Finite Group Databasebeta

← D61×#2123 #29832747

Subgroups — D61×#2123 #29832747

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#536×D61C211yesmaximal, characteristic
2#413×D61C211yesmaximal, characteristic
3#410×D61C211yesmaximal, characteristic
4#21447474C211yesmaximal, characteristic, complemented
5#21447473C211yesmaximal, characteristic, complemented
6#21447472C211yesmaximal, characteristic, complemented
7#21447471C214yesmaximal, complemented
8#352×D61C214yesmaximal, complemented
9C61×#2123C211yesmaximal, characteristic, complemented
10C2×#41×D61C2211yescharacteristic
11C22×Q8×D61C411yescharacteristic, complemented
12C2×M16×D61—21no—
13#16840338C411yescharacteristic, complemented
14#16840337—21no—
15#16840336C411yescharacteristic, complemented
16#16840335—21no—
17#16840335—21no—
18#16840334C412yescomplemented
19#16840334C2212yes—
20#16840333C2211yescharacteristic
21#16840332—21no—
22C4⋊Q8×D61—21no—
23#124×D61—21no—
24#123×D61C412yescomplemented
25#123×D61C2212yes—
26C22⋊Q8×D61—21no—
27C22⋊Q8×D61—21no—
28#117×D61—21no—
29#117×D61C411yescharacteristic, complemented
30#16839746C2211yescharacteristic
31#16839745—21no—
32#16839744—21no—
33#16839743C2212yes—
34#101×D61—21no—
35#100×D61C2212yes—
36#16839736C2211yescharacteristic
37#16839735—21no—
38#16839734—21no—
39#16839734C2212yes—
40#99×D61—21no—
41#99×D61C2212yes—
42#16839553C2214yescomplemented
43#16839552C2214yescomplemented
44#16839551C2214yescomplemented
45C61×#536C2211yescharacteristic
46C61×#413C2211yescharacteristic
47C61×#410C2211yescharacteristic
48C61×#352C2214yescomplemented
49C2×#11758226D411yescharacteristic
50C2×#11758222C2×C411yescharacteristic
51C2×#11758222D411yescharacteristic
52C2×#11758222D411yescharacteristic
53C2×#11758224C2×C411yescharacteristic
54C2×#11758224D411yescharacteristic
55C2×#11758224C2311yescharacteristic
56#41×D61—41no—
57#41×D61—41no—
58#41×D61—41no—
59#41×D61—41no—
60C22×Dic122C2×C411yescharacteristic, complemented
61C22×Dic122C2×C412yescomplemented
62C2×Q8×D61—21no—
63C2×Q8×D61—21no—
64C2×Q8×D61—21no—
65C2×Q8×D61—21no—
66C2×Q8×D61—41no—
67C2×Q8×D61—41no—
68C2×Q8×D61—41no—
69C2×Q8×D61—41no—
70C2×Q8×D61D411yescharacteristic
71C2×D4×D61C2×C411yescharacteristic
72C2×D4×D61D411yescharacteristic
73C2×D4×D61C2311yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C412yes—
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C2×#11758194—21no—
79C2×#11758189—41no—
80M16×D61—22no—
81M16×D61—22no—
82M16×D61—41no—
83M16×D61—41no—
84C2×C8×D61—41no—
85#14519777—21no—
86#14519776—22no—
87#14519776—22no—
88#14519775—21no—
89#14519775—21no—
90#14519766—21no—
91#14519765—21no—
92#14519764—21no—
93#14519763—22no—
94#14519763—22no—
95#14519762—22no—
96#14519762—22no—
97#14519761C2×C412yes—
98#14519761C2×C412yescomplemented
99#14519760C2×C412yes—
100#14519760C2×C412yescomplemented
101#14519759—22no—
102#14519759—22no—
103#14519758C2×C412yescomplemented
104#14519758C2312yes—
105#14519757—21no—
106#14519757—21no—
107#14519756—21no—
108#14519756—21no—
109#14519755—22no—
110#14519755—22no—
111#14519754—22no—
112#14519754—22no—
113#14519753—21no—
114#14519753—21no—
115#14519736—21no—
116#14519736C2×C411yescharacteristic, complemented
117#14519735—21no—
118#14519735—41no—
119#14519734—21no—
120#14519734—41no—
121#14519733—22no—
122#14519733C2×C412yescomplemented
123C4⋊C4×D61—21no—
124C4⋊C4×D61—22no—
125C4⋊C4×D61—22no—
126C4⋊C4×D61—41no—
127C22⋊C4×D61—22no—
128C22⋊C4×D61—22no—
129C22⋊C4×D61—22no—
130C22⋊C4×D61C2×C412yes—
131C42×D61—21no—
132C42×D61—41no—
133#14519696—21no—
134#14519695—22no—
135#14519694C2312yes—
136#14519693—22no—
137#14519692—21no—
138#14519692C2312yes—
139#14519691—22no—
140#14519691—22no—
141C2×#41×C61C2311yescharacteristic
142C22×Q8×C61C2×C411yescharacteristic, complemented
143C2×M16×C61—21no—
144C4⋊Q8×C61—21no—
145#124×C61—21no—
146#123×C61C2×C412yescomplemented
147#123×C61C2312yes—
148C22⋊Q8×C61—21no—
149C22⋊Q8×C61—21no—
150#117×C61—21no—
151#117×C61C2×C411yescharacteristic, complemented
152#101×C61—21no—
153#100×C61C2312yes—
154#99×C61—21no—
155#99×C61C2312yes—
156C23×D61C22⋊C411yescharacteristic
157C23×D61C22×C411yescharacteristic
158C23×D61C2×D411yescharacteristic
159#41×C61—41no—
160#41×C61—41no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—41no—
164C2×Q8×C61—41no—
165C2×Q8×C61C2×D411yescharacteristic
166C2×D4×C61C22×C411yescharacteristic
167C2×D4×C61C2×D411yescharacteristic
168C2×D4×C61C2411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C412yes—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C2×C22⋊D61C22⋊C411yescharacteristic
174C2×C22⋊D61C22⋊C411yescharacteristic
175C2×C22⋊D61C22×C411yescharacteristic
176C2×C22⋊D61C22×C411yescharacteristic
177C2×C22⋊D61C2×D411yescharacteristic
178C2×C22⋊D61C2×D411yescharacteristic
179C22×Dic61C22⋊C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C412yes—
182C22×Dic61C2×D411yescharacteristic
183#11758226—41no—
184#11758226—41no—
185Q8×D61—41no—
186Q8×D61—41no—
187Q8×D61—42no—
188Q8×D61—42no—
189Q8×D61—42no—
190Q8×D61—42no—
191Q8×D61—42no—
192Q8×D61—42no—
193Q8×D61—41no—
194Q8×D61—41no—
195Q8×D61—41no—
196Q8×D61—41no—
197#11758224—41no—
198#11758224—41no—
199#11758224—41no—
200#11758224—41no—
201#11758224—41no—
202#11758224—41no—
203D4×D61—41no—
204D4×D61—41no—
205D4×D61—41no—
206D4×D61—41no—
207D4×D61—41no—
208D4×D61—41no—
209#11758222—41no—
210#11758222—41no—
211#11758222—41no—
212#11758222—41no—
213#11758222—41no—
214#11758222—41no—
215C2×D244C22⋊C411yescharacteristic
216C2×D244C22⋊C411yescharacteristic
217C2×D244C2×D411yescharacteristic
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—22no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61C22⋊C411yescharacteristic
237C2×C4×D61C22⋊C411yescharacteristic
238C2×C4×D61C22⋊C411yescharacteristic
239C2×C4×D61C22⋊C411yescharacteristic
240C2×C4×D61C22⋊C411yescharacteristic
241C2×C4×D61C22⋊C411yescharacteristic
242C2×C4×D61C22⋊C411yescharacteristic
243C2×C4×D61C22⋊C411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—22no—
249C2×Dic122—22no—
250C2×Dic122—42no—
251C2×Dic122—42no—
252C2×Dic122—41no—
253C2×Dic122—41no—
254C2×Dic122C22⋊C411yescharacteristic
255C2×Dic122C22⋊C411yescharacteristic
256C2×Dic122C2×D411yescharacteristic
257M16×C61—22no—
258M16×C61—41no—
259C2×C8×C61—41no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—22no—
263C4⋊C4×C61—41no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—22no—
267C22⋊C4×C61C22×C412yes—
268C42×C61—21no—
269C42×C61—41no—
270C22⋊Dic61—22no—
271C22⋊Dic61—22no—
272C22⋊Dic61—22no—
273C22⋊Dic61C22×C412yes—
274#11758198—22no—
275#11758198—22no—
276#11758198—22no—
277#11758198—22no—
278#11758198—22no—
279#11758198—42no—
280C4⋊Dic61—21no—
281C4⋊Dic61—22no—
282C4⋊Dic61—22no—
283C4⋊Dic61—41no—
284#11758196—22no—
285#11758196—22no—
286#11758196—22no—
287#11758196—22no—
288#11758196—22no—
289#11758196—42no—
290C4×Dic61—21no—
291C4×Dic61—22no—
292C4×Dic61—42no—
293C4×Dic61—41no—
294#11758194—22no—
295#11758194—41no—
296C2×#92418—41no—
297#11758189—42no—
298#11758189—42no—
299C8×D61—42no—
300C8×D61—42no—
301C23×C61C2×C22⋊C411yescharacteristic
302C23×C61C23×C411yescharacteristic
303C23×C61C22×D411yescharacteristic
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61C2×C22⋊C411yescharacteristic
314C22×D61C2×C22⋊C411yescharacteristic
315C22×D61C2×C22⋊C411yescharacteristic
316C22×D61C2×C22⋊C411yescharacteristic
317Q8×C61—41no—
318Q8×C61—42no—
319Q8×C61—41no—
320Q8×C61—41no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61—41no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C2×C22⋊C411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C22⋊D61—41no—
339C22⋊D61—41no—
340C22⋊D61—41no—
341C22⋊D61—41no—
342C22⋊D61—41no—
343C22⋊D61—41no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61C2×C22⋊C411yescharacteristic
357C2×Dic61C2×C22⋊C411yescharacteristic
358D244—41no—
359D244—41no—
360D244—41no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—44no—
380C4×D61—44no—
381C4×D61—42no—
382C4×D61—42no—
383C4×D61—84no—
384C4×D61#9911yescharacteristic
385C4×D61#9911yescharacteristic
386C4×D61#9911yescharacteristic
387C4×D61#9911yescharacteristic
388Dic122—41no—
389Dic122—41no—
390Dic122—41no—
391Dic122—44no—
392Dic122—42no—
393Dic122—41no—
394Dic122—41no—
395Dic122—42no—
396Dic122—42no—
397C8×C61—42no—
398#92418—42no—
399C2×#2123—611nomaximal, Sylow
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61C22×C22⋊C411yescharacteristic
407C2×D61—22no—
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—41no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61C2×#9911yescharacteristic
421C2×D61C2×#9911yescharacteristic
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—42no—
426C4×C61—42no—
427C4×C61—82no—
428C4×C61C2×#9911yescharacteristic
429C4×C61C2×#9911yescharacteristic
430Dic61—21no—
431Dic61—21no—
432Dic61—21no—
433Dic61—42no—
434Dic61—42no—
435Dic61—82no—
436Dic61C2×#9911yescharacteristic
437Dic61C2×#9911yescharacteristic
438C2×#536—611no—
439C2×#413—611no—
440C2×#410—611no—
441#2123—611no—
442#2123—611no—
443#2123—614no—
444#2123—611no—
445#2123D6111yescharacteristic, direct product factor
446C2×#352—614no—
447C2×C61—21no—
448C2×C61—41no—
449C2×C61—41no—
450C2×C61—41no—
451C2×C61C22×#9911yescharacteristic
452D61—21no—
453D61—41no—
454D61—41no—
455D61—41no—
456D61#212312yesdirect product factor
457C22×#41—611no—
458C23×Q8—611no—
459C22×M16—1221no—
460#536—611no—
461#536—611no—
462#536—612no—
463#536—612no—
464#536—611no—
465#536—1221no—
466#536—1221no—
467#536—1221no—
468#536—1221no—
469#536C2×D6111yescharacteristic
470C2×C4⋊Q8—1221no—
471C2×#124—1221no—
472C2×#123—612no—
473C2×#123—612no—
474C2×C22⋊Q8—1221no—
475C2×C22⋊Q8—1221no—
476C2×#117—611no—
477C2×#117—1221no—
478#413—611no—
479#413—612no—
480#413—1221no—
481#413—1221no—
482#413C2×D6111yescharacteristic
483C2×#101—1221no—
484C2×#100—612no—
485#410—611no—
486#410—612no—
487#410—1221no—
488#410—1221no—
489#410C2×D6111yescharacteristic
490C2×#99—612no—
491C2×#99—1221no—
492#352—614no—
493#352—614no—
494#352—614no—
495#352C2×D6114yescomplemented
496C61C2×#212311yescharacteristic, complemented, Sylow
497C2×#41—611no—
498C2×#41—611no—
499C2×#41—611no—
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—2441no—
505C2×#41—2441no—
506C2×#41—2441no—
507C2×#41—2441no—
508C2×#41C22×D6111yescharacteristic
509C22×Q8—611no—
510C22×Q8—612no—
511C22×Q8—611no—
512C22×Q8—1221no—
513C22×Q8—1221no—
514C22×Q8—1221no—
515C22×Q8—1221no—
516C22×Q8—2441no—
517C22×Q8—2441no—
518C22×Q8—2441no—
519C22×Q8—2441no—
520C22×Q8C4×D6111yescharacteristic, complemented
521C22×D4—611no—
522C22×D4—611no—
523C22×D4—611no—
524C23×C4—611no—
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—612no—
528C2×M16—21no—
529C2×M16—1222no—
530C2×M16—1222no—
531C2×M16—1221no—
532C2×M16—2441no—
533C2×M16—2441no—
534C2×M16—2441no—
535C22×C8—2441no—
536C4⋊Q8—21no—
537C4⋊Q8—1221no—
538C4⋊Q8—1222no—
539C4⋊Q8—1222no—
540C4⋊Q8—1221no—
541C4⋊Q8—1221no—
542#124—21no—
543#124—1221no—
544#124—1222no—
545#124—1222no—
546#124—1221no—
547#124—1221no—
548#123—612no—
549#123—612no—
550#123—612no—
551#123—612no—
552#123—612no—
553#123—612no—
554#123—1222no—
555#123—1222no—
556#123—1222no—
557#123—1222no—
558#123C4×D6112yescomplemented
559#123C22×D6112yes—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—1222no—
563C22⋊Q8—1222no—
564C22⋊Q8—1222no—
565C22⋊Q8—1222no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572#117—21no—
573#117—611no—
574#117—612no—
575#117—1221no—
576#117—1221no—
577#117—1222no—
578#117—1221no—
579#117—2441no—
580#117—2441no—
581#117C4×D6111yescharacteristic, complemented
582C2×C4⋊C4—1221no—
583C2×C4⋊C4—1222no—
584C2×C4⋊C4—1222no—
585C2×C4⋊C4—2441no—
586C2×C22⋊C4—612no—
587C2×C22⋊C4—1222no—
588C2×C22⋊C4—1222no—
589C2×C22⋊C4—1222no—
590C2×C42—1221no—
591C2×C42—2441no—
592#101—21no—
593#101—1222no—
594#101—1221no—
595#100—612no—
596#100—1222no—
597#100C22×D6112yes—
598#99—21no—
599#99—612no—
600#99—1222no—
601#99—1222no—
602#99—1221no—
603#99C22×D6112yes—
604C24—611no—
605C24—611no—
606C24—611no—
607#41—41no—
608#41—41no—
609#41—2441no—
610#41—2441no—
611#41—2441no—
612#41—2441no—
613#41—2441no—
614#41—2441no—
615#41—2441no—
616#41—2441no—
617#41—2441no—
618#41—2441no—
619#41—2441no—
620#41—2441no—
621#41—2441no—
622#41—2441no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—41no—
626C2×Q8—41no—
627C2×Q8—611no—
628C2×Q8—611no—
629C2×Q8—611no—
630C2×Q8—1222no—
631C2×Q8—1222no—
632C2×Q8—1221no—
633C2×Q8—1221no—
634C2×Q8—2441no—
635C2×Q8—2441no—
636C2×Q8—2442no—
637C2×Q8—2442no—
638C2×Q8—2441no—
639C2×Q8—2441no—
640C2×Q8—2441no—
641C2×Q8—2441no—
642C2×Q8—2441no—
643C2×Q8—2441no—
644C2×Q8—2442no—
645C2×Q8—2442no—
646C2×Q8—2442no—
647C2×Q8—2442no—
648C2×Q8—2442no—
649C2×Q8—2442no—
650C2×Q8D4×D6111yescharacteristic
651C2×D4—611no—
652C2×D4—611no—
653C2×D4—611no—
654C2×D4—611no—
655C2×D4—611no—
656C2×D4—611no—
657C2×D4—611no—
658C2×D4—611no—
659C2×D4—611no—
660C2×D4—2441no—
661C2×D4—2441no—
662C2×D4—2441no—
663C2×D4—2441no—
664C2×D4—2441no—
665C2×D4—2441no—
666C2×D4C2×C4×D6111yescharacteristic
667C2×D4D4×D6111yescharacteristic
668C2×D4C23×D6111yescharacteristic
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—612no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1222no—
698C22×C4—2442no—
699C22×C4—2442no—
700C22×C4—2442no—
701C22×C4C2×C4×D6111yescharacteristic
702C22×C4C2×C4×D6112yes—
703C22×C4D4×D6111yescharacteristic
704C22×C4D4×D6111yescharacteristic
705M16—22no—
706M16—41no—
707M16—1222no—
708M16—2442no—
709M16—2442no—
710M16—2441no—
711C2×C8—41no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8—2441no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—21no—
718C4⋊C4—41no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1222no—
724C4⋊C4—1222no—
725C4⋊C4—1222no—
726C4⋊C4—1221no—
727C4⋊C4—2441no—
728C4⋊C4—2442no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—612no—
733C22⋊C4—1222no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C22⋊C4—1222no—
739C22⋊C4—1222no—
740C22⋊C4—1222no—
741C22⋊C4—2442no—
742C22⋊C4C2×C4×D6112yes—
743C42—21no—
744C42—41no—
745C42—1222no—
746C42—1221no—
747C42—2441no—
748C42—2442no—
749C23—611no—
750C23—611no—
751C23—611no—
752C23—611no—
753C23—1221no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—2442no—
760C23—2442no—
761C23—2442no—
762C23C22⋊C4×D6111yescharacteristic
763C23C22×C4×D6111yescharacteristic
764C23C2×D4×D6111yescharacteristic
765Q8—41no—
766Q8—42no—
767Q8—41no—
768Q8—41no—
769Q8—2441no—
770Q8—2441no—
771Q8—2441no—
772Q8—2442no—
773Q8—2442no—
774Q8—2442no—
775Q8—2444no—
776Q8—2441no—
777Q8—2441no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—2441no—
782D4—2441no—
783D4—2441no—
784D4—2441no—
785D4—2441no—
786D4—2441no—
787D4—2441no—
788D4—2441no—
789D4—2441no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—4884no—
835C2×C4—2442no—
836C2×C4—2442no—
837C2×C4—2444no—
838C2×C4—2444no—
839C2×C4—2442no—
840C2×C4—2442no—
841C2×C4C22⋊C4×D6111yescharacteristic
842C2×C4C22⋊C4×D6111yescharacteristic
843C2×C4C22⋊C4×D6111yescharacteristic
844C2×C4C2×D4×D6111yescharacteristic
845C8—42no—
846C8—2442no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—611no—
854C22—611no—
855C22—1222no—
856C22—1221no—
857C22—1221no—
858C22—1221no—
859C22—4881no—
860C22—4881no—
861C22—2441no—
862C22—2441no—
863C22—2441no—
864C22—2442no—
865C22—2442no—
866C22—2442no—
867C22—2442no—
868C22C2×C22⋊C4×D6111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—42no—
874C4—82no—
875C4—611no—
876C4—611no—
877C4—1221no—
878C4—1221no—
879C4—1221no—
880C4—4882no—
881C4—2442no—
882C4—2442no—
883C4#99×D6111yescharacteristic
884C4#99×D6111yescharacteristic
885C2—21no—
886C2—41no—
887C2—41no—
888C2—41no—
889C2—612no—
890C2—1221no—
891C2—2441no—
892C2—2441no—
893C2—2441no—
894C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC2C2×#99×D61
commutatorC23×C61C23×C4
FrattiniC2×D4C23×D61
FittingC61×#2123C2
socleC2×C61C22×#99
prime radicalC2×#41×D61C22
cosocleC2×D4×C61C24
hypercenter#2123D61
hypocenterC61C2×#2123
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2123

Complements

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

NH ≅ G/Ntype
4. #21447474C2semidirect
5. #21447473C2semidirect
6. #21447472C2semidirect
7. #21447471C2semidirect
8. #352×D61C2semidirect
9. C61×#2123C2semidirect
11. C22×Q8×D61C4semidirect
13. #16840338C4semidirect
15. #16840336C4semidirect
18. #16840334C4semidirect
24. #123×D61C4semidirect
29. #117×D61C4semidirect
42. #16839553C22semidirect
43. #16839552C22semidirect
44. #16839551C22semidirect
48. C61×#352C22semidirect
60. C22×Dic122C2×C4semidirect
61. C22×Dic122C2×C4semidirect
98. #14519761C2×C4semidirect
100. #14519760C2×C4semidirect
103. #14519758C2×C4semidirect
116. #14519736C2×C4semidirect
122. #14519733C2×C4semidirect
142. C22×Q8×C61C2×C4semidirect
146. #123×C61C2×C4semidirect
151. #117×C61C2×C4semidirect
445. #2123D61direct (N × H)
456. D61#2123direct (N × H)
495. #352C2×D61semidirect
496. C61C2×#2123semidirect
520. C22×Q8C4×D61semidirect
558. #123C4×D61semidirect
581. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#536×D612
#413×D612
#410×D612
#214474742
#214474732
#214474722
#214474712
#352×D612
C61×#21232
C2×#212361