Finite Group Databasebeta

← C2×#21457816 #30556593

Subgroups — C2×#21457816 #30556593

Order 15616.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840418C211yesmaximal, characteristic, complemented
2C2×#16840412C211yesmaximal, characteristic, complemented
3#21457816C2116yesmaximal, direct product factor
4C2×#16840120C211yesmaximal, characteristic, complemented
5C2×#16840099C211yesmaximal, characteristic, complemented
6C2×#16840073C211yesmaximal, characteristic, complemented
7C2×#16840056C211yesmaximal, characteristic, complemented
8C2×#16840007C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839904C211yesmaximal, characteristic, complemented
11C2×#16839900C211yesmaximal, characteristic, complemented
12C2×#16839859C211yesmaximal, characteristic, complemented
13C2×#16839833C211yesmaximal, characteristic, complemented
14C2×#16839760C211yesmaximal, characteristic, complemented
15C22×#14519702C211yesmaximal, characteristic, complemented
16C2×C61×#466C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758224C2211yescharacteristic
19C23×Dic122C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758189C2211yescharacteristic
23#16840418—24no—
24#16840418C2218yescomplemented
25#16840412—24no—
26#16840412C2218yescomplemented
27C2×#14519776C2211yescharacteristic
28C2×#14519764C2211yescharacteristic
29C2×#14519763—21no—
30C2×#14519759—21no—
31C2×#14519758—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519754—21no—
34C2×#14519754—21no—
35C2×#14519749—21no—
36C2×#14519748C2211yescharacteristic
37C2×#14519742C2211yescharacteristic
38C2×D4×Dic61—21no—
39C2×D4×Dic61C2211yescharacteristic
40C2×C4×C22⋊D61C2211yescharacteristic
41C22×C4⋊Dic61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840120C2218yescomplemented
44#16840099C2218yescomplemented
45#16840073C2218yescomplemented
46#16840056C2218yescomplemented
47#16840007C2218yescomplemented
48#16839975C2218yescomplemented
49#16839904C2218yescomplemented
50#16839900C2218yescomplemented
51#16839859C2218yescomplemented
52#16839833C2218yescomplemented
53C2×#14519710C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519706C2211yescharacteristic
56#16839760C2218yescomplemented
57C2×#14519702C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2218yescomplemented
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#466C2218yescomplemented
74C2×#107×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—22no—
79C2×#11758224—24no—
80C2×#11758224—42no—
81C2×#11758224—48no—
82C2×#11758224C2314yes—
83C22×Dic122—24no—
84C22×Dic122—21no—
85C22×Dic122—22no—
86C22×Dic122—21no—
87C22×Dic122—42no—
88C22×Dic122C2311yescharacteristic
89C22×Dic122C2314yes—
90C22×Dic122C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61D411yescharacteristic
94C23×Dic61—21no—
95C23×Dic61—21no—
96C23×Dic61—21no—
97C23×Dic61—21no—
98C22×C4×D61—21no—
99C22×C4×D61C2311yescharacteristic
100C2×#11758200—24no—
101C2×#11758200—42no—
102C2×#11758200C2314yes—
103C2×#11758200C2314yes—
104C2×#11758189—42no—
105C2×#11758189C2314yes—
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108#14519776—22no—
109#14519776C2314yes—
110#14519764—22no—
111#14519764C2314yes—
112#14519763—28no—
113#14519759—28no—
114#14519758—28no—
115#14519757—22no—
116#14519757C2314yes—
117#14519754—28no—
118#14519754—28no—
119#14519749—28no—
120#14519748—22no—
121#14519748C2314yes—
122#14519742—22no—
123#14519742C2314yes—
124D4×Dic61—28no—
125D4×Dic61—22no—
126D4×Dic61C2314yes—
127C4×C22⋊D61D414yes—
128C4×C22⋊D61C2314yes—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—22no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2314yes—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196D411yescharacteristic
139C4⋊C4×D61—22no—
140C4⋊C4×D61C2314yes—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61D411yescharacteristic
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×C4×Dic61—21no—
149C2×C4×Dic61C2311yescharacteristic
150#14519710C2314yes—
151#14519710C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519700C2314yes—
158#14519700C2314yes—
159#14519698C2314yes—
160#14519698C2314yes—
161C22⋊#92418C2314yes—
162#14519689C2314yes—
163#14519687C2314yes—
164C22×D4×C61—21no—
165C22×D4×C61—21no—
166C22×D4×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C23×C4×C61C2311yescharacteristic
169C2×D8×C61—42no—
170C2×D8×C61C2314yes—
171C22×C8×C61—42no—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2314yes—
175#121×C61—22no—
176#121×C61—22no—
177#121×C61C2314yes—
178#121×C61C2314yes—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183#107×C61C2314yes—
184#102×C61C2314yes—
185#102×C61C2314yes—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61C2×D411yescharacteristic
189C23×D61C2×D411yescharacteristic
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—44no—
199C2×D4×C61—44no—
200C2×D4×C61C2412yes—
201C2×D4×C61C2412yes—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2412yes—
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61C2×D414yes—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—24no—
221C22×Dic61—24no—
222C22×Dic61—24no—
223C22×Dic61—24no—
224C22×Dic61—44no—
225C22×Dic61—44no—
226C22×Dic61—44no—
227C22×Dic61—44no—
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231#11758224—28no—
232#11758224—44no—
233#11758224—48no—
234#11758224—432no—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—24no—
238C2×C4×D61—44no—
239C2×C4×D61C2×D412yes—
240C2×C4×D61C2412yes—
241C2×Dic122—21no—
242C2×Dic122—22no—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122—28no—
246C2×Dic122—24no—
247C2×Dic122—21no—
248C2×Dic122—24no—
249C2×Dic122—44no—
250C2×Dic122—48no—
251C2×Dic122—44no—
252C2×Dic122—44no—
253C2×Dic122#4114yescomplemented
254C2×Dic122C2412yes—
255C2×Dic122C2412yes—
256D8×C61—44no—
257C2×C8×C61—22no—
258C2×C8×C61—22no—
259C2×C8×C61—44no—
260C2×C8×C61C2412yes—
261C2×C8×C61C2412yes—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C2412yes—
265C4⋊C4×C61C2412yes—
266C22⋊C4×C61—24no—
267C22⋊C4×C61—24no—
268C22⋊Dic61—24no—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271C22⋊Dic61—24no—
272C22⋊Dic61C2×D414yes—
273#11758200—28no—
274#11758200—44no—
275#11758198—24no—
276#11758198C2×D414yes—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—24no—
280C4⋊Dic61—24no—
281C4⋊Dic61C2412yes—
282C4⋊Dic61C2412yes—
283#11758196—24no—
284#11758196—24no—
285#11758196—24no—
286#11758196C2×D414yes—
287C4×Dic61—24no—
288C4×Dic61C2×D412yes—
289C4×Dic61C2412yes—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294#11758189—44no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61AGL(1,ℤ/8)14yes—
306C23×C61C22×D412yes—
307C23×C61C22×D411yescharacteristic
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61C22×D412yes—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—48no—
317D4×C61—48no—
318D4×C61—42no—
319D4×C61—42no—
320C2×C4×C61—22no—
321C2×C4×C61—24no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4112yes—
331C2×C4×C61H(5,𝔽2)12yes—
332C2×C4×C61C2511yescharacteristic
333C22⋊D61—28no—
334C22⋊D61—48no—
335C22⋊D61—48no—
336C2×Dic61—24no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—48no—
345C2×Dic61—48no—
346C2×Dic61—48no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—48no—
351C2×Dic61C22×D412yes—
352C2×Dic61C22×D412yes—
353C2×Dic61C22×D412yes—
354C4×D61—24no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—48no—
358Dic122—24no—
359Dic122—22no—
360Dic122—22no—
361Dic122—22no—
362Dic122—48no—
363Dic122—48no—
364Dic122—42no—
365Dic122C2×#4114yescomplemented
366C8×C61—22no—
367C8×C61—22no—
368#92418—22no—
369#92418—22no—
370C2×#3308—611nomaximal, Sylow
371C22×C61—22no—
372C22×C61—28no—
373C22×C61—22no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—84no—
381C22×C61—84no—
382C22×C61#54612yes—
383C22×C61C2×AGL(1,ℤ/8)14yes—
384C22×C61C2×AGL(1,ℤ/8)12yes—
385C22×C61#57812yes—
386C22×C61C23×D411yescharacteristic
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—44no—
391C4×C61—22no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61#54612yes—
395C4×C61C22×#4111yescharacteristic
396C4×C61C2×H(5,𝔽2)11yescharacteristic
397Dic61—24no—
398Dic61—22no—
399Dic61—22no—
400Dic61—22no—
401Dic61—42no—
402Dic61—42no—
403Dic61—42no—
404C2×#548—611no—
405C2×#547—611no—
406#3308—6116no—
407C2×#489—611no—
408C2×#484—611no—
409C2×#480—611no—
410C2×#477—611no—
411C2×#468—611no—
412C2×#466D6111yescharacteristic, complemented
413C2×#463—611no—
414C2×#449—611no—
415C2×#448—611no—
416C2×#440—611no—
417C2×#435—611no—
418C2×#417—611no—
419C22×#103—611no—
420C2×C61—24no—
421C2×C61—82no—
422C2×C61—82no—
423C2×C61#330814yescomplemented
424C2×C61C2×#54611yescharacteristic
425C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
426C2×C61C2×#57811yescharacteristic
427D61—42no—
428C22×#41—611no—
429C22×#41—1221no—
430C23×Q8—611no—
431C22×SD16—611no—
432C22×SD16—611no—
433C22×D8C2×D6111yescharacteristic
434C22×M16—611no—
435C23×C8C2×D6111yescharacteristic
436#548—618no—
437#548—1224no—
438#547—618no—
439#547—1224no—
440C2×C4⋊Q8—611no—
441C2×#124—611no—
442C2×#124—1221no—
443C2×#123—1221no—
444C2×#123—1221no—
445C2×C22⋊Q8—611no—
446C2×C22⋊Q8—1221no—
447C2×C22⋊Q8—1221no—
448C2×#121—611no—
449C2×#121—1221no—
450C2×#121C2×D6111yescharacteristic
451C2×#121C2×D6111yescharacteristic
452C2×C4×Q8—611no—
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C2×C4×D4—1221no—
456C22×C4⋊C4—611no—
457C22×C4⋊C4—611no—
458#489—618no—
459#484—618no—
460#480—618no—
461#477—618no—
462#468—618no—
463#466C2×D6118yescomplemented
464#463—618no—
465#449—618no—
466#448—618no—
467#440—618no—
468#435—618no—
469C2×#107—611no—
470C2×#107—611no—
471C2×#107C2×D6111yescharacteristic
472C2×C4⋊C8—611no—
473#417—618no—
474C2×#103—611no—
475C2×#103—611no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#103—618no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102C2×D6111yescharacteristic
484C2×#102C2×D6111yescharacteristic
485C2×C22⋊C8—611no—
486C2×C22⋊C8—611no—
487C2×#97—611no—
488C61C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—614no—
490C2×#41—1222no—
491C2×#41—1228no—
492C2×#41—1224no—
493C2×#41—2442no—
494C2×#41—2448no—
495C22×Q8—611no—
496C22×Q8—611no—
497C22×Q8—614no—
498C22×Q8—1221no—
499C22×Q8—1224no—
500C22×Q8—1221no—
501C22×Q8—1222no—
502C22×Q8—2442no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—611no—
506C22×D4—1221no—
507C22×D4—1221no—
508C22×D4C22×D6111yescharacteristic
509C22×D4C22×D6111yescharacteristic
510C23×C4—611no—
511C23×C4—1221no—
512C23×C4—1221no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4—1221no—
516C23×C4C22×D6111yescharacteristic
517C2×SD16—614no—
518C2×SD16—614no—
519C2×SD16—1224no—
520C2×SD16—2442no—
521C2×D8—42no—
522C2×D8C22×D6114yes—
523C2×M16—614no—
524C2×M16—2442no—
525C22×C8—42no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8C22×D6111yescharacteristic
529C22×C8C22×D6111yescharacteristic
530C22×C8C22×D6114yes—
531C4⋊Q8—614no—
532C4⋊Q8—1222no—
533#124—614no—
534#124—1222no—
535#124—1228no—
536#123—1228no—
537#123—1228no—
538C22⋊Q8—614no—
539C22⋊Q8—1228no—
540C22⋊Q8—1228no—
541C22⋊Q8—1222no—
542#121—22no—
543#121—22no—
544#121—614no—
545#121—1222no—
546#121—1228no—
547#121C22×D6114yes—
548#121C22×D6114yes—
549C4×Q8—614no—
550C4×Q8—1222no—
551C4×D4—614no—
552C4×D4—614no—
553C4×D4—614no—
554C4×D4—1222no—
555C4×D4—1228no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—614no—
560C2×C4⋊C4—614no—
561C2×C4⋊C4—1222no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1222no—
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—611no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C42—611no—
580C2×C42—1221no—
581#107—614no—
582#107—614no—
583#107C22×D6114yes—
584C4⋊C8—614no—
585#103—614no—
586#103—614no—
587#103—614no—
588#103—614no—
589#103—614no—
590#103—614no—
591#102—614no—
592#102—614no—
593#102C22×D6114yes—
594#102C22×D6114yes—
595C22⋊C8—614no—
596C22⋊C8—614no—
597#97—614no—
598C24—21no—
599C24—21no—
600C24—611no—
601C24D4×D6111yescharacteristic
602#41—1228no—
603#41—2444no—
604#41—2448no—
605#41—24432no—
606C2×Q8—614no—
607C2×Q8—612no—
608C2×Q8—612no—
609C2×Q8—1224no—
610C2×Q8—1228no—
611C2×Q8—1221no—
612C2×Q8—1224no—
613C2×Q8—1221no—
614C2×Q8—1222no—
615C2×Q8—1222no—
616C2×Q8—1222no—
617C2×Q8—2444no—
618C2×Q8—2444no—
619C2×Q8—2448no—
620C2×Q8—2444no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—614no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—2444no—
636C2×D4—2444no—
637C2×D4C23×D6112yes—
638C2×D4C23×D6112yes—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—1224no—
649C22×C4—1224no—
650C22×C4—1224no—
651C22×C4—1221no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1224no—
655C22×C4—1224no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—2444no—
660C22×C4—2444no—
661C22×C4—2444no—
662C22×C4—2444no—
663C22×C4—2444no—
664C22×C4D4×D6112yes—
665C22×C4D4×D6111yescharacteristic
666C22×C4C23×D6112yes—
667C22×C4C23×D6111yescharacteristic
668SD16—1228no—
669SD16—2444no—
670D8—44no—
671M16—2444no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—44no—
675C2×C8—612no—
676C2×C8—612no—
677C2×C8—1222no—
678C2×C8—1222no—
679C2×C8C23×D6112yes—
680C2×C8C23×D6112yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—614no—
684C4⋊C4—612no—
685C4⋊C4—612no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1224no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1224no—
693C4⋊C4C23×D6112yes—
694C4⋊C4C23×D6112yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—614no—
698C22⋊C4—614no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C42—612no—
705C42—612no—
706C42—1224no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—612no—
718C23—1222no—
719C23—1222no—
720C23—1222no—
721C23#1451980114yes—
722C23C2×D4×D6112yes—
723C23C2×D4×D6111yescharacteristic
724Q8—614no—
725Q8—1222no—
726Q8—1224no—
727Q8—1222no—
728Q8—1222no—
729Q8—2448no—
730Q8—2448no—
731Q8—2442no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—48no—
737D4—48no—
738D4—42no—
739D4—42no—
740D4—1228no—
741D4—2448no—
742D4—2448no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—612no—
752C2×C4—612no—
753C2×C4—612no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1224no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1224no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—2448no—
766C2×C4—2448no—
767C2×C4—2448no—
768C2×C4—2448no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2448no—
772C2×C4—2442no—
773C2×C4C2×D4×D6112yes—
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4#41×D6112yes—
776C2×C4#1451982212yes—
777C2×C4C24×D6111yescharacteristic
778C8—22no—
779C8—22no—
780C8—1222no—
781C8—1222no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—84no—
792C22—84no—
793C22—1222no—
794C22—1222no—
795C22—1222no—
796C22—2444no—
797C22#1684040112yes—
798C22C2×#1451980114yes—
799C22C2×#1451980112yes—
800C22#1684057612yes—
801C22C22×D4×D6111yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—1222no—
806C4—1224no—
807C4—1222no—
808C4—1222no—
809C4—2442no—
810C4—2442no—
811C4—2442no—
812C4#1684040112yes—
813C4C2×#41×D6111yescharacteristic
814C4C2×#1451982211yescharacteristic
815C2—24no—
816C2—82no—
817C2—82no—
818C2—2442no—
819C2#2145781614yesdirect product factor
820C2C2×#1684040111yescharacteristic
821C2C22×#1451980111yescharacteristic
822C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#466C2
socleC23×C61C22×D4
hypercenterC2×#466D61
hypocenterC61C2×#3308
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#16840418C2semidirect
2. C2×#16840412C2semidirect
3. #21457816C2direct (N × H)
4. C2×#16840120C2semidirect
5. C2×#16840099C2semidirect
6. C2×#16840073C2semidirect
7. C2×#16840056C2semidirect
8. C2×#16840007C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839904C2semidirect
11. C2×#16839900C2semidirect
12. C2×#16839859C2semidirect
13. C2×#16839833C2semidirect
14. C2×#16839760C2semidirect
15. C22×#14519702C2semidirect
16. C2×C61×#466C2semidirect
24. #16840418C22semidirect
26. #16840412C22semidirect
43. #16840120C22semidirect
44. #16840099C22semidirect
45. #16840073C22semidirect
46. #16840056C22semidirect
47. #16840007C22semidirect
48. #16839975C22semidirect
49. #16839904C22semidirect
50. #16839900C22semidirect
51. #16839859C22semidirect
52. #16839833C22semidirect
56. #16839760C22semidirect
61. C2×#14519702C22semidirect
73. C61×#466C22semidirect
253. C2×Dic122#41semidirect
365. Dic122C2×#41semidirect
412. C2×#466D61semidirect
423. C2×C61#3308semidirect
463. #466C2×D61semidirect
488. C61C2×#3308semidirect
819. C2#21457816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404182
C2×#168404122
#214578162
C2×#168401202
C2×#168400992
C2×#168400732
C2×#168400562
C2×#168400072
C2×#168399752
C2×#168399042
C2×#168399002
C2×#168398592
C2×#168398332
C2×#168397602
C22×#145197022
C2×C61×#4662
C2×#330861