Finite Group Databasebeta

← #14797532

Subgroups — #14797532

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622840C211yesmaximal, characteristic
2C2×#10622401C211yesmaximal, characteristic, complemented
3#13072110C211yesmaximal, characteristic
4Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13070162C211yesmaximal, characteristic, complemented
6#13070053C211yesmaximal, characteristic, complemented
7#13069930C211yesmaximal, characteristic, complemented
8#13069799C211yesmaximal, characteristic
9#13069294C211yesmaximal, characteristic, complemented
10#13069225C211yesmaximal, characteristic, complemented
11#13068969C211yesmaximal, characteristic, complemented
12#13068947C211yesmaximal, characteristic, complemented
13#13068872C211yesmaximal, characteristic, complemented
14#13068629C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622843—21no—
30#10622843—21no—
31#10622843C2211yescharacteristic
32#10622843C2211yescharacteristic
33#10622840—24no—
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622825—21no—
37#10622825C2211yescharacteristic
38C4×C22⋊Dic11—21no—
39C4×C22⋊Dic11C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66882C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46#10622601C2211yescharacteristic
47#10622598C2211yescharacteristic
48#10622590C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50#10622574—21no—
51#10622569—21no—
52#10622401—24no—
53#10622287—21no—
54#10622277—21no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—21no—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83Q8×Dic11—22no—
84Q8×Dic11—22no—
85Q8×Dic11—41no—
86Q8×Dic11—41no—
87C2×#4325—22no—
88C2×#4325—22no—
89C2×#4325—22no—
90C2×#4325—22no—
91C2×#4325—41no—
92C2×#4325D414yes—
93#66983—22no—
94#66983—41no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111#66946—22no—
112#66946—41no—
113C11×#103—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#103—41no—
117C11×C22⋊C8—41no—
118C11×#95—21no—
119#66899—22no—
120#66899—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131C22⋊(C11⋊C8)—22no—
132#66885—22no—
133#66885—41no—
134#66882—41no—
135Dic11⋊C8—41no—
136C8×Dic11—22no—
137#66872—22no—
138#24894—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C2×Q8×C11—24no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—42no—
151C2×Q8×C11—42no—
152C2×Q8×C11—44no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11—44no—
156C2×Q8×C11C2×D412yes—
157C2×Q8×C11#4112yes—
158C2×Q8×C11#4112yes—
159C2×Q8×C11#4112yes—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—42no—
176C2×C22⋊D11—42no—
177C2×C22⋊D11—81no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44C2×D412yes—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—81no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C22⋊C4—81no—
205C22⋊Dic11—22no—
206C22⋊Dic11—22no—
207C22⋊Dic11—42no—
208#4325—28no—
209#4325—44no—
210(C2×D11)⋊C4—42no—
211(C2×D11)⋊C4—42no—
212(C2×D11)⋊C4—81no—
213(C2×D11)⋊C4—81no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—42no—
221C4⋊Dic11—42no—
222C4⋊Dic11—81no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—42no—
228C4×Dic11—42no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8C2×D412yes—
235C2×#448—111no—
236C2×C4×SD16—111no—
237#2420—111no—
238Q8×C22⋊C4—111no—
239#2097—111no—
240#2077—111no—
241#2055—111no—
242#2033—111no—
243#1933—111no—
244#1923—111no—
245#1880—111no—
246#1877—111no—
247#1863—111no—
248#1805—111no—
249#1787D1111yescharacteristic, complemented
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11#13512yes—
257C23×C11C22×D411yescharacteristic
258C22×D11—22no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265Q8×C11—22no—
266Q8×C11—22no—
267Q8×C11—22no—
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—48no—
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11#12314yes—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—48no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11C2×#4111yescharacteristic
298C2×C4×C11H(5,𝔽2)11yescharacteristic
299C2×C4×C11H(5,𝔽2)11yescharacteristic
300C22⋊D11—84no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11#13712yes—
322D44—22no—
323D44—22no—
324D44—41no—
325D44—41no—
326C4×D11—84no—
327C8×C11—41no—
328C8×C11—41no—
329C11⋊C8—22no—
330C11⋊C8—41no—
331C23×Q8C2×D1111yescharacteristic
332C22×SD16—111no—
333C22×SD16—111no—
334C2×#121—111no—
335C2×C4×Q8—111no—
336C2×C4×Q8—111no—
337C2×C4×D4—111no—
338#448—224no—
339C4×SD16—224no—
340C2×#107—111no—
341C2×#106—111no—
342C2×C4⋊C8—111no—
343C2×#103—111no—
344C2×#103—111no—
345C2×#103C2×D1111yescharacteristic
346C2×#103C2×D1111yescharacteristic
347C2×#103C2×D1111yescharacteristic
348C2×#103C2×D1111yescharacteristic
349C2×#102—111no—
350C2×#102—111no—
351C2×C22⋊C8—111no—
352C2×C22⋊C8C2×D1111yescharacteristic
353C2×C4×C8—111no—
354#397—221no—
355#394—221no—
356#391—111no—
357#391—111no—
358#391—221no—
359#391—221no—
360#390—111no—
361#389—111no—
362#386—221no—
363#382—111no—
364#381—221no—
365#380—111no—
366#380—221no—
367#380C2×D1111yescharacteristic
368C4×C22⋊C4—111no—
369C4×C22⋊C4—221no—
370#340—111no—
371#340—111no—
372#340—111no—
373#340—111no—
374#336—111no—
375#336—111no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11#52511yescharacteristic
384C22×C11D4211yescharacteristic
385C22×C11#54611yescharacteristic
386C22×C11C2×#13511yescharacteristic
387C22×C11C2×#13711yescharacteristic
388C22×C11#57711yescharacteristic
389C22×C11#57711yescharacteristic
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—42no—
393C2×D11—81no—
394C2×D11—81no—
395C2×D11—81no—
396C2×D11—81no—
397C4×C11—24no—
398C4×C11—41no—
399C4×C11—42no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11C2×#12311yescharacteristic
403C4×C11#53811yescharacteristic
404C4×C11#54611yescharacteristic
405C4×C11#55111yescharacteristic
406Dic11—22no—
407Dic11—41no—
408Dic11—41no—
409Dic11—41no—
410Dic11—81no—
411Dic11—81no—
412Dic11—81no—
413C22×Q8—22no—
414C22×Q8—22no—
415C22×Q8—21no—
416C22×Q8—22no—
417C22×Q8—22no—
418C22×Q8—41no—
419C22×Q8—41no—
420C22×Q8C22×D1111yescharacteristic
421C22×Q8C22×D1111yescharacteristic
422C22×D4—111no—
423C22×D4—221no—
424C23×C4—21no—
425C23×C4—221no—
426C23×C4C22×D1111yescharacteristic
427C2×SD16—114no—
428C2×SD16—222no—
429C2×SD16—222no—
430C2×SD16—222no—
431C2×SD16—222no—
432C2×SD16—441no—
433C22×C8—111no—
434C22×C8—111no—
435C22×C8C22×D1111yescharacteristic
436C22×C8C22×D1111yescharacteristic
437#121—222no—
438#121—441no—
439C4×Q8—222no—
440C4×Q8—222no—
441C4×Q8—441no—
442C4×Q8—441no—
443C4×D4—222no—
444C4×D4—441no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4—111no—
448C2×C4⋊C4—221no—
449C2×C4⋊C4—221no—
450C2×C4⋊C4—221no—
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—111no—
455C2×C22⋊C4—111no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C22⋊C4—221no—
460C2×C22⋊C4—221no—
461C2×C42—111no—
462C2×C42—111no—
463C2×C42—221no—
464C2×C42—221no—
465#107—441no—
466#106—222no—
467C4⋊C8—441no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—41no—
472#103—222no—
473#103—222no—
474#102—222no—
475#102—441no—
476C22⋊C8—41no—
477C22⋊C8—222no—
478C4×C8—222no—
479#95—21no—
480#95—111no—
481#95—111no—
482#95—221no—
483#95—221no—
484#95—221no—
485#95—221no—
486#95—221no—
487#95—221no—
488#95—221no—
489#95—221no—
490C2×C11—42no—
491C2×C11#241811yescharacteristic
492C2×C11#310811yescharacteristic
493C2×C11#312611yescharacteristic
494C2×C11#326611yescharacteristic
495C2×C11#328211yescharacteristic
496C2×C11#330111yescharacteristic
497C2×C11#332911yescharacteristic
498D11—82no—
499C24—221no—
500C24D4×D1111yescharacteristic
501C2×Q8—24no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8#433912yes—
517C2×Q8D4×D1112yes—
518C2×Q8#434112yes—
519C2×Q8#434112yes—
520C2×D4—112no—
521C2×D4—221no—
522C2×D4—221no—
523C2×D4—221no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4—442no—
527C2×D4—442no—
528C2×D4—881no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—111no—
543C22×C4—111no—
544C22×C4—111no—
545C22×C4—111no—
546C22×C4—221no—
547C22×C4—221no—
548C22×C4—221no—
549C22×C4—442no—
550C22×C4—442no—
551C22×C4—881no—
552C22×C4D4×D1111yescharacteristic
553C22×C4C23×D1111yescharacteristic
554SD16—228no—
555SD16—444no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—112no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—442no—
579C4⋊C4—442no—
580C4⋊C4—881no—
581C22⋊C4—81no—
582C22⋊C4—222no—
583C22⋊C4—222no—
584C22⋊C4—442no—
585C22⋊C4—442no—
586C22⋊C4—442no—
587C22⋊C4—881no—
588C22⋊C4—881no—
589C42—221no—
590C42—221no—
591C42—221no—
592C42—221no—
593C42—442no—
594C42—442no—
595C11#2489411yescharacteristic, complemented, Sylow
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—222no—
603C23—441no—
604C23—441no—
605C23—441no—
606C23—441no—
607C23—441no—
608C23—441no—
609C23#6697212yes—
610C23C2×D4×D1111yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—48no—
617Q8—41no—
618Q8—41no—
619Q8#6693614yes—
620D4—222no—
621D4—222no—
622D4—441no—
623D4—441no—
624D4—884no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—48no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—112no—
646C2×C4—221no—
647C2×C4—221no—
648C2×C4—221no—
649C2×C4—221no—
650C2×C4—221no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—221no—
654C2×C4—221no—
655C2×C4—221no—
656C2×C4—221no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4—441no—
665C2×C4—441no—
666C2×C4—884no—
667C2×C4C2×#433911yescharacteristic
668C2×C4C2×D4×D1111yescharacteristic
669C2×C4C2×#434111yescharacteristic
670C2×C4C2×#434111yescharacteristic
671C2×C4#6703711yescharacteristic
672C2×C4#6703711yescharacteristic
673C8—41no—
674C8—41no—
675C8—222no—
676C8—441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—442no—
685C22—442no—
686C22—442no—
687C22—881no—
688C22—881no—
689C22—881no—
690C22—881no—
691C22#1062302111yescharacteristic
692C22#1062311711yescharacteristic
693C22#1062312111yescharacteristic
694C22#1062329311yescharacteristic
695C22C2×#6697211yescharacteristic
696C22D11×#13711yescharacteristic
697C22#1062330911yescharacteristic
698C4—24no—
699C4—41no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—222no—
704C4—441no—
705C4—441no—
706C4—441no—
707C4—881no—
708C4—881no—
709C4—881no—
710C4C2×#6693611yescharacteristic
711C4#1062302611yescharacteristic
712C4#1062312211yescharacteristic
713C4#1062312411yescharacteristic
714C2—42no—
715C2—882no—
716C2#1307208211yescharacteristic
717C2#1307869711yescharacteristic
718C2#1307890111yescharacteristic
719C2#1308012911yescharacteristic
720C2#1308031611yescharacteristic
721C2#1308051411yescharacteristic
722C2#1308090611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1787D11
hypocenterC11#24894
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#10622401C2semidirect
4. Q8×C22⋊Dic11C2semidirect
5. #13070162C2semidirect
6. #13070053C2semidirect
7. #13069930C2semidirect
9. #13069294C2semidirect
10. #13069225C2semidirect
11. #13068969C2semidirect
12. #13068947C2semidirect
13. #13068872C2semidirect
14. #13068629C2semidirect
15. C11×#1787C2semidirect
249. #1787D11semidirect
595. C11#24894semidirect

Maximal subgroups

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

subgroupindex
C2×#106228402
C2×#106224012
#130721102
Q8×C22⋊Dic112
#130701622
#130700532
#130699302
#130697992
#130692942
#130692252
#130689692
#130689472
#130688722
#130686292
C11×#17872
#2489411