Finite Group Databasebeta

← C2×#19143473 #25960755

Subgroups — C2×#19143473 #25960755

Order 11008.

2806 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063346C211yesmaximal, characteristic
2C2×#14583381C211yesmaximal, characteristic, complemented
3C2×#14583378C211yesmaximal, characteristic, complemented
4#19143473C2116yesmaximal, direct product factor
5C2×#14583009C211yesmaximal, characteristic, complemented
6C2×#14583008C211yesmaximal, characteristic, complemented
7C2×#14583004C211yesmaximal, characteristic, complemented
8C2×#14583003C211yesmaximal, characteristic, complemented
9C2×C4×#10621873C211yesmaximal, characteristic, complemented
10C2×SD16×Dic43C211yesmaximal, characteristic, complemented
11C2×#14582986C211yesmaximal, characteristic, complemented
12C2×#106×D43C211yesmaximal, characteristic, complemented
13C2×#14582899C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#14582853C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C2×#13063346C4116yescomplemented
20C2×#13063346C2218yes—
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583381—24no—
27#14583381C2218yescomplemented
28#14583378—24no—
29#14583378C2218yescomplemented
30C2×Q8×Dic43C2211yescharacteristic
31C2×C4×Dic86C2211yescharacteristic
32C2×#13063290C2211yescharacteristic
33C2×C4×D172—21no—
34C2×C4×D172C2211yescharacteristic
35C2×D4×Dic43C2211yescharacteristic
36C2×#13063287—21no—
37C2×#13063287C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063282—21no—
41C2×#13063282C2211yescharacteristic
42C2×#13063281—21no—
43C22×Dic43⋊C4—21no—
44C2×C4⋊C4×D43—21no—
45C2×C4⋊C4×D43C2211yescharacteristic
46C2×C4⋊C4×D43C2211yescharacteristic
47#14583009C2218yescomplemented
48#14583008C2218yescomplemented
49#14583004C2218yescomplemented
50#14583003C2218yescomplemented
51C4×#10621873C2218yescomplemented
52SD16×Dic43C2218yescomplemented
53#14582986C2218yescomplemented
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57#106×D43C2218yescomplemented
58#14582899C2218yescomplemented
59#14582897C2218yescomplemented
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66#14582853C2218yescomplemented
67C2×#13063236C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C2×C8×Dic43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C4×SD16×C43C2218yescomplemented
74C2×#106×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×C4×C8×C43C2211yescharacteristic
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902C2×C418yescomplemented
81C2×#10621902C2314yes—
82C2×#10621900—22no—
83C2×#10621900—24no—
84C2×#10621900C2×C418yescomplemented
85C2×#10621900C2314yes—
86C22×Dic86C2311yescharacteristic
87C22×D172—21no—
88C22×D172C2311yescharacteristic
89C22×C22⋊D43—21no—
90C23×Dic43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98#13063346C2×C4164yescomplemented
99C2×#10621885C2×C418yescomplemented
100C2×#10621885C2314yes—
101C2×#10621873C2×C418yescomplemented
102C2×#10621873C2314yes—
103C2×#10621882C2×C418yescomplemented
104C2×#10621882C2314yes—
105C2×#10621872—24no—
106C2×#10621872C2314yes—
107C22×C43⋊C8C2311yescharacteristic
108C22×C43⋊C8C2311yescharacteristic
109C2×C8×D43C2×C418yescomplemented
110C2×C8×D43C2314yes—
111Q8×Dic43—22no—
112Q8×Dic43C2314yes—
113C4×Dic86—22no—
114C4×Dic86C2314yes—
115#13063290—22no—
116#13063290C2314yes—
117C4×D172—22no—
118C4×D172—28no—
119C4×D172C2314yes—
120D4×Dic43—22no—
121D4×Dic43C2314yes—
122#13063287—28no—
123#13063287—22no—
124#13063287C2314yes—
125C4×C22⋊D43—28no—
126(C22⋊D43)⋊C4—28no—
127#13063282—28no—
128#13063282D414yes—
129#13063282C2314yes—
130#13063281—28no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—28no—
139C2×Dic43⋊C4D411yescharacteristic
140C2×Dic43⋊C4D411yescharacteristic
141C4⋊C4×D43—22no—
142C4⋊C4×D43—22no—
143C4⋊C4×D43—28no—
144C4⋊C4×D43C2314yes—
145C4⋊C4×D43C2314yes—
146C2×C22⋊Dic43—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×(C2×D43)⋊C4D411yescharacteristic
151C2×C4×Dic43—21no—
152C2×C4×Dic43—21no—
153C2×C4×Dic43—21no—
154C2×C4×Dic43C2311yescharacteristic
155#13063257C2314yes—
156#13063256C2314yes—
157#13063256C2314yes—
158#13063250C2314yes—
159#13063249C2314yes—
160#13063248C2314yes—
161#13063247C2314yes—
162#13063246C2314yes—
163#13063245C2314yes—
164#13063236C2314yes—
165#13063235C2314yes—
166C8×Dic43C2314yes—
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C2×SD16×C43C2×C418yescomplemented
171C2×SD16×C43C2314yes—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C4×Q8×C43—22no—
175C4×Q8×C43C2314yes—
176C4×D4×C43—22no—
177C4×D4×C43C2314yes—
178C2×C4⋊C4×C43—21no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C42×C43—21no—
183C2×C42×C43C2311yescharacteristic
184#106×C43C2314yes—
185#103×C43C2314yes—
186#102×C43C2314yes—
187C4×C8×C43C2314yes—
188C24×C43—21no—
189C23×D43—21no—
190C23×D43C2×D411yescharacteristic
191C2×Q8×C43—21no—
192C2×Q8×C43—22no—
193C2×Q8×C43C22×C414yes—
194C2×Q8×C43C2412yes—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43C22×C414yes—
198C2×D4×C43C2412yes—
199C22×C4×C43—24no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—82no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—28no—
208C2×C22⋊D43—24no—
209C22×Dic43—28no—
210C22×Dic43—24no—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—82no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219#10621902—216no—
220#10621902—28no—
221#10621902C22×C4116yescomplemented
222#10621900—216no—
223#10621900—28no—
224#10621900C22×C4116yescomplemented
225C2×D172—21no—
226C2×D172—22no—
227C2×D172—28no—
228C2×D172—24no—
229C2×D172C22×C414yes—
230C2×D172C2412yes—
231C2×C4×D43—28no—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—82no—
238C2×C4×D43—82no—
239C2×C4×D43—82no—
240C2×C4×D43—82no—
241C2×C4×D43C22×C414yes—
242C2×C4×D43C2×D412yes—
243C2×C4×D43#4114yes—
244C2×C4×D43C2412yes—
245C2×Dic86—21no—
246C2×Dic86—22no—
247C2×Dic86C22×C414yes—
248C2×Dic86C2412yes—
249SD16×C43C22×C4116yescomplemented
250C2×C8×C43—22no—
251C2×C8×C43C22×C414yes—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C2412yes—
258C4⋊C4×C43C2412yes—
259C22⋊C4×C43—24no—
260C42×C43—24no—
261C42×C43C2×D412yes—
262C42×C43C2412yes—
263C22⋊Dic43—24no—
264#10621885C22×C4116yescomplemented
265#10621882C22×C4116yescomplemented
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4C2×D414yes—
269(C2×D43)⋊C4C2×D414yes—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—24no—
273C4⋊Dic43C2412yes—
274C4⋊Dic43C2412yes—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4C2×D414yes—
280Dic43⋊C4C2×D414yes—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C4×Dic43—24no—
284C4×Dic43C2×D412yes—
285C4×Dic43C2412yes—
286C2×C43⋊C8—22no—
287C2×C43⋊C8C22×C414yes—
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290#10621873C22×C4116yescomplemented
291#10621872—28no—
292C8×D43C22×C4116yescomplemented
293C23×C43—24no—
294C23×C43—22no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—24no—
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43C4×D414yes—
305C22×D43C22×D412yes—
306Q8×C43—24no—
307Q8×C43—22no—
308Q8×C43C23×C414yes—
309D4×C43—24no—
310D4×C43—22no—
311D4×C43C23×C414yes—
312C2×C4×C43—24no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—84no—
321C2×C4×C43C23×C412yes—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4112yes—
326C2×C4×C43C2511yescharacteristic
327C22⋊D43—216no—
328C2×Dic43—24no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—216no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—84no—
338C2×Dic43C4×D414yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C2×Dic43C22×D412yes—
342D172—216no—
343D172—24no—
344D172—22no—
345D172C23×C414yes—
346C4×D43—216no—
347C4×D43—84no—
348C4×D43—84no—
349C4×D43—84no—
350C4×D43—84no—
351C4×D43C4×D418yes—
352C4×D43C23×C414yes—
353C4×D43C2×#4114yes—
354Dic86—24no—
355Dic86—22no—
356Dic86C23×C414yes—
357C8×C43—22no—
358C8×C43C23×C414yes—
359C43⋊C8—22no—
360C43⋊C8C23×C414yes—
361C2×#2952—431nomaximal, Sylow
362C22×C43—24no—
363C22×C43—48no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43C2×C4×D412yes—
367C22×C43#57712yes—
368C22×C43#57712yes—
369C22×C43C23×D411yescharacteristic
370C2×D43—28no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—24no—
374C2×D43—48no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43C2×C4×D414yes—
378C4×C43—24no—
379C4×C43—22no—
380C4×C43—22no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43C2×C4×D412yes—
384C4×C43C24×C411yescharacteristic
385C4×C43C22×#4111yescharacteristic
386Dic43—24no—
387Dic43—22no—
388Dic43—22no—
389Dic43—42no—
390Dic43—42no—
391Dic43C2×C4×D414yes—
392C22×#135—431no—
393C2×#520—431no—
394C2×#520—431no—
395#2952—4316no—
396C2×#442—431no—
397C2×#442—431no—
398C2×#441—431no—
399C2×#441—431no—
400C2×C4×SD16—431no—
401C2×C4×SD16—431no—
402C2×C4×SD16—431no—
403C2×C4×SD16D4311yescharacteristic, complemented
404C22×#106—431no—
405C2×#417—431no—
406C2×#417—431no—
407C2×#405—431no—
408C2×C43—44no—
409C2×C43#295214yescomplemented
410C2×C43C22×C4×D411yescharacteristic
411C2×C43C2×#57711yescharacteristic
412C2×C43C2×#57711yescharacteristic
413D43—24no—
414D43—44no—
415C22×#41—431no—
416C22×#41—431no—
417C2×#135—438no—
418C2×#135—4316no—
419C22×Q16—431no—
420C22×SD16—431no—
421C22×SD16C2×D4311yescharacteristic
422C22×D8—431no—
423C22×M16—431no—
424C23×C8—431no—
425#520—438no—
426#520—438no—
427#520—864no—
428#520—864no—
429C2×C4×Q8—431no—
430C2×C4×Q8—431no—
431C2×C4×Q8—431no—
432C2×C4×Q8C2×D4311yescharacteristic
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×C4×D4—861no—
439C2×C4×D4—861no—
440C2×C4×D4C2×D4311yescharacteristic
441C2×#117—431no—
442C2×#117—861no—
443C2×#117—861no—
444C22×C4⋊C4—431no—
445C22×C4⋊C4—431no—
446C22×C4⋊C4—861no—
447C22×C4⋊C4—861no—
448#442—438no—
449#442—438no—
450#441—438no—
451#441—438no—
452C4×SD16—438no—
453C4×SD16—438no—
454C4×SD16—438no—
455C4×SD16C2×D4318yescomplemented
456C2×#106—431no—
457C2×#106—431no—
458C2×#106—431no—
459C2×#106—438no—
460C2×#106C2×D4311yescharacteristic
461#417—438no—
462#417—438no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103C2×D4311yescharacteristic
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102C2×D4311yescharacteristic
471#405—438no—
472C2×#97—431no—
473C2×#97—431no—
474C2×C4×C8—431no—
475C2×C4×C8C2×D4311yescharacteristic
476C43C2×#295211yescharacteristic, complemented, Sylow
477C2×#41—438no—
478C2×#41—434no—
479C2×#41—438no—
480C2×#41—434no—
481C2×#41—862no—
482C2×#41—864no—
483C2×#41—862no—
484C2×#41—864no—
485C22×Q8—431no—
486C22×Q8C22×D4311yescharacteristic
487C22×D4—431no—
488C22×D4—861no—
489C22×D4—861no—
490C22×D4C22×D4311yescharacteristic
491C23×C4—21no—
492C23×C4—431no—
493C23×C4—861no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C23×C4—861no—
498C23×C4—861no—
499C23×C4—861no—
500#135—4364no—
501C2×Q16—438no—
502C2×Q16—434no—
503C2×SD16—438no—
504C2×SD16—434no—
505C2×SD16C4×D4318yescomplemented
506C2×SD16C22×D4314yes—
507C2×D8—438no—
508C2×D8—434no—
509C2×M16—434no—
510C2×M16—864no—
511C22×C8—431no—
512C22×C8—438no—
513C22×C8—434no—
514C22×C8—431no—
515C22×C8C22×D4311yescharacteristic
516C22×C8C22×D4311yescharacteristic
517C4×Q8—22no—
518C4×Q8—434no—
519C4×Q8—434no—
520C4×Q8—434no—
521C4×Q8—862no—
522C4×Q8—862no—
523C4×Q8—862no—
524C4×Q8C22×D4314yes—
525C4×D4—22no—
526C4×D4—434no—
527C4×D4—434no—
528C4×D4—434no—
529C4×D4—868no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4—868no—
533C4×D4—868no—
534C4×D4—868no—
535C4×D4—862no—
536C4×D4C22×D4314yes—
537#117—434no—
538#117—434no—
539#117—868no—
540#117—868no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—434no—
547C2×C4⋊C4—434no—
548C2×C4⋊C4—868no—
549C2×C4⋊C4—862no—
550C2×C4⋊C4—862no—
551C2×C4⋊C4—868no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—431no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C42—21no—
566C2×C42—431no—
567C2×C42—861no—
568C2×C42—861no—
569C2×C42—861no—
570C2×C42C22×D4311yescharacteristic
571#106—434no—
572#106—434no—
573#106—434no—
574#106C22×D4314yes—
575#103—434no—
576#103—434no—
577#103—434no—
578#103C22×D4314yes—
579#102—434no—
580#102—434no—
581#102—434no—
582#102C22×D4314yes—
583#97—434no—
584#97—434no—
585C4×C8—434no—
586C4×C8C22×D4314yes—
587C24—21no—
588C24—431no—
589C24—861no—
590#41—4316no—
591#41—4316no—
592#41—8616no—
593#41—868no—
594#41—8616no—
595#41—868no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—434no—
599C2×Q8—432no—
600C2×Q8—861no—
601C2×Q8—862no—
602C2×Q8C2×C4×D4314yes—
603C2×Q8C23×D4312yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—434no—
607C2×D4—432no—
608C2×D4—864no—
609C2×D4—868no—
610C2×D4—864no—
611C2×D4—868no—
612C2×D4—861no—
613C2×D4—862no—
614C2×D4C2×C4×D4314yes—
615C2×D4C23×D4312yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—431no—
622C22×C4—434no—
623C22×C4—432no—
624C22×C4—434no—
625C22×C4—432no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—864no—
629C22×C4—868no—
630C22×C4—864no—
631C22×C4—864no—
632C22×C4—864no—
633C22×C4—864no—
634C22×C4—868no—
635C22×C4—864no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—864no—
640C22×C4—3442no—
641C22×C4—3442no—
642C22×C4—3442no—
643C22×C4—3442no—
644C22×C4—3442no—
645C22×C4D4×D4311yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4C23×D4311yescharacteristic
648Q16—4316no—
649SD16—4316no—
650SD16C2×C4×D43116yescomplemented
651D8—4316no—
652M16—868no—
653C2×C8—22no—
654C2×C8—434no—
655C2×C8—432no—
656C2×C8—4316no—
657C2×C8—432no—
658C2×C8—862no—
659C2×C8C2×C4×D4314yes—
660C2×C8C23×D4312yes—
661C2×C8C23×D4312yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—434no—
666C4⋊C4—434no—
667C4⋊C4—432no—
668C4⋊C4—432no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—864no—
672C4⋊C4—864no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—864no—
676C4⋊C4C23×D4312yes—
677C4⋊C4C23×D4312yes—
678C22⋊C4—24no—
679C22⋊C4—434no—
680C22⋊C4—434no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C42—24no—
685C42—432no—
686C42—432no—
687C42—864no—
688C42—864no—
689C42—864no—
690C42D4×D4312yes—
691C42C23×D4312yes—
692C23—24no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—434no—
697C23—432no—
698C23—862no—
699C23—862no—
700C23—864no—
701C23—862no—
702C23—1722no—
703C23—1722no—
704C23C2×D4×D4311yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—434no—
708Q8—864no—
709Q8—862no—
710Q8C22×C4×D4314yes—
711D4—24no—
712D4—22no—
713D4—434no—
714D4—8616no—
715D4—8616no—
716D4—864no—
717D4—862no—
718D4C22×C4×D4314yes—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—434no—
729C2×C4—432no—
730C2×C4—438no—
731C2×C4—434no—
732C2×C4—434no—
733C2×C4—432no—
734C2×C4—432no—
735C2×C4—8616no—
736C2×C4—8616no—
737C2×C4—864no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—3444no—
744C2×C4—3444no—
745C2×C4—3444no—
746C2×C4—3444no—
747C2×C4—3444no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4C22×C4×D4312yes—
751C2×C4C2×D4×D4312yes—
752C2×C4C2×D4×D4312yes—
753C2×C4C2×D4×D4311yescharacteristic
754C2×C4#41×D4312yes—
755C2×C4C24×D4311yescharacteristic
756C8—22no—
757C8—434no—
758C8—862no—
759C8C22×C4×D4314yes—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—48no—
764C22—434no—
765C22—862no—
766C22—862no—
767C22—868no—
768C22—864no—
769C22—1722no—
770C22—1722no—
771C22—1728no—
772C22C4×D4×D4312yes—
773C22#1458370512yes—
774C22#1458370612yes—
775C22C22×D4×D4311yescharacteristic
776C4—22no—
777C4—22no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—434no—
782C4—862no—
783C4—862no—
784C4—864no—
785C4—1722no—
786C4—1722no—
787C4C4×D4×D4312yes—
788C4C23×C4×D4311yescharacteristic
789C4C2×#41×D4311yescharacteristic
790C2—44no—
791C2—864no—
792C2—1724no—
793C2#1914347314yesdirect product factor
794C2C2×C4×D4×D4311yescharacteristic
795C2C2×#1458370511yescharacteristic
796C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×#13063346C2
cosocleC2×C4×C43C25
hypercenterC2×C4×SD16D43
hypocenterC43C2×#2952
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14583381C2semidirect
3. C2×#14583378C2semidirect
4. #19143473C2direct (N × H)
5. C2×#14583009C2semidirect
6. C2×#14583008C2semidirect
7. C2×#14583004C2semidirect
8. C2×#14583003C2semidirect
9. C2×C4×#10621873C2semidirect
10. C2×SD16×Dic43C2semidirect
11. C2×#14582986C2semidirect
12. C2×#106×D43C2semidirect
13. C2×#14582899C2semidirect
14. C2×#14582897C2semidirect
15. C2×#14582853C2semidirect
16. C2×C4×SD16×C43C2semidirect
19. C2×#13063346C4semidirect
27. #14583381C22semidirect
29. #14583378C22semidirect
47. #14583009C22semidirect
48. #14583008C22semidirect
49. #14583004C22semidirect
50. #14583003C22semidirect
51. C4×#10621873C22semidirect
52. SD16×Dic43C22semidirect
53. #14582986C22semidirect
57. #106×D43C22semidirect
58. #14582899C22semidirect
59. #14582897C22semidirect
66. #14582853C22semidirect
73. C4×SD16×C43C22semidirect
80. C2×#10621902C2×C4semidirect
84. C2×#10621900C2×C4semidirect
98. #13063346C2×C4semidirect
99. C2×#10621885C2×C4semidirect
101. C2×#10621873C2×C4semidirect
103. C2×#10621882C2×C4semidirect
109. C2×C8×D43C2×C4semidirect
170. C2×SD16×C43C2×C4semidirect
221. #10621902C22×C4semidirect
224. #10621900C22×C4semidirect
249. SD16×C43C22×C4semidirect
264. #10621885C22×C4semidirect
265. #10621882C22×C4semidirect
290. #10621873C22×C4semidirect
292. C8×D43C22×C4semidirect
403. C2×C4×SD16D43semidirect
409. C2×C43#2952semidirect
455. C4×SD16C2×D43semidirect
476. C43C2×#2952semidirect
505. C2×SD16C4×D43semidirect
650. SD16C2×C4×D43semidirect
793. C2#19143473direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633462
C2×#145833812
C2×#145833782
#191434732
C2×#145830092
C2×#145830082
C2×#145830042
C2×#145830032
C2×C4×#106218732
C2×SD16×Dic432
C2×#145829862
C2×#106×D432
C2×#145828992
C2×#145828972
C2×#145828532
C2×C4×SD16×C432
C2×#295243