Finite Group Databasebeta

← C2×#13118287 #16030875

Subgroups — C2×#13118287 #16030875

Order 3328.

3830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88178C211yesmaximal, characteristic, complemented
2C22×#88178C211yesmaximal, characteristic, complemented
3C23×C4⋊Dic13C211yesmaximal, characteristic, complemented
4#13118287C2116yesmaximal, direct product factor
5C2×#11718645C212yesmaximal, complemented
6C2×#11718609C212yesmaximal, complemented
7C2×#11718590C211yesmaximal, characteristic, complemented
8C2×#11718589C211yesmaximal, characteristic, complemented
9C2×#11718881C212yesmaximal
10C2×#11718873C211yesmaximal, characteristic, complemented
11C2×#11718603C212yesmaximal, complemented
12C22×C4×D4×C13C211yesmaximal, characteristic
13C23×D4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C24×C4×C13C2211yescharacteristic
16C24×Dic13C2212yes—
17C23×Dic26C2211yescharacteristic
18C2×C4×D4×C13—28no—
19C2×C4×D4×C13C2218yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C22⋊Dic13C2212yes—
25C22×C22⋊Dic13C2212yes—
26C22×C22⋊Dic13C2212yes—
27C22×C4⋊Dic13—28no—
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2212yes—
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4⋊Dic13C2218yescomplemented
33C2×#88178—28no—
34C2×#88178—28no—
35C2×#88178C2218yescomplemented
36C2×#88178C2218yescomplemented
37C22×#6101C2212yes—
38C22×#6101C2212yes—
39C22×#6101C2212yes—
40#11718881C22116yes—
41#11718873C2218yescomplemented
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44C2×#88071C2212yes—
45C2×#88071C2212yes—
46#11718645C22116yescomplemented
47#11718609C22116yescomplemented
48#11718603C22116yescomplemented
49#11718590C2218yescomplemented
50#11718589C2218yescomplemented
51C25×C13C2311yescharacteristic
52C25×C13C2311yescharacteristic
53C22×D4×C13—24no—
54C22×D4×C13—24no—
55C22×D4×C13Q818yescomplemented
56C22×D4×C13C2314yes—
57C23×C4×C13—24no—
58C23×C4×C13—24no—
59C23×C4×C13—24no—
60C23×C4×C13—24no—
61C23×C4×C13—24no—
62C23×C4×C13D418yes—
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2314yes—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2314yes—
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×Dic13—28no—
71C23×Dic13—28no—
72C23×Dic13—44no—
73C23×Dic13C2312yes—
74C23×Dic13C2312yes—
75C23×Dic13C2312yes—
76C23×Dic13C2318yes—
77C23×Dic13C2312yes—
78C22×Dic26—24no—
79C22×Dic26—24no—
80C22×Dic26—24no—
81C22×Dic26C2314yes—
82C4×D4×C13—232no—
83C2×C13×C4⋊C4—24no—
84C2×C13×C4⋊C4C2314yes—
85C2×C13×C22⋊C4—24no—
86C2×C13×C22⋊C4—24no—
87C2×C13×C22⋊C4C2314yes—
88C2×C13×C22⋊C4C2314yes—
89C2×C42×C13—24no—
90C2×C42×C13C2314yes—
91C2×C22⋊Dic13—28no—
92C2×C22⋊Dic13—28no—
93C2×C22⋊Dic13—44no—
94C2×C22⋊Dic13C2318yes—
95C2×C22⋊Dic13C2318yes—
96C2×C22⋊Dic13C2318yes—
97C2×C4⋊Dic13—24no—
98C2×C4⋊Dic13—24no—
99C2×C4⋊Dic13—28no—
100C2×C4⋊Dic13—232no—
101C2×C4⋊Dic13D418yescomplemented
102C2×C4⋊Dic13C2314yes—
103C2×C4⋊Dic13C2314yes—
104C2×C4⋊Dic13C2318yes—
105C2×C4⋊Dic13C2314yes—
106#88178—232no—
107#88178—232no—
108C2×#6101—28no—
109C2×#6101—28no—
110C2×#6101—44no—
111C2×#6101C2318yes—
112C2×#6101C2318yes—
113C2×#6101C2318yes—
114#88071C2318yes—
115#88071C2318yes—
116#88071C2318yes—
117#88071C2318yes—
118C2×#2417—131nomaximal, Sylow
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—22no—
122C24×C13—22no—
123C24×C13—22no—
124C24×C13—22no—
125C24×C13—22no—
126C24×C13—22no—
127C24×C13—22no—
128C24×C13—22no—
129C24×C13C2×D414yes—
130C24×C13C2×Q814yes—
131C24×C13C2×Q814yes—
132C24×C13#4114yes—
133C24×C13C2412yes—
134C24×C13C2412yes—
135C24×C13C2411yescharacteristic
136C2×D4×C13—232no—
137C2×D4×C13—28no—
138C2×D4×C13—28no—
139C2×D4×C13C2×Q8116yescomplemented
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—232no—
145C22×C4×C13—28no—
146C22×C4×C13—28no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—28no—
154C22×C4×C13—28no—
155C22×C4×C13—28no—
156C22×C4×C13—416no—
157C22×C4×C13C2×D414yes—
158C22×C4×C13C2×D414yes—
159C22×C4×C13C2×D4116yes—
160C22×C4×C13C2×D414yes—
161C22×C4×C13C2×Q814yes—
162C22×C4×C13#4114yes—
163C22×C4×C13C2412yes—
164C22×C4×C13C2412yes—
165C22×C4×C13C2412yes—
166C22×C4×C13C2412yes—
167C22×C4×C13C2412yes—
168C22×Dic13—24no—
169C22×Dic13—24no—
170C22×Dic13—24no—
171C22×Dic13—24no—
172C22×Dic13—24no—
173C22×Dic13—24no—
174C22×Dic13—24no—
175C22×Dic13—216no—
176C22×Dic13—24no—
177C22×Dic13—24no—
178C22×Dic13—24no—
179C22×Dic13—24no—
180C22×Dic13—216no—
181C22×Dic13—48no—
182C22×Dic13—432no—
183C22×Dic13C2×D418yes—
184C22×Dic13C2414yes—
185C22×Dic13C2414yes—
186C22×Dic13C2414yes—
187C22×Dic13C2414yes—
188C2×Dic26—28no—
189C2×Dic26—28no—
190C2×Dic26—28no—
191C2×Dic26—416no—
192C13×C4⋊C4—28no—
193C13×C22⋊C4—28no—
194C13×C22⋊C4—28no—
195C42×C13—28no—
196C22⋊Dic13—216no—
197C22⋊Dic13—216no—
198C22⋊Dic13—48no—
199C4⋊Dic13—28no—
200C4⋊Dic13—28no—
201C4⋊Dic13—216no—
202C4⋊Dic13C2×D4116yescomplemented
203#6101—216no—
204#6101—216no—
205#6101—48no—
206C22×C22⋊Q8—131no—
207C22×C22⋊Q8—131no—
208C22×C4×D4D1311yescharacteristic
209C23×C4⋊C4—131no—
210#2417—1316no—
211C2×#398—132no—
212C2×#396—132no—
213C2×#391—131no—
214C2×#389—131no—
215C2×#386—132no—
216C2×#380—131no—
217C2×#380—132no—
218C23×C13—28no—
219C23×C13—28no—
220C23×C13—28no—
221C23×C13—28no—
222C23×C13—28no—
223C23×C13—28no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—28no—
229C23×C13—28no—
230C23×C13—28no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—44no—
238C23×C13—44no—
239C23×C13—44no—
240C23×C13—44no—
241C23×C13C22⋊Q8116yescomplemented
242C23×C13C22×D414yes—
243C23×C13C22×D412yes—
244C23×C13C22×D412yes—
245C23×C13C22×Q814yes—
246C23×C13C22×Q814yes—
247C23×C13C22×Q812yes—
248C23×C13C2×#4114yes—
249C23×C13C2×#4112yes—
250C23×C13C2×#4112yes—
251C23×C13H(5,𝔽2)12yes—
252C23×C132−1+412yes—
253C23×C13C2511yescharacteristic
254D4×C13—232no—
255C2×C4×C13—28no—
256C2×C4×C13—28no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—232no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—44no—
269C2×C4×C13—44no—
270C2×C4×C13—416no—
271C2×C4×C13#121116yes—
272C2×C4×C13C22×D414yes—
273C2×C4×C13C22×D414yes—
274C2×C4×C13C22×D414yes—
275C2×C4×C13C22×Q814yes—
276C2×C4×C13C2×#4114yes—
277C2×Dic13—216no—
278C2×Dic13—24no—
279C2×Dic13—24no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—24no—
287C2×Dic13—24no—
288C2×Dic13—24no—
289C2×Dic13—432no—
290C2×Dic13—48no—
291C2×Dic13—48no—
292C2×Dic13—48no—
293C2×Dic13C22×D418yes—
294Dic26—416no—
295C23×Q8—131no—
296C23×D4C2×D1311yescharacteristic
297C24×C4—132no—
298C24×C4C2×D1311yescharacteristic
299C24×C4C2×D1311yescharacteristic
300C2×C22⋊Q8—138no—
301C2×C22⋊Q8—138no—
302C2×C22⋊Q8—268no—
303C2×C22⋊Q8—268no—
304C2×C4×D4—28no—
305C2×C4×D4C2×D1318yes—
306C22×C4⋊C4—131no—
307C22×C4⋊C4—132no—
308C22×C4⋊C4—132no—
309C22×C4⋊C4—132no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4—131no—
312C22×C4⋊C4—138no—
313C22×C4⋊C4—132no—
314C22×C4⋊C4—268no—
315C22×C4⋊C4C2×D1311yescharacteristic
316C22×C22⋊C4—132no—
317C22×C22⋊C4—132no—
318C22×C22⋊C4—132no—
319C22×C22⋊C4C2×D1311yescharacteristic
320C22×C22⋊C4C2×D1311yescharacteristic
321C22×C42C2×D1311yescharacteristic
322#398—1316no—
323#396—1316no—
324#391—138no—
325#389—138no—
326#386—1316no—
327#380—138no—
328#380—1316no—
329C2×#95—132no—
330C2×#95—132no—
331C2×#95—132no—
332C2×#95—132no—
333C22×C13—24no—
334C22×C13—232no—
335C22×C13—24no—
336C22×C13—24no—
337C22×C13—24no—
338C22×C13—24no—
339C22×C13—24no—
340C22×C13—24no—
341C22×C13—24no—
342C22×C13—24no—
343C22×C13—42no—
344C22×C13—416no—
345C22×C13—42no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13C2×#12114yes—
349C22×C13C2×C22⋊Q814yes—
350C22×C13C2×C22⋊Q818yescomplemented
351C22×C13#53714yes—
352C22×C13#54614yes—
353C22×C13D4×Q814yes—
354C22×C13#55214yes—
355C22×C13#55414yes—
356C22×C13C23×D411yescharacteristic
357C22×C13C23×D411yescharacteristic
358C22×C13C23×Q811yescharacteristic
359C22×C13C22×#4111yescharacteristic
360C22×C13C22×#4111yescharacteristic
361C22×C13C2×H(5,𝔽2)11yescharacteristic
362C22×C13C2×2−1+411yescharacteristic
363C4×C13—24no—
364C4×C13—24no—
365C4×C13—42no—
366C4×C13—42no—
367C4×C13C2×#12118yes—
368Dic13—28no—
369Dic13—44no—
370Dic13—44no—
371Dic13—44no—
372C25C22×D1311yescharacteristic
373C25C22×D1311yescharacteristic
374C22×Q8—134no—
375C22×Q8—264no—
376C22×Q8—264no—
377C22×Q8—264no—
378C22×D4—24no—
379C22×D4—24no—
380C22×D4Dic2618yescomplemented
381C22×D4C22×D1314yes—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—132no—
388C23×C4—132no—
389C23×C4—132no—
390C23×C4—132no—
391C23×C4—138no—
392C23×C4—268no—
393C23×C4—268no—
394C23×C4—524no—
395C23×C4C22⋊D1318yes—
396C23×C4C22×D1314yes—
397C23×C4C22×D1311yescharacteristic
398C23×C4C22×D1311yescharacteristic
399C23×C4C22×D1311yescharacteristic
400C23×C4C22×D1314yes—
401C23×C4C22×D1311yescharacteristic
402C23×C4C22×D1311yescharacteristic
403C22⋊Q8—2632no—
404C22⋊Q8—2632no—
405C4×D4—232no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—138no—
408C2×C4⋊C4—134no—
409C2×C4⋊C4—134no—
410C2×C4⋊C4—138no—
411C2×C4⋊C4—138no—
412C2×C4⋊C4—138no—
413C2×C4⋊C4—134no—
414C2×C4⋊C4—138no—
415C2×C4⋊C4—2632no—
416C2×C4⋊C4—268no—
417C2×C4⋊C4—268no—
418C2×C4⋊C4—264no—
419C2×C4⋊C4—268no—
420C2×C4⋊C4—264no—
421C2×C4⋊C4—524no—
422C2×C4⋊C4C22×D1314yes—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—138no—
426C2×C22⋊C4—138no—
427C2×C22⋊C4—138no—
428C2×C22⋊C4—268no—
429C2×C22⋊C4—268no—
430C2×C22⋊C4—524no—
431C2×C22⋊C4C22×D1314yes—
432C2×C22⋊C4C22×D1314yes—
433C2×C42—24no—
434C2×C42C22×D1314yes—
435#95—138no—
436#95—138no—
437#95—138no—
438#95—138no—
439C2×C13—28no—
440C2×C13—44no—
441C2×C13#241718yescomplemented
442C2×C13C22×#12111yescharacteristic
443C2×C13C22×C22⋊Q811yescharacteristic
444C2×C13C2×#53711yescharacteristic
445C2×C13C2×#54611yescharacteristic
446C2×C13C2×D4×Q811yescharacteristic
447C2×C13C2×#55211yescharacteristic
448C2×C13C2×#55411yescharacteristic
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C2×Dic2614yes—
460C24C2×Dic2614yes—
461C24#612714yes—
462C24C2×C22⋊D1314yes—
463C24C23×D1312yes—
464C24C23×D1312yes—
465C24C23×D1311yescharacteristic
466C2×Q8—268no—
467C2×Q8—268no—
468C2×Q8—268no—
469C2×Q8—5216no—
470C2×D4—232no—
471C2×D4—28no—
472C2×D4—28no—
473C2×D4C2×Dic26116yescomplemented
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—232no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—416no—
491C22×C4—138no—
492C22×C4—134no—
493C22×C4—134no—
494C22×C4—134no—
495C22×C4—134no—
496C22×C4—2616no—
497C22×C4—264no—
498C22×C4—264no—
499C22×C4—2616no—
500C22×C4—264no—
501C22×C4—264no—
502C22×C4—264no—
503C22×C4—264no—
504C22×C4—264no—
505C22×C4—264no—
506C22×C4—264no—
507C22×C4—264no—
508C22×C4—264no—
509C22×C4—528no—
510C22×C4—5232no—
511C22×C4C2×Dic2614yes—
512C22×C4D4×D1314yes—
513C22×C4#612914yes—
514C22×C4C2×C22⋊D1314yes—
515C22×C4C2×C22⋊D13116yes—
516C22×C4C2×C22⋊D1314yes—
517C22×C4C23×D1312yes—
518C22×C4C23×D1312yes—
519C22×C4C23×D1312yes—
520C22×C4C23×D1312yes—
521C22×C4C23×D1312yes—
522C4⋊C4—28no—
523C4⋊C4—1316no—
524C4⋊C4—2616no—
525C4⋊C4—2616no—
526C4⋊C4—268no—
527C4⋊C4—2616no—
528C4⋊C4—268no—
529C4⋊C4—528no—
530C22⋊C4—28no—
531C22⋊C4—28no—
532C22⋊C4—2616no—
533C22⋊C4—2616no—
534C22⋊C4—528no—
535C42—28no—
536C13C2×#241711yescharacteristic, complemented, Sylow
537C23—28no—
538C23—28no—
539C23—28no—
540C23—28no—
541C23—28no—
542C23—28no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—28no—
548C23—28no—
549C23—28no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23#88178116yescomplemented
561C23C22×Dic2614yes—
562C23C22×Dic2614yes—
563C23C22×Dic2612yes—
564C23C2×#612714yes—
565C23C2×#612712yes—
566C23C2×D4×D1312yes—
567C23C2×#612912yes—
568C23#8825612yes—
569C23#8825712yes—
570C23C22×C22⋊D1314yes—
571C23C22×C22⋊D1312yes—
572C23C24×D1311yescharacteristic
573Q8—5216no—
574D4—232no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—232no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—416no—
591C2×C4—138no—
592C2×C4—2616no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4—264no—
596C2×C4—264no—
597C2×C4—264no—
598C2×C4—264no—
599C2×C4—264no—
600C2×C4—264no—
601C2×C4—264no—
602C2×C4—264no—
603C2×C4—264no—
604C2×C4—5232no—
605C2×C4—528no—
606C2×C4—528no—
607C2×C4—528no—
608C2×C4#88193116yes—
609C2×C4C22×Dic2614yes—
610C2×C4C2×D4×D1314yes—
611C2×C4C2×#612914yes—
612C2×C4C22×C22⋊D1314yes—
613C2×C4C22×C22⋊D1314yes—
614C22—232no—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—416no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22D4×Dic2614yes—
630C22#1171924614yes—
631C22#1171924814yes—
632C22#1171925514yes—
633C22C2×#8817814yes—
634C22C2×#8817818yescomplemented
635C22C2×#8819314yes—
636C22#1171953814yes—
637C22C23×Dic2611yescharacteristic
638C22C22×#612711yescharacteristic
639C22C22×D4×D1311yescharacteristic
640C22C22×#612911yescharacteristic
641C22C2×#8825611yescharacteristic
642C22C2×#8825711yescharacteristic
643C22C23×C22⋊D1311yescharacteristic
644C4—24no—
645C4—24no—
646C4—42no—
647C4—42no—
648C4—268no—
649C4—524no—
650C4—524no—
651C4—524no—
652C4C2×#8819318yes—
653C2—28no—
654C2—44no—
655C2#1311828718yesdirect product factor
656C2C22×#8819311yescharacteristic
657C2C22×#8817811yescharacteristic
658C2C2×#1171953811yescharacteristic
659C2C2×#1171925511yescharacteristic
660C2C2×D4×Dic2611yescharacteristic
661C2C2×#1171924611yescharacteristic
662C2C2×#1171924811yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13C2×#2417
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88178C2semidirect
2. C22×#88178C2semidirect
3. C23×C4⋊Dic13C2semidirect
4. #13118287C2direct (N × H)
5. C2×#11718645C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718590C2semidirect
8. C2×#11718589C2semidirect
10. C2×#11718873C2semidirect
11. C2×#11718603C2semidirect
32. C22×C4⋊Dic13C22semidirect
35. C2×#88178C22semidirect
36. C2×#88178C22semidirect
41. #11718873C22semidirect
46. #11718645C22semidirect
47. #11718609C22semidirect
48. #11718603C22semidirect
49. #11718590C22semidirect
50. #11718589C22semidirect
55. C22×D4×C13Q8semidirect
101. C2×C4⋊Dic13D4semidirect
139. C2×D4×C13C2×Q8semidirect
202. C4⋊Dic13C2×D4semidirect
241. C23×C13C22⋊Q8semidirect
350. C22×C13C2×C22⋊Q8semidirect
380. C22×D4Dic26semidirect
441. C2×C13#2417semidirect
473. C2×D4C2×Dic26semidirect
536. C13C2×#2417semidirect
560. C23#88178semidirect
634. C22C2×#88178semidirect
655. C2#13118287direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881782
C23×C4⋊Dic132
#131182872
C2×#117186452
C2×#117186092
C2×#117185902
C2×#117185892
C2×#117188812
C2×#117188732
C2×#117186032
C22×C4×D4×C132
C2×#241713