Finite Group Databasebeta

← C2×#21456675 #30550670

Subgroups — C2×#21456675 #30550670

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×#16840342C211yesmaximal, characteristic, complemented
2C2×#16840329C211yesmaximal, characteristic, complemented
3#21456675C2116yesmaximal, direct product factor
4C2×#16840079C211yesmaximal, characteristic, complemented
5C2×#16840100C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840074C211yesmaximal, characteristic, complemented
8C2×#16840014C211yesmaximal, characteristic, complemented
9C2×#16840005C211yesmaximal, characteristic, complemented
10C2×#16839997C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic, complemented
12C2×#16839906C211yesmaximal, characteristic, complemented
13C2×#16839906C211yesmaximal, characteristic, complemented
14C2×#16839896C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#450C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic, complemented
18C22×#11758222C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758189C2211yescharacteristic, complemented
22C22×C8×D61C2211yescharacteristic, complemented
23#16840342—24no—
24#16840342C2218yescomplemented
25#16840329—24no—
26#16840329C2218yescomplemented
27C2×#14519773—21no—
28C2×#14519764—21no—
29C2×#14519755—21no—
30C2×#14519753C2211yescharacteristic, complemented
31C2×#14519752—21no—
32C2×#14519752C2211yescharacteristic, complemented
33C2×#14519751C2211yescharacteristic
34C2×#14519750—21no—
35C2×#14519750—21no—
36C2×#14519748C2211yescharacteristic
37C2×#14519748C2211yescharacteristic
38C2×#14519748C2211yescharacteristic
39C2×#14519748C2211yescharacteristic
40C2×#14519746—21no—
41C2×#14519746—21no—
42C2×#14519736C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic, complemented
44#16840100C2218yescomplemented
45#16840087C2218yescomplemented
46#16840079C2218yescomplemented
47#16840074C2218yescomplemented
48#16840014C2218yescomplemented
49#16840005C2218yescomplemented
50#16839997C2218yescomplemented
51#16839988C2218yescomplemented
52#16839906C2218yescomplemented
53#16839906C2218yescomplemented
54#16839896C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519709C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519701C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic, complemented
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic, complemented
69C23×D4×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#450C2218yescomplemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—42no—
79C2×#11758226—42no—
80C2×#11758226C2314yescomplemented
81C2×#11758222—42no—
82C2×#11758222—42no—
83C2×#11758222D414yes—
84C2×#11758222C2314yes—
85C22×Dic122D411yescharacteristic
86C22×D244—21no—
87C22×D244—21no—
88C22×D244D411yescharacteristic
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61D411yescharacteristic
96C22×C22⋊D61D411yescharacteristic
97C22×C4×D61—21no—
98C22×C4×D61—21no—
99C22×C4×D61C2311yescharacteristic
100C22×C4×D61C2311yescharacteristic
101C2×#11758199—42no—
102C2×#11758199—42no—
103C2×#11758199C2314yes—
104C2×#11758199C2314yes—
105C2×#11758189—42no—
106C2×#11758189C2314yescomplemented
107C22×#92418C2311yescharacteristic
108C22×#92418C2311yescharacteristic
109C2×C8×D61—42no—
110C2×C8×D61C2314yescomplemented
111#14519773—28no—
112#14519764—28no—
113#14519755—28no—
114#14519753—22no—
115#14519753C2314yescomplemented
116#14519752—28no—
117#14519752—22no—
118#14519752C2314yescomplemented
119#14519751—22no—
120#14519751C2314yes—
121#14519750—28no—
122#14519750—28no—
123#14519748—22no—
124#14519748—22no—
125#14519748—22no—
126#14519748—22no—
127#14519748C2314yes—
128#14519748C2314yes—
129#14519748C2314yes—
130#14519748C2314yes—
131#14519746—28no—
132#14519746—28no—
133#14519736—22no—
134#14519736C2314yes—
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×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yescomplemented
152#14519710C2314yescomplemented
153#14519709C2314yescomplemented
154#14519708C2314yescomplemented
155#14519701C2314yescomplemented
156#14519701C2314yescomplemented
157#14519699C2314yescomplemented
158#14519699C2314yescomplemented
159#14519698C2314yes—
160#14519698C2314yes—
161C22⋊#92418C2314yes—
162#14519689C2314yescomplemented
163#14519689C2314yescomplemented
164C25×C61—21no—
165C22×Q8×C61C2311yescharacteristic
166C22×D4×C61—21no—
167C22×D4×C61—22no—
168C22×D4×C61—42no—
169C22×D4×C61—42no—
170C22×D4×C61C2311yescharacteristic
171C22×D4×C61C2311yescharacteristic
172C22×D4×C61C2314yes—
173C23×C4×C61C2311yescharacteristic
174C2×SD16×C61—42no—
175C2×SD16×C61—42no—
176C2×SD16×C61C2314yes—
177C2×SD16×C61C2314yes—
178C22×C8×C61C2311yescharacteristic
179C22×C8×C61C2311yescharacteristic
180C22⋊Q8×C61—22no—
181C22⋊Q8×C61C2314yes—
182C2×C4⋊C4×C61—21no—
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—24no—
191C24×C61—44no—
192C24×C61—82no—
193C24×C61—82no—
194C24×C61C2×D411yescharacteristic
195C23×D61—21no—
196C23×D61C2×D411yescharacteristic
197C23×D61C2×D411yescharacteristic
198C2×Q8×C61—21no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61C2412yes—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—24no—
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×C61C2412yes—
214C2×D4×C61C2412yes—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—42no—
229C2×C22⋊D61—42no—
230C2×C22⋊D61—82no—
231C2×C22⋊D61—82no—
232C2×C22⋊D61—82no—
233C2×C22⋊D61—82no—
234C2×C22⋊D61—82no—
235C2×C22⋊D61C2×D414yes—
236C2×C22⋊D61C2×D414yes—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242#11758226—44no—
243#11758226—44no—
244#11758226—48no—
245#11758222—48no—
246#11758222—44no—
247#11758222—44no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—24no—
251C2×D244—21no—
252C2×D244—24no—
253C2×D244—42no—
254C2×D244—44no—
255C2×D244—82no—
256C2×D244C2×D414yes—
257C2×D244C2412yes—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—44no—
265C2×C4×D61—82no—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2×D412yes—
268C2×C4×D61C2412yes—
269C2×C4×D61C2412yes—
270C2×Dic122—42no—
271C2×Dic122C2×D414yes—
272SD16×C61—44no—
273SD16×C61—44no—
274C2×C8×C61—22no—
275C2×C8×C61—22no—
276C2×C8×C61C2412yes—
277C2×C8×C61C2412yes—
278C4⋊C4×C61—24no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C2412yes—
281C22⋊C4×C61—24no—
282C22⋊Dic61—24no—
283C22⋊Dic61—24no—
284C22⋊Dic61—24no—
285C22⋊Dic61—24no—
286C22⋊Dic61—24no—
287#11758199—44no—
288#11758199—44no—
289#11758198—24no—
290#11758198—24no—
291#11758198—24no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
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—48no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—84no—
320C23×C61—84no—
321C23×C61—816no—
322C23×C61C22×D412yes—
323C23×C61C22×D411yescharacteristic
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61C22×D412yes—
335C22×D61C22×D412yes—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—42no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—48no—
344D4×C61—42no—
345D4×C61—42no—
346C2×C4×C61—22no—
347C2×C4×C61—24no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61C22×D412yes—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C61H(5,𝔽2)12yes—
358C2×C4×C61C2511yescharacteristic
359C22⋊D61—44no—
360C22⋊D61—44no—
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—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376D244—22no—
377D244—22no—
378D244—44no—
379D244—48no—
380D244—42no—
381D244—84no—
382C4×D61—24no—
383C4×D61—24no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—22no—
387C4×D61—22no—
388C4×D61—48no—
389C4×D61—84no—
390Dic122—44no—
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—816no—
407C22×C61—84no—
408C22×C61—84no—
409C22×C61#53412yes—
410C22×C61#57612yes—
411C22×C61#57712yes—
412C22×C61C23×D411yescharacteristic
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—44no—
420C2×D61—44no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61#53412yes—
429C4×C61C2×H(5,𝔽2)11yescharacteristic
430C4×C61C2×H(5,𝔽2)11yescharacteristic
431Dic61—22no—
432Dic61—22no—
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×#450D6111yescharacteristic, complemented
450C2×#447—611no—
451C2×#408—611no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61—82no—
455C2×C61#319814yescomplemented
456C2×C61C2×#53411yescharacteristic
457C2×C61C2×#57611yescharacteristic
458C2×C61C2×#57711yescharacteristic
459D61—42no—
460D61—42no—
461D61—82no—
462C22×#41—611no—
463C22×#41—611no—
464C23×D4C2×D6111yescharacteristic
465C22×SD16C2×D6111yescharacteristic
466C22×SD16C2×D6111yescharacteristic
467C22×D8—611no—
468C22×D8—611no—
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—1221no—
479C2×C22⋊Q8C2×D6111yescharacteristic
480C2×#121—611no—
481C2×#121—611no—
482C2×#121—611no—
483C2×#121—611no—
484C2×#121—611no—
485C2×#121—611no—
486C2×#121—1221no—
487C2×#121—1221no—
488C2×#121—1221no—
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#450C2×D6118yescomplemented
502#449—618no—
503#449—618no—
504#447—618no—
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×Q8C22×D6111yescharacteristic
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—42no—
537C22×D4—42no—
538C22×D4—611no—
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×D4—1221no—
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—42no—
558C2×SD16—42no—
559C2×SD16C22×D6114yes—
560C2×SD16C22×D6114yes—
561C2×D8—614no—
562C2×D8—614no—
563C2×D8—2442no—
564C2×D8—2442no—
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—22no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8C22×D6114yes—
580#121—614no—
581#121—614no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1228no—
587#121—1228no—
588#121—1222no—
589#121—1228no—
590#121—1222no—
591#121—1222no—
592#121—1222no—
593#121—1222no—
594#121—1222no—
595#120—1228no—
596#120—1228no—
597#117—614no—
598#117—1222no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—614no—
604C2×C4⋊C4—1222no—
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—24no—
637C24—44no—
638C24—82no—
639C24—82no—
640C24—611no—
641C24—611no—
642C24—1221no—
643C24D4×D6111yescharacteristic
644#41—2448no—
645#41—2444no—
646#41—2444no—
647#41—2444no—
648#41—2444no—
649#41—2448no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—614no—
654C2×Q8—2442no—
655C2×Q8C23×D6112yes—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—48no—
667C2×D4—614no—
668C2×D4—614no—
669C2×D4—614no—
670C2×D4—612no—
671C2×D4—1224no—
672C2×D4—1224no—
673C2×D4—1224no—
674C2×D4—1224no—
675C2×D4—1224no—
676C2×D4—1224no—
677C2×D4—1224no—
678C2×D4—1221no—
679C2×D4—1222no—
680C2×D4—1222no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—4882no—
684C2×D4—4882no—
685C2×D4—4882no—
686C2×D4—4882no—
687C2×D4—2442no—
688C2×D4—2444no—
689C2×D4—2442no—
690C2×D4—2442no—
691C2×D4C23×D6112yes—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—612no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—1224no—
704C22×C4—1224no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
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—44no—
719SD16—44no—
720D8—2444no—
721D8—2444no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—612no—
735C4⋊C4—612no—
736C4⋊C4—612no—
737C4⋊C4—1224no—
738C4⋊C4—1224no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
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—48no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—84no—
766C23—84no—
767C23—816no—
768C23—612no—
769C23—612no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—2442no—
778C23—2442no—
779C23—2442no—
780C23C2×D4×D6112yes—
781C23C2×D4×D6111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—2444no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—1222no—
794D4—1222no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—4884no—
801D4—2444no—
802D4—2448no—
803D4—2444no—
804D4—2444no—
805D4—2442no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—612no—
815C2×C4—612no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1224no—
819C2×C4—1224no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—4884no—
828C2×C4—2448no—
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—816no—
852C22—84no—
853C22—84no—
854C22—1222no—
855C22—1222no—
856C22—1222no—
857C22—1222no—
858C22—1222no—
859C22—1222no—
860C22—4884no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2444no—
865C22—2444no—
866C22#1684032212yes—
867C22#1684056612yes—
868C22#1684056812yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1222no—
874C4—1222no—
875C4—2442no—
876C4—2442no—
877C4—2442no—
878C4#1684032212yes—
879C4C2×#1451982211yescharacteristic
880C4C2×#1451982211yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—4882no—
885C2—2442no—
886C2—2442no—
887C2#2145667514yesdirect product factor
888C2C2×#1684032211yescharacteristic
889C2C2×#1684056611yescharacteristic
890C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#450C2
socleC23×C61C22×D4
hypercenterC2×#450D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#16840342C2semidirect
2. C2×#16840329C2semidirect
3. #21456675C2direct (N × H)
4. C2×#16840079C2semidirect
5. C2×#16840100C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840074C2semidirect
8. C2×#16840014C2semidirect
9. C2×#16840005C2semidirect
10. C2×#16839997C2semidirect
11. C2×#16839988C2semidirect
12. C2×#16839906C2semidirect
13. C2×#16839906C2semidirect
14. C2×#16839896C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#450C2semidirect
17. C22×#11758226C22semidirect
21. C22×#11758189C22semidirect
22. C22×C8×D61C22semidirect
24. #16840342C22semidirect
26. #16840329C22semidirect
30. C2×#14519753C22semidirect
32. C2×#14519752C22semidirect
43. C2×C4⋊C4×D61C22semidirect
44. #16840100C22semidirect
45. #16840087C22semidirect
46. #16840079C22semidirect
47. #16840074C22semidirect
48. #16840014C22semidirect
49. #16840005C22semidirect
50. #16839997C22semidirect
51. #16839988C22semidirect
52. #16839906C22semidirect
53. #16839906C22semidirect
54. #16839896C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519709C22semidirect
58. C2×#14519708C22semidirect
59. C2×#14519701C22semidirect
60. C2×#14519701C22semidirect
61. C2×#14519699C22semidirect
62. C2×#14519699C22semidirect
65. #16839727C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
73. C61×#450C22semidirect
80. C2×#11758226C23semidirect
106. C2×#11758189C23semidirect
110. C2×C8×D61C23semidirect
115. #14519753C23semidirect
118. #14519752C23semidirect
141. C4⋊C4×D61C23semidirect
151. #14519711C23semidirect
152. #14519710C23semidirect
153. #14519709C23semidirect
154. #14519708C23semidirect
155. #14519701C23semidirect
156. #14519701C23semidirect
157. #14519699C23semidirect
158. #14519699C23semidirect
162. #14519689C23semidirect
163. #14519689C23semidirect
449. C2×#450D61semidirect
455. C2×C61#3198semidirect
501. #450C2×D61semidirect
522. C61C2×#3198semidirect
887. C2#21456675direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403422
C2×#168403292
#214566752
C2×#168400792
C2×#168401002
C2×#168400872
C2×#168400742
C2×#168400142
C2×#168400052
C2×#168399972
C2×#168399882
C2×#168399062
C2×#168398962
C2×#168397272
C2×C61×#4502
C2×#319861