Finite Group Databasebeta

← C22⋊C4×#10621898 #25255799

Subgroups — C22⋊C4×#10621898 #25255799

Order 11008.

5646 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621898C211yesmaximal, characteristic
2C2×C4×#10621898C212yesmaximal, complemented
3#19137435C212yesmaximal, complemented
4C22⋊C4×Dic86C212yesmaximal, complemented
5#19137426C212yesmaximal, complemented
6#19137422C214yesmaximal, complemented
7C22⋊C4×D172C212yesmaximal, complemented
8C22⋊C4×C22⋊D43C214yesmaximal, complemented
9#19137085C212yesmaximal, complemented
10#19137081C214yesmaximal, complemented
11#19136978C211yesmaximal, characteristic, complemented
12#19136976C212yesmaximal, complemented
13C4×C22⋊C4×D43C212yesmaximal, complemented
14C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
15C22×#10621898—216no—
16C22×#10621898C4116yescomplemented
17C22×#10621898C2212yes—
18C22×#10621898C2211yescharacteristic
19C22×#10621898C2212yes—
20C22×#10621898C2211yescharacteristic
21C22×#10621898C2211yescharacteristic
22C22×#10621898C2211yescharacteristic
23C23×Dic86C2211yescharacteristic
24C23×D172C2211yescharacteristic
25C23×C22⋊D43C2212yes—
26C23×C4×D43C2212yes—
27C4×#10621898—216no—
28C2×C4×Dic86C2214yescomplemented
29C2×C4×D172C2214yescomplemented
30C2×C4×C22⋊D43C2218yescomplemented
31C2×#13063284C2212yescomplemented
32C2×#13063282C2214yescomplemented
33C2×C22⋊C4×D43C2214yes—
34C2×C42×D43C2214yescomplemented
35#14582805C2214yescomplemented
36#14582803C2218yescomplemented
37#14582801C2214yescomplemented
38#14582799C2218yescomplemented
39#14582778C2218yescomplemented
40#14582777C2218yescomplemented
41#14582775C2218yescomplemented
42#14582762C2212yescomplemented
43#14582761C2214yescomplemented
44#14582759C2212yes—
45#14582759C2212yescomplemented
46#14582758C2214yescomplemented
47#14582757C2214yes—
48#14582755C2212yes—
49#14582754C2214yes—
50C22⋊C4×Dic43C2214yes—
51C4×(C2×D43)⋊C4C2214yescomplemented
52C4×(C2×D43)⋊C4C2214yescomplemented
53C4×C22⋊Dic43C2212yes—
54C4×C22⋊Dic43C2212yescomplemented
55#14582746C2214yescomplemented
56#95×D43C2214yescomplemented
57C24×C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2212yes—
59C22×C42×C43C2212yescomplemented
60C4×C22⋊C4×C43C2212yes—
61C4×C22⋊C4×C43C2211yescharacteristic
62C4×C22⋊C4×C43C2211yescharacteristic
63C4×C22⋊C4×C43C2212yescomplemented
64C4×C22⋊C4×C43C2212yescomplemented
65C2×#95×C43C2212yescomplemented
66C24×D43C2312yes—
67C2×#10621898—28no—
68C2×#10621898—216no—
69C2×#10621898—2128no—
70C2×#10621898—28no—
71C2×#10621898—216no—
72C2×#10621898—28no—
73C2×#10621898C2×C418yes—
74C2×#10621898C2×C418yescomplemented
75C2×#10621898C2×C4116yescomplemented
76C2×#10621898C2×C418yescomplemented
77C2×#10621898C2×C4116yescomplemented
78C2×#10621898C2×C418yescomplemented
79C2×#10621898D4116yes—
80C22×Dic86—28no—
81C22×Dic86C2×C418yescomplemented
82C22×Dic86C2312yes—
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2311yescharacteristic
85C22×D172—28no—
86C22×D172C2×C418yescomplemented
87C22×D172C2311yescharacteristic
88C22×D172C2312yes—
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—216no—
91C22×C22⋊D43C2×C4116yescomplemented
92C22×C22⋊D43C2312yes—
93C22×C22⋊D43C2312yes—
94C22×C22⋊D43C2312yes—
95C22×C22⋊D43C2312yes—
96C23×Dic43C2312yes—
97C22×C4×D43—216no—
98C22×C4×D43C2×C4116yescomplemented
99C22×C4×D43C2318yes—
100C22×C4×D43C2312yes—
101C22×C4×D43C2312yes—
102C22×C4×D43C2312yes—
103C22×C4×D43C2312yes—
104C4×Dic86—216no—
105C4×D172—216no—
106C4×C22⋊D43—232no—
107#13063284—28no—
108#13063282—216no—
109C2×C4⋊Dic43C2314yes—
110C2×Dic43⋊C4C2318yes—
111C2×C22⋊Dic43C2314yes—
112C2×C22⋊Dic43C2314yes—
113C2×C22⋊Dic43C2314yes—
114C2×(C2×D43)⋊C4C2318yes—
115C2×(C2×D43)⋊C4C2318yes—
116C2×(C2×D43)⋊C4C2318yes—
117C22⋊C4×D43—216no—
118C2×C4×Dic43C2318yes—
119C2×C4×Dic43C2314yes—
120C42×D43—216no—
121C43⋊#95C2314yes—
122C43⋊#95C2318yes—
123C43⋊#95C2318yes—
124C43⋊#95C2314yes—
125C25×C43C2311yescharacteristic
126C23×C4×C43—28no—
127C23×C4×C43C2×C418yescomplemented
128C23×C4×C43C2314yes—
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—28no—
136C2×C22⋊C4×C43C2314yes—
137C2×C22⋊C4×C43C2312yes—
138C2×C22⋊C4×C43C2312yes—
139C2×C42×C43—28no—
140C2×C42×C43C2314yes—
141C2×C42×C43C2312yes—
142C2×C42×C43C2312yes—
143#95×C43C2314yes—
144#95×C43C2312yes—
145#95×C43C2312yes—
146C24×C43—24no—
147C24×C43—24no—
148C24×C43—42no—
149C24×C43C22×C414yes—
150C24×C43C2411yescharacteristic
151C24×C43C2411yescharacteristic
152C24×C43C2411yescharacteristic
153C23×D43—28no—
154C23×D43—28no—
155C23×D43—44no—
156C23×D43C22×C418yes—
157C23×D43C2412yes—
158C23×D43C2412yes—
159C22×C4×C43—232no—
160C22×C4×C43—24no—
161C22×C4×C43—24no—
162C22×C4×C43—24no—
163C22×C4×C43—24no—
164C22×C4×C43—28no—
165C22×C4×C43—24no—
166C22×C4×C43—28no—
167C22×C4×C43—44no—
168C22×C4×C43C22×C414yes—
169C22×C4×C43C22×C414yes—
170C22×C4×C43C22×C414yes—
171C22×C4×C43C22×C414yes—
172C22×C4×C43C22×C414yes—
173C22×C4×C43C22×C414yes—
174C22×C4×C43C2×D418yes—
175C22×C4×C43C2414yes—
176C22×C4×C43C2411yescharacteristic
177C22×C4×C43C2411yescharacteristic
178C22×C4×C43C2414yes—
179C22×C4×C43C2411yescharacteristic
180C22×C4×C43C2411yescharacteristic
181C2×C22⋊D43—264no—
182C2×C22⋊D43—28no—
183C2×C22⋊D43—28no—
184C2×C22⋊D43—28no—
185C2×C22⋊D43C22×C418yes—
186C2×C22⋊D43C22×C418yes—
187C2×C22⋊D43C22×C418yes—
188C2×C22⋊D43C22×C418yes—
189C2×C22⋊D43C2×D4116yes—
190C22×Dic43—28no—
191C22×Dic43C22×C418yes—
192C22×Dic43C2418yes—
193C22×Dic43C2412yes—
194C22×Dic43C2412yes—
195#10621898—232no—
196#10621898—264no—
197#10621898—232no—
198#10621898—264no—
199#10621898—232no—
200#10621898C22⋊C4164yesdirect product factor
201C2×D172—24no—
202C2×D172—232no—
203C2×D172—28no—
204C2×D172C22×C414yes—
205C2×D172C22×C418yes—
206C2×D172C22×C414yes—
207C2×D172C2×D418yes—
208C2×C4×D43—28no—
209C2×C4×D43—28no—
210C2×C4×D43—264no—
211C2×C4×D43—216no—
212C2×C4×D43—28no—
213C2×C4×D43—216no—
214C2×C4×D43—48no—
215C2×C4×D43C22×C418yes—
216C2×C4×D43C22×C418yes—
217C2×C4×D43C22×C418yes—
218C2×C4×D43C22×C418yes—
219C2×C4×D43C2×D4116yes—
220C2×Dic86—24no—
221C2×Dic86—28no—
222C2×Dic86—232no—
223C2×Dic86C22×C414yes—
224C2×Dic86C22×C418yes—
225C2×Dic86C22×C414yes—
226C2×Dic86C2×D418yes—
227C22⋊C4×C43—28no—
228C22⋊C4×C43—24no—
229C22⋊C4×C43#4118yescomplemented
230C42×C43—24no—
231C42×C43—24no—
232C42×C43—28no—
233C22⋊Dic43—28no—
234C22⋊Dic43—28no—
235C22⋊Dic43—44no—
236(C2×D43)⋊C4—216no—
237(C2×D43)⋊C4—216no—
238(C2×D43)⋊C4—48no—
239C4⋊Dic43—28no—
240Dic43⋊C4—216no—
241C4×Dic43—28no—
242C4×Dic43—216no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—28no—
248C23×C43—28no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—44no—
253C23×C43—416no—
254C23×C43C23×C412yes—
255C23×C43C23×C412yes—
256C23×C43C23×C412yes—
257C23×C43C22×D414yes—
258C23×C43C2×#4114yes—
259C23×C43C2511yescharacteristic
260C22×D43—24no—
261C22×D43—24no—
262C22×D43—216no—
263C22×D43—24no—
264C22×D43—24no—
265C22×D43—24no—
266C22×D43—216no—
267C22×D43—48no—
268C22×D43—432no—
269C22×D43C23×C414yes—
270C22×D43C23×C414yes—
271C22×D43C22×D418yes—
272C2×C4×C43—28no—
273C2×C4×C43—24no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—24no—
277C2×C4×C43—28no—
278C2×C4×C43—28no—
279C2×C4×C43—28no—
280C2×C4×C43—28no—
281C2×C4×C43—24no—
282C2×C4×C43—24no—
283C2×C4×C43—24no—
284C2×C4×C43—416no—
285C2×C4×C43C2×C22⋊C4116yescomplemented
286C2×C4×C43C23×C412yes—
287C2×C4×C43C23×C412yes—
288C2×C4×C43C23×C412yes—
289C2×C4×C43C23×C412yes—
290C2×C4×C43C22×D414yes—
291C2×C4×C43C22×D414yes—
292C2×C4×C43C2×#4118yescomplemented
293C22⋊D43—216no—
294C22⋊D43—216no—
295C22⋊D43—216no—
296C22⋊D43C2×C22⋊C4132yescomplemented
297C2×Dic43—24no—
298C2×Dic43—216no—
299C2×Dic43—28no—
300C2×Dic43—28no—
301C2×Dic43—28no—
302C2×Dic43C23×C414yes—
303C2×Dic43C23×C414yes—
304C2×Dic43C22×D418yes—
305D172—216no—
306D172—28no—
307D172C2×C22⋊C4116yescomplemented
308C4×D43—216no—
309C4×D43—216no—
310C4×D43—216no—
311C4×D43—432no—
312C4×D43C2×C22⋊C4132yescomplemented
313Dic86—28no—
314Dic86—216no—
315Dic86C2×C22⋊C4116yescomplemented
316C22⋊C4×#41—431nomaximal, Sylow
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—28no—
322C22×C43—28no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—416no—
327C22×C43—44no—
328C22×C43C22×C22⋊C414yes—
329C22×C43C4×#4114yescomplemented
330C22×C43C24×C411yescharacteristic
331C22×C43C23×D412yes—
332C22×C43C22×#4112yes—
333C22×C43#58512yes—
334C2×D43—24no—
335C2×D43—24no—
336C2×D43—216no—
337C2×D43—24no—
338C2×D43—24no—
339C2×D43—24no—
340C2×D43—432no—
341C2×D43—48no—
342C2×D43C22×C22⋊C418yes—
343C4×C43—22no—
344C4×C43—22no—
345C4×C43—28no—
346C4×C43—44no—
347C4×C43C22×C22⋊C414yes—
348C4×C43C22×C22⋊C414yes—
349Dic43—24no—
350Dic43—48no—
351Dic43C22×C22⋊C418yes—
352C23×#41—431no—
353C2×C4×#41—432no—
354#2341—432no—
355Q8×C22⋊C4—432no—
356#2339—432no—
357#2339—434no—
358D4×C22⋊C4—432no—
359D4×C22⋊C4—434no—
360#2297—432no—
361#2297—434no—
362#2280—432no—
363#2280—431no—
364C2×C4×C22⋊C4—432no—
365C2×C4×C22⋊C4D4311yescharacteristic, complemented
366C2×C43—24no—
367C2×C43—24no—
368C2×C43—42no—
369C2×C43C23×C22⋊C411yescharacteristic
370C2×C43C2×C4×#4111yescharacteristic
371C2×C43#342811yescharacteristic
372C2×C43D4×#4114yes—
373D43—28no—
374D43—44no—
375C22×#41—431no—
376C22×#41—431no—
377C22×#41—432no—
378C22×#41—431no—
379C22×#41—432no—
380C22×#41—431no—
381C22×#41—4316no—
382C22×#41—8616no—
383C23×Q8—431no—
384C23×D4—432no—
385C23×D4—431no—
386C24×C4—432no—
387C24×C4C2×D4311yescharacteristic
388C4×#41—8616no—
389C2×C4×Q8—434no—
390C2×C4×D4—438no—
391C2×C4×D4—434no—
392C2×#117—432no—
393C2×#117—434no—
394C22×C22⋊C4—434no—
395C22×C22⋊C4C2×D4312yes—
396C22×C42—434no—
397C22×C42C2×D4312yescomplemented
398#391—434no—
399#391—438no—
400#390—438no—
401#390—434no—
402#386—438no—
403#386—438no—
404#386—438no—
405#381—432no—
406#381—434no—
407#380—432no—
408#380—432no—
409#380—434no—
410#380—434no—
411#379—432no—
412#379—434no—
413C4×C22⋊C4—432no—
414C4×C22⋊C4—432no—
415C4×C22⋊C4—434no—
416C4×C22⋊C4—434no—
417C4×C22⋊C4—434no—
418C4×C22⋊C4—434no—
419C4×C22⋊C4C2×D4312yes—
420C4×C22⋊C4C2×D4311yescharacteristic
421C4×C22⋊C4C2×D4311yescharacteristic
422C4×C22⋊C4C2×D4312yescomplemented
423C4×C22⋊C4C2×D4312yescomplemented
424C2×#95—434no—
425C2×#95C2×D4312yescomplemented
426C43C22⋊C4×#4111yescharacteristic, complemented, Sylow
427C25—432no—
428C25C22×D4311yescharacteristic
429C2×#41—438no—
430C2×#41—4316no—
431C2×#41—4316no—
432C2×#41—438no—
433C2×#41—438no—
434C2×#41—438no—
435C2×#41—4316no—
436C2×#41—8616no—
437C2×#41—8616no—
438C2×#41—868no—
439C2×#41—868no—
440C2×#41—86128no—
441C2×#41—868no—
442C22×Q8—438no—
443C22×Q8—431no—
444C22×Q8—432no—
445C22×Q8—431no—
446C22×Q8—868no—
447C22×D4—432no—
448C22×D4—4316no—
449C22×D4—432no—
450C22×D4—432no—
451C22×D4—432no—
452C22×D4—438no—
453C22×D4—431no—
454C22×D4—432no—
455C22×D4—431no—
456C22×D4—868no—
457C22×D4—8616no—
458C23×C4—28no—
459C23×C4—432no—
460C23×C4—432no—
461C23×C4—4316no—
462C23×C4—432no—
463C23×C4—432no—
464C23×C4—432no—
465C23×C4—438no—
466C23×C4—8616no—
467C23×C4C4×D4318yescomplemented
468C23×C4C22×D4314yes—
469C23×C4C22×D4311yescharacteristic
470C23×C4C22×D4311yescharacteristic
471C23×C4C22×D4311yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C23×C4C22×D4311yescharacteristic
475C4×Q8—8616no—
476C4×D4—8616no—
477C4×D4—8632no—
478#117—8616no—
479#117—868no—
480C2×C4⋊C4—438no—
481C2×C4⋊C4—434no—
482C2×C22⋊C4—28no—
483C2×C22⋊C4—434no—
484C2×C22⋊C4—434no—
485C2×C22⋊C4—438no—
486C2×C22⋊C4—438no—
487C2×C22⋊C4—434no—
488C2×C22⋊C4—438no—
489C2×C22⋊C4—8616no—
490C2×C22⋊C4C22×D4312yes—
491C2×C22⋊C4C22×D4314yes—
492C2×C22⋊C4C22×D4312yes—
493C2×C42—28no—
494C2×C42—438no—
495C2×C42—434no—
496C2×C42—8616no—
497C2×C42C22×D4314yes—
498C2×C42C22×D4312yes—
499C2×C42C22×D4312yes—
500#95—434no—
501#95—438no—
502#95—438no—
503#95—434no—
504#95C22×D4312yes—
505#95C22×D4312yes—
506#95C22×D4314yes—
507C24—24no—
508C24—24no—
509C24—42no—
510C24—432no—
511C24—432no—
512C24—438no—
513C24—868no—
514C24—868no—
515C24—1724no—
516C24C2×C4×D4314yes—
517C24C23×D4311yescharacteristic
518C24C23×D4311yescharacteristic
519C24C23×D4311yescharacteristic
520#41—4364no—
521#41—8664no—
522#41—8664no—
523#41—8632no—
524#41—8632no—
525#41—8632no—
526C2×Q8—434no—
527C2×Q8—438no—
528C2×Q8—434no—
529C2×Q8—438no—
530C2×Q8—868no—
531C2×Q8—8632no—
532C2×Q8—864no—
533C2×D4—438no—
534C2×D4—4316no—
535C2×D4—438no—
536C2×D4—438no—
537C2×D4—438no—
538C2×D4—434no—
539C2×D4—438no—
540C2×D4—434no—
541C2×D4—438no—
542C2×D4—8632no—
543C2×D4—868no—
544C2×D4—868no—
545C2×D4—8664no—
546C2×D4—868no—
547C2×D4—868no—
548C2×D4—864no—
549C22×C4—24no—
550C22×C4—232no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—44no—
558C22×C4—432no—
559C22×C4—438no—
560C22×C4—4316no—
561C22×C4—438no—
562C22×C4—432no—
563C22×C4—438no—
564C22×C4—438no—
565C22×C4—438no—
566C22×C4—438no—
567C22×C4—868no—
568C22×C4—8664no—
569C22×C4—868no—
570C22×C4—8616no—
571C22×C4—868no—
572C22×C4—868no—
573C22×C4—8616no—
574C22×C4—1728no—
575C22×C4C2×C4×D4314yes—
576C22×C4C2×C4×D4314yes—
577C22×C4C2×C4×D4314yes—
578C22×C4C2×C4×D4314yes—
579C22×C4C2×C4×D4314yes—
580C22×C4C2×C4×D4314yes—
581C22×C4D4×D4318yes—
582C22×C4C23×D4314yes—
583C22×C4C23×D4311yescharacteristic
584C22×C4C23×D4311yescharacteristic
585C22×C4C23×D4314yes—
586C22×C4C23×D4311yescharacteristic
587C22×C4C23×D4311yescharacteristic
588C4⋊C4—8616no—
589C4⋊C4—868no—
590C22⋊C4—24no—
591C22⋊C4—28no—
592C22⋊C4—8616no—
593C22⋊C4—868no—
594C22⋊C4—868no—
595C22⋊C4—8616no—
596C22⋊C4—1728no—
597C22⋊C4—1724no—
598C22⋊C4#1062189818yesdirect product factor
599C42—24no—
600C42—24no—
601C42—28no—
602C42—8616no—
603C42—868no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—44no—
614C23—416no—
615C23—434no—
616C23—438no—
617C23—434no—
618C23—8616no—
619C23—864no—
620C23—864no—
621C23—8616no—
622C23—864no—
623C23—864no—
624C23—864no—
625C23—1728no—
626C23—17232no—
627C23C22×C4×D4312yes—
628C23C22×C4×D4312yes—
629C23C22×C4×D4312yes—
630C23C2×D4×D4314yes—
631C23C2×#1062189814yes—
632C23C24×D4311yescharacteristic
633Q8—4316no—
634Q8—8616no—
635Q8—868no—
636D4—4332no—
637D4—4316no—
638D4—8616no—
639D4—8616no—
640D4—8616no—
641D4—8616no—
642D4—868no—
643C2×C4—28no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—416no—
656C2×C4—434no—
657C2×C4—438no—
658C2×C4—4332no—
659C2×C4—434no—
660C2×C4—8616no—
661C2×C4—8616no—
662C2×C4—8616no—
663C2×C4—864no—
664C2×C4—8616no—
665C2×C4—868no—
666C2×C4—868no—
667C2×C4—868no—
668C2×C4—17232no—
669C2×C4C22⋊C4×D43116yescomplemented
670C2×C4C22×C4×D4312yes—
671C2×C4C22×C4×D4312yes—
672C2×C4C22×C4×D4312yes—
673C2×C4C22×C4×D4312yes—
674C2×C4C2×D4×D4314yes—
675C2×C4C2×D4×D4314yes—
676C2×C4C2×#1062189818yescomplemented
677C22—22no—
678C22—22no—
679C22—28no—
680C22—28no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—416no—
687C22—44no—
688C22—438no—
689C22—864no—
690C22—8616no—
691C22—864no—
692C22—864no—
693C22—864no—
694C22—864no—
695C22—17232no—
696C22—1728no—
697C22C2×C22⋊C4×D4314yes—
698C22C4×#1062189814yescomplemented
699C22C23×C4×D4311yescharacteristic
700C22C22×D4×D4312yes—
701C22C22×#1062189812yes—
702C22#1458373512yes—
703C4—28no—
704C4—22no—
705C4—22no—
706C4—44no—
707C4—438no—
708C4—864no—
709C4—1728no—
710C4C2×C22⋊C4×D4314yes—
711C4C2×C22⋊C4×D4314yes—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—868no—
716C2—1724no—
717C2C22×C22⋊C4×D4311yescharacteristic
718C2C2×C4×#1062189811yescharacteristic
719C2#1914779611yescharacteristic
720C2D4×#1062189814yes—
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC23×C43C25
prime radicalC23×#10621898C2
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C22⋊C4×#41
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621898C2semidirect
3. #19137435C2semidirect
4. C22⋊C4×Dic86C2semidirect
5. #19137426C2semidirect
6. #19137422C2semidirect
7. C22⋊C4×D172C2semidirect
8. C22⋊C4×C22⋊D43C2semidirect
9. #19137085C2semidirect
10. #19137081C2semidirect
11. #19136978C2semidirect
12. #19136976C2semidirect
13. C4×C22⋊C4×D43C2semidirect
14. C2×C4×C22⋊C4×C43C2semidirect
16. C22×#10621898C4semidirect
28. C2×C4×Dic86C22semidirect
29. C2×C4×D172C22semidirect
30. C2×C4×C22⋊D43C22semidirect
31. C2×#13063284C22semidirect
32. C2×#13063282C22semidirect
34. C2×C42×D43C22semidirect
35. #14582805C22semidirect
36. #14582803C22semidirect
37. #14582801C22semidirect
38. #14582799C22semidirect
39. #14582778C22semidirect
40. #14582777C22semidirect
41. #14582775C22semidirect
42. #14582762C22semidirect
43. #14582761C22semidirect
45. #14582759C22semidirect
46. #14582758C22semidirect
51. C4×(C2×D43)⋊C4C22semidirect
52. C4×(C2×D43)⋊C4C22semidirect
54. C4×C22⋊Dic43C22semidirect
55. #14582746C22semidirect
56. #95×D43C22semidirect
59. C22×C42×C43C22semidirect
63. C4×C22⋊C4×C43C22semidirect
64. C4×C22⋊C4×C43C22semidirect
65. C2×#95×C43C22semidirect
74. C2×#10621898C2×C4semidirect
75. C2×#10621898C2×C4semidirect
76. C2×#10621898C2×C4semidirect
77. C2×#10621898C2×C4semidirect
78. C2×#10621898C2×C4semidirect
81. C22×Dic86C2×C4semidirect
86. C22×D172C2×C4semidirect
91. C22×C22⋊D43C2×C4semidirect
98. C22×C4×D43C2×C4semidirect
127. C23×C4×C43C2×C4semidirect
200. #10621898C22⋊C4direct (N × H)
229. C22⋊C4×C43#41semidirect
285. C2×C4×C43C2×C22⋊C4semidirect
292. C2×C4×C43C2×#41semidirect
296. C22⋊D43C2×C22⋊C4semidirect
307. D172C2×C22⋊C4semidirect
312. C4×D43C2×C22⋊C4semidirect
315. Dic86C2×C22⋊C4semidirect
329. C22×C43C4×#41semidirect
365. C2×C4×C22⋊C4D43semidirect
397. C22×C42C2×D43semidirect
422. C4×C22⋊C4C2×D43semidirect
423. C4×C22⋊C4C2×D43semidirect
425. C2×#95C2×D43semidirect
426. C43C22⋊C4×#41semidirect
467. C23×C4C4×D43semidirect
598. C22⋊C4#10621898direct (N × H)
669. C2×C4C22⋊C4×D43semidirect
676. C2×C4C2×#10621898semidirect
698. C22C4×#10621898semidirect

Maximal subgroups

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

subgroupindex
C23×#106218982
C2×C4×#106218982
#191374352
C22⋊C4×Dic862
#191374262
#191374222
C22⋊C4×D1722
C22⋊C4×C22⋊D432
#191370852
#191370812
#191369782
#191369762
C4×C22⋊C4×D432
C2×C4×C22⋊C4×C432
C22⋊C4×#4143