Finite Group Databasebeta

← #29695896

Subgroups — #29695896

Order 15616.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic
2C2×#16839882C211yesmaximal, characteristic, complemented
3C2×#16839877C211yesmaximal, characteristic, complemented
4#21454265C211yesmaximal, characteristic, complemented
5#21446711C211yesmaximal, characteristic, complemented
6#21446706C211yesmaximal, characteristic, complemented
7#21446149C211yesmaximal, characteristic, complemented
8#21446149C211yesmaximal, characteristic, complemented
9#21446146C211yesmaximal, characteristic, complemented
10#21446146C211yesmaximal, characteristic, complemented
11#21445859C211yesmaximal, characteristic, complemented
12#21445763C211yesmaximal, characteristic, complemented
13#21445762C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C61×#2880C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17#16840560—24no—
18#16840560—24no—
19C2×#14519808C411yescharacteristic, complemented
20C2×#14519808C411yescharacteristic, complemented
21C2×#14519807C411yescharacteristic, complemented
22C2×#14519807C411yescharacteristic, complemented
23C2×#14519803C411yescharacteristic, complemented
24C2×#14519803C411yescharacteristic, complemented
25C2×#14519802C411yescharacteristic, complemented
26C2×#14519802C411yescharacteristic, complemented
27C2×#14519797C2211yescharacteristic
28C2×#14519797C2211yescharacteristic
29C2×#14519797C2211yescharacteristic
30C2×#14519797C2211yescharacteristic
31C2×#14519783C2211yescharacteristic, complemented
32C2×#14519783C2211yescharacteristic, complemented
33C22×#11758194C2211yescharacteristic
34#16839882—24no—
35#16839877—24no—
36C2×#14519712C2211yescharacteristic, complemented
37C2×#14519712C2211yescharacteristic, complemented
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519704C2211yescharacteristic, complemented
40C2×#14519704C2211yescharacteristic, complemented
41C2×#14519704C2211yescharacteristic, complemented
42C2×#14519703C2211yescharacteristic, complemented
43C2×#14519703C2211yescharacteristic, complemented
44C2×#14519703C2211yescharacteristic, complemented
45C2×#14519703C2211yescharacteristic, complemented
46#16839728C2211yescharacteristic, complemented
47#16839728C2211yescharacteristic, complemented
48#16839727—21no—
49#16839727—21no—
50#16839726C2211yescharacteristic
51#16839724—21no—
52C22⋊C8×D61—21no—
53C2×#14519687C2211yescharacteristic, complemented
54C2×C8×Dic61C2211yescharacteristic, complemented
55C4×C22⋊Dic61C2211yescharacteristic
56#16839526C2211yescharacteristic, complemented
57#16839526C2211yescharacteristic, complemented
58#16839516C2211yescharacteristic, complemented
59#16839516C2211yescharacteristic, complemented
60C22×#41×C61C2211yescharacteristic
61C2×#131×C61C2211yescharacteristic, complemented
62C2×#131×C61C2211yescharacteristic, complemented
63C61×#408—21no—
64C61×#408—21no—
65C61×#408C2211yescharacteristic, complemented
66C61×#408C2211yescharacteristic, complemented
67C61×#407—21no—
68C61×#407C2211yescharacteristic
69C2×C22⋊C8×C61—21no—
70C2×C22⋊C8×C61C2211yescharacteristic
71C2×#11758222—21no—
72C2×#11758222—21no—
73C2×#11758222—22no—
74C2×#11758222—22no—
75C2×#11758222—41no—
76C2×#11758222—41no—
77C2×#11758222C2×C411yescharacteristic
78C2×#11758222C2×C411yescharacteristic
79C2×#11758222C2311yescharacteristic
80C2×#11758222C2311yescharacteristic
81C22×Dic122C2×C411yescharacteristic
82C22×D244C2×C411yescharacteristic
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85#14519808—24no—
86#14519808—24no—
87#14519807—24no—
88#14519807—24no—
89#14519803—24no—
90#14519803—24no—
91#14519802—24no—
92#14519802—24no—
93#14519797—22no—
94#14519797—22no—
95#14519797—22no—
96#14519797—22no—
97#14519797—22no—
98#14519797—22no—
99#14519797D414yes—
100#14519797D414yes—
101C2×#11758202C2×C411yescharacteristic
102C2×#11758202C2×C411yescharacteristic
103C2×#11758202C2×C411yescharacteristic
104C2×#11758202C2×C411yescharacteristic
105C2×#11758200C2×C411yescharacteristic
106C2×#11758200C2×C411yescharacteristic
107C2×#11758200C2×C411yescharacteristic
108C2×#11758200C2×C411yescharacteristic
109C2×#11758201C2×C411yescharacteristic
110C2×#11758201C2×C411yescharacteristic
111C2×#11758201C2×C411yescharacteristic
112C2×#11758201C2×C411yescharacteristic
113C2×#11758199C2×C411yescharacteristic
114C2×#11758199C2×C411yescharacteristic
115C2×#11758199C2×C411yescharacteristic
116C2×#11758199C2×C411yescharacteristic
117#14519783—22no—
118#14519783—22no—
119#14519783—41no—
120#14519783—41no—
121C2×#11758194—22no—
122C2×#11758194—22no—
123C2×#11758194C2×C411yescharacteristic
124C2×#11758194C2×C411yescharacteristic
125C2×#11758194C2×C411yescharacteristic
126C2×#11758194C2×C411yescharacteristic
127C2×#11758194C2311yescharacteristic
128C2×#11758194C2311yescharacteristic
129C2×#11758189—21no—
130C2×#11758189—21no—
131C22×#92418C2311yescharacteristic
132C22×#92418C2311yescharacteristic
133C2×C8×D61—21no—
134C2×C8×D61—21no—
135C2×C22⋊Dic61—21no—
136C2×C4×Dic61C2311yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138#14519712—22no—
139#14519712—22no—
140#14519704—22no—
141#14519704—22no—
142#14519704—41no—
143#14519704—41no—
144#14519703—22no—
145#14519703—22no—
146#14519703—41no—
147#14519703—41no—
148C22⋊#92418—21no—
149C22⋊#92418—21no—
150#14519689—21no—
151#14519689—21no—
152#14519689—21no—
153#14519689—21no—
154#14519687—22no—
155C8×Dic61—22no—
156#14519684—21no—
157C2×#41×C61—21no—
158C2×#41×C61—21no—
159C2×#41×C61—22no—
160C2×#41×C61—22no—
161C2×#41×C61—41no—
162C2×#41×C61—41no—
163C2×#41×C61C2×C411yescharacteristic
164C2×#41×C61C2×C411yescharacteristic
165C2×#41×C61C2311yescharacteristic
166C2×#41×C61C2311yescharacteristic
167C22×Q8×C61C2×C411yescharacteristic
168C22×D4×C61—21no—
169C22×D4×C61C2×C411yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172#131×C61—22no—
173#131×C61—22no—
174#131×C61—41no—
175#131×C61—41no—
176C2×M16×C61—21no—
177C2×M16×C61—21no—
178C2×M16×C61C2311yescharacteristic
179C2×M16×C61C2311yescharacteristic
180C22×C8×C61—21no—
181C22×C8×C61—21no—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184C22⋊C8×C61—21no—
185C22⋊C8×C61—21no—
186C22⋊C8×C61—21no—
187C22⋊C8×C61—21no—
188C22⋊C8×C61—21no—
189C22⋊C8×C61—21no—
190C22⋊C8×C61D411yescharacteristic
191C22⋊C8×C61D411yescharacteristic
192C22⋊C8×C61D411yescharacteristic
193C22⋊C8×C61D411yescharacteristic
194C24×C61—21no—
195C24×C61#4111yescharacteristic
196C23×D61—21no—
197#41×C61—21no—
198#41×C61—21no—
199#41×C61—22no—
200#41×C61—22no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—21no—
204#41×C61—21no—
205#41×C61—42no—
206#41×C61—42no—
207#41×C61—41no—
208#41×C61—41no—
209#41×C61—42no—
210#41×C61—42no—
211#41×C61C2×D412yes—
212#41×C61C2×D412yes—
213C2×Q8×C61—21no—
214C2×Q8×C61—22no—
215C2×Q8×C61—41no—
216C2×Q8×C61C22×C411yescharacteristic
217C2×Q8×C61C22×C411yescharacteristic
218C2×D4×C61—21no—
219C2×D4×C61—22no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—41no—
225C2×D4×C61—42no—
226C2×D4×C61—42no—
227C2×D4×C61C22×C411yescharacteristic
228C2×D4×C61C22×C411yescharacteristic
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—42no—
239C22×C4×C61—42no—
240C22×C4×C61C22×C411yescharacteristic
241C22×C4×C61C22×C411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61#4111yescharacteristic
245C22×C4×C61C2411yescharacteristic
246C2×C22⋊D61—21no—
247C2×C22⋊D61—21no—
248C2×C22⋊D61—21no—
249C2×C22⋊D61—21no—
250C2×C22⋊D61—42no—
251C2×C22⋊D61—42no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255#11758222—21no—
256#11758222—21no—
257#11758222—21no—
258#11758222—21no—
259#11758222—21no—
260#11758222—21no—
261#11758222—22no—
262#11758222—22no—
263#11758222—41no—
264#11758222—41no—
265#11758222—42no—
266#11758222—42no—
267#11758222—42no—
268#11758222—42no—
269#11758222C2×D412yes—
270#11758222C2×D412yes—
271C2×D244—22no—
272C2×D244—21no—
273C2×D244—41no—
274C2×D244C22×C411yescharacteristic
275C2×D244C22×C411yescharacteristic
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—42no—
281C2×C4×D61—42no—
282C2×Dic122—22no—
283C2×Dic122—21no—
284C2×Dic122—41no—
285C2×Dic122C22×C411yescharacteristic
286C2×Dic122C22×C411yescharacteristic
287M16×C61—21no—
288M16×C61—21no—
289M16×C61—21no—
290M16×C61—21no—
291M16×C61—42no—
292M16×C61—42no—
293C2×C8×C61—21no—
294C2×C8×C61—21no—
295C2×C8×C61—21no—
296C2×C8×C61—21no—
297C2×C8×C61—21no—
298C2×C8×C61—21no—
299C2×C8×C61—42no—
300C2×C8×C61—42no—
301C2×C8×C61C2×D411yescharacteristic
302C2×C8×C61C2×D411yescharacteristic
303C2×C8×C61C2×D411yescharacteristic
304C2×C8×C61C2×D411yescharacteristic
305C22⋊Dic61—42no—
306#11758202—22no—
307#11758202—22no—
308#11758202—22no—
309#11758202C22⋊C414yescomplemented
310#11758201—22no—
311#11758201—22no—
312#11758201—22no—
313#11758201C22⋊C414yescomplemented
314#11758200—22no—
315#11758200—22no—
316#11758200—22no—
317#11758200C22⋊C414yescomplemented
318#11758199—22no—
319#11758199—22no—
320#11758199—22no—
321#11758199C22⋊C414yescomplemented
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326#11758194—22no—
327#11758194—22no—
328#11758194—22no—
329#11758194—22no—
330#11758194—21no—
331#11758194—21no—
332#11758194—21no—
333#11758194—21no—
334C2×#92418—21no—
335C2×#92418—21no—
336C2×#92418—21no—
337C2×#92418—21no—
338C2×#92418C22×C411yescharacteristic
339C2×#92418C22×C411yescharacteristic
340C2×#92418C22×C411yescharacteristic
341C2×#92418C22×C411yescharacteristic
342C2×#92418C2×D412yes—
343C2×#92418C2×D412yes—
344#11758189—42no—
345#11758189—42no—
346C8×D61—42no—
347C8×D61—42no—
348C23×C61—21no—
349C23×C61—21no—
350C23×C61—21no—
351C23×C61—21no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—42no—
355C23×C61—42no—
356C23×C61—81no—
357C23×C61C4×D411yescharacteristic
358C23×C61C4×D411yescharacteristic
359C23×C61C2×#4111yescharacteristic
360C22×D61—21no—
361C22×D61—21no—
362C22×D61—42no—
363C22×D61—42no—
364C22×D61—81no—
365Q8×C61—21no—
366Q8×C61—21no—
367Q8×C61—21no—
368Q8×C61—42no—
369Q8×C61C2×C22⋊C412yes—
370D4×C61—22no—
371D4×C61—22no—
372D4×C61—21no—
373D4×C61—21no—
374D4×C61—21no—
375D4×C61—42no—
376D4×C61—42no—
377D4×C61—42no—
378D4×C61—41no—
379D4×C61—41no—
380D4×C61C2×C22⋊C412yes—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—42no—
396C2×C4×C61—42no—
397C2×C4×C61—42no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61C4×D411yescharacteristic
401C2×C4×C61C4×D411yescharacteristic
402C2×C4×C61C23×C411yescharacteristic
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61H(5,𝔽2)11yescharacteristic
407C2×C4×C61H(5,𝔽2)11yescharacteristic
408C22⋊D61—22no—
409C22⋊D61—22no—
410C22⋊D61—42no—
411C22⋊D61—42no—
412C22⋊D61—41no—
413C22⋊D61—41no—
414C2×Dic61—21no—
415C2×Dic61—22no—
416C2×Dic61—21no—
417C2×Dic61—42no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423D244—21no—
424D244—21no—
425D244—21no—
426D244—42no—
427D244C2×C22⋊C412yes—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—42no—
431C4×D61—42no—
432C4×D61—41no—
433C4×D61—41no—
434Dic122—21no—
435Dic122—21no—
436Dic122—21no—
437Dic122—42no—
438Dic122C2×C22⋊C412yes—
439C8×C61—21no—
440C8×C61—21no—
441C8×C61—21no—
442C8×C61—21no—
443C8×C61—41no—
444C8×C61—41no—
445#92418—21no—
446#92418—21no—
447#92418—41no—
448#92418—41no—
449#92418C2×C22⋊C412yes—
450#92418C2×C22⋊C412yes—
451#22453—611nomaximal, Sylow
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—22no—
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—41no—
465C22×C61—41no—
466C22×C61—81no—
467C22×C61—81no—
468C22×C61—84no—
469C22×C61C2×C4×D411yescharacteristic
470C22×C61#54611yescharacteristic
471C22×C61#54611yescharacteristic
472C2×D61—22no—
473C2×D61—41no—
474C2×D61—41no—
475C2×D61—41no—
476C2×D61—41no—
477C2×D61—41no—
478C2×D61—84no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—22no—
482C4×C61—41no—
483C4×C61C22×C22⋊C411yescharacteristic
484C4×C61#51811yescharacteristic
485C4×C61D4211yescharacteristic
486C4×C61D4211yescharacteristic
487Dic61—22no—
488Dic61—42no—
489Dic61—41no—
490Dic61—81no—
491C2×#575—611no—
492C2×#444—611no—
493C2×#443—611no—
494#2880—611no—
495#2880D6111yescharacteristic, complemented
496#1975—611no—
497#1974—611no—
498#1876—611no—
499#1876—611no—
500#1876—611no—
501#1876—611no—
502#1811—611no—
503#1789—611no—
504#1789—611no—
505#1753—611no—
506C2×C61—21no—
507C2×C61—21no—
508C2×C61—41no—
509C2×C61—41no—
510C2×C61—42no—
511C2×C61—81no—
512C2×C61D4×C22⋊C411yescharacteristic
513C2×C61#295511yescharacteristic
514C2×C61#295611yescharacteristic
515D61—42no—
516D61—81no—
517C22×#41—611no—
518C22×#41C2×D6111yescharacteristic
519#575—1224no—
520#575—1224no—
521C2×#137—611no—
522C2×#137—611no—
523C2×#137—611no—
524C2×#137—611no—
525C2×AGL(1,ℤ/8)—611no—
526C2×AGL(1,ℤ/8)—611no—
527C2×AGL(1,ℤ/8)—611no—
528C2×AGL(1,ℤ/8)—611no—
529C2×#135—611no—
530C2×#135—611no—
531C2×#135—611no—
532C2×#135—611no—
533C2×#131—611no—
534C2×#131—611no—
535C2×#131C2×D6111yescharacteristic, complemented
536C2×#131C2×D6111yescharacteristic, complemented
537C22×M16—611no—
538#444—1224no—
539#443—1224no—
540C2×#108—611no—
541C2×#108—611no—
542C2×#104—611no—
543C2×#104—611no—
544C2×#104—611no—
545C2×#104—611no—
546C2×#104—611no—
547C2×#104—611no—
548C2×#104—611no—
549C2×#104—611no—
550#408—21no—
551#408—21no—
552#408—611no—
553#408—611no—
554#408—1221no—
555#408—1221no—
556#408C2×D6111yescharacteristic, complemented
557#408C2×D6111yescharacteristic, complemented
558#407—21no—
559#407—611no—
560#407—1221no—
561#407C2×D6111yescharacteristic
562C2×C22⋊C8—21no—
563C2×C22⋊C8—1221no—
564C2×C22⋊C8C2×D6111yescharacteristic
565C2×#97—611no—
566C2×C4×C8—611no—
567C4×C22⋊C4—611no—
568#341—611no—
569#341—611no—
570#336—611no—
571#336—611no—
572C61#2245311yescharacteristic, complemented, Sylow
573C2×#41—21no—
574C2×#41—21no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—41no—
578C2×#41—41no—
579C2×#41—611no—
580C2×#41—611no—
581C2×#41—611no—
582C2×#41—611no—
583C2×#41—1222no—
584C2×#41—1222no—
585C2×#41—1221no—
586C2×#41—1221no—
587C2×#41—2441no—
588C2×#41—2441no—
589C2×#41C4×D6111yescharacteristic
590C2×#41C4×D6111yescharacteristic
591C2×#41C22×D6111yescharacteristic
592C2×#41C22×D6111yescharacteristic
593C22×Q8—611no—
594C22×Q8C4×D6111yescharacteristic
595C22×D4—21no—
596C22×D4—611no—
597C22×D4—1221no—
598C22×D4C4×D6111yescharacteristic
599C23×C4—21no—
600C23×C4—1221no—
601C23×C4C22×D6111yescharacteristic
602#137—1224no—
603#137—1224no—
604#137—1224no—
605#137—1224no—
606AGL(1,ℤ/8)—1224no—
607AGL(1,ℤ/8)—1224no—
608AGL(1,ℤ/8)—1224no—
609AGL(1,ℤ/8)—1224no—
610#135—614no—
611#135—614no—
612#135—1222no—
613#135—1222no—
614#135—1222no—
615#135—1222no—
616#135—1222no—
617#135—1222no—
618C2×Q16—611no—
619C2×Q16—611no—
620C2×Q16—611no—
621C2×Q16—611no—
622C2×SD16—611no—
623C2×SD16—611no—
624C2×SD16—611no—
625C2×SD16—611no—
626C2×SD16—611no—
627C2×SD16—611no—
628C2×SD16—611no—
629C2×SD16—611no—
630C2×D8—611no—
631C2×D8—611no—
632C2×D8—611no—
633C2×D8—611no—
634#131—22no—
635#131—22no—
636#131—41no—
637#131—41no—
638#131—1222no—
639#131—1222no—
640#131—2441no—
641#131—2441no—
642C2×M16—21no—
643C2×M16—21no—
644C2×M16—611no—
645C2×M16—611no—
646C2×M16—611no—
647C2×M16—611no—
648C2×M16—611no—
649C2×M16—611no—
650C2×M16—1222no—
651C2×M16—1222no—
652C2×M16—1221no—
653C2×M16—1221no—
654C2×M16C22×D6111yescharacteristic
655C2×M16C22×D6111yescharacteristic
656C22×C8—21no—
657C22×C8—21no—
658C22×C8—611no—
659C22×C8—611no—
660C22×C8—1221no—
661C22×C8—1221no—
662C22×C8C22×D6111yescharacteristic
663C22×C8C22×D6111yescharacteristic
664C2×C22⋊C4—1221no—
665C2×C42—611no—
666C2×C42—611no—
667#108—1222no—
668#108—1222no—
669#104—1222no—
670#104—1222no—
671#104—1222no—
672#104—1222no—
673#104—2441no—
674#104—2441no—
675#104—2441no—
676#104—2441no—
677C22⋊C8—21no—
678C22⋊C8—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8—21no—
682C22⋊C8—21no—
683C22⋊C8—1221no—
684C22⋊C8—1221no—
685C22⋊C8—1221no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8—1221no—
689C22⋊C8C22⋊D6111yescharacteristic
690C22⋊C8C22⋊D6111yescharacteristic
691C22⋊C8C22⋊D6111yescharacteristic
692C22⋊C8C22⋊D6111yescharacteristic
693#97—1222no—
694C4×C8—1222no—
695#95—1221no—
696C24—21no—
697C24—1221no—
698C24#1175822211yescharacteristic
699#41—21no—
700#41—21no—
701#41—22no—
702#41—22no—
703#41—21no—
704#41—21no—
705#41—21no—
706#41—21no—
707#41—42no—
708#41—42no—
709#41—41no—
710#41—41no—
711#41—42no—
712#41—42no—
713#41—612no—
714#41—612no—
715#41—1222no—
716#41—1222no—
717#41—1221no—
718#41—1221no—
719#41—1221no—
720#41—1221no—
721#41—1221no—
722#41—1221no—
723#41—2442no—
724#41—2442no—
725#41—2441no—
726#41—2441no—
727#41—2442no—
728#41—2442no—
729#41D4×D6112yes—
730#41D4×D6112yes—
731C2×Q8—21no—
732C2×Q8—22no—
733C2×Q8—41no—
734C2×Q8—611no—
735C2×Q8—611no—
736C2×Q8—1222no—
737C2×Q8—1221no—
738C2×Q8—2441no—
739C2×Q8C2×C4×D6111yescharacteristic
740C2×Q8C2×C4×D6111yescharacteristic
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—41no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—611no—
751C2×D4—611no—
752C2×D4—1222no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—1221no—
756C2×D4—1221no—
757C2×D4—1221no—
758C2×D4—2441no—
759C2×D4—2442no—
760C2×D4—2442no—
761C2×D4C2×C4×D6111yescharacteristic
762C2×D4C2×C4×D6111yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—2442no—
782C22×C4—2442no—
783C22×C4C2×C4×D6111yescharacteristic
784C22×C4C2×C4×D6111yescharacteristic
785C22×C4#1175822211yescharacteristic
786C22×C4C2×C22⋊D6111yescharacteristic
787C22×C4C2×C22⋊D6111yescharacteristic
788C22×C4C23×D6111yescharacteristic
789Q16—614no—
790Q16—1222no—
791Q16—1222no—
792Q16—1222no—
793SD16—614no—
794SD16—614no—
795SD16—1222no—
796SD16—1222no—
797SD16—1222no—
798SD16—1222no—
799SD16—1222no—
800SD16—1222no—
801D8—614no—
802D8—1222no—
803D8—1222no—
804D8—1222no—
805M16—21no—
806M16—21no—
807M16—21no—
808M16—21no—
809M16—42no—
810M16—42no—
811M16—1222no—
812M16—1222no—
813M16—1222no—
814M16—1222no—
815M16—1221no—
816M16—1221no—
817M16—1221no—
818M16—1221no—
819M16—2442no—
820M16—2442no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—42no—
828C2×C8—42no—
829C2×C8—611no—
830C2×C8—611no—
831C2×C8—612no—
832C2×C8—612no—
833C2×C8—611no—
834C2×C8—611no—
835C2×C8—1221no—
836C2×C8—1221no—
837C2×C8—1221no—
838C2×C8—1221no—
839C2×C8—2442no—
840C2×C8—2442no—
841C2×C8C2×C22⋊D6111yescharacteristic
842C2×C8C2×C22⋊D6111yescharacteristic
843C2×C8C2×C22⋊D6111yescharacteristic
844C2×C8C2×C22⋊D6111yescharacteristic
845C22⋊C4—2442no—
846C42—1221no—
847C42—1221no—
848C42—1221no—
849C42—1221no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—81no—
859C23—1221no—
860C23—1221no—
861C23—4881no—
862C23—2442no—
863C23—2442no—
864C23C4×C22⋊D6111yescharacteristic
865C23C4×C22⋊D6111yescharacteristic
866C23C2×#1175822211yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—42no—
871Q8—612no—
872Q8—1221no—
873Q8—1221no—
874Q8—1221no—
875Q8—2442no—
876Q8C22⋊C4×D6112yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—41no—
886D4—41no—
887D4—612no—
888D4—1222no—
889D4—1222no—
890D4—1221no—
891D4—1221no—
892D4—1221no—
893D4—2442no—
894D4—2442no—
895D4—2442no—
896D4—2441no—
897D4—2441no—
898D4C22⋊C4×D6112yes—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—1221no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1221no—
923C2×C4—2442no—
924C2×C4—2442no—
925C2×C4—2442no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4C4×C22⋊D6111yescharacteristic
934C2×C4C4×C22⋊D6111yescharacteristic
935C2×C4C22×C4×D6111yescharacteristic
936C2×C4C2×D4×D6111yescharacteristic
937C2×C4C2×D4×D6111yescharacteristic
938C2×C4C22×C22⋊D6111yescharacteristic
939C2×C4#1451982211yescharacteristic
940C2×C4#1451982211yescharacteristic
941C8—21no—
942C8—21no—
943C8—21no—
944C8—21no—
945C8—41no—
946C8—41no—
947C8—612no—
948C8—612no—
949C8—1221no—
950C8—1221no—
951C8—2441no—
952C8—2441no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—81no—
968C22—81no—
969C22—84no—
970C22—1222no—
971C22—4884no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22C2×C4×C22⋊D6111yescharacteristic
978C22#1684040211yescharacteristic
979C22#1684040211yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—41no—
984C4—1222no—
985C4—4881no—
986C4—2442no—
987C4—2441no—
988C4C2×C22⋊C4×D6111yescharacteristic
989C4#1684023511yescharacteristic
990C4D4×C22⋊D6111yescharacteristic
991C4D4×C22⋊D6111yescharacteristic
992C2—21no—
993C2—21no—
994C2—41no—
995C2—41no—
996C2—42no—
997C2—81no—
998C2—4881no—
999C2—2442no—
1000C2C22⋊C4×C22⋊D6111yescharacteristic
1001C2#2145472011yescharacteristic
1002C2#2145472611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2880C2
socleC22×C61C2×C4×D4
prime radicalC2×#16840560C2
cosocleC22×C4×C61C24
hypercenter#2880D61
hypocenterC61#22453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#16839882C2semidirect
3. C2×#16839877C2semidirect
4. #21454265C2semidirect
5. #21446711C2semidirect
6. #21446706C2semidirect
7. #21446149C2semidirect
8. #21446149C2semidirect
9. #21446146C2semidirect
10. #21446146C2semidirect
11. #21445859C2semidirect
12. #21445763C2semidirect
13. #21445762C2semidirect
14. #21445605C2semidirect
15. C61×#2880C2semidirect
19. C2×#14519808C4semidirect
20. C2×#14519808C4semidirect
21. C2×#14519807C4semidirect
22. C2×#14519807C4semidirect
23. C2×#14519803C4semidirect
24. C2×#14519803C4semidirect
25. C2×#14519802C4semidirect
26. C2×#14519802C4semidirect
31. C2×#14519783C22semidirect
32. C2×#14519783C22semidirect
36. C2×#14519712C22semidirect
37. C2×#14519712C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519704C22semidirect
40. C2×#14519704C22semidirect
41. C2×#14519704C22semidirect
42. C2×#14519703C22semidirect
43. C2×#14519703C22semidirect
44. C2×#14519703C22semidirect
45. C2×#14519703C22semidirect
46. #16839728C22semidirect
47. #16839728C22semidirect
53. C2×#14519687C22semidirect
54. C2×C8×Dic61C22semidirect
56. #16839526C22semidirect
57. #16839526C22semidirect
58. #16839516C22semidirect
59. #16839516C22semidirect
61. C2×#131×C61C22semidirect
62. C2×#131×C61C22semidirect
65. C61×#408C22semidirect
66. C61×#408C22semidirect
309. #11758202C22⋊C4semidirect
313. #11758201C22⋊C4semidirect
317. #11758200C22⋊C4semidirect
321. #11758199C22⋊C4semidirect
495. #2880D61semidirect
535. C2×#131C2×D61semidirect
536. C2×#131C2×D61semidirect
556. #408C2×D61semidirect
557. #408C2×D61semidirect
572. C61#22453semidirect

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#168398822
C2×#168398772
#214542652
#214467112
#214467062
#214461492
#214461462
#214458592
#214457632
#214457622
#214456052
C61×#28802
#2245361