Finite Group Databasebeta

← #29695823

Subgroups — #29695823

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839869C211yesmaximal, characteristic, complemented
2C2×Q16×Dic61C211yesmaximal, characteristic, complemented
3#21448660C211yesmaximal, characteristic
4Q8×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446702C211yesmaximal, characteristic, complemented
6#21446675C211yesmaximal, characteristic, complemented
7#21446176C211yesmaximal, characteristic, complemented
8#21446176C211yesmaximal, characteristic, complemented
9#21446162C211yesmaximal, characteristic, complemented
10#21446162C211yesmaximal, characteristic, complemented
11#21445852C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic
13#21445754C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C22×#137×C61C211yesmaximal, characteristic
16C2×Q8×Dic61C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20#16839869—24no—
21Q16×Dic61—24no—
22C2×#14519711C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519687C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35#16839669—21no—
36#16839669—21no—
37#16839669C2211yescharacteristic
38#16839669C2211yescharacteristic
39#16839665—21no—
40#16839665—21no—
41#16839665C2211yescharacteristic
42#16839665C2211yescharacteristic
43#16839622—21no—
44#16839622—21no—
45#16839622C2211yescharacteristic
46#16839622C2211yescharacteristic
47C4×C22⋊Dic61—21no—
48C4×C22⋊Dic61—21no—
49C4×C22⋊Dic61C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C23×Q8×C61C2211yescharacteristic
56C2×#137×C61—24no—
57C2×#137×C61—24no—
58C2×#137×C61C418yescomplemented
59C22×Q16×C61C2211yescharacteristic
60C22×Q16×C61C2211yescharacteristic
61C22×SD16×C61C2211yescharacteristic
62C22×SD16×C61C2211yescharacteristic
63C22×M16×C61C2211yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66Q8×Dic61—22no—
67Q8×Dic61—22no—
68Q8×Dic61—22no—
69Q8×Dic61—22no—
70Q8×Dic61—41no—
71Q8×Dic61—41no—
72Q8×Dic61—41no—
73Q8×Dic61—41no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61D411yescharacteristic
89C2×C22⋊Dic61D411yescharacteristic
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96#14519711—22no—
97#14519709—22no—
98#14519701—22no—
99#14519701—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—41no—
103#14519701—41no—
104#14519698—41no—
105#14519698—41no—
106C22⋊#92418—22no—
107#14519687—22no—
108C8×Dic61—22no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—41no—
121C2×#41×C61—41no—
122C2×#41×C61C2×C414yes—
123C22×Q8×C61—21no—
124C22×Q8×C61—22no—
125C22×Q8×C61—22no—
126C22×Q8×C61—22no—
127C22×Q8×C61—41no—
128C22×Q8×C61—41no—
129C22×Q8×C61C2×C414yes—
130C22×Q8×C61C2311yescharacteristic
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C22×D4×C61—21no—
134C22×D4×C61C2311yescharacteristic
135C23×C4×C61—21no—
136C23×C4×C61—21no—
137C23×C4×C61C2311yescharacteristic
138#137×C61—232no—
139C2×Q16×C61—22no—
140C2×Q16×C61—22no—
141C2×Q16×C61C2×C414yes—
142C2×Q16×C61C2×C414yes—
143C2×Q16×C61D414yes—
144C2×Q16×C61D414yes—
145C2×SD16×C61—22no—
146C2×SD16×C61—22no—
147C2×SD16×C61—22no—
148C2×SD16×C61—22no—
149C2×SD16×C61C2×C414yes—
150C2×SD16×C61C2×C414yes—
151C2×M16×C61—22no—
152C2×M16×C61—22no—
153C2×M16×C61C2×C414yes—
154C22×C8×C61C2311yescharacteristic
155C22×C8×C61C2311yescharacteristic
156C24×C61—21no—
157C24×C61C2×D411yescharacteristic
158#41×C61—28no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162C2×Q8×C61—24no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—28no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—42no—
176C2×Q8×C61—42no—
177C2×Q8×C61—44no—
178C2×Q8×C61—44no—
179C2×Q8×C61—44no—
180C2×Q8×C61C22×C412yes—
181C2×Q8×C61C22×C412yes—
182C2×Q8×C61C22×C412yes—
183C2×Q8×C61C2×D412yes—
184C2×Q8×C61C2×D412yes—
185C2×Q8×C61C2×D412yes—
186C2×Q8×C61C2×D412yes—
187C2×D4×C61—24no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61C22×C412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—24no—
203C22×C4×C61—21no—
204C22×C4×C61—24no—
205C22×C4×C61—42no—
206C22×C4×C61—42no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61#4112yes—
212C22×C4×C61C2411yescharacteristic
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221Q16×C61—28no—
222Q16×C61C22⋊C4116yescomplemented
223SD16×C61—28no—
224SD16×C61—28no—
225M16×C61—28no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61C22×C412yes—
229C2×C8×C61C22×C412yes—
230C2×C8×C61C2×D412yes—
231C2×C8×C61C2×D412yes—
232C22⋊Dic61—22no—
233C22⋊Dic61—41no—
234C22⋊Dic61—42no—
235C22⋊Dic61—42no—
236C22⋊Dic61—42no—
237C22⋊Dic61—81no—
238C22⋊Dic61—81no—
239C22⋊Dic61—81no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—42no—
249C4⋊Dic61—42no—
250C4⋊Dic61—42no—
251C4⋊Dic61—42no—
252C4×Dic61—21no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C4×Dic61—21no—
256C4×Dic61—42no—
257C4×Dic61—42no—
258C4×Dic61—42no—
259C4×Dic61—42no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—22no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61C4×D412yes—
280C23×C61C22×D411yescharacteristic
281Q8×C61—22no—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—48no—
290Q8×C61—41no—
291Q8×C61—41no—
292Q8×C61C2×C22⋊C414yes—
293Q8×C61C2×C22⋊C414yes—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—48no—
297D4×C61—41no—
298D4×C61—41no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—48no—
313C2×C4×C61—48no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61C4×D412yes—
317C2×C4×C61C23×C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61#13712yescomplemented
347C8×C61—22no—
348C8×C61C2×C22⋊C414yes—
349#92418—41no—
350#92418—41no—
351#22445—611nomaximal, Sylow
352C22×C61—22no—
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61C2×C4×D411yescharacteristic
367C22×C61D4211yescharacteristic
368C22×C61D4211yescharacteristic
369C22×C61C2×#13711yescharacteristic
370C22×C61#57511yescharacteristic
371C22×C61#57711yescharacteristic
372C22×C61#57811yescharacteristic
373C4×C61—22no—
374C4×C61—24no—
375C4×C61—24no—
376C4×C61—42no—
377C4×C61C22×C22⋊C411yescharacteristic
378C4×C61#51811yescharacteristic
379C4×C61#54611yescharacteristic
380C4×C61#54611yescharacteristic
381Dic61—22no—
382Dic61—41no—
383Dic61—41no—
384Dic61—41no—
385Dic61—81no—
386Dic61—81no—
387Dic61—81no—
388Dic61—81no—
389C22×#137D6111yescharacteristic
390C2×#441—611no—
391C2×C4×Q16—611no—
392#2341—611no—
393Q8×C22⋊C4—611no—
394#1973—611no—
395#1968—611no—
396#1880—611no—
397#1880—611no—
398#1878—611no—
399#1878—611no—
400#1809—611no—
401#1788—611no—
402#1787—611no—
403#1753—611no—
404C2×C61—42no—
405C2×C61—82no—
406C2×C61D4×C22⋊C411yescharacteristic
407C2×C61C4×#13711yescharacteristic
408C2×C61#294711yescharacteristic
409C2×C61#327011yescharacteristic
410C2×C61#327111yescharacteristic
411C2×C61#327711yescharacteristic
412C2×C61#327811yescharacteristic
413C22×#41C2×D6111yescharacteristic
414C23×Q8C2×D6111yescharacteristic
415C2×#137—24no—
416C2×#137—24no—
417C2×#137Dic6118yescomplemented
418C22×Q16C2×D6111yescharacteristic
419C22×Q16C2×D6111yescharacteristic
420C22×SD16C2×D6111yescharacteristic
421C22×SD16C2×D6111yescharacteristic
422C22×M16C2×D6111yescharacteristic
423C2×C4×Q8—611no—
424C2×C4×Q8—611no—
425C2×C4×Q8—611no—
426C2×C4×Q8—611no—
427#441—1224no—
428C4×Q16—1224no—
429C2×#107—611no—
430C2×#106—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×C22⋊C8—611no—
440C2×#97—611no—
441C2×C4×C8—611no—
442#391—611no—
443#391—611no—
444#391—1221no—
445#391—1221no—
446#390—611no—
447#390—611no—
448#390—1221no—
449#390—1221no—
450#380—611no—
451#380—611no—
452#380—1221no—
453#380—1221no—
454C4×C22⋊C4—611no—
455C4×C22⋊C4—1221no—
456C4×C22⋊C4—1221no—
457#340—611no—
458#340—611no—
459#336—611no—
460#336—611no—
461C61#2244511yescharacteristic, complemented, Sylow
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41C2×Dic6114yes—
468C22×Q8—21no—
469C22×Q8—22no—
470C22×Q8—22no—
471C22×Q8—22no—
472C22×Q8—41no—
473C22×Q8—41no—
474C22×Q8C2×Dic6114yes—
475C22×Q8C22×D6111yescharacteristic
476C22×Q8C22×D6111yescharacteristic
477C22×Q8C22×D6111yescharacteristic
478C22×D4—21no—
479C22×D4C22×D6111yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C22×D6111yescharacteristic
483#137—232no—
484C2×Q16—22no—
485C2×Q16—22no—
486C2×Q16C2×Dic6114yes—
487C2×Q16C2×Dic6114yes—
488C2×Q16C22⋊D6114yes—
489C2×Q16C22⋊D6114yes—
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16C2×Dic6114yes—
495C2×SD16C2×Dic6114yes—
496C2×M16—22no—
497C2×M16—22no—
498C2×M16C2×Dic6114yes—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8C22×D6111yescharacteristic
502C22×C8C22×D6111yescharacteristic
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8—2441no—
508C4×Q8—2441no—
509C4×Q8—2441no—
510C4×Q8—2441no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C42—611no—
528C2×C42—611no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1221no—
533#107—1222no—
534#106—1222no—
535#103—1222no—
536#103—1222no—
537#103—1222no—
538#103—1222no—
539#103—2441no—
540#103—2441no—
541#102—2441no—
542#102—2441no—
543C22⋊C8—1222no—
544#97—1222no—
545C4×C8—1222no—
546#95—611no—
547#95—611no—
548#95—1221no—
549#95—1221no—
550#95—1221no—
551#95—1221no—
552#95—1221no—
553#95—1221no—
554C24—21no—
555C24D4×D6111yescharacteristic
556#41—28no—
557#41—44no—
558#41—44no—
559#41—44no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—24no—
568C2×Q8—28no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8C22×Dic6112yes—
579C2×Q8C22×Dic6112yes—
580C2×Q8C22×Dic6112yes—
581C2×Q8C2×C22⋊D6112yes—
582C2×Q8C2×C22⋊D6112yes—
583C2×Q8C2×C22⋊D6112yes—
584C2×Q8C2×C22⋊D6112yes—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4C22×Dic6112yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4D4×D6111yescharacteristic
616C22×C4#1175822412yes—
617C22×C4C22×Dic6112yes—
618C22×C4C23×D6111yescharacteristic
619Q16—28no—
620Q16C22⋊Dic61116yescomplemented
621SD16—28no—
622SD16—28no—
623M16—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8C22×Dic6112yes—
633C2×C8C22×Dic6112yes—
634C2×C8C2×C22⋊D6112yes—
635C2×C8C2×C22⋊D6112yes—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—2442no—
645C4⋊C4—2442no—
646C4⋊C4—2442no—
647C4⋊C4—2442no—
648C22⋊C4—1222no—
649C22⋊C4—4881no—
650C22⋊C4—4881no—
651C22⋊C4—4881no—
652C22⋊C4—2442no—
653C22⋊C4—2441no—
654C22⋊C4—2442no—
655C22⋊C4—2442no—
656C42—1221no—
657C42—1221no—
658C42—1221no—
659C42—1221no—
660C42—2442no—
661C42—2442no—
662C42—2442no—
663C42—2442no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23D4×Dic6112yes—
678C23C2×D4×D6111yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—48no—
688Q8—41no—
689Q8—41no—
690Q8C2×C22⋊Dic6114yes—
691Q8C2×C22⋊Dic6114yes—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—48no—
711C2×C4—48no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—612no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4D4×Dic6112yes—
739C2×C4C23×Dic6111yescharacteristic
740C2×C4C22×C22⋊D6111yescharacteristic
741C2×C4C22×C22⋊D6111yescharacteristic
742C2×C4C2×#1175822411yescharacteristic
743C2×C4#1451982211yescharacteristic
744C2×C4#1451982211yescharacteristic
745C8—22no—
746C8—2441no—
747C8—2441no—
748C8C2×C22⋊Dic6114yes—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22C2×D4×Dic6111yescharacteristic
764C22D4×C22⋊D6111yescharacteristic
765C22D4×C22⋊D6111yescharacteristic
766C22#137×D6111yescharacteristic
767C22#1684056111yescharacteristic
768C22#1684057111yescharacteristic
769C22#1684057811yescharacteristic
770C4—22no—
771C4—24no—
772C4—24no—
773C4—42no—
774C4—1222no—
775C4—4881no—
776C4—4881no—
777C4—4881no—
778C4—4881no—
779C4—2441no—
780C4—2441no—
781C4—2441no—
782C4C22×C22⋊Dic6111yescharacteristic
783C4#1684023711yescharacteristic
784C4#1684040611yescharacteristic
785C4#1684040611yescharacteristic
786C2—42no—
787C2—82no—
788C2D4×C22⋊Dic6111yescharacteristic
789C2#137×Dic6111yescharacteristic
790C2#2145466311yescharacteristic
791C2#2145738311yescharacteristic
792C2#2145739811yescharacteristic
793C2#2145747011yescharacteristic
794C2#2145747911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#137×C61C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC22×#137D61
hypocenterC61#22445
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16839869C2semidirect
2. C2×Q16×Dic61C2semidirect
4. Q8×C22⋊Dic61C2semidirect
5. #21446702C2semidirect
6. #21446675C2semidirect
7. #21446176C2semidirect
8. #21446176C2semidirect
9. #21446162C2semidirect
10. #21446162C2semidirect
11. #21445852C2semidirect
13. #21445754C2semidirect
14. #21445600C2semidirect
58. C2×#137×C61C4semidirect
222. Q16×C61C22⋊C4semidirect
346. C2×Dic61#137semidirect
417. C2×#137Dic61semidirect
461. C61#22445semidirect
620. Q16C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398692
C2×Q16×Dic612
#214486602
Q8×C22⋊Dic612
#214467022
#214466752
#214461762
#214461622
#214458522
#214457592
#214457542
#214456002
C22×#137×C612
#2244561