Finite Group Databasebeta

← C2×#11754385 #14482731

Subgroups — C2×#11754385 #14482731

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6779C212yesmaximal, complemented
2C2×C4×#1220C211yesmaximal, characteristic, complemented
3C22×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#4076C211yesmaximal, characteristic, complemented
5C2×#91536C212yesmaximal, complemented
6C2×#91470C211yesmaximal, characteristic, complemented
7C2×#91465C211yesmaximal, characteristic, complemented
8C2×#91437C211yesmaximal, characteristic, complemented
9#11754385C2116yesmaximal, direct product factor
10C2×#91434C211yesmaximal, characteristic, complemented
11C2×#91430C212yesmaximal, complemented
12C2×#91356C212yesmaximal, complemented
13C2×#65841—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C23×C5×Dic3C2212yes—
18C22×C3×C22⋊D5C2212yes—
19C22×C3×D20C2211yescharacteristic
20C22×#1204C2212yes—
21C22×#1202C2212yes—
22C22×#1200C2212yes—
23C2×#6779—216no—
24C2×#6779C22116yescomplemented
25C22×D5×Dic3C2212yes—
26C2×#6719C2211yescharacteristic
27C4×#1220C2218yescomplemented
28C2×#6714C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31C2×C5×C4⋊Dic3C2211yescharacteristic
32C2×C5×C4⋊Dic3C2212yes—
33C2×C5×C4⋊Dic3C2211yescharacteristic
34C2×C5×C4⋊Dic3C2218yescomplemented
35C3×#4076C2218yescomplemented
36C2×C3×#685C2212yes—
37C2×C3×C4⋊Dic5C2211yescharacteristic
38C2×#6669C2212yes—
39C2×#6669C2212yes—
40#91536C22116yescomplemented
41C2×#6665C2212yes—
42C2×#6665C2212yes—
43#91470C2218yescomplemented
44#91465C2218yescomplemented
45#91437C2218yescomplemented
46#91434C2218yescomplemented
47#91430C22116yescomplemented
48#91356C22116yescomplemented
49C2×#5611—51nomaximal, Hall
50C22×#709—32no—
51C22×C5×C4⋊C4—31no—
52C2×#4076D311yescharacteristic, complemented
53C2×#4075—32no—
54C2×C4×C22⋊D5—31no—
55C2×#4042—32no—
56#65841—316no—
57C2×#4041—31no—
58C2×#4040—32no—
59C2×#4039—31no—
60C2×D5×C4⋊C4—31no—
61C2×#4034—31no—
62C24×C3×C5C2311yescharacteristic
63C23×D15C2311yescharacteristic
64C23×C3×D5C2312yes—
65C22×C3×C4×C5—24no—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2314yes—
68C22×C3×C4×C5C2311yescharacteristic
69C2×#1220D418yescomplemented
70C2×#1220C2314yes—
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C2×C4×D15—24no—
75C2×C4×D15C2314yes—
76C22×C5×Dic3—28no—
77C22×C5×Dic3C2312yes—
78C22×C5×Dic3C2312yes—
79C22×C5×Dic3C2318yes—
80C2×C3×C22⋊D5—28no—
81C2×C3×C22⋊D5C2318yes—
82C22×C3×Dic5C2312yes—
83C2×C3×D20—24no—
84C2×C3×D20C2314yes—
85C2×#1204—28no—
86C2×#1204C2318yes—
87C2×#1202—28no—
88C2×#1202C2318yes—
89C2×#1200—28no—
90C2×#1200C2318yes—
91#6779—264no—
92C2×D5×Dic3—28no—
93C2×D5×Dic3C2318yes—
94#6719C2314yes—
95#6714C2314yes—
96#6712C2314yes—
97C4×Dic15C2314yes—
98C5×C4⋊Dic3C2318yes—
99C5×C4⋊Dic3C2314yes—
100C5×C4⋊Dic3C2314yes—
101C3×#685C2318yes—
102C3×C4⋊Dic5C2314yes—
103#6669C2318yes—
104#6669C2318yes—
105#6665C2318yes—
106#6665C2318yes—
107C22×#237—52no—
108C2×C3×#121—51no—
109C2×#938—51no—
110C2×#935—52no—
111C2×D4×Dic3—51no—
112C2×C4×#67—51no—
113C22×C4⋊Dic3D511yescharacteristic, complemented
114#5611—516no—
115C2×D3×C4⋊C4—51no—
116C2×#888—51no—
117C2×#883—52no—
118C2×#878—52no—
119C23×C4×C5—32no—
120C23×C4×C5C2×D311yescharacteristic
121C22×C22⋊D5—31no—
122C22×C22⋊D5C2×D312yes—
123C2×#709—316no—
124C2×#709—616no—
125C22×D20—32no—
126C22×D20C2×D311yescharacteristic
127C22×C4×D5—32no—
128C22×C4×D5—31no—
129C22×C4×D5—32no—
130C22×Dic10—32no—
131C2×C5×C4⋊C4—31no—
132C2×C5×C4⋊C4—31no—
133C2×C5×C4⋊C4—32no—
134C2×C5×C4⋊C4—38no—
135C2×C22⋊Dic5—31no—
136#4076C2×D318yescomplemented
137#4075—316no—
138C4×C22⋊D5—38no—
139C2×#685—32no—
140C2×#685—32no—
141C2×#685—31no—
142C2×#685C2×D312yes—
143C2×C4⋊Dic5C2×D311yescharacteristic
144C2×#683—31no—
145C2×#683—32no—
146C2×#683—32no—
147C2×C4×Dic5—31no—
148#4042—316no—
149#4041—38no—
150#4040—316no—
151#4039—38no—
152D5×C4⋊C4—38no—
153#4034—38no—
154C2×#547—151noSylow
155C23×C3×C5—22no—
156C23×C3×C5—22no—
157C23×C3×C5C2×D414yes—
158C23×C3×C5C2412yes—
159C23×C3×C5C2411yescharacteristic
160C22×D15—22no—
161C22×D15—22no—
162C22×D15C2×D414yes—
163C22×D15C2412yes—
164C22×C3×D5—24no—
165C22×C3×D5—24no—
166C22×C3×D5—24no—
167C22×C3×D5C2414yes—
168C2×C3×C4×C5—22no—
169C2×C3×C4×C5—28no—
170C2×C3×C4×C5#4114yescomplemented
171C2×C3×C4×C5C2412yes—
172C2×C3×C4×C5C2412yes—
173#1220C2×D4116yescomplemented
174C2×Dic15—22no—
175C2×Dic15—22no—
176C2×Dic15C2×D414yes—
177C2×Dic15C2412yes—
178C2×Dic15C2412yes—
179C2×Dic15C2412yes—
180C4×D15—28no—
181C2×C5×Dic3—24no—
182C2×C5×Dic3—216no—
183C2×C5×Dic3—24no—
184C2×C5×Dic3C2414yes—
185C2×C5×Dic3C2414yes—
186C3×C22⋊D5—216no—
187C2×C3×Dic5—24no—
188C2×C3×Dic5C2414yes—
189C3×D20—28no—
190#1204—216no—
191#1202—216no—
192#1200—216no—
193D5×Dic3—216no—
194C22×C3×D4—52no—
195C22×C3×D4—51no—
196C23×C3×C4C2×D511yescharacteristic
197C22×#67—51no—
198C22×#67—52no—
199C23×Dic3—52no—
200C23×Dic3C2×D512yes—
201C2×#237—516no—
202C2×#237—1016no—
203C22×C4×D3—51no—
204C22×C4×D3—52no—
205C22×Dic6—52no—
206C3×#121—58no—
207C2×C3×C4⋊C4—51no—
208C2×C3×C22⋊C4—52no—
209C2×#217—51no—
210C2×#217—52no—
211C2×#217—52no—
212#938—58no—
213#935—516no—
214D4×Dic3—58no—
215C4×#67—58no—
216C2×(C2×D3)⋊C4—51no—
217C2×C4⋊Dic3C2×D512yes—
218C2×C4⋊Dic3C2×D511yescharacteristic
219C2×C4⋊Dic3C2×D511yescharacteristic
220C2×C4⋊Dic3C2×D518yescomplemented
221C2×Dic3⋊C4—51no—
222C2×Dic3⋊C4—52no—
223C2×Dic3⋊C4—52no—
224C2×C4×Dic3—51no—
225D3×C4⋊C4—58no—
226#888—58no—
227#883—516no—
228#878—516no—
229C24×C5C22×D311yescharacteristic
230C23×D5—31no—
231C23×D5C22×D312yes—
232C22×C4×C5—24no—
233C22×C4×C5—32no—
234C22×C4×C5—32no—
235C22×C4×C5—38no—
236C22×C4×C5—68no—
237C22×C4×C5C22×D311yescharacteristic
238C22×C4×C5C22×D314yes—
239C22×C4×C5C22×D311yescharacteristic
240C2×C22⋊D5—28no—
241C2×C22⋊D5—38no—
242C2×C22⋊D5—34no—
243C2×C22⋊D5C22×D318yes—
244C22×Dic5—31no—
245C22×Dic5—31no—
246C22×Dic5—31no—
247C22×Dic5C22×D312yes—
248#709—664no—
249C2×D20—24no—
250C2×D20—38no—
251C2×D20—68no—
252C2×D20C22×D314yes—
253C2×C4×D5—38no—
254C2×C4×D5—34no—
255C2×C4×D5—38no—
256C2×C4×D5—68no—
257C2×C4×D5—68no—
258C2×C4×D5—64no—
259C2×Dic10—38no—
260C2×Dic10—68no—
261C5×C4⋊C4—34no—
262C5×C4⋊C4—34no—
263C5×C4⋊C4—38no—
264C22⋊Dic5—34no—
265#685—38no—
266#685—38no—
267#685—34no—
268#685C22×D318yes—
269C4⋊Dic5C22×D314yes—
270#683—34no—
271#683—38no—
272#683—38no—
273C4×Dic5—34no—
274C22×#41—152no—
275#547—1516no—
276C2×C4⋊Q8—151no—
277C2×#123—152no—
278C2×#123—152no—
279C2×C22⋊Q8—152no—
280C2×#121—51no—
281C2×#121—151no—
282C2×C4×D4—151no—
283C2×C4×D4—151no—
284C22×C4⋊C4—31no—
285C22×C4⋊C4—151no—
286C22×C3×C5—28no—
287C22×C3×C5—22no—
288C22×C3×C5—22no—
289C22×C3×C5C22×D414yes—
290C22×C3×C5C22×D412yes—
291C22×C3×C5C2×#4112yes—
292C22×C3×C52−1+412yes—
293C22×C3×C5C2511yescharacteristic
294C2×D15—28no—
295C2×D15—22no—
296C2×D15—22no—
297C2×D15C22×D414yes—
298C2×C3×D5—24no—
299C2×C3×D5—24no—
300C2×C3×D5—24no—
301C2×C3×D5—48no—
302C3×C4×C5—22no—
303C3×C4×C5C2×#4114yescomplemented
304Dic15—22no—
305Dic15—22no—
306Dic15C22×D414yes—
307C3×Dic5—24no—
308C5×Dic3—24no—
309C5×Dic3—24no—
310C24×C3—52no—
311C24×C3C22×D511yescharacteristic
312C23×D3—51no—
313C2×C3×D4—58no—
314C2×C3×D4—54no—
315C2×C3×D4—108no—
316C2×C3×D4—104no—
317C22×C3×C4—24no—
318C22×C3×C4—52no—
319C22×C3×C4C22×D511yescharacteristic
320C22×C3×C4C22×D514yes—
321C22×C3×C4C22×D511yescharacteristic
322C2×#67—58no—
323C2×#67—54no—
324C2×#67—58no—
325C2×#67—108no—
326C22×Dic3—28no—
327C22×Dic3—51no—
328C22×Dic3—51no—
329C22×Dic3—51no—
330C22×Dic3—58no—
331C22×Dic3—108no—
332C22×Dic3C22×D512yes—
333C22×Dic3C22×D512yes—
334C22×Dic3C22×D518yes—
335#237—1064no—
336C2×C4×D3—54no—
337C2×C4×D3—58no—
338C2×C4×D3—108no—
339C2×C4×D3—104no—
340C2×Dic6—58no—
341C2×Dic6—108no—
342C3×C4⋊C4—54no—
343C3×C22⋊C4—58no—
344#217—54no—
345#217—58no—
346#217—58no—
347(C2×D3)⋊C4—54no—
348C4⋊Dic3C22×D518yes—
349C4⋊Dic3C22×D514yes—
350C4⋊Dic3C22×D514yes—
351Dic3⋊C4—54no—
352Dic3⋊C4—58no—
353Dic3⋊C4—58no—
354C4×Dic3—54no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5D3×D414yes—
358C23×C5C23×D312yes—
359C23×C5C23×D311yescharacteristic
360C22×D5—24no—
361C22×D5—24no—
362C22×D5—24no—
363C22×D5—34no—
364C22×D5—32no—
365C22×D5—62no—
366C22×D5—62no—
367C22×D5C23×D314yes—
368C2×C4×C5—22no—
369C2×C4×C5—28no—
370C2×C4×C5—34no—
371C2×C4×C5—34no—
372C2×C4×C5—64no—
373C2×C4×C5—64no—
374C2×C4×C5—616no—
375C2×C4×C5#23714yescomplemented
376C2×C4×C5C23×D312yes—
377C2×C4×C5C23×D312yes—
378C22⋊D5—216no—
379C22⋊D5—316no—
380C2×Dic5—24no—
381C2×Dic5—34no—
382C2×Dic5—32no—
383C2×Dic5—32no—
384C2×Dic5—32no—
385C2×Dic5—62no—
386C2×Dic5—62no—
387C2×Dic5C23×D314yes—
388D20—28no—
389D20—616no—
390C4×D5—616no—
391C4×D5—616no—
392C4×D5—68no—
393Dic10—616no—
394C2×#41—1516no—
395C2×#41—3016no—
396C22×Q8—152no—
397C22×D4—52no—
398C22×D4—51no—
399C22×D4—152no—
400C22×D4—151no—
401C23×C4—32no—
402C23×C4—152no—
403C23×C4—152no—
404C23×C4—151no—
405C23×C4D3×D511yescharacteristic
406C4⋊Q8—158no—
407#123—1516no—
408#123—1516no—
409C22⋊Q8—1516no—
410#121—58no—
411#121—158no—
412C4×D4—158no—
413C4×D4—158no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—32no—
417C2×C4⋊C4—38no—
418C2×C4⋊C4—51no—
419C2×C4⋊C4—158no—
420C2×C4⋊C4—152no—
421C2×C4⋊C4—152no—
422C2×C4⋊C4—151no—
423C2×C22⋊C4—52no—
424C2×C22⋊C4—152no—
425C2×C22⋊C4—152no—
426C2×C22⋊C4—151no—
427C2×C22⋊C4—151no—
428C2×C42—151no—
429C2×C3×C5—24no—
430C2×C3×C5#54714yescomplemented
431C2×C3×C5C23×D411yescharacteristic
432C2×C3×C5C22×#4111yescharacteristic
433C2×C3×C5C2×2−1+411yescharacteristic
434D15—24no—
435C3×D5—44no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—54no—
439C23×C3—104no—
440C23×C3—104no—
441C23×C3—104no—
442C23×C3D4×D514yes—
443C23×C3C23×D512yes—
444C23×C3C23×D511yescharacteristic
445C22×D3—54no—
446C22×D3—52no—
447C22×D3—102no—
448C22×D3—102no—
449C3×D4—1016no—
450C3×D4—108no—
451C2×C3×C4—22no—
452C2×C3×C4—28no—
453C2×C3×C4—54no—
454C2×C3×C4—104no—
455C2×C3×C4#70914yescomplemented
456C2×C3×C4C23×D512yes—
457C2×C3×C4C23×D512yes—
458#67—516no—
459#67—1016no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—216no—
463C2×Dic3—54no—
464C2×Dic3—52no—
465C2×Dic3—52no—
466C2×Dic3—52no—
467C2×Dic3—1016no—
468C2×Dic3—102no—
469C2×Dic3—102no—
470C2×Dic3C23×D514yes—
471C2×Dic3C23×D514yes—
472C4×D3—1016no—
473C4×D3—108no—
474Dic6—1016no—
475C22×C5—22no—
476C22×C5—22no—
477C22×C5—28no—
478C22×C5C2×D3×D414yes—
479C22×C5C2×D3×D412yes—
480C22×C5C2×#23712yes—
481C22×C5#101012yes—
482C22×C5C24×D311yescharacteristic
483C2×D5—24no—
484C2×D5—24no—
485C2×D5—24no—
486C2×D5—34no—
487C2×D5—48no—
488C2×D5—62no—
489C2×D5—62no—
490C2×D5—68no—
491C4×C5—22no—
492C4×C5—64no—
493C4×C5—64no—
494C4×C5C2×#23714yescomplemented
495Dic5—24no—
496Dic5—34no—
497Dic5—62no—
498Dic5—62no—
499C24—52no—
500C24—151no—
501C24C2×D3×D511yescharacteristic
502#41—3064no—
503C2×Q8—158no—
504C2×Q8—308no—
505C2×D4—58no—
506C2×D4—54no—
507C2×D4—108no—
508C2×D4—104no—
509C2×D4—158no—
510C2×D4—158no—
511C2×D4—154no—
512C2×D4—308no—
513C22×C4—24no—
514C22×C4—38no—
515C22×C4—32no—
516C22×C4—32no—
517C22×C4—52no—
518C22×C4—68no—
519C22×C4—158no—
520C22×C4—158no—
521C22×C4—151no—
522C22×C4—151no—
523C22×C4—151no—
524C22×C4—154no—
525C22×C4—308no—
526C22×C4—308no—
527C22×C4—304no—
528C22×C4C2×D3×D514yes—
529C22×C4C2×D3×D511yescharacteristic
530C22×C4C2×D3×D511yescharacteristic
531C4⋊C4—34no—
532C4⋊C4—34no—
533C4⋊C4—38no—
534C4⋊C4—54no—
535C4⋊C4—158no—
536C4⋊C4—158no—
537C4⋊C4—154no—
538C22⋊C4—58no—
539C22⋊C4—158no—
540C22⋊C4—158no—
541C22⋊C4—154no—
542C22⋊C4—154no—
543C42—154no—
544C3×C5C2×#54711yescharacteristic, complemented, Hall
545C22×C3—28no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—104no—
549C22×C3—104no—
550C22×C3—104no—
551C22×C3—208no—
552C22×C3C2×#70912yes—
553C22×C3C2×D4×D514yes—
554C22×C3C2×D4×D512yes—
555C22×C3#414712yes—
556C22×C3C24×D511yescharacteristic
557C2×D3—54no—
558C2×D3—108no—
559C2×D3—102no—
560C2×D3—102no—
561C3×C4—22no—
562C3×C4—104no—
563C3×C4C2×#70914yescomplemented
564Dic3—24no—
565Dic3—24no—
566Dic3—54no—
567Dic3—102no—
568Dic3—102no—
569C2×C5—24no—
570C2×C5#561114yescomplemented
571C2×C5C22×D3×D411yescharacteristic
572C2×C5C22×#23711yescharacteristic
573C2×C5C2×#101011yescharacteristic
574D5—44no—
575D5—64no—
576C23—22no—
577C23—22no—
578C23—54no—
579C23—104no—
580C23—104no—
581C23—104no—
582C23—154no—
583C23—152no—
584C23—302no—
585C23—302no—
586C23#677714yes—
587C23C22×D3×D512yes—
588C23C22×D3×D511yescharacteristic
589Q8—3016no—
590D4—1016no—
591D4—108no—
592D4—1516no—
593D4—3016no—
594C2×C4—22no—
595C2×C4—28no—
596C2×C4—34no—
597C2×C4—34no—
598C2×C4—54no—
599C2×C4—64no—
600C2×C4—64no—
601C2×C4—616no—
602C2×C4—104no—
603C2×C4—154no—
604C2×C4—152no—
605C2×C4—152no—
606C2×C4—152no—
607C2×C4—3016no—
608C2×C4—3016no—
609C2×C4—302no—
610C2×C4—302no—
611C2×C4—308no—
612C2×C4#677914yescomplemented
613C2×C4C22×D3×D512yes—
614C2×C4C22×D3×D512yes—
615C2×C3—24no—
616C2×C3—204no—
617C2×C3#6584114yescomplemented
618C2×C3C22×#70911yescharacteristic
619C2×C3C22×D4×D511yescharacteristic
620C2×C3C2×#414711yescharacteristic
621D3—104no—
622C5C2×#561111yescharacteristic, complemented, Sylow
623C22—22no—
624C22—28no—
625C22—22no—
626C22—104no—
627C22—104no—
628C22—104no—
629C22—154no—
630C22—208no—
631C22—302no—
632C22—308no—
633C22—302no—
634C22#9200012yes—
635C22C2×#677714yes—
636C22C2×#677712yes—
637C22C2×#677912yes—
638C22C23×D3×D511yescharacteristic
639C4—22no—
640C4—64no—
641C4—64no—
642C4—104no—
643C4—154no—
644C4—302no—
645C4—302no—
646C4C2×#677914yescomplemented
647C3C2×#6584111yescharacteristic, complemented, Sylow
648C2—24no—
649C2—204no—
650C2—304no—
651C2#1175438514yesdirect product factor
652C2C2×#9200011yescharacteristic
653C2C22×#677711yescharacteristic
654C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#547
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#6779C2semidirect
2. C2×C4×#1220C2semidirect
3. C22×C5×C4⋊Dic3C2semidirect
4. C2×C3×#4076C2semidirect
5. C2×#91536C2semidirect
6. C2×#91470C2semidirect
7. C2×#91465C2semidirect
8. C2×#91437C2semidirect
9. #11754385C2direct (N × H)
10. C2×#91434C2semidirect
11. C2×#91430C2semidirect
12. C2×#91356C2semidirect
24. C2×#6779C22semidirect
27. C4×#1220C22semidirect
34. C2×C5×C4⋊Dic3C22semidirect
35. C3×#4076C22semidirect
40. #91536C22semidirect
43. #91470C22semidirect
44. #91465C22semidirect
45. #91437C22semidirect
46. #91434C22semidirect
47. #91430C22semidirect
48. #91356C22semidirect
52. C2×#4076D3semidirect
69. C2×#1220D4semidirect
113. C22×C4⋊Dic3D5semidirect
136. #4076C2×D3semidirect
170. C2×C3×C4×C5#41semidirect
173. #1220C2×D4semidirect
220. C2×C4⋊Dic3C2×D5semidirect
303. C3×C4×C5C2×#41semidirect
375. C2×C4×C5#237semidirect
430. C2×C3×C5#547semidirect
455. C2×C3×C4#709semidirect
494. C4×C5C2×#237semidirect
544. C3×C5C2×#547semidirect
563. C3×C4C2×#709semidirect
570. C2×C5#5611semidirect
612. C2×C4#6779semidirect
617. C2×C3#65841semidirect
622. C5C2×#5611semidirect
646. C4C2×#6779semidirect
647. C3C2×#65841semidirect
651. C2#11754385direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67792
C2×C4×#12202
C22×C5×C4⋊Dic32
C2×C3×#40762
C2×#915362
C2×#914702
C2×#914652
C2×#914372
#117543852
C2×#914342
C2×#914302
C2×#913562
C2×#658413
C2×#56115