Finite Group Databasebeta

← C2×#19137402 #25255510

Subgroups — C2×#19137402 #25255510

Order 11008.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063311C211yesmaximal, characteristic
2#19137402C2116yesmaximal, direct product factor
3C2×#14582805C211yesmaximal, characteristic, complemented
4C2×#14582803C211yesmaximal, characteristic, complemented
5C2×#14582793C211yesmaximal, characteristic, complemented
6C2×#14582791C211yesmaximal, characteristic, complemented
7C2×#14582791C211yesmaximal, characteristic, complemented
8C2×#14582776C211yesmaximal, characteristic
9C2×#14582775C211yesmaximal, characteristic
10C2×#14582774C211yesmaximal, characteristic, complemented
11C2×#14582770C211yesmaximal, characteristic, complemented
12C2×#14582766C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063311C4116yescomplemented
22C2×#13063311C2218yes—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582805C2218yescomplemented
38#14582803C2218yescomplemented
39#14582793C2218yescomplemented
40#14582791C2218yescomplemented
41#14582791C2218yescomplemented
42#14582776C2218yes—
43#14582775C2218yes—
44#14582774C2218yescomplemented
45#14582770C2218yescomplemented
46#14582766C2218yescomplemented
47C4⋊C4×Dic43C2218yescomplemented
48C22⋊C4×Dic43C2218yescomplemented
49C4×(C2×D43)⋊C4C2218yescomplemented
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C42×C43C2211yescharacteristic
65C43×#388C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×Dic86—42no—
70C22×Dic86—42no—
71C22×Dic86C2×C418yescomplemented
72C22×Dic86C2314yes—
73C22×C22⋊D43—42no—
74C22×C22⋊D43—42no—
75C22×C22⋊D43C2×C418yes—
76C22×C22⋊D43C2314yes—
77C23×Dic43—24no—
78C23×Dic43—42no—
79C23×Dic43—42no—
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2314yes—
88C22×C4×D43—24no—
89C22×C4×D43—42no—
90C22×C4×D43—42no—
91C22×C4×D43C2314yes—
92#13063311C2×C4164yescomplemented
93C2×C4⋊Dic43—24no—
94C2×C4⋊Dic43—42no—
95C2×C4⋊Dic43C2314yes—
96C2×C4⋊Dic43C2314yes—
97C2×Dic43⋊C4—42no—
98C2×Dic43⋊C4C2314yes—
99C2×C22⋊Dic43—42no—
100C2×C22⋊Dic43C2×C418yescomplemented
101C2×C22⋊Dic43C2314yes—
102C2×C22⋊Dic43C2314yes—
103C2×(C2×D43)⋊C4—24no—
104C2×(C2×D43)⋊C4—42no—
105C2×(C2×D43)⋊C4—42no—
106C2×(C2×D43)⋊C4C2×C418yescomplemented
107C2×(C2×D43)⋊C4C2×C418yescomplemented
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×C4×Dic43—42no—
114C2×C4×Dic43—42no—
115C2×C4×Dic43—42no—
116C2×C4×Dic43C2×C418yescomplemented
117C2×C4×Dic43C2314yes—
118C2×C4×Dic43C2314yes—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C25×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43—24no—
139C2×C4⋊C4×C43C2314yes—
140C2×C22⋊C4×C43—24no—
141C2×C22⋊C4×C43—42no—
142C2×C22⋊C4×C43C2×C418yescomplemented
143C2×C22⋊C4×C43C2314yes—
144C2×C22⋊C4×C43C2314yes—
145C2×C22⋊C4×C43C2314yes—
146C2×C42×C43—42no—
147C2×C42×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43C22×C414yes—
157C24×C43C2412yes—
158C24×C43C2411yescharacteristic
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43C22×C414yes—
166C23×D43C2412yes—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43C22×C414yes—
183C22×C4×C43C22×C414yes—
184C22×C4×C43#4114yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C2×C22⋊D43—416no—
192C2×C22⋊D43—44no—
193C2×C22⋊D43—44no—
194C2×C22⋊D43C22×C4116yes—
195C22×Dic43—28no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—44no—
214C22×Dic43—44no—
215C22×Dic43—416no—
216C22×Dic43C22×C414yes—
217C22×Dic43C22×C414yes—
218C22×Dic43C22×C414yes—
219C22×Dic43#4114yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×C4×D43—28no—
228C2×C4×D43—44no—
229C2×C4×D43—44no—
230C2×C4×D43—416no—
231C2×Dic86—416no—
232C2×Dic86—44no—
233C2×Dic86—44no—
234C2×Dic86C22×C4116yescomplemented
235C4⋊C4×C43—28no—
236C22⋊C4×C43—28no—
237C22⋊C4×C43—44no—
238C22⋊C4×C43C22×C4116yescomplemented
239C42×C43—44no—
240C22⋊Dic43—44no—
241C22⋊Dic43C22×C4116yescomplemented
242(C2×D43)⋊C4—28no—
243(C2×D43)⋊C4—44no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4C22×C4116yescomplemented
246(C2×D43)⋊C4C22×C4116yescomplemented
247C4⋊Dic43—28no—
248C4⋊Dic43—44no—
249Dic43⋊C4—44no—
250C4×Dic43—44no—
251C4×Dic43—44no—
252C4×Dic43—44no—
253C4×Dic43C22×C4116yescomplemented
254C23×C43—28no—
255C23×C43—28no—
256C23×C43—28no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43C23×C414yes—
268C23×C43C23×C412yes—
269C23×C43C2×#4112yes—
270C23×C43C2×#4112yes—
271C23×C43H(5,𝔽2)12yes—
272C23×C43H(5,𝔽2)12yes—
273C23×C43H(5,𝔽2)12yes—
274C23×C432−1+412yes—
275C23×C43C2511yescharacteristic
276C22×D43—28no—
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—44no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43C23×C414yes—
290C2×C4×C43—28no—
291C2×C4×C43—28no—
292C2×C4×C43—28no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—44no—
309C2×C4×C43—44no—
310C2×C4×C43—44no—
311C2×C4×C43C23×C414yes—
312C2×C4×C43C23×C414yes—
313C2×C4×C43C2×#4114yes—
314C22⋊D43—416no—
315C2×Dic43—28no—
316C2×Dic43—28no—
317C2×Dic43—28no—
318C2×Dic43—28no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—416no—
337C2×Dic43—44no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43C23×C414yes—
341C2×Dic43C23×C414yes—
342C2×Dic43C23×C414yes—
343C2×Dic43C2×#4114yes—
344C4×D43—416no—
345Dic86—416no—
346C2×#2337—431nomaximal, Sylow
347C22×C43—24no—
348C22×C43—24no—
349C22×C43—24no—
350C22×C43—416no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43C4×#4114yes—
356C22×C43#51814yes—
357C22×C43#52014yes—
358C22×C43#53814yes—
359C22×C43#53814yes—
360C22×C43#54214yes—
361C22×C43#54214yes—
362C22×C43C24×C411yescharacteristic
363C22×C43C22×#4111yescharacteristic
364C22×C43C22×#4111yescharacteristic
365C22×C43C2×H(5,𝔽2)11yescharacteristic
366C22×C43C2×H(5,𝔽2)11yescharacteristic
367C22×C43C2×H(5,𝔽2)11yescharacteristic
368C22×C43C2×2−1+411yescharacteristic
369C2×D43—24no—
370C2×D43—24no—
371C2×D43—24no—
372C2×D43—416no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C4×C43—24no—
378C4×C43—24no—
379C4×C43—24no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—42no—
383Dic43—24no—
384Dic43—24no—
385Dic43—24no—
386Dic43—24no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390C22×#124—431no—
391#2337—4316no—
392C2×#391—431no—
393C2×#391—431no—
394C2×#388—431no—
395C2×#388—431no—
396C2×#388—431no—
397C2×#388D4311yescharacteristic, complemented
398C2×#386—431no—
399C2×#386—431no—
400C2×#385—431no—
401C2×#385—431no—
402C2×#383—431no—
403C2×C4×C4⋊C4—431no—
404C2×C4×C22⋊C4—431no—
405C2×C4×C22⋊C4—431no—
406C2×C43—44no—
407C2×C43#233718yescomplemented
408C2×C43C2×C4×#4111yescharacteristic
409C2×C43C2×#51811yescharacteristic
410C2×C43C2×#52011yescharacteristic
411C2×C43C2×#53811yescharacteristic
412C2×C43C2×#53811yescharacteristic
413C2×C43C2×#54211yescharacteristic
414C2×C43C2×#54211yescharacteristic
415D43—44no—
416C23×Q8—431no—
417C23×D4—431no—
418C24×C4—431no—
419C24×C4—431no—
420C2×#124—438no—
421C2×#124—4316no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4C2×D4311yescharacteristic
426C22×C22⋊C4—431no—
427C22×C22⋊C4—431no—
428C22×C22⋊C4—431no—
429C22×C22⋊C4—431no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4C2×D4311yescharacteristic
434C22×C22⋊C4C2×D4311yescharacteristic
435C22×C22⋊C4C2×D4311yescharacteristic
436C22×C42—431no—
437C22×C42—431no—
438C22×C42—431no—
439C22×C42—431no—
440C22×C42C2×D4311yescharacteristic
441#391—438no—
442#391—438no—
443#388—438no—
444#388—438no—
445#388—438no—
446#388C2×D4318yescomplemented
447#386—438no—
448#386—438no—
449#385—438no—
450#385—438no—
451#383—438no—
452C4×C4⋊C4—438no—
453C4×C22⋊C4—438no—
454C4×C22⋊C4—438no—
455C2×#95—431no—
456C2×#95—431no—
457C2×#95—431no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95—431no—
464C2×#95—431no—
465C2×#95C2×D4311yescharacteristic
466C2×#95C2×D4311yescharacteristic
467C43C2×#233711yescharacteristic, complemented, Sylow
468C25—431no—
469C25C22×D4311yescharacteristic
470C22×Q8—438no—
471C22×Q8—434no—
472C22×Q8—1722no—
473C22×Q8—1722no—
474C22×D4—438no—
475C22×D4—434no—
476C22×D4—1722no—
477C22×D4—1722no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—434no—
486C23×C4—434no—
487C23×C4—864no—
488C23×C4—864no—
489C23×C4—1722no—
490C23×C4—1722no—
491C23×C4—1722no—
492C23×C4—1722no—
493C23×C4C22×D4311yescharacteristic
494C23×C4C22×D4311yescharacteristic
495C23×C4C22×D4311yescharacteristic
496C23×C4C22×D4311yescharacteristic
497C23×C4C22×D4311yescharacteristic
498C23×C4C22×D4311yescharacteristic
499#124—4364no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—434no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—434no—
504C2×C4⋊C4—864no—
505C2×C4⋊C4—1722no—
506C2×C4⋊C4—1722no—
507C2×C4⋊C4C22×D4314yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—438no—
511C2×C22⋊C4—434no—
512C2×C22⋊C4—438no—
513C2×C22⋊C4—438no—
514C2×C22⋊C4—434no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—434no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—1722no—
522C2×C22⋊C4—1722no—
523C2×C22⋊C4—1722no—
524C2×C22⋊C4C4×D4318yescomplemented
525C2×C22⋊C4C22×D4314yes—
526C2×C22⋊C4C22×D4314yes—
527C2×C22⋊C4C22×D4314yes—
528C2×C42—42no—
529C2×C42—438no—
530C2×C42—434no—
531C2×C42—434no—
532C2×C42—434no—
533C2×C42—434no—
534C2×C42—1722no—
535C2×C42—1722no—
536C2×C42—1722no—
537C2×C42C22×D4314yes—
538#95—434no—
539#95—434no—
540#95—434no—
541#95—434no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95—434no—
548#95C22×D4314yes—
549#95C22×D4314yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—434no—
557C24—432no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24—862no—
564C24C2×C4×D4314yes—
565C24C23×D4312yes—
566C24C23×D4311yescharacteristic
567C2×Q8—4316no—
568C2×Q8—17216no—
569C2×Q8—1724no—
570C2×Q8—1724no—
571C2×D4—4316no—
572C2×D4—17216no—
573C2×D4—1724no—
574C2×D4—1724no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—434no—
591C22×C4—434no—
592C22×C4—434no—
593C22×C4—434no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—868no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—868no—
620C22×C4—1724no—
621C22×C4—1724no—
622C22×C4—17216no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4—17216no—
626C22×C4C2×C4×D4314yes—
627C22×C4C2×C4×D4314yes—
628C22×C4#1062190014yes—
629C22×C4C23×D4312yes—
630C22×C4C23×D4312yes—
631C22×C4C23×D4312yes—
632C22×C4C23×D4312yes—
633C22×C4C23×D4312yes—
634C22×C4C23×D4312yes—
635C4⋊C4—28no—
636C4⋊C4—868no—
637C4⋊C4—1724no—
638C4⋊C4—1724no—
639C22⋊C4—28no—
640C22⋊C4—44no—
641C22⋊C4—4316no—
642C22⋊C4—4316no—
643C22⋊C4—4316no—
644C22⋊C4—868no—
645C22⋊C4—1724no—
646C22⋊C4—1724no—
647C22⋊C4—1724no—
648C22⋊C4C2×C4×D43116yescomplemented
649C42—44no—
650C42—4316no—
651C42—1724no—
652C42—1724no—
653C42—1724no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—434no—
668C23—868no—
669C23—868no—
670C23—868no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—1724no—
678C23—1724no—
679C23—1724no—
680C23—1724no—
681C23C22×C4×D4314yes—
682C23C22×C4×D4312yes—
683C23#41×D4312yes—
684C23C2×#1062190012yes—
685C23#1306337012yes—
686C23#1306337112yes—
687C23#1306337112yes—
688C23#1306337212yes—
689C23C24×D4311yescharacteristic
690Q8—17216no—
691D4—17216no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—434no—
714C2×C4—434no—
715C2×C4—434no—
716C2×C4—434no—
717C2×C4—868no—
718C2×C4—868no—
719C2×C4—868no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—868no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—17216no—
739C2×C4—17216no—
740C2×C4—1724no—
741C2×C4—1724no—
742C2×C4—1724no—
743C2×C4C22×C4×D4314yes—
744C2×C4C22×C4×D4314yes—
745C2×C4C2×#1062190014yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—864no—
755C22—864no—
756C22—864no—
757C22—17216no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22C4×#1062190014yes—
763C22#1458337114yes—
764C22#1458337914yes—
765C22#1458348614yes—
766C22#1458348814yes—
767C22#1458351714yes—
768C22#1458351814yes—
769C22C23×C4×D4311yescharacteristic
770C22C2×#41×D4311yescharacteristic
771C22C22×#1062190011yescharacteristic
772C22C2×#1306337011yescharacteristic
773C22C2×#1306337111yescharacteristic
774C22C2×#1306337111yescharacteristic
775C22C2×#1306337211yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—864no—
783C4—864no—
784C4—864no—
785C4—864no—
786C4—1722no—
787C4—1722no—
788C4—1722no—
789C2—44no—
790C2—1724no—
791C2#1913740218yesdirect product factor
792C2C2×C4×#1062190011yescharacteristic
793C2C2×#1458337111yescharacteristic
794C2C2×#1458337911yescharacteristic
795C2C2×#1458348611yescharacteristic
796C2C2×#1458348811yescharacteristic
797C2C2×#1458351711yescharacteristic
798C2C2×#1458351811yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2337
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #19137402C2direct (N × H)
3. C2×#14582805C2semidirect
4. C2×#14582803C2semidirect
5. C2×#14582793C2semidirect
6. C2×#14582791C2semidirect
7. C2×#14582791C2semidirect
10. C2×#14582774C2semidirect
11. C2×#14582770C2semidirect
12. C2×#14582766C2semidirect
13. C2×C4⋊C4×Dic43C2semidirect
14. C2×C22⋊C4×Dic43C2semidirect
15. C2×C4×(C2×D43)⋊C4C2semidirect
16. C2×C43×#388C2semidirect
21. C2×#13063311C4semidirect
37. #14582805C22semidirect
38. #14582803C22semidirect
39. #14582793C22semidirect
40. #14582791C22semidirect
41. #14582791C22semidirect
44. #14582774C22semidirect
45. #14582770C22semidirect
46. #14582766C22semidirect
47. C4⋊C4×Dic43C22semidirect
48. C22⋊C4×Dic43C22semidirect
49. C4×(C2×D43)⋊C4C22semidirect
65. C43×#388C22semidirect
71. C22×Dic86C2×C4semidirect
92. #13063311C2×C4semidirect
100. C2×C22⋊Dic43C2×C4semidirect
106. C2×(C2×D43)⋊C4C2×C4semidirect
107. C2×(C2×D43)⋊C4C2×C4semidirect
116. C2×C4×Dic43C2×C4semidirect
142. C2×C22⋊C4×C43C2×C4semidirect
234. C2×Dic86C22×C4semidirect
238. C22⋊C4×C43C22×C4semidirect
241. C22⋊Dic43C22×C4semidirect
245. (C2×D43)⋊C4C22×C4semidirect
246. (C2×D43)⋊C4C22×C4semidirect
253. C4×Dic43C22×C4semidirect
397. C2×#388D43semidirect
407. C2×C43#2337semidirect
446. #388C2×D43semidirect
467. C43C2×#2337semidirect
524. C2×C22⋊C4C4×D43semidirect
648. C22⋊C4C2×C4×D43semidirect
791. C2#19137402direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633112
#191374022
C2×#145828052
C2×#145828032
C2×#145827932
C2×#145827912
C2×#145827762
C2×#145827752
C2×#145827742
C2×#145827702
C2×#145827662
C2×C4⋊C4×Dic432
C2×C22⋊C4×Dic432
C2×C4×(C2×D43)⋊C42
C2×C43×#3882
C2×#233743