Finite Group Databasebeta

← C2×#19137276 #25255338

Subgroups — C2×#19137276 #25255338

Order 11008.

3198 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063303C211yesmaximal, characteristic
2C22×C4×Dic86C211yesmaximal, characteristic, complemented
3C22×#13063283C211yesmaximal, characteristic
4#19137276C2116yesmaximal, direct product factor
5C2×#14582803C211yesmaximal, characteristic, complemented
6C2×#14582798C211yesmaximal, characteristic, complemented
7C2×#14582796C211yesmaximal, characteristic, complemented
8C2×#14582796C211yesmaximal, characteristic, complemented
9C2×#14582791C211yesmaximal, characteristic
10C2×#14582791C211yesmaximal, characteristic
11C2×#14582790C211yesmaximal, characteristic
12C2×#14582788C211yesmaximal, characteristic
13C2×#14582780C211yesmaximal, characteristic, complemented
14C2×#14582758C211yesmaximal, characteristic
15C2×#14582750C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063303C4116yescomplemented
20C2×#13063303C2218yes—
21C2×C4×Dic86—28no—
22C2×C4×Dic86C2218yescomplemented
23C2×#13063283—28no—
24C2×#13063283C2218yes—
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×C4⋊Dic43C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43C22×C4×Dic43C2211yescharacteristic
44C22×C4×Dic43C2211yescharacteristic
45#14582803C2218yescomplemented
46#14582798C2218yescomplemented
47#14582796C2218yescomplemented
48#14582796C2218yescomplemented
49#14582791C2218yes—
50#14582791C2218yes—
51#14582790C2218yes—
52#14582788C2218yes—
53#14582780C2218yescomplemented
54#14582758C2218yes—
55#14582750C2218yescomplemented
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C42×C43C2211yescharacteristic
65C43×#387C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×Dic86—24no—
72C22×Dic86—24no—
73C22×Dic86C2×C418yes—
74C22×Dic86C2314yes—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C22×C4×D43—24no—
83C22×C4×D43—24no—
84C22×C4×D43C2×C418yes—
85C22×C4×D43C2314yes—
86#13063303C2×C4164yescomplemented
87C4×Dic86—232no—
88#13063283—232no—
89C2×C4⋊Dic43—24no—
90C2×C4⋊Dic43—24no—
91C2×C4⋊Dic43—42no—
92C2×C4⋊Dic43C2314yes—
93C2×C4⋊Dic43C2314yes—
94C2×C4⋊Dic43C2314yes—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4—24no—
98C2×Dic43⋊C4—42no—
99C2×Dic43⋊C4C2×C418yes—
100C2×Dic43⋊C4C2×C418yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4—24no—
109C2×(C2×D43)⋊C4—42no—
110C2×(C2×D43)⋊C4—42no—
111C2×(C2×D43)⋊C4C2×C418yes—
112C2×(C2×D43)⋊C4C2×C418yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×(C2×D43)⋊C4C2314yes—
118C2×(C2×D43)⋊C4C2314yes—
119C2×C4×Dic43—24no—
120C2×C4×Dic43—24no—
121C2×C4×Dic43—42no—
122C2×C4×Dic43—42no—
123C2×C4×Dic43D418yes—
124C2×C4×Dic43C2314yes—
125C2×C4×Dic43C2314yes—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2314yes—
128C2×C4×Dic43C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43—24no—
143C2×C4⋊C4×C43C2×C418yes—
144C2×C4⋊C4×C43C2314yes—
145C2×C4⋊C4×C43C2314yes—
146C2×C42×C43—24no—
147C2×C42×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150#95×C43C2314yes—
151#95×C43C2314yes—
152C24×C43C2411yescharacteristic
153C23×D43—22no—
154C23×D43—22no—
155C23×D43—22no—
156C23×D43—22no—
157C23×D43—22no—
158C23×D43—22no—
159C23×D43C22×C414yes—
160C23×D43C2412yes—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
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×C43C22×C414yes—
179C22×C4×C43C22×C414yes—
180C22×C4×C43C22×C414yes—
181C22×C4×C43C2×D414yes—
182C22×C4×C43C2412yes—
183C22×C4×C43C2412yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
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×Dic43C22×C414yes—
205C22×Dic43C22×C414yes—
206C22×Dic43C22×C414yes—
207C22×Dic43C2×D414yes—
208C22×Dic43C2×D414yes—
209C22×Dic43#4114yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C22×Dic43C2412yes—
216C22×Dic43C2412yes—
217C2×C4×D43—232no—
218C2×C4×D43—28no—
219C2×C4×D43—28no—
220C2×C4×D43C22×C4116yes—
221C2×Dic86—232no—
222C2×Dic86—28no—
223C2×Dic86—28no—
224C2×Dic86C22×C4116yes—
225C4⋊C4×C43—28no—
226C4⋊C4×C43C22×C4116yes—
227C42×C43—28no—
228(C2×D43)⋊C4—28no—
229(C2×D43)⋊C4—28no—
230(C2×D43)⋊C4—44no—
231(C2×D43)⋊C4—44no—
232(C2×D43)⋊C4C22×C4116yes—
233(C2×D43)⋊C4C22×C4116yes—
234C4⋊Dic43—28no—
235C4⋊Dic43—28no—
236C4⋊Dic43—44no—
237Dic43⋊C4—28no—
238Dic43⋊C4—28no—
239Dic43⋊C4—28no—
240Dic43⋊C4—44no—
241Dic43⋊C4C22×C4116yes—
242Dic43⋊C4C22×C4116yes—
243C4×Dic43—28no—
244C4×Dic43—28no—
245C4×Dic43—44no—
246C4×Dic43—44no—
247C4×Dic43C2×D4116yes—
248C23×C43C23×C412yes—
249C23×C43C22×D412yes—
250C23×C43C2×#4112yes—
251C23×C43H(5,𝔽2)12yes—
252C23×C432−1+412yes—
253C23×C432−1+412yes—
254C23×C432−1+412yes—
255C23×C43C2511yescharacteristic
256C22×D43—28no—
257C22×D43—28no—
258C22×D43—28no—
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—44no—
266C22×D43—44no—
267C22×D43—44no—
268C22×D43—44no—
269C22×D43C23×C414yes—
270C2×C4×C43—28no—
271C2×C4×C43—28no—
272C2×C4×C43—28no—
273C2×C4×C43—28no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—44no—
292C2×C4×C43—44no—
293C2×C4×C43—44no—
294C2×C4×C43C23×C414yes—
295C2×C4×C43C23×C414yes—
296C2×C4×C43C23×C414yes—
297C2×C4×C43C22×D414yes—
298C2×Dic43—28no—
299C2×Dic43—28no—
300C2×Dic43—28no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—44no—
317C2×Dic43—44no—
318C2×Dic43—44no—
319C2×Dic43C4×D4116yes—
320C2×Dic43C23×C414yes—
321C2×Dic43C23×C414yes—
322C2×Dic43C23×C414yes—
323C2×Dic43C22×D414yes—
324C2×Dic43C22×D414yes—
325C2×Dic43C2×#4114yes—
326C4×D43—232no—
327Dic86—232no—
328C2×#2323—431nomaximal, Sylow
329C22×C43C2×C4×D414yes—
330C22×C43#51914yes—
331C22×C43#52014yes—
332C22×C43#53614yes—
333C22×C43#53714yes—
334C22×C43#54114yes—
335C22×C43#54214yes—
336C22×C43C24×C411yescharacteristic
337C22×C43C23×D411yescharacteristic
338C22×C43C22×#4111yescharacteristic
339C22×C43C2×H(5,𝔽2)11yescharacteristic
340C22×C43C2×2−1+411yescharacteristic
341C22×C43C2×2−1+411yescharacteristic
342C22×C43C2×2−1+411yescharacteristic
343C2×D43—24no—
344C2×D43—24no—
345C2×D43—24no—
346C2×D43—416no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C4×C43—24no—
352C4×C43—24no—
353C4×C43—24no—
354C4×C43—24no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—42no—
358Dic43—24no—
359Dic43—24no—
360Dic43—24no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43C2×C4×D418yes—
365C22×C22⋊Q8—431no—
366C22×C4×Q8—431no—
367C22×#117—431no—
368#2323—4316no—
369C2×#391—431no—
370C2×#389—431no—
371C2×#389—431no—
372C2×#389—431no—
373C2×#388—431no—
374C2×#388—431no—
375C2×#388—431no—
376C2×#388—431no—
377C2×#387—431no—
378C2×#387D4311yescharacteristic, complemented
379C2×#380—431no—
380C2×C4×C4⋊C4—431no—
381C2×C43#232318yescomplemented
382C2×C43C22×C4×D411yescharacteristic
383C2×C43C2×#51911yescharacteristic
384C2×C43C2×#52011yescharacteristic
385C2×C43C2×#53611yescharacteristic
386C2×C43C2×#53711yescharacteristic
387C2×C43C2×#54111yescharacteristic
388C2×C43C2×#54211yescharacteristic
389D43—44no—
390C23×Q8—431no—
391C24×C4—431no—
392C2×C22⋊Q8—438no—
393C2×C22⋊Q8—4316no—
394C2×C4×Q8—438no—
395C2×C4×Q8—868no—
396C2×#117—438no—
397C2×#117—868no—
398C22×C4⋊C4—431no—
399C22×C4⋊C4—431no—
400C22×C4⋊C4—431no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4—431no—
404C22×C4⋊C4—431no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4C2×D4311yescharacteristic
408C22×C4⋊C4C2×D4311yescharacteristic
409C22×C22⋊C4—431no—
410C22×C22⋊C4—431no—
411C22×C22⋊C4—431no—
412C22×C22⋊C4—431no—
413C22×C22⋊C4—431no—
414C22×C22⋊C4—431no—
415C22×C42—431no—
416C22×C42—431no—
417C22×C42—431no—
418C22×C42—431no—
419C22×C42—431no—
420C22×C42C2×D4311yescharacteristic
421#391—438no—
422#389—438no—
423#389—438no—
424#389—438no—
425#388—438no—
426#388—438no—
427#388—438no—
428#388—438no—
429#387—438no—
430#387C2×D4318yescomplemented
431#380—438no—
432C4×C4⋊C4—438no—
433C2×#95—431no—
434C2×#95—431no—
435C2×#95—431no—
436C2×#95—431no—
437C2×#95—431no—
438C2×#95—431no—
439C2×#95C2×D4311yescharacteristic
440C2×#95C2×D4311yescharacteristic
441C2×#95C2×D4311yescharacteristic
442C2×#95C2×D4311yescharacteristic
443C43C2×#232311yescharacteristic, complemented, Sylow
444C25—431no—
445C22×Q8—438no—
446C22×Q8—434no—
447C22×Q8—864no—
448C22×Q8—864no—
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—431no—
452C23×C4—431no—
453C23×C4—438no—
454C23×C4—434no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—864no—
459C23×C4—864no—
460C23×C4C22×D4311yescharacteristic
461C23×C4C22×D4311yescharacteristic
462C23×C4C22×D4311yescharacteristic
463C23×C4C22×D4311yescharacteristic
464C23×C4C22×D4311yescharacteristic
465C23×C4C22×D4311yescharacteristic
466C23×C4C22×D4311yescharacteristic
467C22⋊Q8—4364no—
468C4×Q8—8632no—
469#117—8632no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—438no—
472C2×C4⋊C4—438no—
473C2×C4⋊C4—434no—
474C2×C4⋊C4—434no—
475C2×C4⋊C4—434no—
476C2×C4⋊C4—434no—
477C2×C4⋊C4—434no—
478C2×C4⋊C4—434no—
479C2×C4⋊C4—434no—
480C2×C4⋊C4—434no—
481C2×C4⋊C4—434no—
482C2×C4⋊C4—864no—
483C2×C4⋊C4—864no—
484C2×C4⋊C4—864no—
485C2×C4⋊C4—864no—
486C2×C4⋊C4—864no—
487C2×C4⋊C4—1722no—
488C2×C4⋊C4—1722no—
489C2×C4⋊C4C4×D4318yes—
490C2×C4⋊C4C22×D4314yes—
491C2×C4⋊C4C22×D4314yes—
492C2×C22⋊C4—438no—
493C2×C22⋊C4—438no—
494C2×C22⋊C4—434no—
495C2×C22⋊C4—434no—
496C2×C22⋊C4—434no—
497C2×C22⋊C4—434no—
498C2×C22⋊C4—434no—
499C2×C22⋊C4—434no—
500C2×C22⋊C4—864no—
501C2×C22⋊C4—864no—
502C2×C22⋊C4—1722no—
503C2×C22⋊C4—1722no—
504C2×C42—24no—
505C2×C42—438no—
506C2×C42—434no—
507C2×C42—434no—
508C2×C42—434no—
509C2×C42—434no—
510C2×C42—434no—
511C2×C42—864no—
512C2×C42—864no—
513C2×C42—1722no—
514C2×C42—1722no—
515C2×C42C22×D4314yes—
516#95—434no—
517#95—434no—
518#95—434no—
519#95—434no—
520#95—434no—
521#95—434no—
522#95C22×D4314yes—
523#95C22×D4314yes—
524#95C22×D4314yes—
525#95C22×D4314yes—
526C24—434no—
527C24—432no—
528C24—862no—
529C24—862no—
530C24—862no—
531C24—862no—
532C24—862no—
533C24—862no—
534C24C23×D4311yescharacteristic
535C2×Q8—4316no—
536C2×Q8—868no—
537C2×Q8—8632no—
538C2×Q8—868no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—434no—
557C22×C4—434no—
558C22×C4—434no—
559C22×C4—432no—
560C22×C4—434no—
561C22×C4—434no—
562C22×C4—434no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—4316no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—868no—
571C22×C4—8632no—
572C22×C4—868no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4C2×C4×D4314yes—
589C22×C4C2×C4×D4314yes—
590C22×C4C2×C4×D4314yes—
591C22×C4D4×D4314yes—
592C22×C4C23×D4312yes—
593C22×C4C23×D4312yes—
594C22×C4C23×D4312yes—
595C22×C4C23×D4312yes—
596C22×C4C23×D4312yes—
597C22×C4C23×D4312yes—
598C22×C4C23×D4312yes—
599C4⋊C4—28no—
600C4⋊C4—4316no—
601C4⋊C4—4316no—
602C4⋊C4—868no—
603C4⋊C4—868no—
604C4⋊C4—868no—
605C4⋊C4—868no—
606C4⋊C4—868no—
607C4⋊C4—1724no—
608C4⋊C4—1724no—
609C4⋊C4C2×C4×D43116yes—
610C22⋊C4—4316no—
611C22⋊C4—4316no—
612C22⋊C4—868no—
613C22⋊C4—868no—
614C22⋊C4—1724no—
615C22⋊C4—1724no—
616C42—28no—
617C42—4316no—
618C42—868no—
619C42—868no—
620C42—1724no—
621C42—1724no—
622C23—434no—
623C23—868no—
624C23—868no—
625C23—868no—
626C23—862no—
627C23—862no—
628C23—862no—
629C23—862no—
630C23—862no—
631C23—862no—
632C23—1724no—
633C23—1724no—
634C23—1724no—
635C23—1724no—
636C23C22×C4×D4312yes—
637C23C2×D4×D4312yes—
638C23#41×D4312yes—
639C23#1306337112yes—
640C23#1306337212yes—
641C23#1306337212yes—
642C23#1306337312yes—
643C23C24×D4311yescharacteristic
644Q8—8632no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—28no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—4316no—
670C2×C4—434no—
671C2×C4—434no—
672C2×C4—434no—
673C2×C4—434no—
674C2×C4—434no—
675C2×C4—434no—
676C2×C4—8632no—
677C2×C4—868no—
678C2×C4—868no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—868no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—1724no—
696C2×C4—1724no—
697C2×C4—1724no—
698C2×C4C22×C4×D4314yes—
699C2×C4C22×C4×D4314yes—
700C2×C4C22×C4×D4314yes—
701C2×C4C2×D4×D4314yes—
702C22—864no—
703C22—864no—
704C22—864no—
705C22—1722no—
706C22—1722no—
707C22—1722no—
708C22—1722no—
709C22—17216no—
710C22C4×D4×D4314yes—
711C22#1458337514yes—
712C22#1458337914yes—
713C22#1458347114yes—
714C22#1458347914yes—
715C22#1458350814yes—
716C22#1458351514yes—
717C22C23×C4×D4311yescharacteristic
718C22C22×D4×D4311yescharacteristic
719C22C2×#41×D4311yescharacteristic
720C22C2×#1306337111yescharacteristic
721C22C2×#1306337211yescharacteristic
722C22C2×#1306337211yescharacteristic
723C22C2×#1306337311yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—438no—
732C4—864no—
733C4—864no—
734C4—864no—
735C4—1722no—
736C4—1722no—
737C4—1722no—
738C2—1724no—
739C2#1913727618yesdirect product factor
740C2C2×C4×D4×D4311yescharacteristic
741C2C2×#1458337511yescharacteristic
742C2C2×#1458337911yescharacteristic
743C2C2×#1458347111yescharacteristic
744C2C2×#1458347911yescharacteristic
745C2C2×#1458350811yescharacteristic
746C2C2×#1458351511yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×#387D43
hypocenterC43C2×#2323
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic86C2semidirect
4. #19137276C2direct (N × H)
5. C2×#14582803C2semidirect
6. C2×#14582798C2semidirect
7. C2×#14582796C2semidirect
8. C2×#14582796C2semidirect
13. C2×#14582780C2semidirect
15. C2×#14582750C2semidirect
16. C2×C43×#387C2semidirect
19. C2×#13063303C4semidirect
22. C2×C4×Dic86C22semidirect
45. #14582803C22semidirect
46. #14582798C22semidirect
47. #14582796C22semidirect
48. #14582796C22semidirect
53. #14582780C22semidirect
55. #14582750C22semidirect
65. C43×#387C22semidirect
86. #13063303C2×C4semidirect
378. C2×#387D43semidirect
381. C2×C43#2323semidirect
430. #387C2×D43semidirect
443. C43C2×#2323semidirect
739. C2#19137276direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633032
C22×C4×Dic862
C22×#130632832
#191372762
C2×#145828032
C2×#145827982
C2×#145827962
C2×#145827912
C2×#145827902
C2×#145827882
C2×#145827802
C2×#145827582
C2×#145827502
C2×C43×#3872
C2×#232343