Finite Group Databasebeta

← C2×#21457405 #30555075

Subgroups — C2×#21457405 #30555075

Order 15616.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic, complemented
2C22×#14519797C211yesmaximal, characteristic, complemented
3C2×#16840433C211yesmaximal, characteristic, complemented
4#21457405C2116yesmaximal, direct product factor
5C2×#16840152C211yesmaximal, characteristic, complemented
6C2×#16840013C211yesmaximal, characteristic, complemented
7C2×#16839993C211yesmaximal, characteristic, complemented
8C2×#16839981C211yesmaximal, characteristic, complemented
9C2×#16839962C211yesmaximal, characteristic, complemented
10C2×#16839922C211yesmaximal, characteristic, complemented
11C2×#16839907C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic, complemented
13C2×#16839901C211yesmaximal, characteristic, complemented
14C2×#16839867C211yesmaximal, characteristic, complemented
15C2×#16839834C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C2×#14519808—28no—
20C2×#14519808C2218yescomplemented
21C2×#14519797—28no—
22C2×#14519797C2218yescomplemented
23C22×#11758202C2211yescharacteristic
24C22×#11758202C2211yescharacteristic
25C22×#11758200C2211yescharacteristic
26C22×#11758201C2211yescharacteristic
27C22×#11758201C2211yescharacteristic
28C22×#11758201C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758194C2211yescharacteristic
33C23×#92418C2211yescharacteristic
34#16840433—24no—
35#16840433C2218yescomplemented
36C2×#14519774C2211yescharacteristic
37C2×#14519773—21no—
38C2×#14519751C2211yescharacteristic
39C2×#14519751C2211yescharacteristic
40C2×#14519750—21no—
41C2×#14519750—21no—
42C2×C4×Dic122C2211yescharacteristic
43C2×#14519739—21no—
44#16840152C2218yescomplemented
45#16840013C2218yescomplemented
46#16839993C2218yescomplemented
47#16839981C2218yescomplemented
48#16839962C2218yescomplemented
49#16839922C2218yescomplemented
50#16839907C2218yescomplemented
51#16839905C2218yescomplemented
52#16839901C2218yescomplemented
53#16839867C2218yescomplemented
54#16839834C2218yescomplemented
55C2×#14519708C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519701C2211yescharacteristic
59C2×#14519700C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×#14519697C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×C22⋊#92418C2211yescharacteristic
64C2×C22⋊#92418C2211yescharacteristic
65C2×#14519688C2211yescharacteristic
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—22no—
81C2×#11758222—24no—
82C2×#11758222—24no—
83C2×#11758222—42no—
84C2×#11758222—42no—
85C2×#11758222C2314yes—
86C2×#11758222C2314yes—
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#14519808—232no—
99#14519797—232no—
100C2×#11758202—24no—
101C2×#11758202D418yescomplemented
102C2×#11758202C2314yes—
103C2×#11758202C2314yes—
104C2×#11758200—24no—
105C2×#11758200C2314yes—
106C2×#11758201—24no—
107C2×#11758201—24no—
108C2×#11758201—24no—
109C2×#11758201—42no—
110C2×#11758201C2314yes—
111C2×#11758201C2314yes—
112C2×#11758201C2314yes—
113C2×#11758201C2314yes—
114C2×#11758199—24no—
115C2×#11758199—42no—
116C2×#11758199C2314yes—
117C2×#11758199C2314yes—
118C2×#11758194—24no—
119C2×#11758194C2314yes—
120C22×#92418—24no—
121C22×#92418C2311yescharacteristic
122C22×#92418C2311yescharacteristic
123C22×#92418C2311yescharacteristic
124C22×#92418C2314yes—
125C22×#92418C2311yescharacteristic
126#14519774—22no—
127#14519774C2314yes—
128#14519773—28no—
129#14519751—22no—
130#14519751—22no—
131#14519751C2314yes—
132#14519751C2314yes—
133#14519750—28no—
134#14519750—28no—
135C4×Dic122—22no—
136C4×Dic122C2314yes—
137#14519739—28no—
138C2×C4⋊Dic61C2311yescharacteristic
139C2×#11758196—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×C4×Dic61—21no—
143#14519708C2314yes—
144C4⋊#92418C2314yes—
145#14519701C2314yes—
146#14519701C2314yes—
147#14519700C2314yes—
148#14519698C2314yes—
149#14519697C2314yes—
150#14519697C2314yes—
151C22⋊#92418C2314yes—
152C22⋊#92418C2314yes—
153#14519688C2314yes—
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—
203C23×D61—21no—
204#41×C61—28no—
205#41×C61—44no—
206#41×C61—48no—
207C2×Q8×C61—21no—
208C2×Q8×C61—24no—
209C2×Q8×C61—21no—
210C2×Q8×C61—22no—
211C2×Q8×C61—28no—
212C2×Q8×C61—22no—
213C2×Q8×C61—22no—
214C2×Q8×C61—44no—
215C2×Q8×C61—44no—
216C2×Q8×C61—48no—
217C2×Q8×C61C2×D414yes—
218C2×Q8×C61C2412yes—
219C2×Q8×C61C2412yes—
220C2×D4×C61—24no—
221C2×D4×C61—24no—
222C2×D4×C61—22no—
223C2×D4×C61—21no—
224C2×D4×C61—22no—
225C2×D4×C61—42no—
226C2×D4×C61—44no—
227C2×D4×C61—44no—
228C2×D4×C61C2×D414yes—
229C2×D4×C61C2412yes—
230C22×C4×C61—21no—
231C22×C4×C61—22no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—24no—
238C22×C4×C61—24no—
239C22×C4×C61—44no—
240C22×C4×C61—44no—
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2412yes—
248C22×C4×C61C2412yes—
249C22×C4×C61C2411yescharacteristic
250C2×C22⋊D61—24no—
251C2×C22⋊D61—24no—
252C2×C22⋊D61—24no—
253C2×C22⋊D61—24no—
254C2×C22⋊D61—44no—
255C2×C22⋊D61—44no—
256C2×C22⋊D61—82no—
257C2×C22⋊D61—82no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260#11758222—28no—
261#11758222—28no—
262#11758222—44no—
263#11758222—44no—
264#11758222—48no—
265#11758222—48no—
266C2×D244—22no—
267C2×D244—22no—
268C2×D244—22no—
269C2×D244—22no—
270C2×D244—24no—
271C2×D244—21no—
272C2×D244—21no—
273C2×D244—24no—
274C2×D244—44no—
275C2×D244—82no—
276C2×D244C2412yes—
277C2×D244C2412yes—
278C2×C4×D61—24no—
279C2×C4×D61—24no—
280C2×C4×D61—44no—
281C2×C4×D61—44no—
282C2×Dic122—21no—
283C2×Dic122—22no—
284C2×Dic122C2×D414yes—
285C2×Dic122C2412yes—
286C4⋊C4×C61—24no—
287C4⋊C4×C61—24no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61C2×D414yes—
290C4⋊C4×C61C2412yes—
291C22⋊C4×C61—24no—
292C22⋊C4×C61—24no—
293C22⋊C4×C61—24no—
294C22⋊C4×C61—24no—
295C22⋊C4×C61C2×D414yes—
296C22⋊C4×C61C2×D414yes—
297C42×C61—24no—
298C42×C61C2×D412yes—
299C42×C61C2412yes—
300#11758202—28no—
301#11758202C2×D4116yescomplemented
302#11758201—28no—
303#11758201—28no—
304#11758201—28no—
305#11758201—44no—
306#11758200—28no—
307#11758199—28no—
308#11758199—44no—
309#11758198—24no—
310#11758198—24no—
311C4⋊Dic61—21no—
312C4⋊Dic61C2412yes—
313#11758196—24no—
314C4×Dic61—24no—
315#11758194—28no—
316C2×#92418—22no—
317C2×#92418—22no—
318C2×#92418—22no—
319C2×#92418—28no—
320C2×#92418C2×D414yes—
321C2×#92418C2412yes—
322C2×#92418C2412yes—
323C2×#92418C2412yes—
324C2×#92418C2412yes—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—42no—
333C23×C61—42no—
334C23×C61—42no—
335C23×C61C22×D412yes—
336C23×C61C22×D412yes—
337C23×C61C22×D411yescharacteristic
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—42no—
346Q8×C61—24no—
347Q8×C61—22no—
348Q8×C61—22no—
349Q8×C61—22no—
350Q8×C61—48no—
351Q8×C61—42no—
352Q8×C61C22×D414yes—
353D4×C61—22no—
354D4×C61—22no—
355D4×C61—44no—
356D4×C61—48no—
357D4×C61—48no—
358D4×C61—42no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—24no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—24no—
366C2×C4×C61—24no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—48no—
374C2×C4×C61—48no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61C22×D412yes—
378C2×C4×C61C22×D412yes—
379C2×C4×C61C22×D412yes—
380C2×C4×C61C22×D412yes—
381C2×C4×C61C22×D411yescharacteristic
382C2×C4×C61C22×D412yes—
383C2×C4×C61H(5,𝔽2)12yes—
384C2×C4×C61C2511yescharacteristic
385C22⋊D61—48no—
386C22⋊D61—48no—
387C22⋊D61—84no—
388C22⋊D61—84no—
389C2×Dic61—24no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—42no—
393D244—22no—
394D244—22no—
395D244—22no—
396D244—22no—
397D244—48no—
398D244—42no—
399D244—42no—
400D244—84no—
401C4×D61—48no—
402C4×D61—48no—
403Dic122—24no—
404Dic122—22no—
405Dic122C22×D414yes—
406#92418—22no—
407#92418—22no—
408#92418—22no—
409#92418C22×D414yes—
410C2×#3271—611nomaximal, Sylow
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—44no—
418C22×C61—44no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—84no—
423C22×C61D4212yes—
424C22×C61#57512yes—
425C22×C61#57712yes—
426C22×C61C23×D411yescharacteristic
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—84no—
434C2×D61—84no—
435C4×C61—22no—
436C4×C61—22no—
437C4×C61—24no—
438C4×C61—22no—
439C4×C61—22no—
440C4×C61—42no—
441C4×C61—42no—
442C4×C61D4212yes—
443C4×C61C23×D411yescharacteristic
444C4×C61C2×H(5,𝔽2)11yescharacteristic
445Dic61—24no—
446Dic61—42no—
447C22×#137—611no—
448C22×#135—611no—
449C2×#550—611no—
450C2×#548D6111yescharacteristic, complemented
451#3271—6116no—
452C2×#496—611no—
453C2×#469—611no—
454C2×#465—611no—
455C2×#464—611no—
456C2×#460—611no—
457C2×#452—611no—
458C2×#449—611no—
459C2×#449—611no—
460C2×#448—611no—
461C2×#441—611no—
462C2×#435—611no—
463C2×C61—42no—
464C2×C61—42no—
465C2×C61—82no—
466C2×C61#327114yescomplemented
467C2×C61C2×D4211yescharacteristic
468C2×C61C2×#57511yescharacteristic
469C2×C61C2×#57711yescharacteristic
470D61—82no—
471D61—82no—
472C22×#41—611no—
473C22×#41—611no—
474C22×#41C2×D6111yescharacteristic
475C23×Q8C2×D6111yescharacteristic
476C2×#137—618no—
477C2×#137—1228no—
478C2×#135—618no—
479C2×#135—1228no—
480C22×Q16—611no—
481C22×Q16—611no—
482C22×SD16—611no—
483C22×SD16—611no—
484C22×SD16—611no—
485C22×SD16—611no—
486C22×SD16—611no—
487C22×D8—611no—
488C22×D8—611no—
489C22×M16—611no—
490C23×C8—611no—
491#550—618no—
492#550—1224no—
493#548—24no—
494#548C2×D6118yescomplemented
495C2×#127—611no—
496C2×#127—1221no—
497C2×#124—21no—
498C2×#124C2×D6111yescharacteristic
499C2×C22⋊Q8—21no—
500C2×C22⋊Q8C2×D6111yescharacteristic
501C2×#121—21no—
502C2×#121—611no—
503C2×#121—611no—
504C2×#121—1221no—
505C2×#121—1221no—
506C2×#121C2×D6111yescharacteristic
507C2×C4×Q8—611no—
508C2×C4×Q8C2×D6111yescharacteristic
509C2×C4×D4—21no—
510C2×C4×D4—1221no—
511C2×C4×D4C2×D6111yescharacteristic
512#496—618no—
513#469—618no—
514#465—618no—
515#464—618no—
516#460—618no—
517#452—618no—
518#449—618no—
519#449—618no—
520#448—618no—
521#441—618no—
522#435—618no—
523C2×#106—611no—
524C2×C4⋊C8—611no—
525C2×#103—611no—
526C2×#103—611no—
527C2×#103—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—611no—
531C2×C22⋊C8—611no—
532C2×C22⋊C8—611no—
533C2×#97—611no—
534C61C2×#327111yescharacteristic, complemented, Sylow
535C2×#41—22no—
536C2×#41—24no—
537C2×#41—42no—
538C2×#41—614no—
539C2×#41—614no—
540C2×#41—1224no—
541C2×#41—1224no—
542C2×#41—1222no—
543C2×#41—1222no—
544C2×#41—2442no—
545C2×#41—2442no—
546C2×#41C22×D6114yes—
547C22×Q8—21no—
548C22×Q8—22no—
549C22×Q8—24no—
550C22×Q8—42no—
551C22×Q8—611no—
552C22×Q8C22×D6111yescharacteristic
553C22×Q8C22×D6114yes—
554C22×Q8C22×D6111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—611no—
558C22×D4—611no—
559C22×D4—1221no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—1221no—
564C22×D4—1221no—
565C22×D4C22⋊D6111yescharacteristic
566C22×D4C22×D6111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—1221no—
570C23×C4—1221no—
571C23×C4C22×D6111yescharacteristic
572C23×C4C22×D6111yescharacteristic
573#137—12232no—
574#135—12232no—
575C2×Q16—618no—
576C2×Q16—614no—
577C2×Q16—614no—
578C2×Q16—1224no—
579C2×SD16—614no—
580C2×SD16—614no—
581C2×SD16—614no—
582C2×SD16—614no—
583C2×SD16—614no—
584C2×SD16—1224no—
585C2×SD16—1224no—
586C2×SD16—1224no—
587C2×SD16—1224no—
588C2×SD16—2442no—
589C2×D8—614no—
590C2×D8—614no—
591C2×D8—1224no—
592C2×D8—2442no—
593C2×M16—614no—
594C2×M16—1224no—
595C22×C8—611no—
596C22×C8—611no—
597C22×C8—614no—
598C22×C8—611no—
599C22×C8—611no—
600C22×C8—1224no—
601#127—614no—
602#127—1228no—
603#127—1222no—
604#124—28no—
605#124—22no—
606#124C22×D6114yes—
607C22⋊Q8—22no—
608C22⋊Q8—28no—
609C22⋊Q8C22×D6114yes—
610#121—28no—
611#121—22no—
612#121—614no—
613#121—614no—
614#121—1222no—
615#121—1222no—
616#121—1228no—
617#121—1228no—
618#121C22×D6114yes—
619C4×Q8—22no—
620C4×Q8—614no—
621C4×Q8—1222no—
622C4×Q8C22×D6114yes—
623C4×D4—28no—
624C4×D4—1228no—
625C4×D4C22⋊D6114yes—
626C4×D4C22×D6114yes—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4C22⋊D6111yescharacteristic
632C2×C4⋊C4C22×D6111yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4C22⋊D6111yescharacteristic
640C2×C22⋊C4C22⋊D6111yescharacteristic
641C2×C42—21no—
642C2×C42—1221no—
643C2×C42C22×D6111yescharacteristic
644#106—614no—
645C4⋊C8—614no—
646#103—614no—
647#103—614no—
648#103—614no—
649#102—614no—
650#102—614no—
651#102—614no—
652C22⋊C8—614no—
653C22⋊C8—614no—
654#97—614no—
655C24—21no—
656C24—1221no—
657C24—1221no—
658C24C2×C22⋊D6111yescharacteristic
659C24C2×C22⋊D6111yescharacteristic
660#41—28no—
661#41—44no—
662#41—48no—
663#41—1228no—
664#41—1228no—
665#41—2444no—
666#41—2444no—
667#41—2448no—
668#41—2448no—
669C2×Q8—21no—
670C2×Q8—24no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—28no—
674C2×Q8—22no—
675C2×Q8—22no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—48no—
679C2×Q8—614no—
680C2×Q8—612no—
681C2×Q8—1221no—
682C2×Q8—1222no—
683C2×Q8D4×D6114yes—
684C2×Q8C23×D6112yes—
685C2×Q8C23×D6112yes—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—42no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—612no—
695C2×D4—612no—
696C2×D4—1224no—
697C2×D4—1224no—
698C2×D4—1224no—
699C2×D4—1224no—
700C2×D4—1222no—
701C2×D4—1222no—
702C2×D4—1224no—
703C2×D4—1224no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1222no—
707C2×D4—1222no—
708C2×D4—4882no—
709C2×D4—4882no—
710C2×D4—4882no—
711C2×D4—2444no—
712C2×D4—2444no—
713C2×D4—2444no—
714C2×D4C2×C22⋊D6114yes—
715C2×D4C23×D6112yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1224no—
730C22×C4—1224no—
731C22×C4—2444no—
732C22×C4—2444no—
733C22×C4C2×C22⋊D6112yes—
734C22×C4C2×C22⋊D6112yes—
735C22×C4C2×C22⋊D6111yescharacteristic
736C22×C4C2×C22⋊D6111yescharacteristic
737C22×C4C2×C22⋊D6111yescharacteristic
738C22×C4C2×C22⋊D6111yescharacteristic
739C22×C4C23×D6112yes—
740C22×C4C23×D6112yes—
741C22×C4C23×D6111yescharacteristic
742Q16—6116no—
743Q16—1228no—
744SD16—1228no—
745SD16—1228no—
746SD16—1228no—
747SD16—1228no—
748SD16—2444no—
749D8—1228no—
750D8—2444no—
751M16—1228no—
752C2×C8—614no—
753C2×C8—612no—
754C2×C8—612no—
755C2×C8—612no—
756C2×C8—612no—
757C2×C8—1228no—
758C2×C8—1222no—
759C2×C8—1222no—
760C2×C8—1222no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—612no—
765C4⋊C4—1221no—
766C4⋊C4—1224no—
767C4⋊C4C2×C22⋊D6114yes—
768C4⋊C4C23×D6112yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—1224no—
774C22⋊C4—1224no—
775C22⋊C4C2×C22⋊D6114yes—
776C22⋊C4C2×C22⋊D6114yes—
777C42—24no—
778C42—1224no—
779C42C2×C22⋊D6112yes—
780C42C23×D6112yes—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—1222no—
792C23—1222no—
793C23—2442no—
794C23—2442no—
795C23—2442no—
796C23—2442no—
797C23—2442no—
798C23—2442no—
799C23C22×C22⋊D6112yes—
800C23C22×C22⋊D6112yes—
801C23C22×C22⋊D6111yescharacteristic
802Q8—22no—
803Q8—24no—
804Q8—22no—
805Q8—22no—
806Q8—48no—
807Q8—42no—
808Q8—614no—
809Q8—1222no—
810Q8—1224no—
811Q8C2×D4×D6114yes—
812D4—22no—
813D4—22no—
814D4—44no—
815D4—48no—
816D4—48no—
817D4—42no—
818D4—1222no—
819D4—1222no—
820D4—1222no—
821D4—1222no—
822D4—4884no—
823D4—4884no—
824D4—4884no—
825D4—2448no—
826D4—2448no—
827D4—2448no—
828D4—2442no—
829D4—2442no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—48no—
845C2×C4—48no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—1222no—
849C2×C4—1224no—
850C2×C4—1222no—
851C2×C4—2448no—
852C2×C4—2448no—
853C2×C4—2442no—
854C2×C4C2×D4×D6112yes—
855C2×C4C22×C22⋊D6112yes—
856C2×C4C22×C22⋊D6112yes—
857C2×C4C22×C22⋊D6112yes—
858C2×C4C22×C22⋊D6112yes—
859C2×C4C22×C22⋊D6111yescharacteristic
860C2×C4#1451982212yes—
861C2×C4C24×D6111yescharacteristic
862C8—614no—
863C8—1222no—
864C8—1222no—
865C8—1222no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—44no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—84no—
878C22—4884no—
879C22—4884no—
880C22—2442no—
881C22—2442no—
882C22—2442no—
883C22—2442no—
884C22—2442no—
885C22—2442no—
886C22D4×C22⋊D6112yes—
887C22#1684056012yes—
888C22#1684057012yes—
889C22C23×C22⋊D6111yescharacteristic
890C4—22no—
891C4—22no—
892C4—24no—
893C4—22no—
894C4—22no—
895C4—42no—
896C4—42no—
897C4—1224no—
898C4—2442no—
899C4D4×C22⋊D6112yes—
900C4C22×D4×D6111yescharacteristic
901C4C2×#1451982211yescharacteristic
902C2—42no—
903C2—42no—
904C2—82no—
905C2—4882no—
906C2—4882no—
907C2#2145740514yesdirect product factor
908C2C2×D4×C22⋊D6111yescharacteristic
909C2C2×#1684056011yescharacteristic
910C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61C2×#3271
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×#14519797C2semidirect
3. C2×#16840433C2semidirect
4. #21457405C2direct (N × H)
5. C2×#16840152C2semidirect
6. C2×#16840013C2semidirect
7. C2×#16839993C2semidirect
8. C2×#16839981C2semidirect
9. C2×#16839962C2semidirect
10. C2×#16839922C2semidirect
11. C2×#16839907C2semidirect
12. C2×#16839905C2semidirect
13. C2×#16839901C2semidirect
14. C2×#16839867C2semidirect
15. C2×#16839834C2semidirect
16. C2×C61×#548C2semidirect
20. C2×#14519808C22semidirect
22. C2×#14519797C22semidirect
35. #16840433C22semidirect
44. #16840152C22semidirect
45. #16840013C22semidirect
46. #16839993C22semidirect
47. #16839981C22semidirect
48. #16839962C22semidirect
49. #16839922C22semidirect
50. #16839907C22semidirect
51. #16839905C22semidirect
52. #16839901C22semidirect
53. #16839867C22semidirect
54. #16839834C22semidirect
69. C61×#548C22semidirect
101. C2×#11758202D4semidirect
301. #11758202C2×D4semidirect
450. C2×#548D61semidirect
466. C2×C61#3271semidirect
494. #548C2×D61semidirect
534. C61C2×#3271semidirect
907. C2#21457405direct (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×#145197972
C2×#168404332
#214574052
C2×#168401522
C2×#168400132
C2×#168399932
C2×#168399812
C2×#168399622
C2×#168399222
C2×#168399072
C2×#168399052
C2×#168399012
C2×#168398672
C2×#168398342
C2×C61×#5482
C2×#327161