Finite Group Databasebeta

← C2×#21455536 #30547405

Subgroups — C2×#21455536 #30547405

Order 15616.

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×#16840560C211yesmaximal, characteristic, complemented
2C22×#14519797C211yesmaximal, characteristic, complemented
3C22×#14519784C211yesmaximal, characteristic, complemented
4#21455536C2116yesmaximal, direct product factor
5C2×#16840035C212yesmaximal, complemented
6C2×#16840030C212yesmaximal, complemented
7C2×#16840027C212yesmaximal, complemented
8C2×#16840023C212yesmaximal, complemented
9C22×#14519712C211yesmaximal, characteristic, complemented
10C2×#16839746C211yesmaximal, characteristic, complemented
11C2×#16839744C211yesmaximal, characteristic, complemented
12C2×C61×#575C211yesmaximal, characteristic, complemented
13C22×#11758222C2211yescharacteristic
14#16840560—24no—
15#16840560C2218yescomplemented
16C2×#14519808—21no—
17C2×#14519807C2212yes—
18C2×#14519803—21no—
19C2×#14519802C2212yes—
20C2×#14519797—21no—
21C2×#14519797—21no—
22C2×#14519797—21no—
23C2×#14519797—21no—
24C2×#14519797—24no—
25C2×#14519797—22no—
26C2×#14519797C2218yescomplemented
27C22×#11758202C2211yescharacteristic, complemented
28C22×#11758200C2211yescharacteristic, complemented
29C22×#11758201C2211yescharacteristic, complemented
30C22×#11758199C2211yescharacteristic, complemented
31C2×#14519784—21no—
32C2×#14519784—21no—
33C2×#14519784—24no—
34C2×#14519784C2212yes—
35C2×#14519784C2212yes—
36C2×#14519784C2218yescomplemented
37C22×#11758194—21no—
38C22×#11758194C2211yescharacteristic
39C22×#11758194C2211yescharacteristic
40C23×#92418—21no—
41C23×#92418C2211yescharacteristic
42#16840035C22116yescomplemented
43#16840030C22116yescomplemented
44#16840027C22116yescomplemented
45#16840023C22116yescomplemented
46C2×#14519712C2212yescomplemented
47C2×#14519712C2212yescomplemented
48C2×#14519712C2218yescomplemented
49#16839746C2218yescomplemented
50#16839744C2218yescomplemented
51C2×#14519696C2212yescomplemented
52C2×#14519695C2212yescomplemented
53C2×#14519694C2212yescomplemented
54C2×#14519693C2212yescomplemented
55C22×#41×C61C2211yescharacteristic
56C22×#41×C61C2211yescharacteristic
57C61×#575—24no—
58C61×#575C2218yescomplemented
59C2×#137×C61—21no—
60C2×#137×C61C2212yes—
61C2×AGL(1,ℤ/8)×C61—21no—
62C2×AGL(1,ℤ/8)×C61C2212yes—
63C2×#135×C61—22no—
64C22×M16×C61C2211yescharacteristic
65C2×#11758222—22no—
66C2×#11758222—21no—
67C2×#11758222—21no—
68C2×#11758222—22no—
69C2×#11758222—21no—
70C2×#11758222—21no—
71C2×#11758222—22no—
72C2×#11758222C2314yes—
73C22×Dic122C2311yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C4×D61—21no—
77#14519808—28no—
78#14519807—24no—
79#14519807C2318yes—
80#14519803—28no—
81#14519802—24no—
82#14519802C2318yes—
83#14519797—216no—
84#14519797—28no—
85#14519797—28no—
86#14519797—28no—
87#14519797—28no—
88C2×#11758202—22no—
89C2×#11758202—21no—
90C2×#11758202—21no—
91C2×#11758202—22no—
92C2×#11758202C2314yescomplemented
93C2×#11758200—22no—
94C2×#11758200—21no—
95C2×#11758200—21no—
96C2×#11758200—22no—
97C2×#11758200C2314yescomplemented
98C2×#11758201—22no—
99C2×#11758201—21no—
100C2×#11758201—21no—
101C2×#11758201—22no—
102C2×#11758201C2314yescomplemented
103C2×#11758199—22no—
104C2×#11758199—21no—
105C2×#11758199—21no—
106C2×#11758199—22no—
107C2×#11758199C2314yescomplemented
108#14519784—24no—
109#14519784—24no—
110#14519784—28no—
111#14519784—28no—
112#14519784C2318yes—
113#14519784C2318yes—
114C2×#11758194—21no—
115C2×#11758194—22no—
116C2×#11758194—21no—
117C2×#11758194—22no—
118C2×#11758194—22no—
119C2×#11758194—22no—
120C2×#11758194—28no—
121C2×#11758194C2312yes—
122C2×#11758194C2312yes—
123C2×#11758194C2314yes—
124C2×#11758194C2314yes—
125C22×#92418—21no—
126C22×#92418—21no—
127C22×#92418—22no—
128C22×#92418—22no—
129C22×#92418—28no—
130C22×#92418D411yescharacteristic
131C22×#92418D411yescharacteristic
132C22×#92418D411yescharacteristic
133C22×#92418D411yescharacteristic
134C22×#92418D414yes—
135C22×#92418C2311yescharacteristic
136C22×#92418C2311yescharacteristic
137C22×#92418C2314yes—
138#14519712C2318yescomplemented
139#14519712C2318yescomplemented
140#14519696C2318yescomplemented
141#14519695C2318yescomplemented
142#14519694C2318yescomplemented
143#14519693C2318yescomplemented
144C2×#41×C61—21no—
145C2×#41×C61—22no—
146C2×#41×C61—21no—
147C2×#41×C61—22no—
148C2×#41×C61—22no—
149C2×#41×C61—21no—
150C2×#41×C61—21no—
151C2×#41×C61—22no—
152C2×#41×C61—21no—
153C2×#41×C61—21no—
154C2×#41×C61—22no—
155C2×#41×C61D412yes—
156C2×#41×C61D414yes—
157C2×#41×C61C2312yes—
158C2×#41×C61C2314yes—
159C2×#41×C61C2314yes—
160C22×Q8×C61D411yescharacteristic
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61—21no—
163C22×D4×C61—21no—
164C22×D4×C61D411yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C23×C4×C61—21no—
167C23×C4×C61—21no—
168C23×C4×C61C2311yescharacteristic
169#137×C61—24no—
170#137×C61—28no—
171#137×C61C2318yes—
172AGL(1,ℤ/8)×C61—24no—
173AGL(1,ℤ/8)×C61—28no—
174AGL(1,ℤ/8)×C61C2318yes—
175#135×C61—216no—
176C2×Q16×C61—22no—
177C2×SD16×C61—22no—
178C2×SD16×C61—22no—
179C2×D8×C61—22no—
180C2×M16×C61—21no—
181C2×M16×C61—22no—
182C2×M16×C61C2312yes—
183C2×M16×C61C2314yes—
184C22×C8×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61#4111yescharacteristic
188C23×D61—21no—
189#41×C61—24no—
190#41×C61—24no—
191#41×C61—24no—
192#41×C61—22no—
193#41×C61—24no—
194#41×C61—22no—
195#41×C61—24no—
196#41×C61—24no—
197#41×C61—24no—
198#41×C61—24no—
199#41×C61—24no—
200#41×C61—42no—
201#41×C61—42no—
202#41×C61—42no—
203#41×C61—42no—
204#41×C61C2×D418yes—
205#41×C61C2×D414yes—
206#41×C61C2414yes—
207C2×Q8×C61—21no—
208C2×Q8×C61—22no—
209C2×Q8×C61—21no—
210C2×Q8×C61—21no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61C2×D414yes—
215C2×Q8×C61C2×D412yes—
216C2×Q8×C61C2412yes—
217C2×D4×C61—22no—
218C2×D4×C61—24no—
219C2×D4×C61—22no—
220C2×D4×C61—24no—
221C2×D4×C61—24no—
222C2×D4×C61—21no—
223C2×D4×C61—22no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—41no—
230C2×D4×C61—41no—
231C2×D4×C61—42no—
232C2×D4×C61C2×D412yes—
233C2×D4×C61C2×D414yes—
234C2×D4×C61C2412yes—
235C22×C4×C61—21no—
236C22×C4×C61—24no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—24no—
240C22×C4×C61—21no—
241C22×C4×C61—24no—
242C22×C4×C61—41no—
243C22×C4×C61—42no—
244C22×C4×C61—41no—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D412yes—
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D412yes—
251C22×C4×C61#4111yescharacteristic
252C22×C4×C61#4112yes—
253C22×C4×C61C2411yescharacteristic
254C22×C4×C61C2412yes—
255C2×C22⋊D61—24no—
256C2×C22⋊D61—41no—
257C2×C22⋊D61—41no—
258C2×C22⋊D61—42no—
259C22×Dic61—21no—
260#11758222—24no—
261#11758222—24no—
262#11758222—24no—
263#11758222—24no—
264#11758222—42no—
265#11758222—42no—
266#11758222—42no—
267#11758222—42no—
268C2×D244—21no—
269C2×D244—21no—
270C2×D244—21no—
271C2×D244—21no—
272C2×D244—21no—
273C2×D244C2412yes—
274C2×C4×D61—24no—
275C2×C4×D61—41no—
276C2×C4×D61—42no—
277C2×C4×D61—41no—
278C2×Dic122—21no—
279C2×Dic122—21no—
280C2×Dic122—21no—
281C2×Dic122—21no—
282C2×Dic122—21no—
283C2×Dic122C2412yes—
284Q16×C61—28no—
285SD16×C61—28no—
286SD16×C61—28no—
287D8×C61—28no—
288M16×C61—22no—
289M16×C61—24no—
290M16×C61C2414yes—
291C2×C8×C61—22no—
292C2×C8×C61—24no—
293#11758202—28no—
294#11758202—24no—
295#11758202—24no—
296#11758201—28no—
297#11758201—24no—
298#11758201—24no—
299#11758200—28no—
300#11758200—24no—
301#11758200—24no—
302#11758199—28no—
303#11758199—24no—
304#11758199—24no—
305#11758194—24no—
306#11758194—22no—
307#11758194—24no—
308#11758194—22no—
309#11758194—28no—
310#11758194—28no—
311#11758194C2414yes—
312#11758194C2414yes—
313C2×#92418—22no—
314C2×#92418—24no—
315C2×#92418—22no—
316C2×#92418—24no—
317C2×#92418—28no—
318C2×#92418—28no—
319C2×#92418C2×D411yescharacteristic
320C2×#92418C2×D411yescharacteristic
321C2×#92418C2×D414yes—
322C2×#92418C2×D411yescharacteristic
323C2×#92418C2×D411yescharacteristic
324C2×#92418C2×D414yes—
325C2×#92418C2×D412yes—
326C2×#92418C2×D412yes—
327C2×#92418C2×D414yes—
328C2×#92418C2×D414yes—
329C2×#92418C2412yes—
330C2×#92418C2412yes—
331C23×C61—24no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—42no—
335C23×C61—44no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—82no—
339C23×C61#12111yescharacteristic
340C23×C61#12111yescharacteristic
341C23×C61#12112yes—
342C23×C61C2×#4111yescharacteristic
343C23×C61C2×#4112yes—
344C22×D61—22no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—82no—
348Q8×C61—22no—
349Q8×C61—24no—
350Q8×C61—22no—
351Q8×C61—22no—
352Q8×C61—41no—
353Q8×C61—41no—
354Q8×C61C22×D414yes—
355D4×C61—24no—
356D4×C61—28no—
357D4×C61—24no—
358D4×C61—22no—
359D4×C61—24no—
360D4×C61—22no—
361D4×C61—22no—
362D4×C61—44no—
363D4×C61—44no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61C22×D414yes—
367C2×C4×C61—24no—
368C2×C4×C61—22no—
369C2×C4×C61—24no—
370C2×C4×C61—28no—
371C2×C4×C61—24no—
372C2×C4×C61—22no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—44no—
376C2×C4×C61—44no—
377C2×C4×C61#12111yescharacteristic
378C2×C4×C61#12112yes—
379C2×C4×C61#12112yes—
380C2×C4×C61#12112yes—
381C2×C4×C61#12112yes—
382C2×C4×C61#12112yes—
383C2×C4×C61#12111yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C22×D412yes—
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C22×D412yes—
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61C22×D412yes—
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C22×D412yes—
392C2×C4×C61C2×#4111yescharacteristic
393C2×C4×C61C2×#4112yes—
394C2×C4×C61C2511yescharacteristic
395C22⋊D61—44no—
396C22⋊D61—44no—
397C2×Dic61—22no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400D244—22no—
401D244—22no—
402D244—41no—
403D244—41no—
404C4×D61—44no—
405C4×D61—44no—
406Dic122—22no—
407Dic122—22no—
408Dic122—41no—
409Dic122—41no—
410C8×C61—24no—
411#92418—24no—
412#92418—24no—
413#92418C22×D412yes—
414#92418C22×D412yes—
415#92418C22×D412yes—
416#92418C22×D412yes—
417C2×#3067—611nomaximal, Sylow
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—24no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—48no—
425C22×C61—44no—
426C22×C61—42no—
427C22×C61—82no—
428C22×C61—82no—
429C22×C61—82no—
430C22×C61C2×#12111yescharacteristic
431C22×C61C2×#12112yes—
432C22×C61C2×#12112yes—
433C22×C61C2×#12111yescharacteristic
434C22×C61C22×#4111yescharacteristic
435C2×D61—42no—
436C2×D61—82no—
437C2×D61—82no—
438C2×D61—82no—
439C4×C61—24no—
440C4×C61—42no—
441C4×C61C2×#12111yescharacteristic
442C4×C61C2×#12111yescharacteristic
443C4×C61C2×#12112yes—
444C4×C61C2×#12112yes—
445C4×C61C23×D411yescharacteristic
446C4×C61C23×D411yescharacteristic
447Dic61—42no—
448C2×#575—611no—
449C2×#575D6111yescharacteristic, complemented
450C22×#135—611no—
451C22×#131—611no—
452#3067—6116no—
453C2×#473—612no—
454C2×#472—612no—
455C2×#471—612no—
456C2×#471—612no—
457C22×#108—611no—
458C2×#413—611no—
459C2×#413—611no—
460C2×C61—21no—
461C2×C61—21no—
462C2×C61—22no—
463C2×C61—22no—
464C2×C61—44no—
465C2×C61—82no—
466C2×C61#306712yescomplemented
467C2×C61C22×#12111yescharacteristic
468D61—82no—
469C22×#41—611no—
470C22×#41C2×D6111yescharacteristic
471C22×#41C2×D6111yescharacteristic
472#575—24no—
473#575—618no—
474#575—1224no—
475#575C2×D6118yescomplemented
476C2×#137—21no—
477C2×#137—612no—
478C2×#137—1221no—
479C2×#137C2×D6112yes—
480C2×AGL(1,ℤ/8)—21no—
481C2×AGL(1,ℤ/8)—612no—
482C2×AGL(1,ℤ/8)—1221no—
483C2×AGL(1,ℤ/8)C2×D6112yes—
484C2×#135—22no—
485C2×#135—618no—
486C2×#135—1221no—
487C2×#135—1221no—
488C2×#135—1221no—
489C2×#135—1221no—
490C2×#135—1224no—
491C2×#135—1222no—
492C22×Q16—611no—
493C22×SD16—611no—
494C22×SD16—611no—
495C22×D8—611no—
496C2×#131—612no—
497C2×#131—612no—
498C2×#131—618no—
499C2×#131—1221no—
500C2×#131—1221no—
501C2×#131—1224no—
502C22×M16—611no—
503C22×M16—611no—
504C22×M16—1221no—
505C22×M16C2×D6111yescharacteristic
506C23×C8—611no—
507C23×C8—1221no—
508#473—6116no—
509#472—6116no—
510#471—6116no—
511#471—6116no—
512C2×#108—612no—
513C2×#108—612no—
514C2×#108—618no—
515#413—618no—
516#413—618no—
517C2×#101—612no—
518C2×#101—612no—
519C2×#100—612no—
520C2×#100—612no—
521C61C2×#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—614no—
534C2×#41—1222no—
535C2×#41—1221no—
536C2×#41—1222no—
537C2×#41—1221no—
538C2×#41—1221no—
539C2×#41—1221no—
540C2×#41—1222no—
541C2×#41C22⋊D6112yes—
542C2×#41C22⋊D6114yes—
543C2×#41C22×D6112yes—
544C2×#41C22×D6114yes—
545C2×#41C22×D6114yes—
546C22×Q8—611no—
547C22×Q8C22⋊D6111yescharacteristic
548C22×Q8C22×D6111yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—611no—
552C22×D4—1221no—
553C22×D4C22⋊D6111yescharacteristic
554C22×D4C22×D6111yescharacteristic
555C23×C4—21no—
556C23×C4—21no—
557C23×C4—1221no—
558C23×C4C22×D6111yescharacteristic
559#137—24no—
560#137—28no—
561#137—618no—
562#137—1224no—
563#137—1228no—
564#137C22×D6118yes—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—28no—
567AGL(1,ℤ/8)—618no—
568AGL(1,ℤ/8)—1224no—
569AGL(1,ℤ/8)—1228no—
570AGL(1,ℤ/8)C22×D6118yes—
571#135—216no—
572#135—1228no—
573#135—1228no—
574#135—1228no—
575#135—1228no—
576#135—12216no—
577C2×Q16—22no—
578C2×Q16—614no—
579C2×Q16—1221no—
580C2×Q16—1221no—
581C2×Q16—1222no—
582C2×Q16—1222no—
583C2×SD16—22no—
584C2×SD16—22no—
585C2×SD16—614no—
586C2×SD16—614no—
587C2×SD16—1221no—
588C2×SD16—1221no—
589C2×SD16—1222no—
590C2×SD16—1221no—
591C2×SD16—1221no—
592C2×SD16—1222no—
593C2×SD16—1222no—
594C2×SD16—1222no—
595C2×D8—22no—
596C2×D8—614no—
597C2×D8—1221no—
598C2×D8—1221no—
599C2×D8—1222no—
600C2×D8—1222no—
601#131—618no—
602#131—618no—
603#131—1224no—
604#131—1224no—
605#131—1228no—
606#131—1228no—
607C2×M16—21no—
608C2×M16—22no—
609C2×M16—612no—
610C2×M16—614no—
611C2×M16—612no—
612C2×M16—614no—
613C2×M16—1222no—
614C2×M16—1222no—
615C2×M16—1228no—
616C2×M16—1221no—
617C2×M16—1222no—
618C2×M16—1221no—
619C2×M16—1222no—
620C2×M16C22×D6112yes—
621C2×M16C22×D6114yes—
622C22×C8—21no—
623C22×C8—611no—
624C22×C8—611no—
625C22×C8—611no—
626C22×C8—611no—
627C22×C8—614no—
628C22×C8—611no—
629C22×C8—611no—
630C22×C8—614no—
631C22×C8—1222no—
632C22×C8—1222no—
633C22×C8—1228no—
634C22×C8—1221no—
635C22×C8—1221no—
636#108—618no—
637#108—618no—
638#101—618no—
639#101—618no—
640#100—618no—
641#100—618no—
642C24—21no—
643C24—21no—
644C24—1221no—
645C24#1175822411yescharacteristic
646#41—22no—
647#41—24no—
648#41—24no—
649#41—22no—
650#41—24no—
651#41—24no—
652#41—24no—
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—1224no—
662#41—1224no—
663#41—1224no—
664#41—1224no—
665#41—2442no—
666#41—2442no—
667#41—2442no—
668#41—2442no—
669#41C2×C22⋊D6118yes—
670#41C2×C22⋊D6114yes—
671#41C23×D6114yes—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—22no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—612no—
680C2×Q8—1221no—
681C2×Q8—1221no—
682C2×Q8—1221no—
683C2×Q8—1221no—
684C2×Q8—1221no—
685C2×Q8C2×C22⋊D6112yes—
686C2×Q8C2×C22⋊D6114yes—
687C2×Q8C23×D6112yes—
688C2×D4—22no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—22no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—42no—
703C2×D4—612no—
704C2×D4—1224no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—2441no—
711C2×D4—2441no—
712C2×D4—2442no—
713C2×D4C2×C22⋊D6112yes—
714C2×D4C2×C22⋊D6114yes—
715C2×D4C23×D6112yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—24no—
723C22×C4—41no—
724C22×C4—42no—
725C22×C4—41no—
726C22×C4—1221no—
727C22×C4—1224no—
728C22×C4—2441no—
729C22×C4—2442no—
730C22×C4—2441no—
731C22×C4D4×D6111yescharacteristic
732C22×C4D4×D6112yes—
733C22×C4D4×D6111yescharacteristic
734C22×C4#1175822412yes—
735C22×C4#1175822411yescharacteristic
736C22×C4C2×C22⋊D6111yescharacteristic
737C22×C4C2×C22⋊D6112yes—
738C22×C4C2×C22⋊D6111yescharacteristic
739C22×C4C23×D6111yescharacteristic
740C22×C4C23×D6112yes—
741Q16—28no—
742Q16—1224no—
743Q16—1224no—
744Q16—1228no—
745SD16—28no—
746SD16—28no—
747SD16—1224no—
748SD16—1224no—
749SD16—1224no—
750SD16—1224no—
751SD16—1228no—
752SD16—1228no—
753D8—28no—
754D8—1224no—
755D8—1224no—
756D8—1228no—
757M16—22no—
758M16—24no—
759M16—614no—
760M16—614no—
761M16—1228no—
762M16—1228no—
763M16—1222no—
764M16—1224no—
765M16—1222no—
766M16—1224no—
767M16C23×D6114yes—
768C2×C8—22no—
769C2×C8—24no—
770C2×C8—611no—
771C2×C8—611no—
772C2×C8—614no—
773C2×C8—611no—
774C2×C8—611no—
775C2×C8—614no—
776C2×C8—612no—
777C2×C8—612no—
778C2×C8—614no—
779C2×C8—614no—
780C2×C8—612no—
781C2×C8—612no—
782C2×C8—1228no—
783C2×C8—1228no—
784C2×C8—1222no—
785C2×C8—1224no—
786C2×C8—1222no—
787C2×C8—1224no—
788C23—24no—
789C23—22no—
790C23—22no—
791C23—42no—
792C23—44no—
793C23—41no—
794C23—41no—
795C23—82no—
796C23—1222no—
797C23—4882no—
798C23—2441no—
799C23—2441no—
800C23#1451974911yescharacteristic
801C23#1451974911yescharacteristic
802C23#1451974912yes—
803C23C2×#1175822411yescharacteristic
804C23C2×#1175822412yes—
805Q8—24no—
806Q8—22no—
807Q8—22no—
808Q8—22no—
809Q8—41no—
810Q8—41no—
811Q8—1222no—
812Q8—1222no—
813Q8—2441no—
814Q8—2441no—
815Q8C22×C22⋊D6114yes—
816D4—24no—
817D4—28no—
818D4—24no—
819D4—24no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—44no—
824D4—44no—
825D4—41no—
826D4—41no—
827D4—1222no—
828D4—1222no—
829D4—2444no—
830D4—2444no—
831D4—2441no—
832D4—2441no—
833D4C22×C22⋊D6114yes—
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—1222no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2444no—
848C2×C4—2444no—
849C2×C4#1451974912yes—
850C2×C4#1451974911yescharacteristic
851C2×C4#1451974912yes—
852C2×C4#1451974912yes—
853C2×C4#1451974912yes—
854C2×C4#1451974912yes—
855C2×C4#1451974911yescharacteristic
856C2×C4C2×D4×D6111yescharacteristic
857C2×C4C2×D4×D6112yes—
858C2×C4C2×D4×D6111yescharacteristic
859C2×C4C2×D4×D6112yes—
860C2×C4C22×C22⋊D6111yescharacteristic
861C2×C4C22×C22⋊D6112yes—
862C2×C4C22×C22⋊D6111yescharacteristic
863C2×C4C22×C22⋊D6112yes—
864C2×C4C2×#1175822412yes—
865C2×C4C2×#1175822411yescharacteristic
866C2×C4C24×D6111yescharacteristic
867C8—24no—
868C8—612no—
869C8—612no—
870C8—612no—
871C8—612no—
872C8—1224no—
873C8—1224no—
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—4882no—
887C22—4882no—
888C22—4882no—
889C22—2442no—
890C22C2×#1451974912yes—
891C22C2×#1451974911yescharacteristic
892C22C2×#1451974912yes—
893C22C2×#1451974911yescharacteristic
894C22C22×#1175822411yescharacteristic
895C4—24no—
896C4—42no—
897C4—2442no—
898C4C2×#1451974912yes—
899C4C2×#1451974911yescharacteristic
900C4C2×#1451974912yes—
901C4C2×#1451974911yescharacteristic
902C4C22×D4×D6111yescharacteristic
903C4C23×C22⋊D6111yescharacteristic
904C2—22no—
905C2—21no—
906C2—21no—
907C2—22no—
908C2—44no—
909C2—82no—
910C2—4882no—
911C2#2145553612yesdirect product factor
912C2C22×#1451974911yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#575C2
socleC22×C61C2×#121
hypercenterC2×#575D61
hypocenterC61C2×#3067
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#16840560C2semidirect
2. C22×#14519797C2semidirect
3. C22×#14519784C2semidirect
4. #21455536C2direct (N × H)
5. C2×#16840035C2semidirect
6. C2×#16840030C2semidirect
7. C2×#16840027C2semidirect
8. C2×#16840023C2semidirect
9. C22×#14519712C2semidirect
10. C2×#16839746C2semidirect
11. C2×#16839744C2semidirect
12. C2×C61×#575C2semidirect
15. #16840560C22semidirect
26. C2×#14519797C22semidirect
27. C22×#11758202C22semidirect
28. C22×#11758200C22semidirect
29. C22×#11758201C22semidirect
30. C22×#11758199C22semidirect
36. C2×#14519784C22semidirect
42. #16840035C22semidirect
43. #16840030C22semidirect
44. #16840027C22semidirect
45. #16840023C22semidirect
46. C2×#14519712C22semidirect
47. C2×#14519712C22semidirect
48. C2×#14519712C22semidirect
49. #16839746C22semidirect
50. #16839744C22semidirect
51. C2×#14519696C22semidirect
52. C2×#14519695C22semidirect
53. C2×#14519694C22semidirect
54. C2×#14519693C22semidirect
58. C61×#575C22semidirect
92. C2×#11758202C23semidirect
97. C2×#11758200C23semidirect
102. C2×#11758201C23semidirect
107. C2×#11758199C23semidirect
138. #14519712C23semidirect
139. #14519712C23semidirect
140. #14519696C23semidirect
141. #14519695C23semidirect
142. #14519694C23semidirect
143. #14519693C23semidirect
449. C2×#575D61semidirect
466. C2×C61#3067semidirect
475. #575C2×D61semidirect
521. C61C2×#3067semidirect
911. C2#21455536direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405602
C22×#145197972
C22×#145197842
#214555362
C2×#168400352
C2×#168400302
C2×#168400272
C2×#168400232
C22×#145197122
C2×#168397462
C2×#168397442
C2×C61×#5752
C2×#306761