Dic86—41no—
410C8×C43—24no—
411C43⋊C8—24no—
412C43⋊C8—24no—
413C43⋊C8C22×D412yes—
414C43⋊C8C22×D412yes—
415C43⋊C8C22×D412yes—
416C43⋊C8C22×D412yes—
417C2×#3067—431nomaximal, Sylow
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—22no—
421C22×C43—24no—
422C22×C43—42no—
423C22×C43—42no—
424C22×C43—48no—
425C22×C43—44no—
426C22×C43—42no—
427C22×C43—82no—
428C22×C43—82no—
429C22×C43—82no—
430C22×C43C2×#12111yescharacteristic
431C22×C43C2×#12112yes—
432C22×C43C2×#12112yes—
433C22×C43C2×#12111yescharacteristic
434C22×C43C22×#4111yescharacteristic
435C2×D43—42no—
436C2×D43—82no—
437C2×D43—82no—
438C2×D43—82no—
439C4×C43—24no—
440C4×C43—42no—
441C4×C43C2×#12111yescharacteristic
442C4×C43C2×#12111yescharacteristic
443C4×C43C2×#12112yes—
444C4×C43C2×#12112yes—
445C4×C43C23×D411yescharacteristic
446C4×C43C23×D411yescharacteristic
447Dic43—42no—
448C2×#575—431no—
449C2×#575D4311yescharacteristic, complemented
450C22×#135—431no—
451C22×#131—431no—
452#3067—4316no—
453C2×#473—432no—
454C2×#472—432no—
455C2×#471—432no—
456C2×#471—432no—
457C22×#108—431no—
458C2×#413—431no—
459C2×#413—431no—
460C2×C43—21no—
461C2×C43—21no—
462C2×C43—22no—
463C2×C43—22no—
464C2×C43—44no—
465C2×C43—82no—
466C2×C43#306712yescomplemented
467C2×C43C22×#12111yescharacteristic
468D43—82no—
469C22×#41—431no—
470C22×#41C2×D4311yescharacteristic
471C22×#41C2×D4311yescharacteristic
472#575—24no—
473#575—438no—
474#575—864no—
475#575C2×D4318yescomplemented
476C2×#137—21no—
477C2×#137—432no—
478C2×#137—861no—
479C2×#137C2×D4312yes—
480C2×AGL(1,ℤ/8)—21no—
481C2×AGL(1,ℤ/8)—432no—
482C2×AGL(1,ℤ/8)—861no—
483C2×AGL(1,ℤ/8)C2×D4312yes—
484C2×#135—22no—
485C2×#135—438no—
486C2×#135—861no—
487C2×#135—861no—
488C2×#135—861no—
489C2×#135—861no—
490C2×#135—864no—
491C2×#135—862no—
492C22×Q16—431no—
493C22×SD16—431no—
494C22×SD16—431no—
495C22×D8—431no—
496C2×#131—432no—
497C2×#131—432no—
498C2×#131—438no—
499C2×#131—861no—
500C2×#131—861no—
501C2×#131—864no—
502C22×M16—431no—
503C22×M16—431no—
504C22×M16—861no—
505C22×M16C2×D4311yescharacteristic
506C23×C8—431no—
507C23×C8—861no—
508#473—4316no—
509#472—4316no—
510#471—4316no—
511#471—4316no—
512C2×#108—432no—
513C2×#108—432no—
514C2×#108—438no—
515#413—438no—
516#413—438no—
517C2×#101—432no—
518C2×#101—432no—
519C2×#100—432no—
520C2×#100—432no—
521C43C2×#306711yescharacteristic, complemented, Sylow
522C2×#41—21no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—21no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—22no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—22no—
533C2×#41—434no—
534C2×#41—862no—
535C2×#41—861no—
536C2×#41—862no—
537C2×#41—861no—
538C2×#41—861no—
539C2×#41—861no—
540C2×#41—862no—
541C2×#41C22⋊D4312yes—
542C2×#41C22⋊D4314yes—
543C2×#41C22×D4312yes—
544C2×#41C22×D4314yes—
545C2×#41C22×D4314yes—
546C22×Q8—431no—
547C22×Q8C22⋊D4311yescharacteristic
548C22×Q8C22×D4311yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—431no—
552C22×D4—861no—
553C22×D4C22⋊D4311yescharacteristic
554C22×D4C22×D4311yescharacteristic
555C23×C4—21no—
556C23×C4—21no—
557C23×C4—861no—
558C23×C4C22×D4311yescharacteristic
559#137—24no—
560#137—28no—
561#137—438no—
562#137—864no—
563#137—868no—
564#137C22×D4318yes—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—28no—
567AGL(1,ℤ/8)—438no—
568AGL(1,ℤ/8)—864no—
569AGL(1,ℤ/8)—868no—
570AGL(1,ℤ/8)C22×D4318yes—
571#135—216no—
572#135—868no—
573#135—868no—
574#135—868no—
575#135—868no—
576#135—8616no—
577C2×Q16—22no—
578C2×Q16—434no—
579C2×Q16—861no—
580C2×Q16—861no—
581C2×Q16—862no—
582C2×Q16—862no—
583C2×SD16—22no—
584C2×SD16—22no—
585C2×SD16—434no—
586C2×SD16—434no—
587C2×SD16—861no—
588C2×SD16—861no—
589C2×SD16—862no—
590C2×SD16—861no—
591C2×SD16—861no—
592C2×SD16—862no—
593C2×SD16—862no—
594C2×SD16—862no—
595C2×D8—22no—
596C2×D8—434no—
597C2×D8—861no—
598C2×D8—861no—
599C2×D8—862no—
600C2×D8—862no—
601#131—438no—
602#131—438no—
603#131—864no—
604#131—864no—
605#131—868no—
606#131—868no—
607C2×M16—21no—
608C2×M16—22no—
609C2×M16—432no—
610C2×M16—434no—
611C2×M16—432no—
612C2×M16—434no—
613C2×M16—862no—
614C2×M16—862no—
615C2×M16—868no—
616C2×M16—861no—
617C2×M16—862no—
618C2×M16—861no—
619C2×M16—862no—
620C2×M16C22×D4312yes—
621C2×M16C22×D4314yes—
622C22×C8—21no—
623C22×C8—431no—
624C22×C8—431no—
625C22×C8—431no—
626C22×C8—431no—
627C22×C8—434no—
628C22×C8—431no—
629C22×C8—431no—
630C22×C8—434no—
631C22×C8—862no—
632C22×C8—862no—
633C22×C8—868no—
634C22×C8—861no—
635C22×C8—861no—
636#108—438no—
637#108—438no—
638#101—438no—
639#101—438no—
640#100—438no—
641#100—438no—
642C24—21no—
643C24—21no—
644C24—861no—
645C24#1062190011yescharacteristic
646#41—24no—
647#41—24no—
648#41—24no—
649#41—22no—
650#41—24no—
651#41—24no—
652#41—22no—
653#41—24no—
654#41—24no—
655#41—24no—
656#41—24no—
657#41—42no—
658#41—42no—
659#41—42no—
660#41—42no—
661#41—864no—
662#41—864no—
663#41—864no—
664#41—864no—
665#41—1722no—
666#41—1722no—
667#41—1722no—
668#41—1722no—
669#41C2×C22⋊D4318yes—
670#41C2×C22⋊D4314yes—
671#41C23×D4314yes—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—432no—
680C2×Q8—861no—
681C2×Q8—861no—
682C2×Q8—861no—
683C2×Q8—861no—
684C2×Q8—861no—
685C2×Q8C2×C22⋊D4312yes—
686C2×Q8C2×C22⋊D4314yes—
687C2×Q8C23×D4312yes—
688C2×D4—22no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—21no—
694C2×D4—22no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—42no—
703C2×D4—432no—
704C2×D4—864no—
705C2×D4—861no—
706C2×D4—861no—
707C2×D4—861no—
708C2×D4—861no—
709C2×D4—861no—
710C2×D4—1721no—
711C2×D4—1721no—
712C2×D4—1722no—
713C2×D4C2×C22⋊D4312yes—
714C2×D4C2×C22⋊D4314yes—
715C2×D4C23×D4312yes—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—21no—
722C22×C4—24no—
723C22×C4—41no—
724C22×C4—42no—
725C22×C4—41no—
726C22×C4—861no—
727C22×C4—864no—
728C22×C4—1721no—
729C22×C4—1722no—
730C22×C4—1721no—
731C22×C4D4×D4311yescharacteristic
732C22×C4D4×D4312yes—
733C22×C4D4×D4311yescharacteristic
734C22×C4#1062190012yes—
735C22×C4#1062190011yescharacteristic
736C22×C4C2×C22⋊D4311yescharacteristic
737C22×C4C2×C22⋊D4312yes—
738C22×C4C2×C22⋊D4311yescharacteristic
739C22×C4C23×D4311yescharacteristic
740C22×C4C23×D4312yes—
741Q16—28no—
742Q16—864no—
743Q16—864no—
744Q16—868no—
745SD16—28no—
746SD16—28no—
747SD16—864no—
748SD16—864no—
749SD16—864no—
750SD16—864no—
751SD16—868no—
752SD16—868no—
753D8—28no—
754D8—864no—
755D8—864no—
756D8—868no—
757M16—22no—
758M16—24no—
759M16—434no—
760M16—434no—
761M16—868no—
762M16—868no—
763M16—862no—
764M16—864no—
765M16—862no—
766M16—864no—
767M16C23×D4314yes—
768C2×C8—22no—
769C2×C8—24no—
770C2×C8—431no—
771C2×C8—431no—
772C2×C8—434no—
773C2×C8—431no—
774C2×C8—431no—
775C2×C8—434no—
776C2×C8—432no—
777C2×C8—432no—
778C2×C8—434no—
779C2×C8—434no—
780C2×C8—432no—
781C2×C8—432no—
782C2×C8—868no—
783C2×C8—868no—
784C2×C8—862no—
785C2×C8—864no—
786C2×C8—862no—
787C2×C8—864no—
788C23—24no—
789C23—22no—
790C23—22no—
791C23—42no—
792C23—44no—
793C23—41no—
794C23—41no—
795C23—82no—
796C23—862no—
797C23—3442no—
798C23—1721no—
799C23—1721no—
800C23#1306329711yescharacteristic
801C23#1306329711yescharacteristic
802C23#1306329712yes—
803C23C2×#1062190011yescharacteristic
804C23C2×#1062190012yes—
805Q8—24no—
806Q8—22no—
807Q8—22no—
808Q8—22no—
809Q8—41no—
810Q8—41no—
811Q8—862no—
812Q8—862no—
813Q8—1721no—
814Q8—1721no—
815Q8C22×C22⋊D4314yes—
816D4—24no—
817D4—28no—
818D4—24no—
819D4—24no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—44no—
824D4—44no—
825D4—41no—
826D4—41no—
827D4—862no—
828D4—862no—
829D4—1724no—
830D4—1724no—
831D4—1721no—
832D4—1721no—
833D4C22×C22⋊D4314yes—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—28no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—862no—
845C2×C4—1721no—
846C2×C4—1721no—
847C2×C4—1724no—
848C2×C4—1724no—
849C2×C4#1306329712yes—
850C2×C4#1306329711yescharacteristic
851C2×C4#1306329712yes—
852C2×C4#1306329712yes—
853C2×C4#1306329712yes—
854C2×C4#1306329712yes—
855C2×C4#1306329711yescharacteristic
856C2×C4C2×D4×D4311yescharacteristic
857C2×C4C2×D4×D4312yes—
858C2×C4C2×D4×D4311yescharacteristic
859C2×C4C2×D4×D4312yes—
860C2×C4C22×C22⋊D4311yescharacteristic
861C2×C4C22×C22⋊D4312yes—
862C2×C4C22×C22⋊D4311yescharacteristic
863C2×C4C22×C22⋊D4312yes—
864C2×C4C2×#1062190012yes—
865C2×C4C2×#1062190011yescharacteristic
866C2×C4C24×D4311yescharacteristic
867C8—24no—
868C8—432no—
869C8—432no—
870C8—432no—
871C8—432no—
872C8—864no—
873C8—864no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—24no—
878C22—42no—
879C22—42no—
880C22—48no—
881C22—44no—
882C22—42no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—3442no—
887C22—3442no—
888C22—3442no—
889C22—1722no—
890C22C2×#1306329712yes—
891C22C2×#1306329711yescharacteristic
892C22C2×#1306329712yes—
893C22C2×#1306329711yescharacteristic
894C22C22×#1062190011yescharacteristic
895C4—24no—
896C4—42no—
897C4—1722no—
898C4C2×#1306329712yes—
899C4C2×#1306329711yescharacteristic
900C4C2×#1306329712yes—
901C4C2×#1306329711yescharacteristic
902C4C22×D4×D4311yescharacteristic
903C4C23×C22⋊D4311yescharacteristic
904C2—22no—
905C2—21no—
906C2—21no—
907C2—22no—
908C2—44no—
909C2—82no—
910C2—3442no—
911C2#1914431212yesdirect product factor
912C2C22×#1306329711yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#575C2
socleC22×C43C2×#121
hypercenterC2×#575D43
hypocenterC43C2×#3067
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#14583697C2semidirect
2. C22×#13063345C2semidirect
3. C22×#13063332C2semidirect
4. #19144312C2direct (N × H)
5. C2×#14583172C2semidirect
6. C2×#14583167C2semidirect
7. C2×#14583164C2semidirect
8. C2×#14583160C2semidirect
9. C22×#13063260C2semidirect
10. C2×#14582883C2semidirect
11. C2×#14582881C2semidirect
12. C2×C43×#575C2semidirect
15. #14583697C22semidirect
26. C2×#13063345C22semidirect
27. C22×#10621885C22semidirect
28. C22×#10621883C22semidirect
29. C22×#10621884C22semidirect
30. C22×#10621882C22semidirect
36. C2×#13063332C22semidirect
42. #14583172C22semidirect
43. #14583167C22semidirect
44. #14583164C22semidirect
45. #14583160C22semidirect
46. C2×#13063260C22semidirect
47. C2×#13063260C22semidirect
48. C2×#13063260C22semidirect
49. #14582883C22semidirect
50. #14582881C22semidirect
51. C2×#13063244C22semidirect
52. C2×#13063243C22semidirect
53. C2×#13063242C22semidirect
54. C2×#13063241C22semidirect
58. C43×#575C22semidirect
92. C2×#10621885C23semidirect
97. C2×#10621883C23semidirect
102. C2×#10621884C23semidirect
107. C2×#10621882C23semidirect
138. #13063260C23semidirect
139. #13063260C23semidirect
140. #13063244C23semidirect
141. #13063243C23semidirect
142. #13063242C23semidirect
143. #13063241C23semidirect
449. C2×#575D43semidirect
466. C2×C43#3067semidirect
475. #575C2×D43semidirect
521. C43C2×#3067semidirect
911. C2#19144312direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836972
C22×#130633452
C22×#130633322
#191443122
C2×#145831722
C2×#145831672
C2×#145831642
C2×#145831602
C22×#130632602
C2×#145828832
C2×#145828812
C2×C43×#5752
C2×#306743