Finite Group Databasebeta

← C22×#11719343 #16769658

Subgroups — C22×#11719343 #16769658

Order 3328.

8062 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719343C2148yesmaximal, direct product factor
2C22×#88152C211yesmaximal, characteristic, complemented
3C22×#88133C211yesmaximal, characteristic, complemented
4C22×#88143C211yesmaximal, characteristic, complemented
5C22×#88143C211yesmaximal, characteristic, complemented
6C22×#88148C211yesmaximal, characteristic, complemented
7C22×#88183C211yesmaximal, characteristic, complemented
8C22×#88137C211yesmaximal, characteristic, complemented
9C22×#88137C211yesmaximal, characteristic, complemented
10C22×#88200C211yesmaximal, characteristic, complemented
11C22×#88200C211yesmaximal, characteristic, complemented
12C22×#88138C211yesmaximal, characteristic
13C22×#88147C211yesmaximal, characteristic, complemented
14C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
15C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
16C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×D52C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C2×C13×C22⋊Q8C22124yescomplemented
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C2×#88200C22124yescomplemented
35C2×#88200C22124yescomplemented
36C2×#88183C22124yescomplemented
37C2×C4×C22⋊D13C22124yescomplemented
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C22×#6103C2211yescharacteristic
44C22×C4⋊Dic13C2211yescharacteristic
45C22×C4⋊Dic13C2211yescharacteristic
46C22×C4⋊Dic13C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2211yescharacteristic
50C22×#6101C2211yescharacteristic
51C22×#6101C2211yescharacteristic
52C22×#6101C2211yescharacteristic
53C22×#6101C2211yescharacteristic
54C22×#6101C2211yescharacteristic
55C22×C4×Dic13C2211yescharacteristic
56C22×C4×Dic13C2211yescharacteristic
57#11719343C221256yesdirect product factor
58C2×#88152C22124yescomplemented
59C2×#88148C22124yescomplemented
60C2×#88147C22124yescomplemented
61C2×C4⋊C4×D13C22124yescomplemented
62C2×#88143C22124yescomplemented
63C2×#88143C22124yescomplemented
64C2×#88138C22124yes—
65C2×#88137C22124yescomplemented
66C2×#88137C22124yescomplemented
67C2×#88133C22124yescomplemented
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C22×Q8×C13—44no—
72C22×Q8×C13C23112yes—
73C23×C4×C13—44no—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C23112yes—
81C22×C22⋊D13—28no—
82C22×C22⋊D13—44no—
83C22×C22⋊D13C23112yes—
84C22×C22⋊D13C23112yes—
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C22×D52—28no—
92C22×D52C23112yes—
93C22×C4×D13—28no—
94C22×C4×D13—44no—
95C22×C4×D13—44no—
96C22×C4×D13—44no—
97C22×C4×D13C23112yes—
98C22×C4×D13C23112yes—
99C22×C4×D13C23112yes—
100C22×C4×D13C23112yes—
101C13×C22⋊Q8C23164yescomplemented
102C2×C13×C4⋊C4C23112yes—
103C2×C13×C4⋊C4C23112yes—
104C2×C13×C4⋊C4C23112yes—
105C2×C13×C22⋊C4C23112yes—
106C2×C13×C22⋊C4C23112yes—
107C2×C22⋊Dic13C23112yes—
108C2×C22⋊Dic13C23112yes—
109#88200C23164yescomplemented
110#88200C23164yescomplemented
111#88183C23164yescomplemented
112C4×C22⋊D13C23164yescomplemented
113C2×#6103C23112yes—
114C2×#6103C23112yes—
115C2×#6103C23112yes—
116C2×#6103C23112yes—
117C2×#6103C23112yes—
118C2×#6103C23112yes—
119C2×C4⋊Dic13C23112yes—
120C2×C4⋊Dic13C23112yes—
121C2×C4⋊Dic13C23112yes—
122C2×#6101C23112yes—
123C2×#6101C23112yes—
124C2×#6101C23112yes—
125C2×#6101C23112yes—
126C2×#6101C23112yes—
127C2×#6101C23112yes—
128C2×#6101C23112yes—
129C2×#6101C23112yes—
130C2×C4×Dic13C23112yes—
131C2×C4×Dic13C23112yes—
132#88152C23164yescomplemented
133#88148C23164yescomplemented
134#88147C23164yescomplemented
135C4⋊C4×D13C23164yescomplemented
136#88143C23164yescomplemented
137#88143C23164yescomplemented
138#88138C23164yes—
139#88137C23164yescomplemented
140#88137C23164yescomplemented
141#88133C23164yescomplemented
142C22×#539—131nomaximal, Sylow
143C24×C13—24no—
144C24×C13—24no—
145C24×C13—24no—
146C24×C13C2416yes—
147C24×C13C2411yescharacteristic
148C23×D13—24no—
149C23×D13—24no—
150C23×D13—24no—
151C23×D13—24no—
152C23×D13—24no—
153C23×D13#4118yes—
154C23×D13C2416yes—
155C23×D13C2416yes—
156C2×Q8×C13—424no—
157C2×Q8×C13C24116yes—
158C22×C4×C13—24no—
159C22×C4×C13—24no—
160C22×C4×C13—24no—
161C22×C4×C13—24no—
162C22×C4×C13—24no—
163C22×C4×C13—24no—
164C22×C4×C13—424no—
165C22×C4×C13C2416yes—
166C22×C4×C13C2416yes—
167C22×C4×C13C2416yes—
168C22×C4×C13C2416yes—
169C22×C4×C13C2416yes—
170C22×C4×C13C2416yes—
171C22×C4×C13C24116yes—
172C2×C22⋊D13—248no—
173C2×C22⋊D13—424no—
174C2×C22⋊D13C24116yes—
175C2×C22⋊D13C24116yes—
176C22×Dic13—24no—
177C22×Dic13—24no—
178C22×Dic13—24no—
179C22×Dic13—24no—
180C22×Dic13—24no—
181C22×Dic13—24no—
182C22×Dic13C2416yes—
183C22×Dic13C2416yes—
184C22×Dic13C2416yes—
185C22×Dic13C2416yes—
186C22×Dic13C2416yes—
187C22×Dic13C2416yes—
188C2×D52—248no—
189C2×D52C24116yes—
190C2×C4×D13—248no—
191C2×C4×D13—424no—
192C2×C4×D13—424no—
193C2×C4×D13—424no—
194C2×C4×D13C24116yes—
195C2×C4×D13C24116yes—
196C2×C4×D13C24116yes—
197C2×C4×D13C24116yes—
198C13×C4⋊C4C24116yes—
199C13×C4⋊C4C24116yes—
200C13×C4⋊C4C24116yes—
201C13×C22⋊C4C24116yes—
202C13×C22⋊C4C24116yes—
203C22⋊Dic13C24116yes—
204C22⋊Dic13C24116yes—
205#6103C24116yes—
206#6103C24116yes—
207#6103C24116yes—
208#6103C24116yes—
209#6103C24116yes—
210#6103C24116yes—
211C4⋊Dic13C24116yes—
212C4⋊Dic13C24116yes—
213C4⋊Dic13C24116yes—
214#6101C24116yes—
215#6101C24116yes—
216#6101C24116yes—
217#6101C24116yes—
218#6101C24116yes—
219#6101C24116yes—
220#6101C24116yes—
221#6101C24116yes—
222C4×Dic13C24116yes—
223C4×Dic13C24116yes—
224C2×#539—1348no—
225C22×#126—131no—
226C22×#126—131no—
227C22×#125—131no—
228C22×#125—131no—
229C22×#123—131no—
230C22×#123—131no—
231C22×#123—131no—
232C22×#123—131no—
233C22×C22⋊Q8—131no—
234C22×C22⋊Q8—131no—
235C22×C22⋊Q8D1311yescharacteristic, complemented
236C22×#121—131no—
237C22×C4×D4—131no—
238C22×C4×D4—131no—
239C23×C4⋊C4—131no—
240C23×C13—212no—
241C23×C13—212no—
242C23×C13—212no—
243C23×C13—416no—
244C23×C13C2×#4114yes—
245C23×C13H(5,𝔽2)14yes—
246C23×C132−1+414yes—
247C23×C13C2514yes—
248C23×C13C2513yes—
249C22×D13—232no—
250C22×D13—212no—
251C22×D13—212no—
252C22×D13—212no—
253C22×D13—212no—
254C22×D13—212no—
255C22×D13—416no—
256C22×D13C2×#41124yes—
257C22×D13C2514yes—
258C22×D13C2514yes—
259Q8×C13—416no—
260C2×C4×C13—212no—
261C2×C4×C13—212no—
262C2×C4×C13—212no—
263C2×C4×C13—212no—
264C2×C4×C13—212no—
265C2×C4×C13—212no—
266C2×C4×C13—416no—
267C2×C4×C13C2514yes—
268C2×C4×C13C2514yes—
269C2×C4×C13C2514yes—
270C2×C4×C13C2514yes—
271C2×C4×C13C2514yes—
272C2×C4×C13C2514yes—
273C22⋊D13—232no—
274C22⋊D13—416no—
275C2×Dic13—212no—
276C2×Dic13—212no—
277C2×Dic13—212no—
278C2×Dic13—212no—
279C2×Dic13—212no—
280C2×Dic13—212no—
281C2×Dic13C2514yes—
282C2×Dic13C2514yes—
283C2×Dic13C2514yes—
284C2×Dic13C2514yes—
285C2×Dic13C2514yes—
286C2×Dic13C2514yes—
287D52—232no—
288C4×D13—232no—
289C4×D13—416no—
290C4×D13—416no—
291C4×D13—416no—
292C23×Q8C2×D1311yescharacteristic
293C23×D4—131no—
294C23×D4—131no—
295C23×D4—131no—
296C24×C4—131no—
297C24×C4—131no—
298C24×C4—131no—
299C24×C4—131no—
300C24×C4C2×D1311yescharacteristic
301#539—13256no—
302C2×#126—1324no—
303C2×#126—1324no—
304C2×#125—1324no—
305C2×#125—1324no—
306C2×#123—1324no—
307C2×#123—1324no—
308C2×#123—1324no—
309C2×#123—1324no—
310C2×C22⋊Q8—1324no—
311C2×C22⋊Q8—1324no—
312C2×C22⋊Q8C2×D13124yescomplemented
313C2×#121—1324no—
314C2×C4×D4—1324no—
315C2×C4×D4—1324no—
316C22×C4⋊C4—131no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4—131no—
319C22×C4⋊C4—131no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—131no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4—131no—
324C22×C4⋊C4—131no—
325C22×C4⋊C4—131no—
326C22×C4⋊C4—131no—
327C22×C4⋊C4—1324no—
328C22×C4⋊C4C2×D1311yescharacteristic
329C22×C4⋊C4C2×D1311yescharacteristic
330C22×C4⋊C4C2×D1311yescharacteristic
331C22×C22⋊C4—131no—
332C22×C22⋊C4—131no—
333C22×C22⋊C4—131no—
334C22×C22⋊C4—131no—
335C22×C22⋊C4—131no—
336C22×C22⋊C4—131no—
337C22×C22⋊C4—131no—
338C22×C22⋊C4—131no—
339C22×C22⋊C4C2×D1311yescharacteristic
340C22×C22⋊C4C2×D1311yescharacteristic
341C22×C42—131no—
342C22×C42—131no—
343C22×C13—24no—
344C22×C13—24no—
345C22×C13—24no—
346C22×C13—424no—
347C22×C13#539116yescomplemented
348C22×C13C22×#4116yes—
349C22×C13C2×H(5,𝔽2)16yes—
350C22×C13C2×2−1+416yes—
351C22×C13C2611yescharacteristic
352C2×D13—24no—
353C2×D13—24no—
354C2×D13—248no—
355C2×D13—24no—
356C2×D13—24no—
357C2×D13—24no—
358C2×D13—424no—
359C2×D13C22×#4118yes—
360C4×C13—24no—
361C4×C13—24no—
362C4×C13—24no—
363C4×C13—24no—
364C4×C13—24no—
365C4×C13—24no—
366Dic13—24no—
367Dic13—24no—
368Dic13—24no—
369Dic13—24no—
370Dic13—24no—
371Dic13—24no—
372C25—131no—
373C25—131no—
374C25C22×D1311yescharacteristic
375C22×Q8—44no—
376C22×Q8C22×D13112yes—
377C22×D4—1312no—
378C22×D4—1312no—
379C22×D4—1312no—
380C22×D4—268no—
381C22×D4—268no—
382C22×D4—524no—
383C23×C4—44no—
384C23×C4—131no—
385C23×C4—131no—
386C23×C4—131no—
387C23×C4—131no—
388C23×C4—131no—
389C23×C4—131no—
390C23×C4—1312no—
391C23×C4—1312no—
392C23×C4—1312no—
393C23×C4—1312no—
394C23×C4—268no—
395C23×C4—524no—
396C23×C4—524no—
397C23×C4—524no—
398C23×C4C22×D1311yescharacteristic
399C23×C4C22×D1311yescharacteristic
400C23×C4C22×D1311yescharacteristic
401C23×C4C22×D1311yescharacteristic
402C23×C4C22×D1311yescharacteristic
403C23×C4C22×D1311yescharacteristic
404C23×C4C22×D13112yes—
405#126—1364no—
406#126—1364no—
407#125—1364no—
408#125—1364no—
409#123—1364no—
410#123—1364no—
411#123—1364no—
412#123—1364no—
413C22⋊Q8—1364no—
414C22⋊Q8—1364no—
415C22⋊Q8C22×D13164yescomplemented
416#121—1364no—
417C4×D4—1364no—
418C4×D4—1364no—
419C2×C4⋊C4—1312no—
420C2×C4⋊C4—1312no—
421C2×C4⋊C4—1312no—
422C2×C4⋊C4—1312no—
423C2×C4⋊C4—1312no—
424C2×C4⋊C4—1312no—
425C2×C4⋊C4—1312no—
426C2×C4⋊C4—1312no—
427C2×C4⋊C4—1312no—
428C2×C4⋊C4—1312no—
429C2×C4⋊C4—1312no—
430C2×C4⋊C4—1364no—
431C2×C4⋊C4C22×D13112yes—
432C2×C4⋊C4C22×D13112yes—
433C2×C4⋊C4C22×D13112yes—
434C2×C22⋊C4—1312no—
435C2×C22⋊C4—1312no—
436C2×C22⋊C4—1312no—
437C2×C22⋊C4—1312no—
438C2×C22⋊C4—1312no—
439C2×C22⋊C4—1312no—
440C2×C22⋊C4—1312no—
441C2×C22⋊C4—1312no—
442C2×C22⋊C4C22×D13112yes—
443C2×C22⋊C4C22×D13112yes—
444C2×C42—1312no—
445C2×C42—1312no—
446C2×C13—44no—
447C2×C13C2×#539112yescomplemented
448C2×C13C23×#4111yescharacteristic
449C2×C13C22×H(5,𝔽2)11yescharacteristic
450C2×C13C22×2−1+411yescharacteristic
451D13—28no—
452D13—44no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24—138no—
457C24—136no—
458C24—136no—
459C24—264no—
460C24—264no—
461C24—264no—
462C24—264no—
463C24—264no—
464C24C23×D1316yes—
465C24C23×D1311yescharacteristic
466C2×Q8—424no—
467C2×Q8C23×D13116yes—
468C2×D4—1316no—
469C2×D4—1316no—
470C2×D4—1316no—
471C2×D4—2648no—
472C2×D4—2648no—
473C2×D4—5224no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—424no—
481C22×C4—136no—
482C22×C4—136no—
483C22×C4—136no—
484C22×C4—136no—
485C22×C4—136no—
486C22×C4—136no—
487C22×C4—1316no—
488C22×C4—1316no—
489C22×C4—1316no—
490C22×C4—1316no—
491C22×C4—2648no—
492C22×C4—264no—
493C22×C4—264no—
494C22×C4—264no—
495C22×C4—264no—
496C22×C4—264no—
497C22×C4—264no—
498C22×C4—5224no—
499C22×C4—5224no—
500C22×C4—5224no—
501C22×C4C23×D1316yes—
502C22×C4C23×D1316yes—
503C22×C4C23×D1316yes—
504C22×C4C23×D1316yes—
505C22×C4C23×D1316yes—
506C22×C4C23×D1316yes—
507C22×C4C23×D13116yes—
508C4⋊C4—1316no—
509C4⋊C4—1316no—
510C4⋊C4—1316no—
511C4⋊C4—1316no—
512C4⋊C4—1316no—
513C4⋊C4—1316no—
514C4⋊C4—1316no—
515C4⋊C4—1316no—
516C4⋊C4—1316no—
517C4⋊C4—1316no—
518C4⋊C4—1316no—
519C4⋊C4C23×D13116yes—
520C4⋊C4C23×D13116yes—
521C4⋊C4C23×D13116yes—
522C22⋊C4—1316no—
523C22⋊C4—1316no—
524C22⋊C4—1316no—
525C22⋊C4—1316no—
526C22⋊C4—1316no—
527C22⋊C4—1316no—
528C22⋊C4—1316no—
529C22⋊C4—1316no—
530C22⋊C4C23×D13116yes—
531C22⋊C4C23×D13116yes—
532C42—1316no—
533C42—1316no—
534C13C22×#53911yescharacteristic, complemented, Sylow
535C23—212no—
536C23—212no—
537C23—212no—
538C23—416no—
539C23—1324no—
540C23—134no—
541C23—134no—
542C23—2632no—
543C23—2612no—
544C23—2612no—
545C23—2612no—
546C23—2612no—
547C23—2612no—
548C23—5216no—
549C23#8825114yes—
550C23#8825414yes—
551C23#41×D1314yes—
552C23C24×D1314yes—
553C23C24×D1313yes—
554Q8—416no—
555D4—2632no—
556D4—2632no—
557D4—5216no—
558C2×C4—212no—
559C2×C4—212no—
560C2×C4—212no—
561C2×C4—212no—
562C2×C4—212no—
563C2×C4—212no—
564C2×C4—416no—
565C2×C4—134no—
566C2×C4—134no—
567C2×C4—134no—
568C2×C4—134no—
569C2×C4—134no—
570C2×C4—134no—
571C2×C4—2632no—
572C2×C4—2612no—
573C2×C4—2612no—
574C2×C4—2612no—
575C2×C4—2612no—
576C2×C4—2612no—
577C2×C4—2612no—
578C2×C4—5216no—
579C2×C4—5216no—
580C2×C4—5216no—
581C2×C4C24×D1314yes—
582C2×C4C24×D1314yes—
583C2×C4C24×D1314yes—
584C2×C4C24×D1314yes—
585C2×C4C24×D1314yes—
586C2×C4C24×D1314yes—
587C22—24no—
588C22—24no—
589C22—24no—
590C22—424no—
591C22—138no—
592C22—264no—
593C22—264no—
594C22—2648no—
595C22—264no—
596C22—264no—
597C22—264no—
598C22—5224no—
599C22#11719343116yesdirect product factor
600C22C2×#8825116yes—
601C22C2×#8825416yes—
602C22C2×#41×D1316yes—
603C22C25×D1311yescharacteristic
604C4—24no—
605C4—24no—
606C4—24no—
607C4—24no—
608C4—24no—
609C4—24no—
610C4—264no—
611C4—264no—
612C4—264no—
613C4—264no—
614C4—264no—
615C4—264no—
616C2—44no—
617C2—268no—
618C2—524no—
619C2C2×#11719343112yesdirect product factor
620C2C22×#41×D1311yescharacteristic
621C2C22×#8825111yescharacteristic
622C2C22×#8825411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC22×#88138C2
hypercenterC22×C22⋊Q8D13
hypocenterC13C22×#539
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11719343C2direct (N × H)
2. C22×#88152C2semidirect
3. C22×#88133C2semidirect
4. C22×#88143C2semidirect
5. C22×#88143C2semidirect
6. C22×#88148C2semidirect
7. C22×#88183C2semidirect
8. C22×#88137C2semidirect
9. C22×#88137C2semidirect
10. C22×#88200C2semidirect
11. C22×#88200C2semidirect
13. C22×#88147C2semidirect
14. C22×C4×C22⋊D13C2semidirect
15. C22×C4⋊C4×D13C2semidirect
16. C22×C13×C22⋊Q8C2semidirect
26. C2×C13×C22⋊Q8C22semidirect
34. C2×#88200C22semidirect
35. C2×#88200C22semidirect
36. C2×#88183C22semidirect
37. C2×C4×C22⋊D13C22semidirect
57. #11719343C22direct (N × H)
58. C2×#88152C22semidirect
59. C2×#88148C22semidirect
60. C2×#88147C22semidirect
61. C2×C4⋊C4×D13C22semidirect
62. C2×#88143C22semidirect
63. C2×#88143C22semidirect
65. C2×#88137C22semidirect
66. C2×#88137C22semidirect
67. C2×#88133C22semidirect
101. C13×C22⋊Q8C23semidirect
109. #88200C23semidirect
110. #88200C23semidirect
111. #88183C23semidirect
112. C4×C22⋊D13C23semidirect
132. #88152C23semidirect
133. #88148C23semidirect
134. #88147C23semidirect
135. C4⋊C4×D13C23semidirect
136. #88143C23semidirect
137. #88143C23semidirect
139. #88137C23semidirect
140. #88137C23semidirect
141. #88133C23semidirect
235. C22×C22⋊Q8D13semidirect
312. C2×C22⋊Q8C2×D13semidirect
347. C22×C13#539semidirect
415. C22⋊Q8C22×D13semidirect
447. C2×C13C2×#539semidirect
534. C13C22×#539semidirect
599. C22#11719343direct (N × H)
619. C2C2×#11719343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193432
C22×#881522
C22×#881332
C22×#881432
C22×#881482
C22×#881832
C22×#881372
C22×#882002
C22×#881382
C22×#881472
C22×C4×C22⋊D132
C22×C4⋊C4×D132
C22×C13×C22⋊Q82
C22×#53913