Finite Group Databasebeta

← C2×#21456727 #30550728

Subgroups — C2×#21456727 #30550728

Order 15616.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840342C211yesmaximal, characteristic, complemented
2C2×#16840340C211yesmaximal, characteristic, complemented
3#21456727C2116yesmaximal, direct product factor
4C2×#16840081C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic, complemented
6C2×#16840091C211yesmaximal, characteristic, complemented
7C2×#16840090C211yesmaximal, characteristic, complemented
8C2×#16840017C211yesmaximal, characteristic, complemented
9C2×#16840014C211yesmaximal, characteristic, complemented
10C2×#16839994C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic, complemented
12C2×#16839923C211yesmaximal, characteristic, complemented
13C2×#16839907C211yesmaximal, characteristic, complemented
14C2×#16839906C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840342—24no—
24#16840342C2218yescomplemented
25#16840340—24no—
26#16840340C2218yescomplemented
27C2×#14519756—21no—
28C2×#14519755—21no—
29C2×#14519753C2211yescharacteristic
30C2×#14519753C2211yescharacteristic
31C2×#14519753C2211yescharacteristic
32C2×#14519752—21no—
33C2×#14519752C2211yescharacteristic
34C2×#14519751—21no—
35C2×#14519751C2211yescharacteristic
36C2×#14519750—21no—
37C2×#14519750—21no—
38C2×#14519749—21no—
39C2×#14519749—21no—
40C2×#14519748C2211yescharacteristic
41C2×#14519748C2211yescharacteristic
42C22×C4⋊Dic61C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840091C2218yescomplemented
45#16840090C2218yescomplemented
46#16840081C2218yescomplemented
47#16840079C2218yescomplemented
48#16840017C2218yescomplemented
49#16840014C2218yescomplemented
50#16839994C2218yescomplemented
51#16839988C2218yescomplemented
52#16839923C2218yescomplemented
53#16839907C2218yescomplemented
54#16839906C2218yescomplemented
55C2×#14519709C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#452C2218yescomplemented
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—42no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
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⋊D61D411yescharacteristic
94C22×C22⋊D61D411yescharacteristic
95C23×Dic61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61C2311yescharacteristic
99C22×C4×D61C2311yescharacteristic
100C2×#11758201—42no—
101C2×#11758201C2314yes—
102C2×#11758199—42no—
103C2×#11758199C2314yes—
104C2×#11758189—42no—
105C2×#11758189C2314yes—
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108C2×C8×D61—42no—
109C2×C8×D61C2314yes—
110#14519756—28no—
111#14519755—28no—
112#14519753—22no—
113#14519753—22no—
114#14519753—22no—
115#14519753C2314yes—
116#14519753C2314yes—
117#14519753C2314yes—
118#14519752—28no—
119#14519752—22no—
120#14519752C2314yes—
121#14519751—22no—
122#14519751—28no—
123#14519751C2314yes—
124#14519750—28no—
125#14519750—28no—
126#14519749—28no—
127#14519749—28no—
128#14519748—22no—
129#14519748—22no—
130#14519748C2314yes—
131#14519748C2314yes—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61—22no—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2314yes—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C4⋊C4×D61—22no—
143C4⋊C4×D61C2314yes—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151#14519709C2314yes—
152#14519709C2314yes—
153#14519708C2314yes—
154#14519708C2314yes—
155#14519701C2314yes—
156#14519701C2314yes—
157#14519701C2314yes—
158#14519699C2314yes—
159#14519699C2314yes—
160#14519698C2314yes—
161C22⋊#92418C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164C2×#41×C61—22no—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C22×Q8×C61C2311yescharacteristic
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C23×C4×C61—21no—
173C23×C4×C61C2311yescharacteristic
174C2×Q16×C61—42no—
175C2×Q16×C61C2314yes—
176C2×SD16×C61—42no—
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#103×C61C2314yes—
186#102×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191C23×D61C2×D411yescharacteristic
192C23×D61C2×D411yescharacteristic
193#41×C61—44no—
194#41×C61—44no—
195#41×C61—48no—
196C2×Q8×C61—21no—
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61—22no—
202C2×Q8×C61C2412yes—
203C2×Q8×C61C2412yes—
204C2×D4×C61—24no—
205C2×D4×C61—21no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61—44no—
209C2×D4×C61C2412yes—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—24no—
216C22×C4×C61—44no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D412yes—
219C22×C4×C61C2412yes—
220C22×C4×C61C2411yescharacteristic
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—42no—
226C2×C22⋊D61—82no—
227C2×C22⋊D61—82no—
228C2×C22⋊D61—82no—
229C2×C22⋊D61C2×D414yes—
230C2×C22⋊D61C2×D414yes—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—24no—
235C22×Dic61—82no—
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238#11758226—44no—
239#11758226—44no—
240#11758226—48no—
241#11758222—48no—
242#11758222—44no—
243#11758222—44no—
244C2×D244—22no—
245C2×D244—22no—
246C2×D244—24no—
247C2×D244—21no—
248C2×D244—24no—
249C2×D244—42no—
250C2×D244—44no—
251C2×D244—82no—
252C2×D244C2×D414yes—
253C2×D244C2412yes—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—24no—
259C2×C4×D61—24no—
260C2×C4×D61—44no—
261C2×C4×D61—82no—
262C2×C4×D61C2×D412yes—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—42no—
267C2×Dic122C2×D414yes—
268Q16×C61—44no—
269SD16×C61—44no—
270C2×C8×C61—22no—
271C2×C8×C61—22no—
272C2×C8×C61C2412yes—
273C2×C8×C61C2412yes—
274C4⋊C4×C61—24no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61C2412yes—
277C22⋊C4×C61—24no—
278C22⋊Dic61—24no—
279C22⋊Dic61—24no—
280#11758201—44no—
281#11758199—44no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286#11758198—24no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—24no—
291C4⋊Dic61C2412yes—
292C4⋊Dic61C2412yes—
293C4⋊Dic61C2412yes—
294#11758196—24no—
295#11758196—24no—
296#11758196—24no—
297#11758196—24no—
298C2×#92418—22no—
299C2×#92418—22no—
300C2×#92418C2412yes—
301C2×#92418C2412yes—
302#11758189—44no—
303C8×D61—44no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61C22×D412yes—
312C23×C61C22×D411yescharacteristic
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61C22×D412yes—
324C22×D61C22×D412yes—
325Q8×C61—22no—
326Q8×C61—22no—
327Q8×C61—22no—
328Q8×C61—22no—
329Q8×C61—42no—
330Q8×C61—42no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—48no—
334D4×C61—42no—
335C2×C4×C61—22no—
336C2×C4×C61—24no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—48no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61C22×D412yes—
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61H(5,𝔽2)12yes—
349C2×C4×C61H(5,𝔽2)12yes—
350C2×C4×C61C2511yescharacteristic
351C22⋊D61—44no—
352C22⋊D61—44no—
353C22⋊D61—84no—
354C22⋊D61—84no—
355C22⋊D61—84no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61—84no—
365C2×Dic61C22×D412yes—
366C2×Dic61C22×D412yes—
367D244—22no—
368D244—22no—
369D244—44no—
370D244—48no—
371D244—42no—
372D244—84no—
373C4×D61—24no—
374C4×D61—24no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—48no—
380C4×D61—84no—
381Dic122—44no—
382C8×C61—22no—
383C8×C61—22no—
384#92418—22no—
385#92418—22no—
386C2×#3204—611nomaximal, Sylow
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—44no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—84no—
395C22×C61#53412yes—
396C22×C61#57712yes—
397C22×C61#57712yes—
398C22×C61C23×D411yescharacteristic
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—44no—
406C2×D61—44no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—84no—
411C4×C61—22no—
412C4×C61—42no—
413C4×C61—42no—
414C4×C61—42no—
415C4×C61#53412yes—
416C4×C61C2×H(5,𝔽2)11yescharacteristic
417C4×C61C2×H(5,𝔽2)11yescharacteristic
418Dic61—22no—
419Dic61—22no—
420Dic61—42no—
421Dic61—42no—
422Dic61—42no—
423C2×#537—611no—
424C2×#537—611no—
425#3204—6116no—
426C2×#481—611no—
427C2×#481—611no—
428C2×#483—611no—
429C2×#483—611no—
430C2×#470—611no—
431C2×#469—611no—
432C2×#465—611no—
433C2×#465—611no—
434C2×#452—611no—
435C2×#452D6111yescharacteristic, complemented
436C2×#449—611no—
437C2×#449—611no—
438C2×#408—611no—
439C2×C61—42no—
440C2×C61—82no—
441C2×C61#320414yescomplemented
442C2×C61C2×#53411yescharacteristic
443C2×C61C2×#57711yescharacteristic
444C2×C61C2×#57711yescharacteristic
445D61—42no—
446D61—42no—
447D61—82no—
448C22×#41—611no—
449C22×#41—611no—
450C22×#41C2×D6111yescharacteristic
451C22×Q16C2×D6111yescharacteristic
452C22×SD16—611no—
453C22×SD16C2×D6111yescharacteristic
454C22×D8—611no—
455C22×M16—611no—
456C23×C8—611no—
457#537—618no—
458#537—618no—
459#537—1224no—
460#537—1224no—
461C2×C22⋊Q8—611no—
462C2×C22⋊Q8—611no—
463C2×C22⋊Q8—611no—
464C2×C22⋊Q8—1221no—
465C2×C22⋊Q8—1221no—
466C2×C22⋊Q8C2×D6111yescharacteristic
467C2×#121—611no—
468C2×#121—611no—
469C2×#121—611no—
470C2×#121—611no—
471C2×#121—1221no—
472C2×#121—1221no—
473C2×#121—1221no—
474C2×#121—1221no—
475C2×#121—1221no—
476C2×#121—1221no—
477C22×C4⋊C4—611no—
478C22×C4⋊C4—611no—
479#483—618no—
480#483—618no—
481#481—618no—
482#481—618no—
483#470—618no—
484#469—618no—
485#465—618no—
486#465—618no—
487#452—618no—
488#452C2×D6118yescomplemented
489#449—618no—
490#449—618no—
491C2×#106—611no—
492C2×#106—611no—
493C2×#106—611no—
494C2×#106—611no—
495C2×#103—611no—
496C2×#103—611no—
497C2×#103—611no—
498C2×#103C2×D6111yescharacteristic
499C2×#102—611no—
500C2×#102—611no—
501C2×#102—611no—
502C2×#102C2×D6111yescharacteristic
503#408—618no—
504C2×C22⋊C8—611no—
505C2×C22⋊C8—611no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8C2×D6111yescharacteristic
508C61C2×#320411yescharacteristic, complemented, Sylow
509C2×#41—22no—
510C2×#41—42no—
511C2×#41—42no—
512C2×#41—614no—
513C2×#41—614no—
514C2×#41—614no—
515C2×#41—1222no—
516C2×#41—2442no—
517C2×#41—2442no—
518C2×#41—2442no—
519C2×#41—2442no—
520C2×#41C22×D6114yes—
521C22×Q8—611no—
522C22×Q8C22×D6111yescharacteristic
523C22×Q8C22×D6111yescharacteristic
524C22×D4—21no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—611no—
528C22×D4—611no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4C22×D6111yescharacteristic
535C23×C4—21no—
536C23×C4—611no—
537C23×C4—611no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
542C2×Q16—42no—
543C2×Q16C22×D6114yes—
544C2×SD16—42no—
545C2×SD16—614no—
546C2×SD16—2442no—
547C2×SD16C22×D6114yes—
548C2×D8—614no—
549C2×D8—2442no—
550C2×M16—614no—
551C2×M16—2442no—
552C22×C8—611no—
553C22×C8—611no—
554C22×C8—614no—
555C22×C8—2442no—
556C22×C8C22×D6111yescharacteristic
557C22×C8C22×D6111yescharacteristic
558C22⋊Q8—22no—
559C22⋊Q8—614no—
560C22⋊Q8—614no—
561C22⋊Q8—614no—
562C22⋊Q8—1228no—
563C22⋊Q8—1228no—
564C22⋊Q8—1222no—
565C22⋊Q8—1222no—
566C22⋊Q8—1222no—
567C22⋊Q8C22×D6114yes—
568#121—614no—
569#121—614no—
570#121—614no—
571#121—614no—
572#121—1228no—
573#121—1228no—
574#121—1222no—
575#121—1228no—
576#121—1228no—
577#121—1222no—
578#121—1222no—
579#121—1228no—
580#121—1228no—
581#121—1222no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—614no—
587C2×C4⋊C4—614no—
588C2×C4⋊C4—1222no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4—1222no—
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604#106—614no—
605#106—614no—
606#106—614no—
607#106—614no—
608#103—614no—
609#103—614no—
610#103—614no—
611#103C22×D6114yes—
612#102—614no—
613#102—614no—
614#102—614no—
615#102C22×D6114yes—
616C22⋊C8—614no—
617C22⋊C8—614no—
618C22⋊C8—614no—
619C22⋊C8C22×D6114yes—
620C24—21no—
621C24—611no—
622C24—611no—
623C24—1221no—
624C24D4×D6111yescharacteristic
625#41—44no—
626#41—44no—
627#41—48no—
628#41—2448no—
629#41—2444no—
630#41—2444no—
631#41—2444no—
632#41—2444no—
633#41—2448no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—22no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—614no—
641C2×Q8—2442no—
642C2×Q8C23×D6112yes—
643C2×Q8C23×D6112yes—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—44no—
649C2×D4—614no—
650C2×D4—614no—
651C2×D4—614no—
652C2×D4—612no—
653C2×D4—1224no—
654C2×D4—1224no—
655C2×D4—1224no—
656C2×D4—1224no—
657C2×D4—1224no—
658C2×D4—1221no—
659C2×D4—1222no—
660C2×D4—1222no—
661C2×D4—4882no—
662C2×D4—4882no—
663C2×D4—4882no—
664C2×D4—4882no—
665C2×D4—2442no—
666C2×D4—2444no—
667C2×D4—2442no—
668C2×D4—2442no—
669C2×D4C23×D6112yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—44no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—1224no—
684C22×C4—1224no—
685C22×C4—1222no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—1222no—
689C22×C4—1224no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—4882no—
694C22×C4—4882no—
695C22×C4—2444no—
696C22×C4D4×D6112yes—
697C22×C4D4×D6111yescharacteristic
698C22×C4C23×D6112yes—
699C22×C4C23×D6111yescharacteristic
700Q16—44no—
701SD16—44no—
702SD16—2444no—
703D8—2444no—
704M16—2444no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—612no—
708C2×C8—612no—
709C2×C8—1222no—
710C2×C8—1222no—
711C2×C8—2444no—
712C2×C8C23×D6112yes—
713C2×C8C23×D6112yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—612no—
717C4⋊C4—612no—
718C4⋊C4—612no—
719C4⋊C4—1224no—
720C4⋊C4—1224no—
721C4⋊C4—1224no—
722C4⋊C4—1224no—
723C4⋊C4—1224no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4C23×D6112yes—
728C22⋊C4—24no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—612no—
744C23—612no—
745C23—1222no—
746C23—1222no—
747C23—1222no—
748C23—1222no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—2442no—
753C23—2442no—
754C23—2442no—
755C23C2×D4×D6112yes—
756C23C2×D4×D6111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—42no—
762Q8—42no—
763Q8—2444no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—42no—
768D4—1222no—
769D4—1222no—
770D4—4884no—
771D4—4884no—
772D4—4884no—
773D4—4884no—
774D4—2444no—
775D4—2448no—
776D4—2444no—
777D4—2444no—
778D4—2442no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—48no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—612no—
791C2×C4—612no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1224no—
795C2×C4—1224no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—4884no—
804C2×C4—4884no—
805C2×C4—2448no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4C2×D4×D6112yes—
810C2×C4C2×D4×D6111yescharacteristic
811C2×C4#1451982212yes—
812C2×C4#1451982212yes—
813C2×C4C24×D6111yescharacteristic
814C8—22no—
815C8—22no—
816C8—1222no—
817C8—1222no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—84no—
826C22—1222no—
827C22—1222no—
828C22—1222no—
829C22—1222no—
830C22—1222no—
831C22—1222no—
832C22—4884no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22—2444no—
837C22—2444no—
838C22#1684032212yes—
839C22#1684056912yes—
840C22#1684057112yes—
841C22C22×D4×D6111yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—1222no—
847C4—1222no—
848C4—2442no—
849C4—2442no—
850C4—2442no—
851C4#1684032212yes—
852C4C2×#1451982211yescharacteristic
853C4C2×#1451982211yescharacteristic
854C2—42no—
855C2—82no—
856C2—4882no—
857C2—2442no—
858C2—2442no—
859C2#2145672714yesdirect product factor
860C2C2×#1684032211yescharacteristic
861C2C2×#1684056911yescharacteristic
862C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
hypercenterC2×#452D61
hypocenterC61C2×#3204
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16840342C2semidirect
2. C2×#16840340C2semidirect
3. #21456727C2direct (N × H)
4. C2×#16840081C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840091C2semidirect
7. C2×#16840090C2semidirect
8. C2×#16840017C2semidirect
9. C2×#16840014C2semidirect
10. C2×#16839994C2semidirect
11. C2×#16839988C2semidirect
12. C2×#16839923C2semidirect
13. C2×#16839907C2semidirect
14. C2×#16839906C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#452C2semidirect
24. #16840342C22semidirect
26. #16840340C22semidirect
44. #16840091C22semidirect
45. #16840090C22semidirect
46. #16840081C22semidirect
47. #16840079C22semidirect
48. #16840017C22semidirect
49. #16840014C22semidirect
50. #16839994C22semidirect
51. #16839988C22semidirect
52. #16839923C22semidirect
53. #16839907C22semidirect
54. #16839906C22semidirect
65. #16839727C22semidirect
73. C61×#452C22semidirect
435. C2×#452D61semidirect
441. C2×C61#3204semidirect
488. #452C2×D61semidirect
508. C61C2×#3204semidirect
859. C2#21456727direct (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×#168403402
#214567272
C2×#168400812
C2×#168400792
C2×#168400912
C2×#168400902
C2×#168400172
C2×#168400142
C2×#168399942
C2×#168399882
C2×#168399232
C2×#168399072
C2×#168399062
C2×#168397272
C2×C61×#4522
C2×#320461