Finite Group Databasebeta

← C2×#26023118 #36713661

Subgroups — C2×#26023118 #36713661

Order 22784.

3526 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667970C211yesmaximal, characteristic
2C22×#15667969C211yesmaximal, characteristic
3C22×C4⋊C4×D89C211yesmaximal, characteristic
4#26023118C2116yesmaximal, direct product factor
5C2×#19151495C211yesmaximal, characteristic, complemented
6C2×#19151493C211yesmaximal, characteristic, complemented
7C2×#19151484C211yesmaximal, characteristic, complemented
8C2×#19151483C211yesmaximal, characteristic, complemented
9C2×#19151481C211yesmaximal, characteristic, complemented
10C2×#19151460C211yesmaximal, characteristic
11C2×#19151460C211yesmaximal, characteristic
12C2×#19151457C211yesmaximal, characteristic
13C2×C4×#13083553C211yesmaximal, characteristic, complemented
14C2×#19151449C211yesmaximal, characteristic, complemented
15C2×#19151445C211yesmaximal, characteristic
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×C4×D89C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C2×#15667970—28no—
21C2×#15667970C2218yes—
22C2×#15667969—28no—
23C2×#15667969C2218yes—
24C22×C4⋊Dic89C2211yescharacteristic
25C22×C4⋊Dic89C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083553C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×#13083553C2211yescharacteristic
32C2×C4⋊C4×D89C4116yescomplemented
33C2×C4⋊C4×D89C2218yes—
34C22×#13083551C2211yescharacteristic
35C22×#13083551C2211yescharacteristic
36C22×#13083551C2211yescharacteristic
37C22×#13083551C2211yescharacteristic
38C22×C4×Dic89C2211yescharacteristic
39C22×C4×Dic89C2211yescharacteristic
40C22×C4×Dic89C2211yescharacteristic
41C22×C4×Dic89C2211yescharacteristic
42C22×C4×Dic89C2211yescharacteristic
43#19151495C2218yescomplemented
44#19151493C2218yescomplemented
45#19151484C2218yescomplemented
46#19151483C2218yescomplemented
47#19151481C2218yescomplemented
48#19151460C2218yes—
49#19151460C2218yes—
50#19151457C2218yes—
51C4×#13083553C2218yescomplemented
52#19151449C2218yescomplemented
53#19151445C2218yes—
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C2×#15667919C2211yescharacteristic
62C22×C4⋊C4×C89C2211yescharacteristic
63C22×C4⋊C4×C89C2211yescharacteristic
64C22×C42×C89C2211yescharacteristic
65#387×C89C2218yescomplemented
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C2×#95×C89C2211yescharacteristic
69C2×#95×C89C2211yescharacteristic
70C24×D89C2311yescharacteristic
71C23×Dic89C2311yescharacteristic
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C22×C4×D89—24no—
79C22×C4×D89—24no—
80C22×C4×D89—24no—
81C22×C4×D89—24no—
82C22×C4×D89—24no—
83C22×C4×D89—24no—
84C22×C4×D89C2×C418yes—
85C22×C4×D89C2×C418yes—
86C22×C4×D89C2×C418yes—
87C22×C4×D89C2314yes—
88C22×C4×D89C2314yes—
89C22×C4×D89C2314yes—
90#15667970—232no—
91#15667969—232no—
92C2×C4⋊Dic89—24no—
93C2×C4⋊Dic89C2×C418yes—
94C2×C4⋊Dic89C2314yes—
95C2×C4⋊Dic89C2314yes—
96C2×#13083553—24no—
97C2×#13083553—24no—
98C2×#13083553—24no—
99C2×#13083553—24no—
100C2×#13083553C2×C418yes—
101C2×#13083553C2×C418yes—
102C2×#13083553C2314yes—
103C2×#13083553C2314yes—
104C2×#13083553C2314yes—
105C2×#13083553C2314yes—
106C2×#13083553C2314yes—
107C2×#13083553C2314yes—
108C4⋊C4×D89C2×C4164yescomplemented
109C2×#13083551—24no—
110C2×#13083551—24no—
111C2×#13083551—24no—
112C2×#13083551D418yes—
113C2×#13083551C2314yes—
114C2×#13083551C2314yes—
115C2×#13083551C2314yes—
116C2×#13083551C2314yes—
117C2×C4×Dic89—24no—
118C2×C4×Dic89—24no—
119C2×C4×Dic89—24no—
120C2×C4×Dic89—24no—
121C2×C4×Dic89—24no—
122C2×C4×Dic89C2314yes—
123C2×C4×Dic89C2314yes—
124C2×C4×Dic89C2314yes—
125C2×C4×Dic89C2314yes—
126C2×C4×Dic89C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131#15667919C2314yes—
132#15667919C2314yes—
133#15667919C2314yes—
134#15667919C2314yes—
135C23×C4×C89C2311yescharacteristic
136C23×C4×C89C2311yescharacteristic
137C23×C4×C89C2311yescharacteristic
138C23×C4×C89C2311yescharacteristic
139C23×C4×C89C2311yescharacteristic
140C23×C4×C89C2311yescharacteristic
141C23×C4×C89C2311yescharacteristic
142C2×C4⋊C4×C89—24no—
143C2×C4⋊C4×C89C2×C418yes—
144C2×C4⋊C4×C89C2314yes—
145C2×C4⋊C4×C89C2314yes—
146C2×C42×C89—24no—
147C2×C42×C89C2314yes—
148#95×C89C2314yes—
149#95×C89C2314yes—
150#95×C89C2314yes—
151#95×C89C2314yes—
152C23×D89—22no—
153C23×D89—22no—
154C23×D89—22no—
155C23×D89—22no—
156C23×D89C22×C414yes—
157C23×D89C2×D414yes—
158C23×D89#4114yes—
159C23×D89C2412yes—
160C22×Dic89—22no—
161C22×Dic89—22no—
162C22×Dic89—22no—
163C22×Dic89—22no—
164C22×Dic89—22no—
165C22×Dic89—22no—
166C22×Dic89—22no—
167C22×Dic89—22no—
168C22×Dic89—22no—
169C22×Dic89—22no—
170C22×Dic89—22no—
171C22×Dic89—22no—
172C22×Dic89—22no—
173C22×Dic89—22no—
174C22×Dic89—22no—
175C22×Dic89C22×C414yes—
176C22×Dic89C22×C414yes—
177C22×Dic89C22×C414yes—
178C22×Dic89C2×D414yes—
179C22×Dic89#4114yes—
180C22×Dic89#4114yes—
181C22×Dic89C2412yes—
182C22×Dic89C2412yes—
183C22×Dic89C2412yes—
184C22×Dic89C2412yes—
185C22×Dic89C2412yes—
186C22×Dic89C2412yes—
187C22×Dic89C2412yes—
188C2×C4×D89—232no—
189C2×C4×D89—232no—
190C2×C4×D89—28no—
191C2×C4×D89—28no—
192C2×C4×D89—28no—
193C2×C4×D89—28no—
194C2×C4×D89—232no—
195C2×C4×D89—28no—
196C2×C4×D89—28no—
197C2×C4×D89C22×C4116yes—
198C2×C4×D89C22×C4116yes—
199C2×C4×D89C22×C4116yes—
200C4⋊Dic89—28no—
201C4⋊Dic89C22×C4116yes—
202#13083553—28no—
203#13083553—28no—
204#13083553—28no—
205#13083553—28no—
206#13083553C22×C4116yes—
207#13083553C22×C4116yes—
208#13083551—28no—
209#13083551—28no—
210#13083551—28no—
211#13083551C2×D4116yes—
212C4×Dic89—28no—
213C4×Dic89—28no—
214C4×Dic89—28no—
215C4×Dic89—28no—
216C4×Dic89—28no—
217C24×C89C2411yescharacteristic
218C22×C4×C89—22no—
219C22×C4×C89—22no—
220C22×C4×C89—22no—
221C22×C4×C89—22no—
222C22×C4×C89—22no—
223C22×C4×C89—22no—
224C22×C4×C89—22no—
225C22×C4×C89—22no—
226C22×C4×C89—22no—
227C22×C4×C89—22no—
228C22×C4×C89—22no—
229C22×C4×C89—22no—
230C22×C4×C89—22no—
231C22×C4×C89—22no—
232C22×C4×C89—22no—
233C22×C4×C89—22no—
234C22×C4×C89—22no—
235C22×C4×C89C22×C414yes—
236C22×C4×C89C22×C414yes—
237C22×C4×C89C22×C414yes—
238C22×C4×C89C2×D414yes—
239C22×C4×C89C2412yes—
240C22×C4×C89C2412yes—
241C22×C4×C89C2412yes—
242C22×C4×C89C2412yes—
243C22×C4×C89C2412yes—
244C22×C4×C89C2412yes—
245C22×C4×C89C2412yes—
246C4⋊C4×C89—28no—
247C4⋊C4×C89C22×C4116yes—
248C42×C89—28no—
249C23×C89C23×C412yes—
250C23×C89C22×D412yes—
251C23×C89C2×#4112yes—
252C23×C89C2×#4112yes—
253C23×C89C2×#4112yes—
254C23×C892−1+412yes—
255C23×C892−1+412yes—
256C23×C89C2511yescharacteristic
257C22×D89—28no—
258C22×D89—28no—
259C22×D89—28no—
260C22×D89—28no—
261C22×D89—28no—
262C22×D89—28no—
263C22×D89—22no—
264C22×D89—22no—
265C22×D89—22no—
266C22×D89—22no—
267C22×D89C4×D4116yes—
268C22×D89C23×C414yes—
269C22×D89C22×D414yes—
270C22×D89C2×#4114yes—
271C2×C4×C89—28no—
272C2×C4×C89—28no—
273C2×C4×C89—28no—
274C2×C4×C89—28no—
275C2×C4×C89—22no—
276C2×C4×C89—22no—
277C2×C4×C89—22no—
278C2×C4×C89—22no—
279C2×C4×C89—22no—
280C2×C4×C89—22no—
281C2×C4×C89—22no—
282C2×C4×C89—22no—
283C2×C4×C89—22no—
284C2×C4×C89—22no—
285C2×C4×C89—22no—
286C2×C4×C89—22no—
287C2×C4×C89—22no—
288C2×C4×C89—22no—
289C2×C4×C89—22no—
290C2×C4×C89—22no—
291C2×C4×C89—22no—
292C2×C4×C89—44no—
293C2×C4×C89—44no—
294C2×C4×C89—44no—
295C2×C4×C89C23×C414yes—
296C2×C4×C89C23×C414yes—
297C2×C4×C89C23×C414yes—
298C2×C4×C89C22×D414yes—
299C2×Dic89—28no—
300C2×Dic89—28no—
301C2×Dic89—28no—
302C2×Dic89—22no—
303C2×Dic89—22no—
304C2×Dic89—22no—
305C2×Dic89—22no—
306C2×Dic89—22no—
307C2×Dic89—22no—
308C2×Dic89—22no—
309C2×Dic89—22no—
310C2×Dic89—22no—
311C2×Dic89—22no—
312C2×Dic89—22no—
313C2×Dic89—22no—
314C2×Dic89—22no—
315C2×Dic89—22no—
316C2×Dic89—22no—
317C2×Dic89—44no—
318C2×Dic89—44no—
319C2×Dic89—44no—
320C2×Dic89#117116yescomplemented
321C2×Dic89C23×C414yes—
322C2×Dic89C23×C414yes—
323C2×Dic89C23×C414yes—
324C2×Dic89C22×D414yes—
325C2×Dic89C2×#4114yes—
326C2×Dic89C2×#4114yes—
327C4×D89—232no—
328C4×D89—232no—
329C4×D89—232no—
330C22×C89C2×#11714yes—
331C22×C89C2×C4×D414yes—
332C22×C89#51914yes—
333C22×C89#54714yes—
334C22×C89#54714yes—
335C22×C89#55214yes—
336C22×C89#55214yes—
337C22×C89C24×C411yescharacteristic
338C22×C89C23×D411yescharacteristic
339C22×C89C22×#4111yescharacteristic
340C22×C89C22×#4111yescharacteristic
341C22×C89C22×#4111yescharacteristic
342C22×C89C2×2−1+411yescharacteristic
343C22×C89C2×2−1+411yescharacteristic
344C2×D89—232no—
345C2×D89—24no—
346C2×D89—24no—
347C2×D89—24no—
348C2×D89—24no—
349C2×D89—24no—
350C2×D89—24no—
351C2×D89C2×C4×D418yes—
352C4×C89—24no—
353C4×C89—24no—
354C4×C89—24no—
355C4×C89—24no—
356C4×C89—42no—
357C4×C89—42no—
358C4×C89—42no—
359Dic89—24no—
360Dic89—24no—
361Dic89—24no—
362Dic89—42no—
363Dic89—42no—
364Dic89—42no—
365Dic89C2×#11718yescomplemented
366C2×#2344—891nomaximal, Sylow
367C2×C89#234418yescomplemented
368C2×C89C22×#11711yescharacteristic
369C2×C89C22×C4×D411yescharacteristic
370C2×C89C2×#51911yescharacteristic
371C2×C89C2×#54711yescharacteristic
372C2×C89C2×#54711yescharacteristic
373C2×C89C2×#55211yescharacteristic
374C2×C89C2×#55211yescharacteristic
375D89—28no—
376C22×#117—891no—
377C22×#117—891no—
378C23×C4⋊C4—891no—
379#2344—8916no—
380C2×#389—891no—
381C2×#389—891no—
382C2×#387—891no—
383C2×#387—891no—
384C2×#387—891no—
385C2×#387D8911yescharacteristic, complemented
386C2×#381—891no—
387C2×#381—891no—
388C2×#380—891no—
389C2×C4×C4⋊C4—891no—
390C2×C4×C4⋊C4—891no—
391C2×C4×C22⋊C4—891no—
392C89C2×#234411yescharacteristic, complemented, Sylow
393C24×C4—891no—
394C24×C4—891no—
395C24×C4—891no—
396C2×#117—898no—
397C2×#117—898no—
398C2×#117—1788no—
399C2×#117—1788no—
400C22×C4⋊C4—891no—
401C22×C4⋊C4—891no—
402C22×C4⋊C4—891no—
403C22×C4⋊C4—8916no—
404C22×C4⋊C4—898no—
405C22×C4⋊C4—891no—
406C22×C4⋊C4—891no—
407C22×C4⋊C4—891no—
408C22×C4⋊C4—891no—
409C22×C4⋊C4—891no—
410C22×C4⋊C4C2×D8911yescharacteristic
411C22×C4⋊C4C2×D8911yescharacteristic
412C22×C22⋊C4—891no—
413C22×C22⋊C4—891no—
414C22×C22⋊C4—891no—
415C22×C22⋊C4—891no—
416C22×C42—891no—
417C22×C42—891no—
418C22×C42—891no—
419C22×C42—891no—
420C22×C42—891no—
421C22×C42C2×D8911yescharacteristic
422#389—898no—
423#389—898no—
424#387—898no—
425#387—898no—
426#387—898no—
427#387C2×D8918yescomplemented
428#381—898no—
429#381—898no—
430#380—898no—
431C4×C4⋊C4—898no—
432C4×C4⋊C4—898no—
433C4×C22⋊C4—898no—
434C2×#95—891no—
435C2×#95—891no—
436C2×#95—891no—
437C2×#95—891no—
438C2×#95—891no—
439C2×#95—891no—
440C2×#95—891no—
441C2×#95—891no—
442C2×#95C2×D8911yescharacteristic
443C2×#95C2×D8911yescharacteristic
444C2×#95C2×D8911yescharacteristic
445C2×#95C2×D8911yescharacteristic
446C25—891no—
447C23×C4—891no—
448C23×C4—891no—
449C23×C4—891no—
450C23×C4—891no—
451C23×C4—898no—
452C23×C4—898no—
453C23×C4—898no—
454C23×C4—894no—
455C23×C4—894no—
456C23×C4—894no—
457C23×C4—891no—
458C23×C4—891no—
459C23×C4—891no—
460C23×C4—1784no—
461C23×C4—1784no—
462C23×C4—1784no—
463C23×C4—1784no—
464C23×C4—1784no—
465C23×C4—1784no—
466C23×C4C22×D8911yescharacteristic
467C23×C4C22×D8911yescharacteristic
468C23×C4C22×D8911yescharacteristic
469C23×C4C22×D8911yescharacteristic
470C23×C4C22×D8911yescharacteristic
471C23×C4C22×D8911yescharacteristic
472C23×C4C22×D8911yescharacteristic
473#117—17832no—
474#117—17832no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—898no—
477C2×C4⋊C4—898no—
478C2×C4⋊C4—898no—
479C2×C4⋊C4—894no—
480C2×C4⋊C4—894no—
481C2×C4⋊C4—894no—
482C2×C4⋊C4—8964no—
483C2×C4⋊C4—894no—
484C2×C4⋊C4—894no—
485C2×C4⋊C4—894no—
486C2×C4⋊C4—894no—
487C2×C4⋊C4—894no—
488C2×C4⋊C4—1784no—
489C2×C4⋊C4—1784no—
490C2×C4⋊C4—1784no—
491C2×C4⋊C4—1784no—
492C2×C4⋊C4—1784no—
493C2×C4⋊C4C4×D8918yes—
494C2×C4⋊C4C22×D8914yes—
495C2×C4⋊C4C22×D8914yes—
496C2×C22⋊C4—898no—
497C2×C22⋊C4—894no—
498C2×C22⋊C4—894no—
499C2×C22⋊C4—894no—
500C2×C22⋊C4—894no—
501C2×C22⋊C4—1784no—
502C2×C22⋊C4—1784no—
503C2×C22⋊C4—1784no—
504C2×C42—24no—
505C2×C42—894no—
506C2×C42—894no—
507C2×C42—894no—
508C2×C42—894no—
509C2×C42—894no—
510C2×C42—1784no—
511C2×C42—1784no—
512C2×C42—1784no—
513C2×C42—1784no—
514C2×C42—1784no—
515C2×C42C22×D8914yes—
516#95—894no—
517#95—894no—
518#95—894no—
519#95—894no—
520#95—894no—
521#95—894no—
522#95—894no—
523#95—894no—
524#95C22×D8914yes—
525#95C22×D8914yes—
526#95C22×D8914yes—
527#95C22×D8914yes—
528C24—894no—
529C24—894no—
530C24—894no—
531C24—892no—
532C24—1782no—
533C24—1782no—
534C24—1782no—
535C24—1782no—
536C24C23×D8911yescharacteristic
537C22×C4—22no—
538C22×C4—22no—
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—894no—
555C22×C4—894no—
556C22×C4—894no—
557C22×C4—892no—
558C22×C4—894no—
559C22×C4—894no—
560C22×C4—894no—
561C22×C4—892no—
562C22×C4—892no—
563C22×C4—892no—
564C22×C4—8916no—
565C22×C4—8916no—
566C22×C4—8916no—
567C22×C4—892no—
568C22×C4—892no—
569C22×C4—892no—
570C22×C4—1788no—
571C22×C4—1788no—
572C22×C4—17832no—
573C22×C4—1788no—
574C22×C4—1788no—
575C22×C4—1788no—
576C22×C4—1788no—
577C22×C4—17832no—
578C22×C4—17832no—
579C22×C4—1782no—
580C22×C4—1782no—
581C22×C4—1782no—
582C22×C4—1782no—
583C22×C4—1782no—
584C22×C4—1782no—
585C22×C4—1782no—
586C22×C4—1782no—
587C22×C4—1782no—
588C22×C4—1782no—
589C22×C4—1782no—
590C22×C4—1782no—
591C22×C4—1782no—
592C22×C4—1782no—
593C22×C4—1782no—
594C22×C4C2×C4×D8914yes—
595C22×C4C2×C4×D8914yes—
596C22×C4C2×C4×D8914yes—
597C22×C4D4×D8914yes—
598C22×C4C23×D8912yes—
599C22×C4C23×D8912yes—
600C22×C4C23×D8912yes—
601C22×C4C23×D8912yes—
602C22×C4C23×D8912yes—
603C22×C4C23×D8912yes—
604C22×C4C23×D8912yes—
605C4⋊C4—28no—
606C4⋊C4—8916no—
607C4⋊C4—8916no—
608C4⋊C4—8916no—
609C4⋊C4—1788no—
610C4⋊C4—1788no—
611C4⋊C4—1788no—
612C4⋊C4—1788no—
613C4⋊C4—1788no—
614C4⋊C4C2×C4×D89116yes—
615C22⋊C4—8916no—
616C22⋊C4—1788no—
617C22⋊C4—1788no—
618C22⋊C4—1788no—
619C42—28no—
620C42—1788no—
621C42—1788no—
622C42—1788no—
623C42—1788no—
624C42—1788no—
625C23—894no—
626C23—894no—
627C23—894no—
628C23—8916no—
629C23—1782no—
630C23—1782no—
631C23—1782no—
632C23—1782no—
633C23—1788no—
634C23—1788no—
635C23—1788no—
636C23—1788no—
637C23—1788no—
638C23—1788no—
639C23C22×C4×D8912yes—
640C23C2×D4×D8912yes—
641C23#41×D8912yes—
642C23#41×D8912yes—
643C23#41×D8912yes—
644C23#1566805912yes—
645C23#1566806012yes—
646C23C24×D8911yescharacteristic
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—894no—
672C2×C4—894no—
673C2×C4—894no—
674C2×C4—8916no—
675C2×C4—894no—
676C2×C4—894no—
677C2×C4—894no—
678C2×C4—3564no—
679C2×C4—3564no—
680C2×C4—3564no—
681C2×C4—17832no—
682C2×C4—17832no—
683C2×C4—17832no—
684C2×C4—1782no—
685C2×C4—1782no—
686C2×C4—1782no—
687C2×C4—1782no—
688C2×C4—1782no—
689C2×C4—1782no—
690C2×C4—1782no—
691C2×C4—1782no—
692C2×C4—1782no—
693C2×C4—1782no—
694C2×C4—1782no—
695C2×C4—1782no—
696C2×C4—1782no—
697C2×C4—1782no—
698C2×C4—1782no—
699C2×C4—1788no—
700C2×C4—1788no—
701C2×C4—1788no—
702C2×C4C22×C4×D8914yes—
703C2×C4C22×C4×D8914yes—
704C2×C4C22×C4×D8914yes—
705C2×C4C2×D4×D8914yes—
706C22—898no—
707C22—1784no—
708C22—1784no—
709C22—1784no—
710C22—1784no—
711C22—1784no—
712C22—1784no—
713C22—17832no—
714C22#117×D8914yes—
715C22C4×D4×D8914yes—
716C22#1915207414yes—
717C22#1915224614yes—
718C22#1915225014yes—
719C22#1915228014yes—
720C22#1915228414yes—
721C22C23×C4×D8911yescharacteristic
722C22C22×D4×D8911yescharacteristic
723C22C2×#41×D8911yescharacteristic
724C22C2×#41×D8911yescharacteristic
725C22C2×#41×D8911yescharacteristic
726C22C2×#1566805911yescharacteristic
727C22C2×#1566806011yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—898no—
736C4—3562no—
737C4—3562no—
738C4—3562no—
739C4—1784no—
740C4—1784no—
741C4—1784no—
742C2—1788no—
743C2#2602311818yesdirect product factor
744C2C2×#117×D8911yescharacteristic
745C2C2×C4×D4×D8911yescharacteristic
746C2C2×#1915207411yescharacteristic
747C2C2×#1915224611yescharacteristic
748C2C2×#1915225011yescharacteristic
749C2C2×#1915228011yescharacteristic
750C2C2×#1915228411yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC24×D89C23
cosocleC23×C89C25
hypercenterC2×#387D89
hypocenterC89C2×#2344
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
4. #26023118C2direct (N × H)
5. C2×#19151495C2semidirect
6. C2×#19151493C2semidirect
7. C2×#19151484C2semidirect
8. C2×#19151483C2semidirect
9. C2×#19151481C2semidirect
13. C2×C4×#13083553C2semidirect
14. C2×#19151449C2semidirect
16. C2×#387×C89C2semidirect
32. C2×C4⋊C4×D89C4semidirect
43. #19151495C22semidirect
44. #19151493C22semidirect
45. #19151484C22semidirect
46. #19151483C22semidirect
47. #19151481C22semidirect
51. C4×#13083553C22semidirect
52. #19151449C22semidirect
65. #387×C89C22semidirect
108. C4⋊C4×D89C2×C4semidirect
320. C2×Dic89#117semidirect
365. Dic89C2×#117semidirect
367. C2×C89#2344semidirect
385. C2×#387D89semidirect
392. C89C2×#2344semidirect
427. #387C2×D89semidirect
743. C2#26023118direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679702
C22×#156679692
C22×C4⋊C4×D892
#260231182
C2×#191514952
C2×#191514932
C2×#191514842
C2×#191514832
C2×#191514812
C2×#191514602
C2×#191514572
C2×C4×#130835532
C2×#191514492
C2×#191514452
C2×#387×C892
C2×#234489