Finite Group Databasebeta

← #30620207

Subgroups — #30620207

Order 15616.

1434 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840801C211yesmaximal, characteristic, complemented
2C2×SD16×#6923C211yesmaximal, characteristic, complemented
3Q8×C22⋊#6923C211yesmaximal, characteristic, complemented
4#21462322C211yesmaximal, characteristic
5#21461967C211yesmaximal, characteristic, complemented
6#21461965C211yesmaximal, characteristic, complemented
7#21461813C211yesmaximal, characteristic, complemented
8#21461813C211yesmaximal, characteristic, complemented
9#21461812C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461697C211yesmaximal, characteristic, complemented
12#21461659C211yesmaximal, characteristic
13#21461658C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15C2×#137×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840801—24no—
21SD16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32D61⋊(C22⋊C8)C2211yescharacteristic
33C2×#14519831C2211yescharacteristic
34C2×C8×#6923C2211yescharacteristic
35(C2×#6923)⋊Q8—21no—
36(C2×#6923)⋊Q8—21no—
37(C2×#6923)⋊Q8C2211yescharacteristic
38(C2×#6923)⋊Q8C2211yescharacteristic
39(C2×#6923)⋊Q8C2211yescharacteristic
40(C2×#6923)⋊Q8C2211yescharacteristic
41#16840710—21no—
42#16840710—21no—
43#16840705—21no—
44#16840704—21no—
45#16840704C2211yescharacteristic
46#16840704C2211yescharacteristic
47C4×C22⋊#6923—21no—
48C4×C22⋊#6923C2211yescharacteristic
49C2×(C2×#6923)⋊C4—21no—
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C22×Q8×D61C2211yescharacteristic
56C2×#14519810C411yescharacteristic, complemented
57C2×#14519809C411yescharacteristic, complemented
58C2×#14519809C411yescharacteristic, complemented
59C2×#14519808C411yescharacteristic, complemented
60C2×#14519807C411yescharacteristic, complemented
61C2×#14519806C411yescharacteristic, complemented
62C2×#14519806C411yescharacteristic, complemented
63#137×D61—24no—
64#137×D61—24no—
65C2×Q16×D61C2211yescharacteristic
66C2×Q16×D61C2211yescharacteristic
67C2×SD16×D61C2211yescharacteristic
68C2×SD16×D61C2211yescharacteristic
69C2×M16×D61C2211yescharacteristic
70C2×#137×C61C411yescharacteristic, complemented
71C23×#6923—21no—
72C23×#6923—21no—
73C2×D61⋊C8C2311yescharacteristic
74C2×D61⋊C8C2311yescharacteristic
75Q8×#6923—22no—
76Q8×#6923—22no—
77Q8×#6923—41no—
78Q8×#6923—41no—
79D4×#6923—22no—
80D4×#6923—22no—
81D4×#6923—41no—
82D4×#6923—41no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923D411yescharacteristic
94C2×C22⋊#6923D411yescharacteristic
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923C2311yescharacteristic
98C2×C4×#6923C2311yescharacteristic
99#14519846—22no—
100#14519845—22no—
101#14519840—22no—
102#14519840—22no—
103#14519840—41no—
104#14519840—41no—
105#14519840—41no—
106#14519840—41no—
107#14519839—22no—
108#14519839—22no—
109#14519834—21no—
110C22⋊#92420—21no—
111#14519831—22no—
112C8×#6923—22no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122(C2×#6923)⋊C4—21no—
123(C2×#6923)⋊C4D411yescharacteristic
124(C2×#6923)⋊C4D411yescharacteristic
125C2×#11758226C2×C411yescharacteristic
126C2×#11758222—21no—
127C2×#11758222C2×C411yescharacteristic
128C2×#11758224—21no—
129C2×#11758224C2×C411yescharacteristic
130#41×D61—22no—
131#41×D61—22no—
132#41×D61—41no—
133#41×D61—41no—
134C22×Dic122—21no—
135C22×Dic122C2×C411yescharacteristic, complemented
136C2×Q8×D61—21no—
137C2×Q8×D61—21no—
138C2×Q8×D61—22no—
139C2×Q8×D61—22no—
140C2×Q8×D61—41no—
141C2×Q8×D61—41no—
142C2×Q8×D61C2×C411yescharacteristic, complemented
143C2×Q8×D61C2×C411yescharacteristic, complemented
144C2×Q8×D61C2311yescharacteristic
145C2×Q8×D61C2311yescharacteristic
146C2×Q8×D61C2311yescharacteristic
147C2×D4×D61—21no—
148C2×D4×D61C2311yescharacteristic
149C22×C4×D61—21no—
150C22×C4×D61—21no—
151C22×C4×D61C2311yescharacteristic
152#14519810—24no—
153#14519809—24no—
154#14519809—24no—
155#14519808—24no—
156#14519807—24no—
157#14519806—24no—
158#14519806—24no—
159C2×Dic244C2×C411yescharacteristic, complemented
160C2×Dic244C2×C411yescharacteristic, complemented
161C2×#11758202C2×C411yescharacteristic, complemented
162C2×#11758202C2×C411yescharacteristic, complemented
163C2×#11758202C2×C411yescharacteristic, complemented
164C2×#11758202C2×C411yescharacteristic, complemented
165Q16×D61—22no—
166Q16×D61—22no—
167Q16×D61—22no—
168Q16×D61—22no—
169C2×#11758190C2×C411yescharacteristic
170C2×#11758190C2×C411yescharacteristic
171C2×#11758200C2×C411yescharacteristic
172C2×#11758200C2×C411yescharacteristic
173C2×#11758201C2×C411yescharacteristic
174C2×#11758201C2×C411yescharacteristic
175SD16×D61—22no—
176SD16×D61—22no—
177SD16×D61D414yes—
178SD16×D61D414yes—
179C2×#11758194C2×C411yescharacteristic, complemented
180C2×#11758189C2×C411yescharacteristic, complemented
181C2×#11758189C2×C411yescharacteristic, complemented
182M16×D61—22no—
183M16×D61—22no—
184C2×C8×D61C2311yescharacteristic
185C2×C8×D61C2311yescharacteristic
186C2×#41×C61C2×C411yescharacteristic
187C22×Q8×C61C2×C411yescharacteristic, complemented
188#137×C61—24no—
189C2×Q16×C61C2×C411yescharacteristic, complemented
190C2×Q16×C61C2×C411yescharacteristic, complemented
191C2×SD16×C61C2×C411yescharacteristic
192C2×SD16×C61C2×C411yescharacteristic
193C2×M16×C61C2×C411yescharacteristic, complemented
194C23×D61—21no—
195C23×D61C2×D411yescharacteristic
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—42no—
201C22×#6923—42no—
202C22×#6923—42no—
203C22×#6923—42no—
204C22×#6923—81no—
205C22×#6923—81no—
206C22×#6923C2×D411yescharacteristic
207C22×#6923C2×D411yescharacteristic
208C22×#6923C2×D411yescharacteristic
209C22×#6923C2×D411yescharacteristic
210#41×C61—22no—
211#41×C61—41no—
212C2×Q8×C61—21no—
213C2×Q8×C61—22no—
214C2×Q8×C61—41no—
215C2×Q8×C61C22×C411yescharacteristic
216C2×Q8×C61C22×C411yescharacteristic
217C2×Q8×C61C22×C411yescharacteristic
218C2×D4×C61—21no—
219C2×D4×C61C22×C411yescharacteristic
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61C22×C411yescharacteristic
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61#4111yescharacteristic
229#11758226—22no—
230#11758226—41no—
231Q8×D61—21no—
232Q8×D61—21no—
233Q8×D61—22no—
234Q8×D61—21no—
235Q8×D61—21no—
236Q8×D61—21no—
237Q8×D61—21no—
238Q8×D61—21no—
239Q8×D61—21no—
240Q8×D61—21no—
241Q8×D61—21no—
242Q8×D61—22no—
243Q8×D61—41no—
244Q8×D61—41no—
245Q8×D61—42no—
246Q8×D61—42no—
247Q8×D61—42no—
248Q8×D61—42no—
249Q8×D61C2×D412yes—
250Q8×D61C2×D412yes—
251#11758224—22no—
252#11758224—41no—
253#11758224—42no—
254#11758224—42no—
255D4×D61—21no—
256D4×D61—21no—
257D4×D61—42no—
258D4×D61—42no—
259D4×D61C2×D412yes—
260D4×D61C2×D412yes—
261#11758222—22no—
262#11758222—41no—
263#11758222—42no—
264#11758222—42no—
265C2×D244—21no—
266C2×D244C22×C411yescharacteristic
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—42no—
279C2×C4×D61—42no—
280C2×C4×D61—42no—
281C2×C4×D61—42no—
282C2×C4×D61C22×C411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×C4×D61#4111yescharacteristic
285C2×C4×D61C2411yescharacteristic
286C2×Dic122—21no—
287C2×Dic122—22no—
288C2×Dic122—21no—
289C2×Dic122—21no—
290C2×Dic122—21no—
291C2×Dic122—21no—
292C2×Dic122—21no—
293C2×Dic122—41no—
294C2×Dic122—42no—
295C2×Dic122—42no—
296C2×Dic122C22×C411yescharacteristic
297C2×Dic122C22×C411yescharacteristic
298C2×Dic122C22×C411yescharacteristic
299C22⋊#6923—22no—
300C22⋊#6923—41no—
301C22⋊#6923—42no—
302C22⋊#6923—42no—
303C22⋊#6923—42no—
304C22⋊#6923—81no—
305C2×#92420—21no—
306C2×#92420—21no—
307C4⋊#6923—21no—
308C4⋊#6923—21no—
309C4⋊#6923—21no—
310C4⋊#6923—21no—
311C4⋊#6923—21no—
312C4⋊#6923—21no—
313C4⋊#6923—21no—
314C4⋊#6923—21no—
315C4⋊#6923—42no—
316C4⋊#6923—42no—
317C4×#6923—21no—
318C4×#6923—21no—
319C4×#6923—21no—
320C4×#6923—21no—
321C4×#6923—42no—
322C4×#6923—42no—
323D61⋊C8—21no—
324D61⋊C8—21no—
325D61⋊C8—21no—
326D61⋊C8—21no—
327Q16×C61—22no—
328Q16×C61—22no—
329SD16×C61—22no—
330SD16×C61C22⋊C414yescomplemented
331M16×C61—22no—
332C2×C8×C61C22×C411yescharacteristic
333C2×C8×C61C22×C411yescharacteristic
334#11758202—22no—
335#11758202—22no—
336#11758202—22no—
337#11758202—22no—
338#11758201—22no—
339#11758201C22⋊C414yescomplemented
340#11758200—22no—
341#11758200C22⋊C414yescomplemented
342#11758194—22no—
343C2×#92418C22×C411yescharacteristic
344C2×#92418C22×C411yescharacteristic
345Dic244—22no—
346Dic244—22no—
347#11758190—22no—
348#11758190C22⋊C414yescomplemented
349#11758189—22no—
350#11758189—22no—
351C8×D61—21no—
352C8×D61—21no—
353C8×D61C2×D412yes—
354C8×D61C2×D412yes—
355C23×C61—21no—
356C23×C61C4×D411yescharacteristic
357C22×D61—21no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—21no—
361C22×D61—21no—
362C22×D61—21no—
363C22×D61—21no—
364C22×D61—21no—
365C22×D61—21no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61C4×D411yescharacteristic
371C22×D61C22×D411yescharacteristic
372C2×#6923—21no—
373C2×#6923—21no—
374C2×#6923—21no—
375C2×#6923—21no—
376C2×#6923—21no—
377C2×#6923—21no—
378C2×#6923—21no—
379C2×#6923—21no—
380C2×#6923—21no—
381C2×#6923—21no—
382C2×#6923—21no—
383C2×#6923—41no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—84no—
396C2×#6923—84no—
397C2×#6923#13712yescomplemented
398Q8×C61—21no—
399Q8×C61—21no—
400Q8×C61—21no—
401Q8×C61—21no—
402Q8×C61—21no—
403Q8×C61—42no—
404Q8×C61C2×C22⋊C412yes—
405D4×C61—21no—
406D4×C61—42no—
407D4×C61C2×C22⋊C412yes—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—42no—
414C2×C4×C61—42no—
415C2×C4×C61C4×D411yescharacteristic
416C2×C4×C61C23×C411yescharacteristic
417C22⋊D61—22no—
418C22⋊D61—22no—
419C22⋊D61—42no—
420C22⋊D61—42no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—42no—
427C2×Dic61—42no—
428C2×Dic61C4×D411yescharacteristic
429C2×Dic61C2×#4111yescharacteristic
430D244—21no—
431D244—42no—
432D244C2×C22⋊C412yes—
433C4×D61—22no—
434C4×D61—22no—
435C4×D61—21no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—21no—
439C4×D61—21no—
440C4×D61—21no—
441C4×D61—42no—
442C4×D61—42no—
443C4×D61—42no—
444C4×D61—42no—
445C4×D61—41no—
446C4×D61—41no—
447C4×D61—41no—
448C4×D61—41no—
449C4×D61C22×D411yescharacteristic
450C4×D61C22×D411yescharacteristic
451C4×D61H(5,𝔽2)11yescharacteristic
452C4×D61H(5,𝔽2)11yescharacteristic
453Dic122—21no—
454Dic122—22no—
455Dic122—22no—
456Dic122—21no—
457Dic122—21no—
458Dic122—21no—
459Dic122—21no—
460Dic122—42no—
461Dic122—42no—
462Dic122—42no—
463Dic122—41no—
464Dic122—41no—
465Dic122—41no—
466Dic122—41no—
467Dic122C2×C22⋊C412yes—
468#92420—41no—
469#92420—41no—
470C8×C61—21no—
471C8×C61C2×C22⋊C412yes—
472#92418—21no—
473#92418C2×C22⋊C412yes—
474#22444—611nomaximal, Sylow
475C22×C61—21no—
476C22×C61—22no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—41no—
480C22×C61—41no—
481C22×C61C2×C4×D411yescharacteristic
482C2×D61—21no—
483C2×D61—22no—
484C2×D61—21no—
485C2×D61—21no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—42no—
489C2×D61—41no—
490C2×D61—41no—
491C2×D61—42no—
492C2×D61—42no—
493C2×D61—41no—
494C2×D61—41no—
495C2×D61—42no—
496C2×D61D4211yescharacteristic
497C2×D61D4211yescharacteristic
498C2×D61C2×#13711yescharacteristic
499C2×D61#57511yescharacteristic
500C2×D61#57711yescharacteristic
501C2×D61#57811yescharacteristic
502#6923—22no—
503#6923—41no—
504#6923—41no—
505#6923—41no—
506#6923—81no—
507#6923—81no—
508#6923—81no—
509#6923—81no—
510C4×C61—22no—
511C4×C61—21no—
512C4×C61—41no—
513C4×C61—41no—
514C4×C61C22×C22⋊C411yescharacteristic
515C4×C61#51811yescharacteristic
516Dic61—22no—
517Dic61—21no—
518Dic61—41no—
519Dic61—41no—
520Dic61#54611yescharacteristic
521Dic61#54611yescharacteristic
522C22×#137—611no—
523C2×#440—611no—
524C2×C4×SD16—611no—
525Q8×C22⋊C4—611no—
526#2339—611no—
527#1971—611no—
528#1969—611no—
529#1878—611no—
530#1878—611no—
531#1877—611no—
532#1877—611no—
533#1809—611no—
534#1788—611no—
535#1787—611no—
536#1753—611no—
537C2×C61—41no—
538C2×C61—42no—
539C2×C61D4×C22⋊C411yescharacteristic
540C2×C61C4×#13711yescharacteristic
541C2×C61#294711yescharacteristic
542D61—41no—
543D61—42no—
544D61#326611yescharacteristic
545D61#326911yescharacteristic
546D61#327511yescharacteristic
547D61#327611yescharacteristic
548C22×#41—611no—
549C23×Q8—611no—
550C2×#137—611no—
551C2×#137—611no—
552C2×#137—611no—
553C2×#137—611no—
554C2×#137—611no—
555C2×#137—611no—
556C2×#137—611no—
557C2×#137—1224no—
558C2×#137—1224no—
559C2×#137#692311yescharacteristic, complemented
560C22×Q16—611no—
561C22×Q16—611no—
562C22×SD16—611no—
563C22×SD16—611no—
564C22×M16—611no—
565C2×C4×Q8—611no—
566C2×C4×Q8—611no—
567C2×C4×D4—611no—
568C2×C4×D4—611no—
569#440—1224no—
570C4×SD16—1224no—
571C2×#107—611no—
572C2×#106—611no—
573C2×#103—611no—
574C2×#103—611no—
575C2×#103—611no—
576C2×#103—611no—
577C2×#103—611no—
578C2×#103—611no—
579C2×#102—611no—
580C2×#102—611no—
581C2×C22⋊C8—611no—
582C2×#97—611no—
583C2×C4×C8—611no—
584#391—611no—
585#391—611no—
586#391—611no—
587#391—611no—
588#391—1221no—
589#391—1221no—
590#386—1221no—
591#386—1221no—
592#381—1221no—
593#380—611no—
594#380—611no—
595#380—1221no—
596C4×C22⋊C4—611no—
597C4×C22⋊C4—1221no—
598C2×#95—1221no—
599#340—611no—
600#340—611no—
601#336—611no—
602#336—611no—
603C61#2244411yescharacteristic, complemented, Sylow
604C2×#41—611no—
605C2×#41—611no—
606C2×#41—611no—
607C2×#41—1221no—
608C2×#41—1221no—
609C2×#41—1222no—
610C2×#41—1222no—
611C2×#41—2441no—
612C2×#41—2441no—
613C2×#41C2×#692311yescharacteristic
614C22×Q8—611no—
615C22×Q8—611no—
616C22×Q8—611no—
617C22×Q8—611no—
618C22×Q8—611no—
619C22×Q8—611no—
620C22×Q8—1221no—
621C22×Q8—1221no—
622C22×Q8—1221no—
623C22×Q8—1222no—
624C22×Q8—1222no—
625C22×Q8—2441no—
626C22×Q8—2441no—
627C22×Q8C2×#692311yescharacteristic, complemented
628C22×D4—611no—
629C22×D4—1221no—
630C23×C4—611no—
631C23×C4—1221no—
632C23×C4—1221no—
633C23×C4—1221no—
634C23×C4—1221no—
635#137—24no—
636#137—1224no—
637#137—1224no—
638#137—1224no—
639#137—1224no—
640#137—1224no—
641#137—1224no—
642#137—1224no—
643C2×Q16—611no—
644C2×Q16—611no—
645C2×Q16—611no—
646C2×Q16—611no—
647C2×Q16—611no—
648C2×Q16—611no—
649C2×Q16—1222no—
650C2×Q16—1222no—
651C2×Q16—1222no—
652C2×Q16—1222no—
653C2×Q16C2×#692311yescharacteristic, complemented
654C2×Q16C2×#692311yescharacteristic, complemented
655C2×SD16—611no—
656C2×SD16—611no—
657C2×SD16—614no—
658C2×SD16—614no—
659C2×SD16—611no—
660C2×SD16—611no—
661C2×SD16—611no—
662C2×SD16—611no—
663C2×SD16—1222no—
664C2×SD16—1222no—
665C2×SD16C2×#692311yescharacteristic
666C2×SD16C2×#692311yescharacteristic
667C2×M16—611no—
668C2×M16—611no—
669C2×M16—611no—
670C2×M16—1222no—
671C2×M16—1222no—
672C2×M16C2×#692311yescharacteristic, complemented
673C22×C8—611no—
674C22×C8—611no—
675C22×C8—611no—
676C22×C8—611no—
677C4×Q8—1222no—
678C4×Q8—1222no—
679C4×Q8—2441no—
680C4×Q8—2441no—
681C4×D4—1222no—
682C4×D4—1222no—
683C4×D4—2441no—
684C4×D4—2441no—
685C2×C4⋊C4—611no—
686C2×C4⋊C4—611no—
687C2×C4⋊C4—611no—
688C2×C4⋊C4—611no—
689C2×C4⋊C4—1221no—
690C2×C4⋊C4—1221no—
691C2×C22⋊C4—611no—
692C2×C22⋊C4—611no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C22⋊C4—1221no—
696C2×C22⋊C4—1221no—
697C2×C42—611no—
698C2×C42—611no—
699C2×C42—1221no—
700C2×C42—1221no—
701#107—1222no—
702#106—1222no—
703#103—1222no—
704#103—1222no—
705#103—2441no—
706#103—2441no—
707#103—2441no—
708#103—2441no—
709#102—1222no—
710#102—1222no—
711C22⋊C8—1221no—
712C22⋊C8—1221no—
713#97—1222no—
714C4×C8—1222no—
715#95—611no—
716#95—611no—
717#95—1221no—
718#95—1221no—
719#95—1221no—
720#95—1221no—
721#95—1221no—
722#95—1221no—
723#95—1221no—
724#95—1221no—
725#95—1221no—
726#95—1221no—
727C24—611no—
728C24—1221no—
729#41—22no—
730#41—41no—
731#41—1222no—
732#41—1222no—
733#41—1222no—
734#41—2441no—
735#41—2442no—
736#41—2442no—
737#41—2441no—
738#41—2442no—
739#41—2442no—
740#41—2441no—
741C2×Q8—21no—
742C2×Q8—22no—
743C2×Q8—41no—
744C2×Q8—612no—
745C2×Q8—612no—
746C2×Q8—611no—
747C2×Q8—611no—
748C2×Q8—611no—
749C2×Q8—1221no—
750C2×Q8—1221no—
751C2×Q8—1221no—
752C2×Q8—1221no—
753C2×Q8—1221no—
754C2×Q8—1222no—
755C2×Q8—1221no—
756C2×Q8—1221no—
757C2×Q8—1221no—
758C2×Q8—1221no—
759C2×Q8—1221no—
760C2×Q8—1221no—
761C2×Q8—1221no—
762C2×Q8—1221no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×Q8—1221no—
766C2×Q8—1222no—
767C2×Q8—1222no—
768C2×Q8—2441no—
769C2×Q8—2442no—
770C2×Q8—2442no—
771C2×Q8—2442no—
772C2×Q8—2442no—
773C2×Q8—2441no—
774C2×Q8—2441no—
775C2×Q8—2442no—
776C2×Q8—2442no—
777C2×Q8C22×#692311yescharacteristic
778C2×Q8C22×#692311yescharacteristic
779C2×Q8C22×#692311yescharacteristic
780C2×D4—21no—
781C2×D4—612no—
782C2×D4—612no—
783C2×D4—611no—
784C2×D4—1221no—
785C2×D4—1221no—
786C2×D4—1221no—
787C2×D4—1221no—
788C2×D4—1221no—
789C2×D4—1221no—
790C2×D4—2442no—
791C2×D4—2442no—
792C2×D4C22×#692311yescharacteristic
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—4881no—
822C22×C4—4881no—
823C22×C4—2442no—
824C22×C4—2442no—
825C22×C4—2442no—
826C22×C4—2442no—
827C22×C4—2442no—
828C22×C4—2442no—
829C22×C4—2442no—
830C22×C4—2442no—
831C22×C4C22×#692311yescharacteristic
832Q16—22no—
833Q16—22no—
834Q16—1222no—
835Q16—1222no—
836Q16—1222no—
837Q16—1222no—
838Q16—1222no—
839Q16—1222no—
840SD16—22no—
841SD16—614no—
842SD16—614no—
843SD16—614no—
844SD16—1222no—
845SD16—1222no—
846SD16—1222no—
847SD16C22⋊#692314yescomplemented
848M16—22no—
849M16—1222no—
850M16—1222no—
851M16—1222no—
852C2×C8—611no—
853C2×C8—612no—
854C2×C8—612no—
855C2×C8—611no—
856C2×C8—1221no—
857C2×C8—1221no—
858C2×C8—1221no—
859C2×C8—1221no—
860C2×C8—1221no—
861C2×C8—1221no—
862C2×C8—1221no—
863C2×C8—1221no—
864C2×C8C22×#692311yescharacteristic
865C2×C8C22×#692311yescharacteristic
866C4⋊C4—1221no—
867C4⋊C4—1221no—
868C4⋊C4—1221no—
869C4⋊C4—1221no—
870C4⋊C4—1221no—
871C4⋊C4—1221no—
872C4⋊C4—1221no—
873C4⋊C4—1221no—
874C4⋊C4—2442no—
875C4⋊C4—2442no—
876C22⋊C4—1222no—
877C22⋊C4—4881no—
878C22⋊C4—2441no—
879C22⋊C4—2442no—
880C22⋊C4—2442no—
881C22⋊C4—2442no—
882C42—1221no—
883C42—1221no—
884C42—1221no—
885C42—1221no—
886C42—2442no—
887C42—2442no—
888C23—21no—
889C23—611no—
890C23—611no—
891C23—1221no—
892C23—1221no—
893C23—1221no—
894C23—1222no—
895C23—1222no—
896C23—1221no—
897C23—1221no—
898C23—1221no—
899C23—1221no—
900C23—2441no—
901C23—2441no—
902C23—2441no—
903C23—2441no—
904C23D4×#692311yescharacteristic
905Q8—21no—
906Q8—21no—
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—42no—
911Q8—612no—
912Q8—1222no—
913Q8—1222no—
914Q8—1221no—
915Q8—1221no—
916Q8—1221no—
917Q8—1221no—
918Q8—1221no—
919Q8—2442no—
920Q8—2442no—
921Q8—2441no—
922Q8—2441no—
923Q8—2441no—
924Q8—2441no—
925Q8—2442no—
926Q8C2×C22⋊#692312yes—
927D4—21no—
928D4—42no—
929D4—612no—
930D4—1222no—
931D4—1222no—
932D4—1221no—
933D4—2442no—
934D4—2442no—
935D4—2442no—
936D4C2×C22⋊#692312yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—611no—
945C2×C4—611no—
946C2×C4—611no—
947C2×C4—611no—
948C2×C4—611no—
949C2×C4—612no—
950C2×C4—611no—
951C2×C4—1221no—
952C2×C4—1221no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1221no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—1221no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—4884no—
976C2×C4—4884no—
977C2×C4—2442no—
978C2×C4—2442no—
979C2×C4—2442no—
980C2×C4—2442no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2442no—
986C2×C4—2442no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4D4×#692311yescharacteristic
1000C2×C4C23×#692311yescharacteristic
1001C8—21no—
1002C8—612no—
1003C8—1221no—
1004C8—2441no—
1005C8—2441no—
1006C8C2×C22⋊#692312yes—
1007C22—21no—
1008C22—21no—
1009C22—22no—
1010C22—21no—
1011C22—41no—
1012C22—41no—
1013C22—611no—
1014C22—611no—
1015C22—611no—
1016C22—611no—
1017C22—611no—
1018C22—611no—
1019C22—1221no—
1020C22—1221no—
1021C22—1222no—
1022C22—1221no—
1023C22—2442no—
1024C22—2442no—
1025C22—2441no—
1026C22—2441no—
1027C22—2441no—
1028C22—2441no—
1029C22—2442no—
1030C22—2442no—
1031C22—2441no—
1032C22—2441no—
1033C22C2×D4×#692311yescharacteristic
1034C4—21no—
1035C4—22no—
1036C4—41no—
1037C4—41no—
1038C4—611no—
1039C4—611no—
1040C4—1222no—
1041C4—1221no—
1042C4—1222no—
1043C4—4881no—
1044C4—4881no—
1045C4—4881no—
1046C4—4881no—
1047C4—2441no—
1048C4—2441no—
1049C4—2441no—
1050C4—2441no—
1051C4—2441no—
1052C4C22×C22⋊#692311yescharacteristic
1053C4#1684082911yescharacteristic
1054C2—41no—
1055C2—42no—
1056C2—611no—
1057C2—611no—
1058C2—611no—
1059C2—611no—
1060C2—2441no—
1061C2—2442no—
1062C2D4×C22⋊#692311yescharacteristic
1063C2#137×#692311yescharacteristic
1064C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#137×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#137#6923
hypocenterC61#22444
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16840801C2semidirect
2. C2×SD16×#6923C2semidirect
3. Q8×C22⋊#6923C2semidirect
5. #21461967C2semidirect
6. #21461965C2semidirect
7. #21461813C2semidirect
8. #21461813C2semidirect
9. #21461812C2semidirect
10. #21461812C2semidirect
11. #21461697C2semidirect
13. #21461658C2semidirect
14. #21461559C2semidirect
56. C2×#14519810C4semidirect
57. C2×#14519809C4semidirect
58. C2×#14519809C4semidirect
59. C2×#14519808C4semidirect
60. C2×#14519807C4semidirect
61. C2×#14519806C4semidirect
62. C2×#14519806C4semidirect
70. C2×#137×C61C4semidirect
135. C22×Dic122C2×C4semidirect
142. C2×Q8×D61C2×C4semidirect
143. C2×Q8×D61C2×C4semidirect
159. C2×Dic244C2×C4semidirect
160. C2×Dic244C2×C4semidirect
161. C2×#11758202C2×C4semidirect
162. C2×#11758202C2×C4semidirect
163. C2×#11758202C2×C4semidirect
164. C2×#11758202C2×C4semidirect
179. C2×#11758194C2×C4semidirect
180. C2×#11758189C2×C4semidirect
181. C2×#11758189C2×C4semidirect
187. C22×Q8×C61C2×C4semidirect
189. C2×Q16×C61C2×C4semidirect
190. C2×Q16×C61C2×C4semidirect
193. C2×M16×C61C2×C4semidirect
330. SD16×C61C22⋊C4semidirect
339. #11758201C22⋊C4semidirect
341. #11758200C22⋊C4semidirect
348. #11758190C22⋊C4semidirect
397. C2×#6923#137semidirect
559. C2×#137#6923semidirect
603. C61#22444semidirect
627. C22×Q8C2×#6923semidirect
653. C2×Q16C2×#6923semidirect
654. C2×Q16C2×#6923semidirect
672. C2×M16C2×#6923semidirect
847. SD16C22⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408012
C2×SD16×#69232
Q8×C22⋊#69232
#214623222
#214619672
#214619652
#214618132
#214618122
#214616972
#214616592
#214616582
#214615592
C2×#137×D612
#2244461