Finite Group Databasebeta

← #29695893

Subgroups — #29695893

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×#16839881C211yesmaximal, characteristic, complemented
3C2×#16839876C211yesmaximal, characteristic, complemented
4#21454269C211yesmaximal, characteristic, complemented
5#21454268C211yesmaximal, characteristic, complemented
6#21446709C211yesmaximal, characteristic, complemented
7#21446704C211yesmaximal, characteristic, complemented
8#21446144C211yesmaximal, characteristic, complemented
9#21446144C211yesmaximal, characteristic, complemented
10#21446143C211yesmaximal, characteristic, complemented
11#21446143C211yesmaximal, characteristic, complemented
12#21445859C211yesmaximal, characteristic, complemented
13#21445764C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#1789C211yesmaximal, 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×#14519785C2211yescharacteristic, complemented
32C2×#14519785C2211yescharacteristic, complemented
33C2×#14519784C2211yescharacteristic, complemented
34C2×#14519784C2211yescharacteristic, complemented
35C22×#11758194C2211yescharacteristic
36#16839881—24no—
37#16839876—24no—
38C2×#14519712C2211yescharacteristic, complemented
39C2×#14519712C2211yescharacteristic, complemented
40C2×#14519705C2211yescharacteristic, complemented
41C2×#14519705C2211yescharacteristic, complemented
42C2×#14519705C2211yescharacteristic, complemented
43C2×#14519705C2211yescharacteristic, complemented
44#16839730C2211yescharacteristic, complemented
45#16839730C2211yescharacteristic, complemented
46#16839729—21no—
47#16839729—21no—
48#16839729C2211yescharacteristic, complemented
49#16839729C2211yescharacteristic, complemented
50#16839727—21no—
51#16839727—21no—
52#16839726—21no—
53#16839726C2211yescharacteristic
54#16839724—21no—
55C2×C22⋊#92418—21no—
56C2×C22⋊#92418C2211yescharacteristic
57C22⋊C8×D61—21no—
58C2×#14519688C2211yescharacteristic, complemented
59C2×C4×#92418C2211yescharacteristic, complemented
60#16839526C2211yescharacteristic, complemented
61#16839526C2211yescharacteristic, complemented
62#16839517C2211yescharacteristic, complemented
63#16839517C2211yescharacteristic, complemented
64C22×#41×C61C2211yescharacteristic
65C2×#104×C61C2211yescharacteristic, complemented
66C2×#104×C61C2211yescharacteristic, complemented
67C2×#104×C61C2211yescharacteristic, complemented
68C2×#104×C61C2211yescharacteristic, complemented
69C61×#407C2211yescharacteristic
70C4×C22⋊C4×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#14519785—22no—
118#14519785—22no—
119#14519785—41no—
120#14519785—41no—
121#14519784—22no—
122#14519784—22no—
123#14519784—41no—
124#14519784—41no—
125C2×#11758194—22no—
126C2×#11758194—22no—
127C2×#11758194—21no—
128C2×#11758194—21no—
129C2×#11758194C2×C411yescharacteristic
130C2×#11758194C2×C411yescharacteristic
131C2×#11758194C2×C411yescharacteristic
132C2×#11758194C2×C411yescharacteristic
133C2×#11758194C2311yescharacteristic
134C2×#11758194C2311yescharacteristic
135C2×#11758189—21no—
136C2×#11758189—21no—
137C22×#92418—21no—
138C22×#92418—21no—
139C22×#92418C2311yescharacteristic
140C22×#92418C2311yescharacteristic
141C22×#92418C2311yescharacteristic
142C22×#92418C2311yescharacteristic
143C2×C8×D61—21no—
144C2×C8×D61—21no—
145#14519712—22no—
146#14519712—22no—
147#14519705—22no—
148#14519705—22no—
149#14519705—41no—
150#14519705—41no—
151C22⋊#92418—21no—
152C22⋊#92418—21no—
153C22⋊#92418—21no—
154C22⋊#92418—21no—
155C22⋊#92418—21no—
156C22⋊#92418—21no—
157C22⋊#92418D411yescharacteristic
158C22⋊#92418D411yescharacteristic
159C22⋊#92418D411yescharacteristic
160C22⋊#92418D411yescharacteristic
161#14519689—21no—
162#14519689—21no—
163#14519689—21no—
164#14519689—21no—
165#14519688—22no—
166C4×#92418—22no—
167C2×#41×C61—21no—
168C2×#41×C61—21no—
169C2×#41×C61—22no—
170C2×#41×C61—22no—
171C2×#41×C61—41no—
172C2×#41×C61—41no—
173C2×#41×C61C2×C411yescharacteristic
174C2×#41×C61C2×C411yescharacteristic
175C2×#41×C61C2311yescharacteristic
176C2×#41×C61C2311yescharacteristic
177C22×Q8×C61C2×C411yescharacteristic
178C22×D4×C61—21no—
179C22×D4×C61C2×C411yescharacteristic
180C23×C4×C61—21no—
181C23×C4×C61C2311yescharacteristic
182C2×M16×C61C2311yescharacteristic
183C2×M16×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185C2×C42×C61C2311yescharacteristic
186C2×C42×C61C2311yescharacteristic
187#104×C61—22no—
188#104×C61—22no—
189#104×C61—41no—
190#104×C61—41no—
191C22⋊C8×C61—21no—
192C22⋊C8×C61—21no—
193#95×C61—21no—
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—21no—
239C22×C4×C61—21no—
240C22×C4×C61—42no—
241C22×C4×C61—42no—
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61#4111yescharacteristic
247C22×C4×C61C2411yescharacteristic
248C2×C22⋊D61—21no—
249C2×C22⋊D61—21no—
250C2×C22⋊D61—21no—
251C2×C22⋊D61—21no—
252C2×C22⋊D61—42no—
253C2×C22⋊D61—42no—
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—
291C2×C8×C61—21no—
292C2×C8×C61—21no—
293C22⋊C4×C61—42no—
294C42×C61—21no—
295C42×C61—21no—
296C42×C61—21no—
297C42×C61—21no—
298#11758202—22no—
299#11758202—22no—
300#11758202—22no—
301#11758202C22⋊C414yescomplemented
302#11758201—22no—
303#11758201—22no—
304#11758201—22no—
305#11758201C22⋊C414yescomplemented
306#11758200—22no—
307#11758200—22no—
308#11758200—22no—
309#11758200C22⋊C414yescomplemented
310#11758199—22no—
311#11758199—22no—
312#11758199—22no—
313#11758199C22⋊C414yescomplemented
314#11758194—22no—
315#11758194—22no—
316#11758194—22no—
317#11758194—22no—
318#11758194—21no—
319#11758194—21no—
320#11758194—21no—
321#11758194—21no—
322#11758194—42no—
323#11758194—42no—
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328C2×#92418—21no—
329C2×#92418—21no—
330C2×#92418—21no—
331C2×#92418—21no—
332C2×#92418—42no—
333C2×#92418—42no—
334C2×#92418C22×C411yescharacteristic
335C2×#92418C22×C411yescharacteristic
336C2×#92418C22×C411yescharacteristic
337C2×#92418C22×C411yescharacteristic
338C2×#92418C2×D411yescharacteristic
339C2×#92418C2×D411yescharacteristic
340C2×#92418C2×D411yescharacteristic
341C2×#92418C2×D411yescharacteristic
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—22no—
395C2×C4×C61—21no—
396C2×C4×C61—42no—
397C2×C4×C61—42no—
398C2×C4×C61—42no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61C4×D411yescharacteristic
407C2×C4×C61C4×D411yescharacteristic
408C2×C4×C61C23×C411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61C22×D411yescharacteristic
412C2×C4×C61H(5,𝔽2)11yescharacteristic
413C2×C4×C61H(5,𝔽2)11yescharacteristic
414C22⋊D61—22no—
415C22⋊D61—22no—
416C22⋊D61—42no—
417C22⋊D61—42no—
418C22⋊D61—41no—
419C22⋊D61—41no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—42no—
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—41no—
440C8×C61—41no—
441#92418—21no—
442#92418—21no—
443#92418—21no—
444#92418—21no—
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—42no—
483C4×C61—41no—
484C4×C61—81no—
485C4×C61C22×C22⋊C411yescharacteristic
486C4×C61#51811yescharacteristic
487C4×C61D4211yescharacteristic
488C4×C61D4211yescharacteristic
489Dic61—22no—
490Dic61—41no—
491C2×#575—611no—
492C2×#444—611no—
493C2×#443—611no—
494#2880—611no—
495#2880—611no—
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#1789D6111yescharacteristic, complemented
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×#131—611no—
536C2×#131—611no—
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×#104C2×D6111yescharacteristic, complemented
547C2×#104C2×D6111yescharacteristic, complemented
548C2×#104C2×D6111yescharacteristic, complemented
549C2×#104C2×D6111yescharacteristic, complemented
550#408—611no—
551#408—611no—
552#408—611no—
553#408—611no—
554#408—1221no—
555#408—1221no—
556#408—1221no—
557#408—1221no—
558#407—611no—
559#407—1221no—
560#407—1221no—
561#407C2×D6111yescharacteristic
562C2×C22⋊C8—611no—
563C2×C22⋊C8—1221no—
564C2×C22⋊C8—1221no—
565C2×#97—611no—
566C2×C4×C8—611no—
567C4×C22⋊C4C2×D6111yescharacteristic
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—1222no—
635#131—1222no—
636#131—1222no—
637#131—1222no—
638#131—2441no—
639#131—2441no—
640#131—2441no—
641#131—2441no—
642C2×M16—611no—
643C2×M16—611no—
644C2×M16—611no—
645C2×M16—611no—
646C2×M16—611no—
647C2×M16—611no—
648C2×M16—1221no—
649C2×M16—1221no—
650C2×M16—1222no—
651C2×M16—1222no—
652C2×M16—1221no—
653C2×M16—1221no—
654C2×M16C22×D6111yescharacteristic
655C2×M16C22×D6111yescharacteristic
656C22×C8—611no—
657C22×C8—611no—
658C22×C8—611no—
659C22×C8—611no—
660C22×C8—1221no—
661C22×C8—1221no—
662C22×C8—1221no—
663C22×C8—1221no—
664C2×C22⋊C4—21no—
665C2×C42C22×D6111yescharacteristic
666C2×C42C22×D6111yescharacteristic
667#108—1222no—
668#108—1222no—
669#104—22no—
670#104—22no—
671#104—41no—
672#104—41no—
673#104—1222no—
674#104—1222no—
675#104—2441no—
676#104—2441no—
677C22⋊C8—21no—
678C22⋊C8—21no—
679C22⋊C8—611no—
680C22⋊C8—611no—
681C22⋊C8—611no—
682C22⋊C8—611no—
683C22⋊C8—1221no—
684C22⋊C8—1221no—
685C22⋊C8—1221no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8—1221no—
689C22⋊C8—1221no—
690C22⋊C8—1221no—
691C22⋊C8—1221no—
692C22⋊C8—1221no—
693#97—1222no—
694C4×C8—1222no—
695#95—21no—
696C24—21no—
697C24—1221no—
698C24#1175822411yescharacteristic
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—21no—
773C22×C4—21no—
774C22×C4—42no—
775C22×C4—42no—
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×C4D4×D6111yescharacteristic
786C22×C4D4×D6111yescharacteristic
787C22×C4#1175822411yescharacteristic
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—1222no—
810M16—1222no—
811M16—1222no—
812M16—1222no—
813M16—1221no—
814M16—1221no—
815M16—1221no—
816M16—1221no—
817M16—2442no—
818M16—2442no—
819M16—2442no—
820M16—2442no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—611no—
824C2×C8—611no—
825C2×C8—612no—
826C2×C8—612no—
827C2×C8—611no—
828C2×C8—611no—
829C2×C8—611no—
830C2×C8—611no—
831C2×C8—611no—
832C2×C8—611no—
833C2×C8—1221no—
834C2×C8—1221no—
835C2×C8—1221no—
836C2×C8—1221no—
837C2×C8—1221no—
838C2×C8—1221no—
839C2×C8—1221no—
840C2×C8—1221no—
841C2×C8—2442no—
842C2×C8—2442no—
843C2×C8—2442no—
844C2×C8—2442no—
845C22⋊C4—42no—
846C42—21no—
847C42—21no—
848C42—21no—
849C42—21no—
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—
864C23#1451973711yescharacteristic
865C23#1451973711yescharacteristic
866C23C2×#1175822411yescharacteristic
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—22no—
913C2×C4—21no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—1221no—
925C2×C4—1222no—
926C2×C4—1222no—
927C2×C4—1221no—
928C2×C4—2442no—
929C2×C4—2442no—
930C2×C4—2442no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4#1451973711yescharacteristic
934C2×C4#1451973711yescharacteristic
935C2×C4C22×C4×D6111yescharacteristic
936C2×C4C2×D4×D6111yescharacteristic
937C2×C4C2×D4×D6111yescharacteristic
938C2×C4C2×D4×D6111yescharacteristic
939C2×C4#1451982211yescharacteristic
940C2×C4#1451982211yescharacteristic
941C8—41no—
942C8—41no—
943C8—612no—
944C8—612no—
945C8—1221no—
946C8—1221no—
947C8—1221no—
948C8—1221no—
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×#1451973711yescharacteristic
978C22#1684039911yescharacteristic
979C22#1684039911yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—81no—
986C4—1222no—
987C4—2441no—
988C4C2×C22⋊C4×D6111yescharacteristic
989C4#1684023511yescharacteristic
990C4#1684039411yescharacteristic
991C4#1684039411yescharacteristic
992C2—21no—
993C2—21no—
994C2—41no—
995C2—41no—
996C2—42no—
997C2—81no—
998C2—4881no—
999C2—2442no—
1000C2#2144863511yescharacteristic
1001C2#2145471811yescharacteristic
1002C2#2145472511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1789C2
socleC22×C61C2×C4×D4
prime radicalC2×#16840560C2
cosocleC22×C4×C61C24
hypercenter#1789D61
hypocenterC61#22453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. C2×#16839881C2semidirect
3. C2×#16839876C2semidirect
4. #21454269C2semidirect
5. #21454268C2semidirect
6. #21446709C2semidirect
7. #21446704C2semidirect
8. #21446144C2semidirect
9. #21446144C2semidirect
10. #21446143C2semidirect
11. #21446143C2semidirect
12. #21445859C2semidirect
13. #21445764C2semidirect
14. #21445603C2semidirect
15. C61×#1789C2semidirect
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×#14519785C22semidirect
32. C2×#14519785C22semidirect
33. C2×#14519784C22semidirect
34. C2×#14519784C22semidirect
38. C2×#14519712C22semidirect
39. C2×#14519712C22semidirect
40. C2×#14519705C22semidirect
41. C2×#14519705C22semidirect
42. C2×#14519705C22semidirect
43. C2×#14519705C22semidirect
44. #16839730C22semidirect
45. #16839730C22semidirect
48. #16839729C22semidirect
49. #16839729C22semidirect
58. C2×#14519688C22semidirect
59. C2×C4×#92418C22semidirect
60. #16839526C22semidirect
61. #16839526C22semidirect
62. #16839517C22semidirect
63. #16839517C22semidirect
65. C2×#104×C61C22semidirect
66. C2×#104×C61C22semidirect
67. C2×#104×C61C22semidirect
68. C2×#104×C61C22semidirect
301. #11758202C22⋊C4semidirect
305. #11758201C22⋊C4semidirect
309. #11758200C22⋊C4semidirect
313. #11758199C22⋊C4semidirect
504. #1789D61semidirect
546. C2×#104C2×D61semidirect
547. C2×#104C2×D61semidirect
548. C2×#104C2×D61semidirect
549. C2×#104C2×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×#168398812
C2×#168398762
#214542692
#214542682
#214467092
#214467042
#214461442
#214461432
#214458592
#214457642
#214456032
C61×#17892
#2245361