Finite Group Databasebeta

← C2×#21457472 #30555167

Subgroups — C2×#21457472 #30555167

Order 15616.

2762 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic, complemented
2C22×#14519807C211yesmaximal, characteristic, complemented
3C2×#16840421C211yesmaximal, characteristic, complemented
4#21457472C2116yesmaximal, direct product factor
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16840010C211yesmaximal, characteristic, complemented
7C2×#16840006C211yesmaximal, characteristic, complemented
8C2×#16839984C211yesmaximal, characteristic, complemented
9C2×#16839981C211yesmaximal, characteristic, complemented
10C2×#16839907C211yesmaximal, characteristic, complemented
11C2×#16839905C211yesmaximal, characteristic, complemented
12C2×#16839918C211yesmaximal, characteristic, complemented
13C2×#16839917C211yesmaximal, characteristic, complemented
14C2×C4×#11758202C211yesmaximal, characteristic, complemented
15C2×#16839840C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C2×#14519808—28no—
20C2×#14519808C2218yescomplemented
21C2×#14519807—28no—
22C2×#14519807C2218yescomplemented
23C22×#11758202C2211yescharacteristic
24C22×#11758202C2211yescharacteristic
25C22×#11758202C2211yescharacteristic
26C22×#11758202C2211yescharacteristic
27C22×#11758200C2211yescharacteristic
28C22×#11758200C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758201C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758194C2211yescharacteristic
33C22×#11758194C2211yescharacteristic
34#16840421—24no—
35#16840421C2218yescomplemented
36C2×#14519765C2211yescharacteristic
37C2×#14519763—21no—
38C2×#14519756C2211yescharacteristic
39C2×#14519755—21no—
40C2×#14519751C2211yescharacteristic
41C2×#14519749—21no—
42C2×C4×Dic122C2211yescharacteristic
43C2×#14519737—21no—
44#16840144C2218yescomplemented
45#16840010C2218yescomplemented
46#16840006C2218yescomplemented
47#16839984C2218yescomplemented
48#16839981C2218yescomplemented
49#16839918C2218yescomplemented
50#16839917C2218yescomplemented
51#16839907C2218yescomplemented
52#16839905C2218yescomplemented
53C4×#11758202C2218yescomplemented
54#16839840C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519701C2211yescharacteristic
59C2×#14519700C2211yescharacteristic
60C2×#14519700C2211yescharacteristic
61C2×#14519698C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×C22⋊#92418C2211yescharacteristic
64C2×C22⋊#92418C2211yescharacteristic
65C2×C4×#92418C2211yescharacteristic
66C22×#41×C61C2211yescharacteristic
67C23×Q8×C61C2211yescharacteristic
68C61×#548—24no—
69C61×#548C2218yescomplemented
70C2×#124×C61—21no—
71C2×#124×C61C2211yescharacteristic
72C2×C22⋊Q8×C61—21no—
73C2×C22⋊Q8×C61C2211yescharacteristic
74C2×#121×C61—21no—
75C2×#121×C61C2211yescharacteristic
76C2×C4×Q8×C61C2211yescharacteristic
77C2×C4×D4×C61—21no—
78C2×C4×D4×C61C2211yescharacteristic
79C2×#11758222—22no—
80C2×#11758222—24no—
81C2×#11758222—42no—
82C2×#11758222C2314yes—
83C22×Dic122—24no—
84C22×Dic122—21no—
85C22×Dic122—22no—
86C22×Dic122—42no—
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2314yes—
89C22×Dic122C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C23×Dic61—21no—
94C22×C4×D61—21no—
95#14519808—232no—
96#14519807—232no—
97C2×#11758202—24no—
98C2×#11758202—24no—
99C2×#11758202—42no—
100C2×#11758202D418yescomplemented
101C2×#11758202C2314yes—
102C2×#11758202C2314yes—
103C2×#11758202C2314yes—
104C2×#11758202C2314yes—
105C2×#11758200—24no—
106C2×#11758200—24no—
107C2×#11758200C2314yes—
108C2×#11758200C2314yes—
109C2×#11758201—24no—
110C2×#11758201—24no—
111C2×#11758201C2314yes—
112C2×#11758201C2314yes—
113C2×#11758199—42no—
114C2×#11758199C2314yes—
115C2×#11758194—24no—
116C2×#11758194—24no—
117C2×#11758194C2314yes—
118C2×#11758194C2314yes—
119C22×#92418C2311yescharacteristic
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C22×#92418C2311yescharacteristic
123#14519765—22no—
124#14519765C2314yes—
125#14519763—28no—
126#14519756—22no—
127#14519756C2314yes—
128#14519755—28no—
129#14519751—22no—
130#14519751C2314yes—
131#14519749—28no—
132C4×Dic122—22no—
133C4×Dic122C2314yes—
134#14519737—28no—
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×C22⋊Dic61—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×C4×Dic61—21no—
143#14519710C2314yes—
144C4⋊#92418C2314yes—
145#14519701C2314yes—
146#14519701C2314yes—
147#14519700C2314yes—
148#14519700C2314yes—
149#14519698C2314yes—
150#14519697C2314yes—
151C22⋊#92418C2314yes—
152C22⋊#92418C2314yes—
153C4×#92418C2314yes—
154C2×#41×C61—22no—
155C2×#41×C61—24no—
156C2×#41×C61—42no—
157C2×#41×C61C2314yes—
158C22×Q8×C61—22no—
159C22×Q8×C61—21no—
160C22×Q8×C61—24no—
161C22×Q8×C61—42no—
162C22×Q8×C61C2311yescharacteristic
163C22×Q8×C61C2314yes—
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61—21no—
166C22×D4×C61—21no—
167C22×D4×C61D411yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C23×C4×C61C2311yescharacteristic
173#124×C61—28no—
174#124×C61—22no—
175#124×C61C2314yes—
176C22⋊Q8×C61—22no—
177C22⋊Q8×C61—28no—
178C22⋊Q8×C61C2314yes—
179#121×C61—28no—
180#121×C61—22no—
181#121×C61C2314yes—
182C4×Q8×C61—22no—
183C4×Q8×C61C2314yes—
184C4×D4×C61—28no—
185C4×D4×C61D414yes—
186C4×D4×C61C2314yes—
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61D411yescharacteristic
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193C2×C22⋊C4×C61—21no—
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61D411yescharacteristic
196C2×C22⋊C4×C61D411yescharacteristic
197C2×C42×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C24×C61—21no—
200C24×C61C2×D411yescharacteristic
201C24×C61C2×D411yescharacteristic
202C23×D61—21no—
203#41×C61—28no—
204#41×C61—44no—
205#41×C61—48no—
206C2×Q8×C61—21no—
207C2×Q8×C61—24no—
208C2×Q8×C61—21no—
209C2×Q8×C61—22no—
210C2×Q8×C61—28no—
211C2×Q8×C61—22no—
212C2×Q8×C61—22no—
213C2×Q8×C61—44no—
214C2×Q8×C61—44no—
215C2×Q8×C61—48no—
216C2×Q8×C61C2×D414yes—
217C2×Q8×C61C2412yes—
218C2×Q8×C61C2412yes—
219C2×D4×C61—24no—
220C2×D4×C61—24no—
221C2×D4×C61—22no—
222C2×D4×C61—21no—
223C2×D4×C61—22no—
224C2×D4×C61—42no—
225C2×D4×C61—44no—
226C2×D4×C61—44no—
227C2×D4×C61C2×D414yes—
228C2×D4×C61C2412yes—
229C22×C4×C61—21no—
230C22×C4×C61—22no—
231C22×C4×C61—22no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—24no—
237C22×C4×C61—24no—
238C22×C4×C61—44no—
239C22×C4×C61—44no—
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2412yes—
247C22×C4×C61C2412yes—
248C22×C4×C61C2411yescharacteristic
249C2×C22⋊D61—24no—
250C2×C22⋊D61—24no—
251C2×C22⋊D61—44no—
252C2×C22⋊D61—44no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—24no—
256C22×Dic61—21no—
257C22×Dic61—44no—
258#11758222—28no—
259#11758222—44no—
260#11758222—48no—
261C2×D244—22no—
262C2×D244—22no—
263C2×D244—21no—
264C2×D244C2412yes—
265C2×C4×D61—24no—
266C2×C4×D61—44no—
267C2×Dic122—21no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—22no—
271C2×Dic122—28no—
272C2×Dic122—24no—
273C2×Dic122—21no—
274C2×Dic122—44no—
275C2×Dic122—48no—
276C2×Dic122—44no—
277C2×Dic122C2×D414yes—
278C2×Dic122C2412yes—
279C2×Dic122C2412yes—
280C4⋊C4×C61—24no—
281C4⋊C4×C61—24no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61C2×D414yes—
284C4⋊C4×C61C2412yes—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—24no—
288C22⋊C4×C61—24no—
289C22⋊C4×C61C2×D414yes—
290C22⋊C4×C61C2×D414yes—
291C42×C61—24no—
292C42×C61C2×D412yes—
293C42×C61C2412yes—
294C22⋊Dic61—24no—
295#11758202—28no—
296#11758202—28no—
297#11758202—44no—
298#11758202C2×D4116yescomplemented
299#11758201—28no—
300#11758201—28no—
301#11758200—28no—
302#11758200—28no—
303#11758199—44no—
304#11758198—24no—
305#11758198—24no—
306#11758198—24no—
307C4⋊Dic61—21no—
308C4⋊Dic61C2412yes—
309#11758196—24no—
310#11758196—24no—
311C4×Dic61—24no—
312#11758194—28no—
313#11758194—28no—
314C2×#92418—22no—
315C2×#92418—22no—
316C2×#92418—22no—
317C2×#92418C2×D414yes—
318C2×#92418C2412yes—
319C2×#92418C2412yes—
320C2×#92418C2412yes—
321C2×#92418C2412yes—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—42no—
330C23×C61—42no—
331C23×C61—42no—
332C23×C61C22×D412yes—
333C23×C61C22×D412yes—
334C23×C61C22×D411yescharacteristic
335C22×D61—22no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339Q8×C61—24no—
340Q8×C61—22no—
341Q8×C61—22no—
342Q8×C61—22no—
343Q8×C61—48no—
344Q8×C61—42no—
345Q8×C61C22×D414yes—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—44no—
349D4×C61—48no—
350D4×C61—48no—
351D4×C61—42no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—24no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—24no—
359C2×C4×C61—24no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—48no—
367C2×C4×C61—48no—
368C2×C4×C61—42no—
369C2×C4×C61—42no—
370C2×C4×C61C22×D412yes—
371C2×C4×C61C22×D412yes—
372C2×C4×C61C22×D412yes—
373C2×C4×C61C22×D412yes—
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D412yes—
376C2×C4×C61H(5,𝔽2)12yes—
377C2×C4×C61C2511yescharacteristic
378C22⋊D61—48no—
379C22⋊D61—48no—
380C2×Dic61—24no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—48no—
385C2×Dic61—42no—
386C2×Dic61—42no—
387D244—22no—
388D244—22no—
389D244—42no—
390C4×D61—48no—
391Dic122—24no—
392Dic122—22no—
393Dic122—22no—
394Dic122—22no—
395Dic122—48no—
396Dic122—42no—
397Dic122C22×D414yes—
398#92418—22no—
399#92418—22no—
400#92418—22no—
401#92418C22×D414yes—
402C2×#3277—611nomaximal, Sylow
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—44no—
410C22×C61—44no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—84no—
415C22×C61D4212yes—
416C22×C61#57512yes—
417C22×C61#57812yes—
418C22×C61C23×D411yescharacteristic
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—84no—
423C4×C61—22no—
424C4×C61—22no—
425C4×C61—24no—
426C4×C61—22no—
427C4×C61—22no—
428C4×C61—42no—
429C4×C61—42no—
430C4×C61D4212yes—
431C4×C61C23×D411yescharacteristic
432C4×C61C2×H(5,𝔽2)11yescharacteristic
433Dic61—24no—
434Dic61—42no—
435Dic61—42no—
436C22×#137—611no—
437C22×#137—611no—
438C2×#548—611no—
439C2×#548D6111yescharacteristic, complemented
440#3277—6116no—
441C2×#495—611no—
442C2×#468—611no—
443C2×#468—611no—
444C2×#464—611no—
445C2×#464—611no—
446C2×#449—611no—
447C2×#449—611no—
448C2×#451—611no—
449C2×#451—611no—
450C2×C4×Q16—611no—
451C2×#436—611no—
452C2×C61—42no—
453C2×C61—42no—
454C2×C61—82no—
455C2×C61#327714yescomplemented
456C2×C61C2×D4211yescharacteristic
457C2×C61C2×#57511yescharacteristic
458C2×C61C2×#57811yescharacteristic
459D61—82no—
460C22×#41—611no—
461C22×#41C2×D6111yescharacteristic
462C23×Q8—611no—
463C23×Q8C2×D6111yescharacteristic
464C2×#137—618no—
465C2×#137—618no—
466C2×#137—1228no—
467C2×#137—1228no—
468C22×Q16—611no—
469C22×Q16—611no—
470C22×Q16—611no—
471C22×Q16—611no—
472C22×SD16—611no—
473C22×SD16—611no—
474C22×SD16—611no—
475C22×SD16—611no—
476C22×D8—611no—
477C22×M16—611no—
478C22×M16—611no—
479#548—24no—
480#548—618no—
481#548—1224no—
482#548C2×D6118yescomplemented
483C2×#124—21no—
484C2×#124—611no—
485C2×#124—1221no—
486C2×#124C2×D6111yescharacteristic
487C2×C22⋊Q8—21no—
488C2×C22⋊Q8—611no—
489C2×C22⋊Q8—1221no—
490C2×C22⋊Q8C2×D6111yescharacteristic
491C2×#121—21no—
492C2×#121—611no—
493C2×#121—1221no—
494C2×#121C2×D6111yescharacteristic
495C2×C4×Q8—611no—
496C2×C4×Q8C2×D6111yescharacteristic
497C2×C4×D4—21no—
498C2×C4×D4—1221no—
499C2×C4×D4C2×D6111yescharacteristic
500#495—618no—
501#468—618no—
502#468—618no—
503#464—618no—
504#464—618no—
505#451—618no—
506#451—618no—
507#449—618no—
508#449—618no—
509C4×Q16—618no—
510#436—618no—
511C2×#107—611no—
512C2×C4⋊C8—611no—
513C2×#103—611no—
514C2×#103—611no—
515C2×#103—611no—
516C2×#103—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×C22⋊C8—611no—
520C2×C22⋊C8—611no—
521C2×C4×C8—611no—
522C61C2×#327711yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—614no—
527C2×#41—1224no—
528C2×#41—1222no—
529C2×#41—2442no—
530C2×#41C22×D6114yes—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—24no—
534C22×Q8—42no—
535C22×Q8—611no—
536C22×Q8—611no—
537C22×Q8—614no—
538C22×Q8—1224no—
539C22×Q8—1221no—
540C22×Q8—1222no—
541C22×Q8—2442no—
542C22×Q8C22×D6111yescharacteristic
543C22×Q8C22×D6114yes—
544C22×Q8C22×D6111yescharacteristic
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—611no—
548C22×D4—1221no—
549C22×D4—1221no—
550C22×D4C22⋊D6111yescharacteristic
551C22×D4C22×D6111yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C23×C4C22×D6111yescharacteristic
558#137—12232no—
559#137—12232no—
560C2×Q16—618no—
561C2×Q16—614no—
562C2×Q16—614no—
563C2×Q16—614no—
564C2×Q16—614no—
565C2×Q16—1224no—
566C2×Q16—1224no—
567C2×Q16—2442no—
568C2×SD16—614no—
569C2×SD16—614no—
570C2×SD16—614no—
571C2×SD16—614no—
572C2×SD16—1224no—
573C2×SD16—1224no—
574C2×SD16—1224no—
575C2×SD16—1224no—
576C2×D8—614no—
577C2×D8—2442no—
578C2×M16—614no—
579C2×M16—614no—
580C2×M16—1224no—
581C2×M16—1224no—
582C22×C8—611no—
583C22×C8—611no—
584C22×C8—611no—
585C22×C8—611no—
586#124—28no—
587#124—22no—
588#124—614no—
589#124—1228no—
590#124—1222no—
591#124C22×D6114yes—
592C22⋊Q8—22no—
593C22⋊Q8—28no—
594C22⋊Q8—614no—
595C22⋊Q8—1222no—
596C22⋊Q8—1228no—
597C22⋊Q8C22×D6114yes—
598#121—28no—
599#121—22no—
600#121—614no—
601#121—1228no—
602#121—1222no—
603#121C22×D6114yes—
604C4×Q8—22no—
605C4×Q8—614no—
606C4×Q8—1222no—
607C4×Q8C22×D6114yes—
608C4×D4—28no—
609C4×D4—1228no—
610C4×D4C22⋊D6114yes—
611C4×D4C22×D6114yes—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4C22⋊D6111yescharacteristic
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4C22⋊D6111yescharacteristic
628C2×C22⋊C4C22⋊D6111yescharacteristic
629C2×C42—21no—
630C2×C42—1221no—
631C2×C42C22×D6111yescharacteristic
632#107—614no—
633C4⋊C8—614no—
634#103—614no—
635#103—614no—
636#103—614no—
637#103—614no—
638#102—614no—
639#102—614no—
640C22⋊C8—614no—
641C22⋊C8—614no—
642C4×C8—614no—
643C24—21no—
644C24—1221no—
645C24C2×C22⋊D6111yescharacteristic
646C24C2×C22⋊D6111yescharacteristic
647#41—28no—
648#41—44no—
649#41—48no—
650#41—1228no—
651#41—2444no—
652#41—2448no—
653C2×Q8—21no—
654C2×Q8—24no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—28no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—48no—
663C2×Q8—614no—
664C2×Q8—612no—
665C2×Q8—612no—
666C2×Q8—1228no—
667C2×Q8—1221no—
668C2×Q8—1224no—
669C2×Q8—1221no—
670C2×Q8—1222no—
671C2×Q8—1222no—
672C2×Q8—1222no—
673C2×Q8—2444no—
674C2×Q8—2444no—
675C2×Q8—2448no—
676C2×Q8D4×D6114yes—
677C2×Q8C23×D6112yes—
678C2×Q8C23×D6112yes—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—22no—
682C2×D4—21no—
683C2×D4—22no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—612no—
688C2×D4—1224no—
689C2×D4—1224no—
690C2×D4—1222no—
691C2×D4—1221no—
692C2×D4—1222no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4C2×C22⋊D6114yes—
696C2×D4C23×D6112yes—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—24no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—24no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—1221no—
709C22×C4—1224no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1224no—
713C22×C4—2444no—
714C22×C4—2444no—
715C22×C4C2×C22⋊D6112yes—
716C22×C4C2×C22⋊D6112yes—
717C22×C4C2×C22⋊D6111yescharacteristic
718C22×C4C2×C22⋊D6111yescharacteristic
719C22×C4C2×C22⋊D6111yescharacteristic
720C22×C4C2×C22⋊D6111yescharacteristic
721C22×C4C23×D6112yes—
722C22×C4C23×D6112yes—
723C22×C4C23×D6111yescharacteristic
724Q16—6116no—
725Q16—1228no—
726Q16—1228no—
727Q16—2444no—
728SD16—1228no—
729SD16—1228no—
730SD16—1228no—
731SD16—1228no—
732D8—2444no—
733M16—1228no—
734M16—1228no—
735C2×C8—614no—
736C2×C8—612no—
737C2×C8—612no—
738C2×C8—612no—
739C2×C8—612no—
740C2×C8—1222no—
741C2×C8—1222no—
742C2×C8—1222no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—21no—
746C4⋊C4—612no—
747C4⋊C4—1221no—
748C4⋊C4—1224no—
749C4⋊C4—1224no—
750C4⋊C4C2×C22⋊D6114yes—
751C4⋊C4C23×D6112yes—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—1224no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C22⋊C4—1224no—
760C22⋊C4C2×C22⋊D6114yes—
761C22⋊C4C2×C22⋊D6114yes—
762C42—24no—
763C42—1224no—
764C42C2×C22⋊D6112yes—
765C42C23×D6112yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—1222no—
777C23—2442no—
778C23—2442no—
779C23—2442no—
780C23C22×C22⋊D6112yes—
781C23C22×C22⋊D6112yes—
782C23C22×C22⋊D6111yescharacteristic
783Q8—22no—
784Q8—24no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—42no—
789Q8—614no—
790Q8—1222no—
791Q8—1224no—
792Q8—1222no—
793Q8—1222no—
794Q8—2448no—
795Q8—2442no—
796Q8C2×D4×D6114yes—
797D4—22no—
798D4—22no—
799D4—44no—
800D4—48no—
801D4—48no—
802D4—42no—
803D4—1222no—
804D4—1222no—
805D4—2448no—
806D4—2448no—
807D4—2442no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—48no—
823C2×C4—48no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—1222no—
827C2×C4—1224no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—2448no—
831C2×C4—2448no—
832C2×C4—2442no—
833C2×C4—2442no—
834C2×C4C2×D4×D6112yes—
835C2×C4C22×C22⋊D6112yes—
836C2×C4C22×C22⋊D6112yes—
837C2×C4C22×C22⋊D6112yes—
838C2×C4C22×C22⋊D6112yes—
839C2×C4C22×C22⋊D6111yescharacteristic
840C2×C4#1451982212yes—
841C2×C4C24×D6111yescharacteristic
842C8—614no—
843C8—1222no—
844C8—1222no—
845C8—1222no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—84no—
858C22—4884no—
859C22—2442no—
860C22—2442no—
861C22—2442no—
862C22D4×C22⋊D6112yes—
863C22#1684056012yes—
864C22#1684057712yes—
865C22C23×C22⋊D6111yescharacteristic
866C4—22no—
867C4—22no—
868C4—24no—
869C4—22no—
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1224no—
874C4—2442no—
875C4—2442no—
876C4D4×C22⋊D6112yes—
877C4C22×D4×D6111yescharacteristic
878C4C2×#1451982211yescharacteristic
879C2—42no—
880C2—42no—
881C2—82no—
882C2—4882no—
883C2#2145747214yesdirect product factor
884C2C2×D4×C22⋊D6111yescharacteristic
885C2C2×#1684056011yescharacteristic
886C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61C2×#3277
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14519808C2semidirect
2. C22×#14519807C2semidirect
3. C2×#16840421C2semidirect
4. #21457472C2direct (N × H)
5. C2×#16840144C2semidirect
6. C2×#16840010C2semidirect
7. C2×#16840006C2semidirect
8. C2×#16839984C2semidirect
9. C2×#16839981C2semidirect
10. C2×#16839907C2semidirect
11. C2×#16839905C2semidirect
12. C2×#16839918C2semidirect
13. C2×#16839917C2semidirect
14. C2×C4×#11758202C2semidirect
15. C2×#16839840C2semidirect
16. C2×C61×#548C2semidirect
20. C2×#14519808C22semidirect
22. C2×#14519807C22semidirect
35. #16840421C22semidirect
44. #16840144C22semidirect
45. #16840010C22semidirect
46. #16840006C22semidirect
47. #16839984C22semidirect
48. #16839981C22semidirect
49. #16839918C22semidirect
50. #16839917C22semidirect
51. #16839907C22semidirect
52. #16839905C22semidirect
53. C4×#11758202C22semidirect
54. #16839840C22semidirect
69. C61×#548C22semidirect
100. C2×#11758202D4semidirect
298. #11758202C2×D4semidirect
439. C2×#548D61semidirect
455. C2×C61#3277semidirect
482. #548C2×D61semidirect
522. C61C2×#3277semidirect
883. C2#21457472direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C22×#145198072
C2×#168404212
#214574722
C2×#168401442
C2×#168400102
C2×#168400062
C2×#168399842
C2×#168399812
C2×#168399072
C2×#168399052
C2×#168399182
C2×#168399172
C2×C4×#117582022
C2×#168398402
C2×C61×#5482
C2×#327761