Finite Group Databasebeta

← C2×#21456667 #30550662

Subgroups — C2×#21456667 #30550662

Order 15616.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840341C211yesmaximal, characteristic, complemented
2C2×#16840329C211yesmaximal, characteristic, complemented
3#21456667C2116yesmaximal, direct product factor
4C2×#16840079C211yesmaximal, characteristic, complemented
5C2×#16840104C211yesmaximal, characteristic, complemented
6C2×#16840083C211yesmaximal, characteristic, complemented
7C2×#16840074C211yesmaximal, characteristic, complemented
8C2×#16840012C211yesmaximal, characteristic, complemented
9C2×#16840007C211yesmaximal, characteristic, complemented
10C2×#16839995C211yesmaximal, characteristic, complemented
11C2×#16839990C211yesmaximal, characteristic, complemented
12C2×#16839904C211yesmaximal, characteristic, complemented
13C2×#16839904C211yesmaximal, characteristic, complemented
14C2×#16839913C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#447C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224C2211yescharacteristic, complemented
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758189C2211yescharacteristic, complemented
22C22×C8×D61C2211yescharacteristic, complemented
23#16840341—24no—
24#16840341C2218yescomplemented
25#16840329—24no—
26#16840329C2218yescomplemented
27C2×#14519773—21no—
28C2×#14519764—21no—
29C2×#14519757C2211yescharacteristic, complemented
30C2×#14519756C2211yescharacteristic
31C2×#14519754—21no—
32C2×#14519750—21no—
33C2×#14519749—21no—
34C2×#14519748—21no—
35C2×#14519748C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×#14519748C2211yescharacteristic
38C2×#14519748C2211yescharacteristic
39C2×#14519748C2211yescharacteristic, complemented
40C2×#14519746—21no—
41C2×#14519746—21no—
42C2×#14519736C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic, complemented
44#16840104C2218yescomplemented
45#16840083C2218yescomplemented
46#16840079C2218yescomplemented
47#16840074C2218yescomplemented
48#16840012C2218yescomplemented
49#16840007C2218yescomplemented
50#16839995C2218yescomplemented
51#16839990C2218yescomplemented
52#16839913C2218yescomplemented
53#16839904C2218yescomplemented
54#16839904C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519709C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519698C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic, complemented
64C2×#14519698C2211yescharacteristic, complemented
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic, complemented
69C23×D4×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#447C2218yescomplemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—42no—
78C2×#11758222—42no—
79C2×#11758222D414yes—
80C2×#11758222C2314yes—
81C2×#11758224—22no—
82C2×#11758224—42no—
83C2×#11758224—42no—
84C2×#11758224C2314yescomplemented
85C22×Dic122D411yescharacteristic
86C22×Dic122C2311yescharacteristic
87C22×D244D411yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61D411yescharacteristic
95C22×C22⋊D61D411yescharacteristic
96C23×Dic61—21no—
97C22×C4×D61—21no—
98C22×C4×D61C2311yescharacteristic
99C22×C4×D61C2311yescharacteristic
100C2×#11758200—42no—
101C2×#11758200—42no—
102C2×#11758200C2314yes—
103C2×#11758200C2314yes—
104C2×#11758189—42no—
105C2×#11758189C2314yescomplemented
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108C2×C8×D61—42no—
109C2×C8×D61C2314yescomplemented
110#14519773—28no—
111#14519764—28no—
112#14519757—22no—
113#14519757C2314yescomplemented
114#14519756—22no—
115#14519756C2314yes—
116#14519754—28no—
117#14519750—28no—
118#14519749—28no—
119#14519748—28no—
120#14519748—22no—
121#14519748—22no—
122#14519748—22no—
123#14519748—22no—
124#14519748—22no—
125#14519748C2314yes—
126#14519748C2314yes—
127#14519748C2314yes—
128#14519748C2314yes—
129#14519748C2314yescomplemented
130#14519746—28no—
131#14519746—28no—
132#14519736—22no—
133#14519736C2314yes—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196—21no—
139C2×#11758196—21no—
140C4⋊C4×D61—22no—
141C4⋊C4×D61C2314yescomplemented
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×C22⋊Dic61—21no—
149C2×#11758198—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yescomplemented
152#14519710C2314yescomplemented
153#14519709C2314yescomplemented
154#14519708C2314yescomplemented
155#14519702C2314yescomplemented
156#14519702C2314yescomplemented
157#14519698C2314yes—
158#14519698C2314yes—
159#14519698C2314yescomplemented
160#14519698C2314yescomplemented
161C22⋊#92418C2314yes—
162#14519689C2314yescomplemented
163#14519689C2314yescomplemented
164C25×C61—21no—
165C22×D4×C61—21no—
166C22×D4×C61—21no—
167C22×D4×C61—22no—
168C22×D4×C61—42no—
169C22×D4×C61—42no—
170C22×D4×C61C2311yescharacteristic
171C22×D4×C61C2311yescharacteristic
172C22×D4×C61C2311yescharacteristic
173C22×D4×C61C2314yes—
174C23×C4×C61C2311yescharacteristic
175C2×D8×C61—42no—
176C2×D8×C61—42no—
177C2×D8×C61C2314yes—
178C2×D8×C61C2314yes—
179C22×C8×C61C2311yescharacteristic
180C22×C8×C61C2311yescharacteristic
181#121×C61—22no—
182#121×C61C2314yes—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#102×C61C2314yes—
186#102×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—24no—
192C24×C61—44no—
193C24×C61—82no—
194C24×C61—82no—
195C24×C61C2×D411yescharacteristic
196C23×D61C2×D411yescharacteristic
197C23×D61C2×D411yescharacteristic
198C2×D4×C61—24no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—24no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—48no—
213C2×D4×C61—82no—
214C2×D4×C61C2412yes—
215C2×D4×C61C2412yes—
216C2×D4×C61C2412yes—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—21no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2411yescharacteristic
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—42no—
231C2×C22⋊D61—42no—
232C2×C22⋊D61—44no—
233C2×C22⋊D61—82no—
234C2×C22⋊D61—82no—
235C2×C22⋊D61—82no—
236C2×C22⋊D61—82no—
237C2×C22⋊D61—82no—
238C2×C22⋊D61C2×D414yes—
239C2×C22⋊D61C2×D414yes—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—24no—
245C22×Dic61—44no—
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248#11758224—44no—
249#11758224—44no—
250#11758224—48no—
251#11758222—48no—
252#11758222—44no—
253#11758222—44no—
254C2×D244—42no—
255C2×D244C2×D414yes—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—24no—
261C2×C4×D61—82no—
262C2×C4×D61C2×D412yes—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—21no—
269C2×Dic122—42no—
270C2×Dic122C2×D414yes—
271C2×Dic122C2412yes—
272D8×C61—44no—
273D8×C61—44no—
274C2×C8×C61—22no—
275C2×C8×C61—22no—
276C2×C8×C61C2412yes—
277C2×C8×C61C2412yes—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2412yes—
280C22⋊C4×C61—24no—
281C22⋊Dic61—24no—
282C22⋊Dic61—24no—
283C22⋊Dic61—24no—
284C22⋊Dic61—24no—
285C22⋊Dic61—24no—
286C22⋊Dic61—24no—
287C22⋊Dic61—24no—
288#11758200—44no—
289#11758200—44no—
290#11758198—24no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—24no—
295C4⋊Dic61C2412yes—
296C4⋊Dic61C2412yes—
297C4⋊Dic61C2412yes—
298#11758196—24no—
299#11758196—24no—
300C4×Dic61—24no—
301C2×#92418—22no—
302C2×#92418—22no—
303C2×#92418C2412yes—
304C2×#92418C2412yes—
305#11758189—44no—
306C8×D61—44no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—48no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61—42no—
323C23×C61—84no—
324C23×C61—84no—
325C23×C61—816no—
326C23×C61C22×D412yes—
327C23×C61C22×D411yescharacteristic
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61C22×D412yes—
335C22×D61C22×D412yes—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—48no—
343D4×C61—42no—
344D4×C61—42no—
345D4×C61—42no—
346D4×C61—84no—
347C2×C4×C61—22no—
348C2×C4×C61—24no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—42no—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61H(5,𝔽2)12yes—
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C61C2511yescharacteristic
358C22⋊D61—44no—
359C22⋊D61—44no—
360C22⋊D61—48no—
361C22⋊D61—84no—
362C22⋊D61—84no—
363C22⋊D61—84no—
364C22⋊D61—84no—
365C22⋊D61—84no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—48no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61C22×D412yes—
378C2×Dic61C22×D412yes—
379D244—44no—
380C4×D61—24no—
381C4×D61—24no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—84no—
387Dic122—22no—
388Dic122—22no—
389Dic122—44no—
390Dic122—42no—
391C8×C61—22no—
392C8×C61—22no—
393#92418—22no—
394#92418—22no—
395C2×#3198—611nomaximal, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—44no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—816no—
410C22×C61—84no—
411C22×C61—84no—
412C22×C61—84no—
413C22×C61#53412yes—
414C22×C61#57612yes—
415C22×C61#57712yes—
416C22×C61C23×D411yescharacteristic
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—22no—
423C2×D61—44no—
424C2×D61—44no—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61#53412yes—
428C4×C61C2×H(5,𝔽2)11yescharacteristic
429C4×C61C2×H(5,𝔽2)11yescharacteristic
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433Dic61—42no—
434Dic61—42no—
435Dic61—42no—
436C2×#537—611no—
437C2×#535—611no—
438#3198—6116no—
439C2×#481—611no—
440C2×#485—611no—
441C2×#482—611no—
442C2×#480—611no—
443C2×#469—611no—
444C2×#468—611no—
445C2×#466—611no—
446C2×#465—611no—
447C2×#449—611no—
448C2×#449—611no—
449C2×#450—611no—
450C2×#447D6111yescharacteristic, complemented
451C2×#408—611no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61—82no—
455C2×C61—82no—
456C2×C61#319814yescomplemented
457C2×C61C2×#53411yescharacteristic
458C2×C61C2×#57611yescharacteristic
459C2×C61C2×#57711yescharacteristic
460D61—42no—
461D61—42no—
462C22×#41—611no—
463C22×#41—611no—
464C23×D4C2×D6111yescharacteristic
465C22×SD16—611no—
466C22×SD16—611no—
467C22×D8C2×D6111yescharacteristic
468C22×D8C2×D6111yescharacteristic
469C22×M16—611no—
470C23×C8—611no—
471#537—618no—
472#537—1224no—
473#535—618no—
474#535—1224no—
475C2×#127—1221no—
476C2×#124—1221no—
477C2×C22⋊Q8—611no—
478C2×C22⋊Q8—611no—
479C2×C22⋊Q8—1221no—
480C2×#121—611no—
481C2×#121—611no—
482C2×#121—611no—
483C2×#121—611no—
484C2×#121—611no—
485C2×#121—1221no—
486C2×#121—1221no—
487C2×#121—1221no—
488C2×#121C2×D6111yescharacteristic
489C2×#120—1221no—
490C2×#120—1221no—
491C2×#117—611no—
492C22×C4⋊C4—611no—
493#485—618no—
494#482—618no—
495#481—618no—
496#480—618no—
497#469—618no—
498#468—618no—
499#466—618no—
500#465—618no—
501#450—618no—
502#449—618no—
503#449—618no—
504#447C2×D6118yescomplemented
505C2×#107—611no—
506C2×#107—611no—
507C2×#106—611no—
508C2×#106—611no—
509C2×#103—611no—
510C2×#103—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102C2×D6111yescharacteristic
516C2×#102C2×D6111yescharacteristic
517#408—618no—
518C2×C22⋊C8—611no—
519C2×C22⋊C8—611no—
520C2×C22⋊C8—611no—
521C2×C22⋊C8C2×D6111yescharacteristic
522C61C2×#319811yescharacteristic, complemented, Sylow
523C25—21no—
524C2×#41—614no—
525C2×#41—614no—
526C2×#41—614no—
527C2×#41—1222no—
528C2×#41—2442no—
529C2×#41—2442no—
530C2×#41—2442no—
531C2×#41—2442no—
532C22×Q8—611no—
533C22×Q8—611no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—42no—
538C22×D4—42no—
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—611no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1221no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4C22×D6111yescharacteristic
549C22×D4C22×D6111yescharacteristic
550C22×D4C22×D6111yescharacteristic
551C22×D4C22×D6114yes—
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C2×SD16—614no—
558C2×SD16—614no—
559C2×SD16—2442no—
560C2×SD16—2442no—
561C2×D8—42no—
562C2×D8—42no—
563C2×D8C22×D6114yes—
564C2×D8C22×D6114yes—
565C2×M16—614no—
566C2×M16—2442no—
567C22×C8—611no—
568C22×C8—611no—
569C22×C8—614no—
570C22×C8—2442no—
571C22×C8C22×D6111yescharacteristic
572C22×C8C22×D6111yescharacteristic
573#127—1228no—
574#124—1228no—
575C22⋊Q8—614no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8—1222no—
580#121—22no—
581#121—614no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1228no—
587#121—1222no—
588#121—1222no—
589#121—1222no—
590#121—1222no—
591#121—1222no—
592#121—1228no—
593#121—1228no—
594#121C22×D6114yes—
595#120—1228no—
596#120—1228no—
597#117—614no—
598#117—1222no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—614no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C42—1221no—
618#107—614no—
619#107—614no—
620#106—614no—
621#106—614no—
622#103—614no—
623#103—614no—
624#102—614no—
625#102—614no—
626#102—614no—
627#102—614no—
628#102C22×D6114yes—
629#102C22×D6114yes—
630C22⋊C8—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633C22⋊C8C22×D6114yes—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—24no—
638C24—44no—
639C24—82no—
640C24—82no—
641C24—611no—
642C24—611no—
643C24D4×D6111yescharacteristic
644#41—2448no—
645#41—2444no—
646#41—2444no—
647#41—2444no—
648#41—2444no—
649#41—2448no—
650C2×Q8—614no—
651C2×Q8—612no—
652C2×Q8—1221no—
653C2×Q8—1222no—
654C2×Q8—1222no—
655C2×Q8—2442no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—24no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—48no—
671C2×D4—82no—
672C2×D4—614no—
673C2×D4—614no—
674C2×D4—614no—
675C2×D4—1224no—
676C2×D4—1224no—
677C2×D4—1224no—
678C2×D4—1224no—
679C2×D4—1224no—
680C2×D4—1224no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—4882no—
684C2×D4—4882no—
685C2×D4—4882no—
686C2×D4—2442no—
687C2×D4—2442no—
688C2×D4—2442no—
689C2×D4—2444no—
690C2×D4C23×D6112yes—
691C2×D4C23×D6112yes—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—612no—
699C22×C4—612no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—1224no—
703C22×C4—1224no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—4882no—
713C22×C4—2444no—
714C22×C4D4×D6112yes—
715C22×C4D4×D6111yescharacteristic
716C22×C4C23×D6112yes—
717C22×C4C23×D6111yescharacteristic
718SD16—2444no—
719SD16—2444no—
720D8—44no—
721D8—44no—
722M16—2444no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—612no—
726C2×C8—612no—
727C2×C8—1222no—
728C2×C8—1222no—
729C2×C8—2444no—
730C2×C8C23×D6112yes—
731C2×C8C23×D6112yes—
732C4⋊C4—21no—
733C4⋊C4—612no—
734C4⋊C4—612no—
735C4⋊C4—612no—
736C4⋊C4—1224no—
737C4⋊C4—1224no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1224no—
742C4⋊C4C23×D6112yes—
743C22⋊C4—24no—
744C22⋊C4—1224no—
745C22⋊C4—1224no—
746C22⋊C4—1224no—
747C22⋊C4—1224no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C42—1224no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—48no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—84no—
770C23—84no—
771C23—816no—
772C23—612no—
773C23—612no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—1222no—
779C23—1222no—
780C23C2×D4×D6112yes—
781C23C2×D4×D6111yescharacteristic
782Q8—1222no—
783Q8—1222no—
784Q8—2444no—
785Q8—2442no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—48no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—84no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—4884no—
801D4—4884no—
802D4—2444no—
803D4—2444no—
804D4—2444no—
805D4—2448no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—42no—
812C2×C4—612no—
813C2×C4—612no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1224no—
817C2×C4—1224no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—4884no—
827C2×C4—2448no—
828C2×C4—2442no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4C2×D4×D6112yes—
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4#1451982212yes—
835C2×C4#1451982212yes—
836C2×C4C24×D6111yescharacteristic
837C8—22no—
838C8—22no—
839C8—1222no—
840C8—1222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—84no—
856C22—84no—
857C22—84no—
858C22—1222no—
859C22—1222no—
860C22—1222no—
861C22—1222no—
862C22—1222no—
863C22—1222no—
864C22—2444no—
865C22—2444no—
866C22#1684032212yes—
867C22#1684056312yes—
868C22#1684057212yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—1222no—
873C4—1222no—
874C4—2442no—
875C4—2442no—
876C4—2442no—
877C4—2442no—
878C4#1684032212yes—
879C4C2×#1451982211yescharacteristic
880C4C2×#1451982211yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—82no—
885C2—2442no—
886C2—2442no—
887C2#2145666714yesdirect product factor
888C2C2×#1684032211yescharacteristic
889C2C2×#1684056311yescharacteristic
890C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#447C2
socleC23×C61C22×D4
hypercenterC2×#447D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#16840341C2semidirect
2. C2×#16840329C2semidirect
3. #21456667C2direct (N × H)
4. C2×#16840079C2semidirect
5. C2×#16840104C2semidirect
6. C2×#16840083C2semidirect
7. C2×#16840074C2semidirect
8. C2×#16840012C2semidirect
9. C2×#16840007C2semidirect
10. C2×#16839995C2semidirect
11. C2×#16839990C2semidirect
12. C2×#16839904C2semidirect
13. C2×#16839904C2semidirect
14. C2×#16839913C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#447C2semidirect
18. C22×#11758224C22semidirect
21. C22×#11758189C22semidirect
22. C22×C8×D61C22semidirect
24. #16840341C22semidirect
26. #16840329C22semidirect
29. C2×#14519757C22semidirect
39. C2×#14519748C22semidirect
43. C2×C4⋊C4×D61C22semidirect
44. #16840104C22semidirect
45. #16840083C22semidirect
46. #16840079C22semidirect
47. #16840074C22semidirect
48. #16840012C22semidirect
49. #16840007C22semidirect
50. #16839995C22semidirect
51. #16839990C22semidirect
52. #16839913C22semidirect
53. #16839904C22semidirect
54. #16839904C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519709C22semidirect
58. C2×#14519708C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519702C22semidirect
63. C2×#14519698C22semidirect
64. C2×#14519698C22semidirect
65. #16839727C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
73. C61×#447C22semidirect
84. C2×#11758224C23semidirect
105. C2×#11758189C23semidirect
109. C2×C8×D61C23semidirect
113. #14519757C23semidirect
129. #14519748C23semidirect
141. C4⋊C4×D61C23semidirect
151. #14519711C23semidirect
152. #14519710C23semidirect
153. #14519709C23semidirect
154. #14519708C23semidirect
155. #14519702C23semidirect
156. #14519702C23semidirect
159. #14519698C23semidirect
160. #14519698C23semidirect
162. #14519689C23semidirect
163. #14519689C23semidirect
450. C2×#447D61semidirect
456. C2×C61#3198semidirect
504. #447C2×D61semidirect
522. C61C2×#3198semidirect
887. C2#21456667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403412
C2×#168403292
#214566672
C2×#168400792
C2×#168401042
C2×#168400832
C2×#168400742
C2×#168400122
C2×#168400072
C2×#168399952
C2×#168399902
C2×#168399042
C2×#168399132
C2×#168397272
C2×C61×#4472
C2×#319861