Finite Group Databasebeta

← C2×#21457355 #30555022

Subgroups — C2×#21457355 #30555022

Order 15616.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519803C211yesmaximal, characteristic, complemented
2C22×#14519797C211yesmaximal, characteristic, complemented
3C2×#16840433C211yesmaximal, characteristic, complemented
4#21457355C2116yesmaximal, direct product factor
5C2×#16840152C211yesmaximal, characteristic, complemented
6C2×#16840010C211yesmaximal, characteristic, complemented
7C2×#16839996C211yesmaximal, characteristic, complemented
8C2×#16839981C211yesmaximal, characteristic, complemented
9C2×#16839957C211yesmaximal, characteristic, complemented
10C2×#16839922C211yesmaximal, characteristic, complemented
11C2×#16839907C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic, complemented
13C2×#16839896C211yesmaximal, characteristic, complemented
14C2×#16839862C211yesmaximal, characteristic, complemented
15C2×#16839834C211yesmaximal, characteristic, complemented
16C2×C61×#546C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758222C2211yescharacteristic, complemented
19C2×#14519803—28no—
20C2×#14519803C2218yescomplemented
21C2×#14519797—28no—
22C2×#14519797C2218yescomplemented
23C22×#11758202C2211yescharacteristic, complemented
24C22×#11758200C2211yescharacteristic
25C22×#11758200C2211yescharacteristic
26C22×#11758201C2211yescharacteristic, complemented
27C22×#11758201C2211yescharacteristic, complemented
28C22×#11758199C2211yescharacteristic
29C22×#11758199C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758194C2211yescharacteristic
33C23×#92418C2211yescharacteristic, complemented
34#16840433—24no—
35#16840433C2218yescomplemented
36C2×#14519774C2211yescharacteristic, complemented
37C2×#14519773—21no—
38C2×#14519751C2211yescharacteristic
39C2×#14519751C2211yescharacteristic, complemented
40C2×#14519750—21no—
41C2×#14519750—21no—
42C2×C4×Dic122C2211yescharacteristic, complemented
43C2×#14519739—21no—
44#16840152C2218yescomplemented
45#16840010C2218yescomplemented
46#16839996C2218yescomplemented
47#16839981C2218yescomplemented
48#16839957C2218yescomplemented
49#16839922C2218yescomplemented
50#16839907C2218yescomplemented
51#16839905C2218yescomplemented
52#16839896C2218yescomplemented
53#16839862C2218yescomplemented
54#16839834C2218yescomplemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×C4⋊#92418C2211yescharacteristic, complemented
57C2×#14519701C2211yescharacteristic, complemented
58C2×#14519700C2211yescharacteristic, complemented
59C2×#14519698C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×#14519697C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic, complemented
63C2×C22⋊#92418C2211yescharacteristic
64C2×C22⋊#92418C2211yescharacteristic, complemented
65C2×#14519688C2211yescharacteristic, complemented
66C22×#41×C61C2211yescharacteristic
67C23×D4×C61C2211yescharacteristic
68C61×#546—24no—
69C61×#546C2218yescomplemented
70C2×#124×C61C2211yescharacteristic
71C2×#123×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×#121×C61—21no—
74C2×#121×C61C2211yescharacteristic
75C2×#120×C61—21no—
76C2×C4×D4×C61C2211yescharacteristic
77C2×C4×D4×C61C2211yescharacteristic
78C22×C22⋊C4×C61—21no—
79C2×#11758222—22no—
80C2×#11758222—22no—
81C2×#11758222—24no—
82C2×#11758222—24no—
83C2×#11758222—42no—
84C2×#11758222—42no—
85C2×#11758222C2314yes—
86C2×#11758222C2314yescomplemented
87C22×Dic122C2311yescharacteristic
88C22×D244—21no—
89C22×D244—21no—
90C22×D244C2311yescharacteristic
91C22×D244C2311yescharacteristic
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98#14519803—232no—
99#14519797—232no—
100C2×#11758202—24no—
101C2×#11758202C2314yescomplemented
102C2×#11758200—24no—
103C2×#11758200D418yescomplemented
104C2×#11758200C2314yes—
105C2×#11758200C2314yes—
106C2×#11758201—24no—
107C2×#11758201—42no—
108C2×#11758201C2314yescomplemented
109C2×#11758201C2314yescomplemented
110C2×#11758199—24no—
111C2×#11758199—24no—
112C2×#11758199—24no—
113C2×#11758199—42no—
114C2×#11758199C2314yes—
115C2×#11758199C2314yes—
116C2×#11758199C2314yes—
117C2×#11758199C2314yes—
118C2×#11758194—24no—
119C2×#11758194C2314yes—
120C22×#92418—24no—
121C22×#92418C2311yescharacteristic
122C22×#92418C2311yescharacteristic
123C22×#92418C2311yescharacteristic
124C22×#92418C2311yescharacteristic
125C22×#92418C2314yescomplemented
126#14519774—22no—
127#14519774C2314yescomplemented
128#14519773—28no—
129#14519751—22no—
130#14519751—22no—
131#14519751C2314yes—
132#14519751C2314yescomplemented
133#14519750—28no—
134#14519750—28no—
135C4×Dic122—22no—
136C4×Dic122C2314yescomplemented
137#14519739—28no—
138C2×C4⋊Dic61C2311yescharacteristic
139C2×#11758196—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×C4×Dic61—21no—
143#14519710C2314yescomplemented
144C4⋊#92418C2314yescomplemented
145#14519701C2314yescomplemented
146#14519700C2314yescomplemented
147#14519698C2314yes—
148#14519698C2314yes—
149#14519697C2314yescomplemented
150#14519697C2314yescomplemented
151C22⋊#92418C2314yes—
152C22⋊#92418C2314yescomplemented
153#14519688C2314yescomplemented
154C25×C61—21no—
155C2×#41×C61—22no—
156C2×#41×C61—24no—
157C2×#41×C61—42no—
158C2×#41×C61C2314yes—
159C22×Q8×C61C2311yescharacteristic
160C22×D4×C61—24no—
161C22×D4×C61—21no—
162C22×D4×C61—21no—
163C22×D4×C61—22no—
164C22×D4×C61—21no—
165C22×D4×C61—42no—
166C22×D4×C61D411yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C22×D4×C61C2314yes—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61—21no—
172C23×C4×C61C2311yescharacteristic
173C23×C4×C61C2311yescharacteristic
174#124×C61—22no—
175#124×C61C2314yes—
176#123×C61—28no—
177C22⋊Q8×C61—22no—
178C22⋊Q8×C61C2314yes—
179#121×C61—22no—
180#121×C61—28no—
181#121×C61C2314yes—
182#120×C61—28no—
183C4×D4×C61—22no—
184C4×D4×C61D414yes—
185C4×D4×C61C2314yes—
186C4×D4×C61C2314yes—
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61D411yescharacteristic
189C2×C4⋊C4×C61C2311yescharacteristic
190C2×C22⋊C4×C61—21no—
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193C2×C22⋊C4×C61—21no—
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61—28no—
196C2×C22⋊C4×C61D411yescharacteristic
197C2×C22⋊C4×C61D411yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—24no—
202C24×C61—44no—
203C24×C61—44no—
204C24×C61—82no—
205C24×C61C2×D411yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209#41×C61—28no—
210#41×C61—44no—
211#41×C61—48no—
212C2×Q8×C61—21no—
213C2×Q8×C61—22no—
214C2×Q8×C61—22no—
215C2×Q8×C61C2412yes—
216C2×D4×C61—28no—
217C2×D4×C61—24no—
218C2×D4×C61—24no—
219C2×D4×C61—21no—
220C2×D4×C61—22no—
221C2×D4×C61—24no—
222C2×D4×C61—21no—
223C2×D4×C61—22no—
224C2×D4×C61—22no—
225C2×D4×C61—44no—
226C2×D4×C61—48no—
227C2×D4×C61—42no—
228C2×D4×C61—44no—
229C2×D4×C61—44no—
230C2×D4×C61—82no—
231C2×D4×C61C2×D414yes—
232C2×D4×C61C2×D414yes—
233C2×D4×C61C2412yes—
234C2×D4×C61C2412yes—
235C22×C4×C61—22no—
236C22×C4×C61—22no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—24no—
242C22×C4×C61—24no—
243C22×C4×C61—44no—
244C22×C4×C61—82no—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D412yes—
250C22×C4×C61C2×D412yes—
251C22×C4×C61C2412yes—
252C22×C4×C61C2412yes—
253C22×C4×C61C2411yescharacteristic
254C2×C22⋊D61—24no—
255C2×C22⋊D61—24no—
256C2×C22⋊D61—24no—
257C2×C22⋊D61—24no—
258C2×C22⋊D61—44no—
259C2×C22⋊D61—44no—
260C2×C22⋊D61—82no—
261C2×C22⋊D61—82no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264#11758222—28no—
265#11758222—28no—
266#11758222—44no—
267#11758222—44no—
268#11758222—48no—
269#11758222—48no—
270C2×D244—22no—
271C2×D244—22no—
272C2×D244—22no—
273C2×D244—22no—
274C2×D244—24no—
275C2×D244—21no—
276C2×D244—21no—
277C2×D244—24no—
278C2×D244—44no—
279C2×D244—82no—
280C2×D244C2412yes—
281C2×D244C2412yes—
282C2×C4×D61—24no—
283C2×C4×D61—24no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×Dic122—21no—
287C2×Dic122—22no—
288C2×Dic122C2×D414yes—
289C2×Dic122C2412yes—
290C4⋊C4×C61—24no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61C2×D414yes—
293C4⋊C4×C61C2412yes—
294C22⋊C4×C61—24no—
295C22⋊C4×C61—24no—
296C22⋊C4×C61—24no—
297C22⋊C4×C61—24no—
298C22⋊C4×C61—24no—
299C22⋊C4×C61C2×D414yes—
300C22⋊C4×C61C2×D414yes—
301C42×C61C2×D412yes—
302C42×C61C2412yes—
303#11758202—28no—
304#11758201—28no—
305#11758201—44no—
306#11758200—28no—
307#11758200C2×D4116yescomplemented
308#11758199—28no—
309#11758199—28no—
310#11758199—28no—
311#11758199—44no—
312#11758198—24no—
313#11758198—24no—
314C4⋊Dic61—21no—
315C4⋊Dic61C2412yes—
316#11758196—24no—
317C4×Dic61—24no—
318#11758194—28no—
319C2×#92418—22no—
320C2×#92418—22no—
321C2×#92418—22no—
322C2×#92418—28no—
323C2×#92418C2×D414yes—
324C2×#92418C2412yes—
325C2×#92418C2412yes—
326C2×#92418C2412yes—
327C2×#92418C2412yes—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—24no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—48no—
338C23×C61—48no—
339C23×C61—42no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61—42no—
343C23×C61—42no—
344C23×C61—84no—
345C23×C61—816no—
346C23×C61C22×D412yes—
347C23×C61C22×D412yes—
348C23×C61C22×D411yescharacteristic
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—42no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357Q8×C61—22no—
358Q8×C61—22no—
359Q8×C61—42no—
360D4×C61—24no—
361D4×C61—22no—
362D4×C61—22no—
363D4×C61—22no—
364D4×C61—44no—
365D4×C61—48no—
366D4×C61—48no—
367D4×C61—42no—
368D4×C61—84no—
369D4×C61C22×D414yes—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—24no—
375C2×C4×C61—24no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—48no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—84no—
386C2×C4×C61C22×D412yes—
387C2×C4×C61C22×D412yes—
388C2×C4×C61C22×D412yes—
389C2×C4×C61C22×D412yes—
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C22×D412yes—
392C2×C4×C61H(5,𝔽2)12yes—
393C2×C4×C61C2511yescharacteristic
394C22⋊D61—48no—
395C22⋊D61—48no—
396C22⋊D61—84no—
397C22⋊D61—84no—
398C2×Dic61—24no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—42no—
402D244—22no—
403D244—22no—
404D244—22no—
405D244—22no—
406D244—48no—
407D244—42no—
408D244—42no—
409D244—84no—
410C4×D61—48no—
411C4×D61—48no—
412Dic122—24no—
413Dic122—22no—
414Dic122C22×D414yes—
415#92418—22no—
416#92418—22no—
417#92418—22no—
418#92418C22×D414yes—
419C2×#3268—611nomaximal, Sylow
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—24no—
423C22×C61—22no—
424C22×C61—22no—
425C22×C61—22no—
426C22×C61—22no—
427C22×C61—44no—
428C22×C61—44no—
429C22×C61—48no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—816no—
436C22×C61—84no—
437C22×C61D4212yes—
438C22×C61#57512yes—
439C22×C61#57612yes—
440C22×C61C23×D411yescharacteristic
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—84no—
448C2×D61—84no—
449C4×C61—22no—
450C4×C61—22no—
451C4×C61—22no—
452C4×C61—22no—
453C4×C61—42no—
454C4×C61—42no—
455C4×C61D4212yes—
456C4×C61C23×D411yescharacteristic
457C4×C61C2×H(5,𝔽2)11yescharacteristic
458Dic61—24no—
459Dic61—42no—
460C22×AGL(1,ℤ/8)—611no—
461C22×#135—611no—
462C2×#550—611no—
463C2×#546D6111yescharacteristic, complemented
464#3268—6116no—
465C2×#496—611no—
466C2×#468—611no—
467C2×#466—611no—
468C2×#464—611no—
469C2×#459—611no—
470C2×#452—611no—
471C2×#449—611no—
472C2×#449—611no—
473C2×#447—611no—
474C2×#440—611no—
475C2×#435—611no—
476C2×C61—42no—
477C2×C61—42no—
478C2×C61—44no—
479C2×C61—82no—
480C2×C61#326814yescomplemented
481C2×C61C2×D4211yescharacteristic
482C2×C61C2×#57511yescharacteristic
483C2×C61C2×#57611yescharacteristic
484D61—82no—
485D61—82no—
486C22×#41—611no—
487C22×#41—611no—
488C22×#41C2×D6111yescharacteristic
489C23×D4C2×D6111yescharacteristic
490C2×AGL(1,ℤ/8)—618no—
491C2×AGL(1,ℤ/8)—1228no—
492C2×#135—618no—
493C2×#135—1228no—
494C22×Q16—611no—
495C22×SD16—611no—
496C22×SD16—611no—
497C22×SD16—611no—
498C22×SD16—611no—
499C22×D8—611no—
500C22×D8—611no—
501C22×D8—611no—
502C22×D8—611no—
503C22×M16—611no—
504C23×C8—611no—
505#550—618no—
506#550—1224no—
507#546—24no—
508#546C2×D6118yescomplemented
509C2×#127—611no—
510C2×#127—1221no—
511C2×#124C2×D6111yescharacteristic
512C2×#123—21no—
513C2×C22⋊Q8C2×D6111yescharacteristic
514C2×#121—21no—
515C2×#121—611no—
516C2×#121—611no—
517C2×#121—1221no—
518C2×#121—1221no—
519C2×#121C2×D6111yescharacteristic
520C2×#120—21no—
521C2×C4×Q8—611no—
522C2×C4×D4—1221no—
523C2×C4×D4C2×D6111yescharacteristic
524C2×C4×D4C2×D6111yescharacteristic
525C22×C22⋊C4—21no—
526#496—618no—
527#468—618no—
528#466—618no—
529#464—618no—
530#459—618no—
531#452—618no—
532#449—618no—
533#449—618no—
534#447—618no—
535#440—618no—
536#435—618no—
537C2×#107—611no—
538C2×C4⋊C8—611no—
539C2×#103—611no—
540C2×#103—611no—
541C2×#102—611no—
542C2×#102—611no—
543C2×#102—611no—
544C2×#102—611no—
545C2×C22⋊C8—611no—
546C2×C22⋊C8—611no—
547C2×#97—611no—
548C61C2×#326811yescharacteristic, complemented, Sylow
549C25—21no—
550C2×#41—22no—
551C2×#41—24no—
552C2×#41—42no—
553C2×#41—614no—
554C2×#41—614no—
555C2×#41—1224no—
556C2×#41—1224no—
557C2×#41—1222no—
558C2×#41—1222no—
559C2×#41—2442no—
560C2×#41—2442no—
561C2×#41C22×D6114yes—
562C22×Q8—611no—
563C22×Q8C22×D6111yescharacteristic
564C22×D4—24no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—22no—
569C22×D4—42no—
570C22×D4—611no—
571C22×D4—611no—
572C22×D4—1221no—
573C22×D4—1221no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4—1221no—
577C22×D4—1221no—
578C22×D4C22⋊D6111yescharacteristic
579C22×D4C22×D6111yescharacteristic
580C22×D4C22×D6114yes—
581C22×D4C22×D6111yescharacteristic
582C23×C4—21no—
583C23×C4—21no—
584C23×C4—1221no—
585C23×C4—1221no—
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588AGL(1,ℤ/8)—12232no—
589#135—12232no—
590C2×Q16—614no—
591C2×Q16—1224no—
592C2×SD16—618no—
593C2×SD16—614no—
594C2×SD16—614no—
595C2×SD16—614no—
596C2×SD16—614no—
597C2×SD16—1224no—
598C2×SD16—1224no—
599C2×SD16—2442no—
600C2×D8—614no—
601C2×D8—614no—
602C2×D8—614no—
603C2×D8—614no—
604C2×D8—1224no—
605C2×D8—1224no—
606C2×D8—1224no—
607C2×D8—2442no—
608C2×M16—614no—
609C2×M16—1224no—
610C22×C8—611no—
611C22×C8—611no—
612C22×C8—614no—
613C22×C8—611no—
614C22×C8—611no—
615C22×C8—1224no—
616#127—614no—
617#127—1228no—
618#127—1222no—
619#124—22no—
620#124C22×D6114yes—
621#123—28no—
622C22⋊Q8—22no—
623C22⋊Q8C22×D6114yes—
624#121—22no—
625#121—28no—
626#121—614no—
627#121—614no—
628#121—1222no—
629#121—1222no—
630#121—1228no—
631#121—1228no—
632#121C22×D6114yes—
633#120—28no—
634C4×Q8—614no—
635C4×Q8—1222no—
636C4×D4—22no—
637C4×D4—1228no—
638C4×D4C22⋊D6114yes—
639C4×D4C22×D6114yes—
640C4×D4C22×D6114yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4C22⋊D6111yescharacteristic
645C2×C4⋊C4C22×D6111yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—28no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1221no—
654C2×C22⋊C4C22⋊D6111yescharacteristic
655C2×C22⋊C4C22⋊D6111yescharacteristic
656C2×C42—1221no—
657C2×C42C22×D6111yescharacteristic
658#107—614no—
659C4⋊C8—614no—
660#103—614no—
661#103—614no—
662#102—614no—
663#102—614no—
664#102—614no—
665#102—614no—
666C22⋊C8—614no—
667C22⋊C8—614no—
668#97—614no—
669C24—21no—
670C24—21no—
671C24—24no—
672C24—44no—
673C24—44no—
674C24—82no—
675C24—1221no—
676C24—1221no—
677C24C2×C22⋊D6111yescharacteristic
678C24C2×C22⋊D6111yescharacteristic
679#41—28no—
680#41—44no—
681#41—48no—
682#41—1228no—
683#41—1228no—
684#41—2444no—
685#41—2444no—
686#41—2448no—
687#41—2448no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—22no—
691C2×Q8—614no—
692C2×Q8—612no—
693C2×Q8—1221no—
694C2×Q8—1222no—
695C2×Q8C23×D6112yes—
696C2×D4—28no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—21no—
701C2×D4—24no—
702C2×D4—21no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—44no—
706C2×D4—48no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—82no—
711C2×D4—612no—
712C2×D4—612no—
713C2×D4—1224no—
714C2×D4—1224no—
715C2×D4—1224no—
716C2×D4—1224no—
717C2×D4—1222no—
718C2×D4—1222no—
719C2×D4—1224no—
720C2×D4—1224no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1222no—
724C2×D4—1222no—
725C2×D4—4882no—
726C2×D4—4882no—
727C2×D4—4882no—
728C2×D4—2444no—
729C2×D4—2444no—
730C2×D4—2444no—
731C2×D4D4×D6114yes—
732C2×D4C2×C22⋊D6114yes—
733C2×D4C23×D6112yes—
734C2×D4C23×D6112yes—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—44no—
744C22×C4—82no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1224no—
748C22×C4—1224no—
749C22×C4—2444no—
750C22×C4—2444no—
751C22×C4C2×C22⋊D6112yes—
752C22×C4C2×C22⋊D6112yes—
753C22×C4C2×C22⋊D6111yescharacteristic
754C22×C4C2×C22⋊D6111yescharacteristic
755C22×C4C2×C22⋊D6111yescharacteristic
756C22×C4C2×C22⋊D6111yescharacteristic
757C22×C4C23×D6112yes—
758C22×C4C23×D6112yes—
759C22×C4C23×D6111yescharacteristic
760Q16—1228no—
761SD16—6116no—
762SD16—1228no—
763SD16—1228no—
764SD16—2444no—
765D8—1228no—
766D8—1228no—
767D8—1228no—
768D8—2444no—
769M16—1228no—
770C2×C8—614no—
771C2×C8—612no—
772C2×C8—612no—
773C2×C8—612no—
774C2×C8—612no—
775C2×C8—1228no—
776C2×C8—1222no—
777C2×C8—1222no—
778C2×C8—1222no—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—612no—
782C4⋊C4—1221no—
783C4⋊C4—1224no—
784C4⋊C4C2×C22⋊D6114yes—
785C4⋊C4C23×D6112yes—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—1224no—
792C22⋊C4—1224no—
793C22⋊C4C2×C22⋊D6114yes—
794C22⋊C4C2×C22⋊D6114yes—
795C42—1224no—
796C42C2×C22⋊D6112yes—
797C42C23×D6112yes—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—24no—
806C23—22no—
807C23—48no—
808C23—48no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—84no—
815C23—816no—
816C23—1222no—
817C23—1222no—
818C23—2442no—
819C23—2442no—
820C23—2442no—
821C23—2442no—
822C23—2442no—
823C23—2442no—
824C23C22×C22⋊D6112yes—
825C23C22×C22⋊D6112yes—
826C23C22×C22⋊D6111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—42no—
830Q8—614no—
831Q8—1222no—
832Q8—1224no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—24no—
837D4—44no—
838D4—48no—
839D4—48no—
840D4—42no—
841D4—84no—
842D4—1222no—
843D4—1222no—
844D4—1222no—
845D4—1222no—
846D4—4884no—
847D4—4884no—
848D4—4884no—
849D4—2448no—
850D4—2448no—
851D4—2448no—
852D4—2442no—
853D4—2442no—
854D4C2×D4×D6114yes—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—48no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—84no—
871C2×C4—1222no—
872C2×C4—1224no—
873C2×C4—1222no—
874C2×C4—2448no—
875C2×C4—2448no—
876C2×C4—2442no—
877C2×C4C2×D4×D6112yes—
878C2×C4C22×C22⋊D6112yes—
879C2×C4C22×C22⋊D6112yes—
880C2×C4C22×C22⋊D6112yes—
881C2×C4C22×C22⋊D6112yes—
882C2×C4C22×C22⋊D6111yescharacteristic
883C2×C4#1451982212yes—
884C2×C4C24×D6111yescharacteristic
885C8—614no—
886C8—1222no—
887C8—1222no—
888C8—1222no—
889C22—22no—
890C22—22no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—42no—
897C22—42no—
898C22—44no—
899C22—44no—
900C22—48no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—816no—
905C22—84no—
906C22—4884no—
907C22—4884no—
908C22—2442no—
909C22—2442no—
910C22—2442no—
911C22—2442no—
912C22—2442no—
913C22—2442no—
914C22D4×C22⋊D6112yes—
915C22#1684056012yes—
916C22#1684056512yes—
917C22C23×C22⋊D6111yescharacteristic
918C4—22no—
919C4—22no—
920C4—22no—
921C4—22no—
922C4—42no—
923C4—42no—
924C4—1224no—
925C4—2442no—
926C4D4×C22⋊D6112yes—
927C4C22×D4×D6111yescharacteristic
928C4C2×#1451982211yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—4882no—
934C2—4882no—
935C2#2145735514yesdirect product factor
936C2C2×D4×C22⋊D6111yescharacteristic
937C2C2×#1684056011yescharacteristic
938C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61C2×#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C22×#14519803C2semidirect
2. C22×#14519797C2semidirect
3. C2×#16840433C2semidirect
4. #21457355C2direct (N × H)
5. C2×#16840152C2semidirect
6. C2×#16840010C2semidirect
7. C2×#16839996C2semidirect
8. C2×#16839981C2semidirect
9. C2×#16839957C2semidirect
10. C2×#16839922C2semidirect
11. C2×#16839907C2semidirect
12. C2×#16839905C2semidirect
13. C2×#16839896C2semidirect
14. C2×#16839862C2semidirect
15. C2×#16839834C2semidirect
16. C2×C61×#546C2semidirect
18. C22×#11758222C22semidirect
20. C2×#14519803C22semidirect
22. C2×#14519797C22semidirect
23. C22×#11758202C22semidirect
26. C22×#11758201C22semidirect
27. C22×#11758201C22semidirect
33. C23×#92418C22semidirect
35. #16840433C22semidirect
36. C2×#14519774C22semidirect
39. C2×#14519751C22semidirect
42. C2×C4×Dic122C22semidirect
44. #16840152C22semidirect
45. #16840010C22semidirect
46. #16839996C22semidirect
47. #16839981C22semidirect
48. #16839957C22semidirect
49. #16839922C22semidirect
50. #16839907C22semidirect
51. #16839905C22semidirect
52. #16839896C22semidirect
53. #16839862C22semidirect
54. #16839834C22semidirect
55. C2×#14519710C22semidirect
56. C2×C4⋊#92418C22semidirect
57. C2×#14519701C22semidirect
58. C2×#14519700C22semidirect
61. C2×#14519697C22semidirect
62. C2×#14519697C22semidirect
64. C2×C22⋊#92418C22semidirect
65. C2×#14519688C22semidirect
69. C61×#546C22semidirect
86. C2×#11758222C23semidirect
101. C2×#11758202C23semidirect
103. C2×#11758200D4semidirect
108. C2×#11758201C23semidirect
109. C2×#11758201C23semidirect
125. C22×#92418C23semidirect
127. #14519774C23semidirect
132. #14519751C23semidirect
136. C4×Dic122C23semidirect
143. #14519710C23semidirect
144. C4⋊#92418C23semidirect
145. #14519701C23semidirect
146. #14519700C23semidirect
149. #14519697C23semidirect
150. #14519697C23semidirect
152. C22⋊#92418C23semidirect
153. #14519688C23semidirect
307. #11758200C2×D4semidirect
463. C2×#546D61semidirect
480. C2×C61#3268semidirect
508. #546C2×D61semidirect
548. C61C2×#3268semidirect
935. C2#21457355direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198032
C22×#145197972
C2×#168404332
#214573552
C2×#168401522
C2×#168400102
C2×#168399962
C2×#168399812
C2×#168399572
C2×#168399222
C2×#168399072
C2×#168399052
C2×#168398962
C2×#168398622
C2×#168398342
C2×C61×#5462
C2×#326861