Finite Group Databasebeta

← #11802776

Subgroups — #11802776

Order 1152.

1597 conjugacy classes of subgroups.

The subgroup lattice has 691 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3722C211yesmaximal, characteristic
2#10592654C211yesmaximal, characteristic
3C3×#4942C211yesmaximal, characteristic, complemented
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5#10591716C211yesmaximal, characteristic, complemented
6#10591714C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591289C212yesmaximal, complemented
9#10591259C212yesmaximal, complemented
10#10591258C212yesmaximal, complemented
11#10591194C212yesmaximal, complemented
12#74004—31nomaximal
13#73567—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×#3752C2212yes—
20C2×#3752C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yescomplemented
24C2×C3×C4×Dic3C2212yescomplemented
25C2×Dic3⋊Dic3C2212yescomplemented
26C2×#3722C418yescomplemented
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C2×#3722C2211yescharacteristic
30C2×#3722C2211yescharacteristic
31C2×#3722C2211yescharacteristic
32C2×#3722C2211yescharacteristic
33C2×Dic32C2212yescomplemented
34C3×C3⋊#95C2212yescomplemented
35C3×C3⋊#95C2212yescomplemented
36#63579C2212yescomplemented
37#63579C2212yescomplemented
38C22×(C2×D3)⋊C4—31no—
39C22×(C2×D3)⋊C4—31no—
40C3×#380—31no—
41C3×C4×C22⋊C4—31no—
42#5212—31no—
43C4×#217—31no—
44#4990—32no—
45#4990—32no—
46#4955—31no—
47#4955—31no—
48#4955—31no—
49#4955—31no—
50#4955—61no—
51#4942—31no—
52#4942D311yescharacteristic, complemented
53Dic3×C22⋊C4—31no—
54Dic3×C22⋊C4D311yescharacteristic, complemented
55#4940—32no—
56#4940—32no—
57#4670—32no—
58#4670—32no—
59#4669—32no—
60#4669—32no—
61C24×C32C2311yescharacteristic
62C23×C3⋊D3—22no—
63C23×C3⋊D3—22no—
64C23×C3⋊D3—42no—
65C23×C3⋊D3—42no—
66C23×C3⋊D3C2×C414yes—
67C23×C3⋊D3C2311yescharacteristic
68C23×C3⋊D3C2311yescharacteristic
69C22×C32×C4C2312yes—
70C22×C3⋊Dic3C2312yes—
71C22×C3×Dic3—42no—
72C22×C3×Dic3—42no—
73C22×C3×Dic3C2×C414yes—
74C22×C3×Dic3C2×C414yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C32×C22⋊C4—22no—
82#3757—22no—
83#3752—42no—
84#3752—42no—
85C3×#217—22no—
86C3×#217—22no—
87C3×Dic3⋊C4—42no—
88C3×C4×Dic3—42no—
89Dic3⋊Dic3—42no—
90#3722—42no—
91#3722—42no—
92#3722C2×C414yes—
93#3722C2×C414yes—
94#3722C2×C414yes—
95#3722C2×C414yes—
96Dic32—42no—
97#2312—91noSylow
98C24×D3—31no—
99C24×D3—31no—
100C24×D3—61no—
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×Dic3C2×D311yescharacteristic
104C23×Dic3C2×D311yescharacteristic
105C2×C3×C4⋊C4—32no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C22⋊C4—31no—
109C2×C3×C22⋊C4C2×D311yescharacteristic
110C2×C3×C22⋊C4C2×D311yescharacteristic
111C2×C3×C42—32no—
112C2×#217—31no—
113C2×#217—31no—
114C2×#217—61no—
115C2×#217C2×D311yescharacteristic
116C2×#217C2×D311yescharacteristic
117C2×(C2×D3)⋊C4—38no—
118C2×(C2×D3)⋊C4—38no—
119C2×(C2×D3)⋊C4—31no—
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—62no—
136C2×(C2×D3)⋊C4—62no—
137C2×C4⋊Dic3—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4C2×D312yescomplemented
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3C2×D312yescomplemented
143C3×#95—32no—
144C3×#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95C2×D312yescomplemented
150C3⋊#95C2×D312yescomplemented
151C23×C32—22no—
152C23×C32—22no—
153C23×C32C22×C412yes—
154C23×C32#4112yes—
155C23×C32#4112yes—
156C23×C32C2411yescharacteristic
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3—28no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—44no—
167C22×C3⋊D3—44no—
168C22×C3⋊D3—48no—
169C22×C3⋊D3—48no—
170C22×C3⋊D3C22×C412yes—
171C22×C3⋊D3C22×C412yes—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—44no—
189C2×C3×Dic3—44no—
190C2×C3×Dic3C22×C412yes—
191C2×C3×Dic3C22×C412yes—
192C2×C3×Dic3C22×C412yes—
193C2×C3×Dic3C22×C412yes—
194C22×C22⋊C4—91no—
195#388—92no—
196#388—92no—
197#388—92no—
198#388—92no—
199#380—31no—
200#380—91no—
201#379—91no—
202#379—91no—
203C4×C22⋊C4—31no—
204C4×C22⋊C4—91no—
205C24×C3—21no—
206C24×C3C22×D311yescharacteristic
207C24×C3C22×D311yescharacteristic
208C23×D3—31no—
209C23×D3—31no—
210C23×D3—31no—
211C23×D3—31no—
212C23×D3—34no—
213C23×D3—34no—
214C23×D3—61no—
215C23×D3—61no—
216C23×D3—64no—
217C23×D3—62no—
218C23×D3—62no—
219C23×D3—62no—
220C23×D3—62no—
221C23×D3—122no—
222C23×D3—122no—
223C23×D3—122no—
224C23×D3—122no—
225C23×D3—122no—
226C23×D3—122no—
227C23×D3—124no—
228C23×D3—124no—
229C22×C3×C4—22no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—34no—
235C22×C3×C4—34no—
236C22×C3×C4—32no—
237C22×C3×C4—32no—
238C22×C3×C4—122no—
239C22×C3×C4—122no—
240C22×C3×C4C22×D312yes—
241C22×C3×C4C22×D312yes—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—42no—
245C22×Dic3—42no—
246C22×Dic3—62no—
247C22×Dic3C4×D314yes—
248C22×Dic3C4×D314yes—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D311yescharacteristic
252C22×Dic3C22×D311yescharacteristic
253C22×Dic3C22×D311yescharacteristic
254C22×Dic3C22×D311yescharacteristic
255C3×C4⋊C4—122no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—42no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—62no—
261C3×C42—122no—
262#217—22no—
263#217—22no—
264#217—62no—
265#217—62no—
266#217—122no—
267(C2×D3)⋊C4—34no—
268(C2×D3)⋊C4—34no—
269(C2×D3)⋊C4—34no—
270(C2×D3)⋊C4—34no—
271(C2×D3)⋊C4—34no—
272(C2×D3)⋊C4—34no—
273(C2×D3)⋊C4—34no—
274(C2×D3)⋊C4—34no—
275(C2×D3)⋊C4—122no—
276(C2×D3)⋊C4—122no—
277(C2×D3)⋊C4—122no—
278(C2×D3)⋊C4—122no—
279(C2×D3)⋊C4—122no—
280(C2×D3)⋊C4—122no—
281(C2×D3)⋊C4—122no—
282(C2×D3)⋊C4—122no—
283(C2×D3)⋊C4—124no—
284(C2×D3)⋊C4—124no—
285C4⋊Dic3—122no—
286Dic3⋊C4—42no—
287Dic3⋊C4—122no—
288C4×Dic3—42no—
289C4×Dic3—122no—
290C4×Dic3—122no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—24no—
294C22×C32—24no—
295C22×C32#11714yes—
296C22×C32C23×C411yescharacteristic
297C22×C32C2×#4111yescharacteristic
298C22×C32C2×#4111yescharacteristic
299C22×C32H(5,𝔽2)12yes—
300C22×C32H(5,𝔽2)12yes—
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3⋊D3—22no—
304C2×C3⋊D3—22no—
305C2×C3⋊D3—22no—
306C2×C3⋊D3—22no—
307C2×C3⋊D3—416no—
308C2×C3⋊D3—42no—
309C2×C3⋊D3—42no—
310C2×C3⋊D3—42no—
311C2×C3⋊D3—42no—
312C32×C4—42no—
313C3⋊Dic3—42no—
314C3×Dic3—22no—
315C3×Dic3—22no—
316C3×Dic3—22no—
317C3×Dic3—22no—
318C3×Dic3—42no—
319C3×Dic3—42no—
320C25—91no—
321C23×C4—31no—
322C23×C4—31no—
323C2×C4⋊C4—32no—
324C2×C4⋊C4—92no—
325C2×C22⋊C4—31no—
326C2×C22⋊C4—31no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—91no—
329C2×C22⋊C4—91no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—98no—
332C2×C22⋊C4—91no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4D3211yescharacteristic
338C2×C42—32no—
339C2×C42—92no—
340#95—32no—
341#95—32no—
342#95—92no—
343#95—92no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—21no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3C2×C4×D312yes—
355C23×C3C2×C4×D312yes—
356C23×C3#23512yes—
357C23×C3#23512yes—
358C23×C3#23712yes—
359C23×C3#23912yes—
360C23×C3C23×D311yescharacteristic
361C23×C3C23×D311yescharacteristic
362C22×D3—32no—
363C22×D3—32no—
364C22×D3—32no—
365C22×D3—32no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—68no—
371C22×D3—68no—
372C22×D3—61no—
373C22×D3—61no—
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3—121no—
389C22×D3—121no—
390C22×D3—122no—
391C22×D3—122no—
392C22×D3—121no—
393C22×D3—121no—
394C22×D3—128no—
395C22×D3—124no—
396C22×D3—124no—
397C22×D3—124no—
398C22×D3—124no—
399C22×D3—128no—
400C22×D3—128no—
401C22×D3—128no—
402C22×D3—128no—
403C22×D3—128no—
404C22×D3—128no—
405C22×D3—1216no—
406C22×D3—1216no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—124no—
431C2×C3×C4—124no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—44no—
443C2×Dic3—44no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—122no—
451C2×Dic3—122no—
452C2×Dic3—122no—
453C2×Dic3C2×C4×D312yes—
454C2×Dic3C2×C4×D312yes—
455C2×Dic3C2×C4×D312yes—
456C2×Dic3C2×C4×D312yes—
457C2×C32—24no—
458C2×C32C2×#11711yescharacteristic
459C2×C32#51811yescharacteristic
460C2×C32#51811yescharacteristic
461C2×C32#53812yes—
462C2×C32#53812yes—
463C3⋊D3—42no—
464C3⋊D3—42no—
465C24—91no—
466C24—91no—
467C24—94no—
468C24—182no—
469C24—182no—
470C24—362no—
471C24—362no—
472C24C2×D3211yescharacteristic
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—34no—
478C22×C4—34no—
479C22×C4—32no—
480C22×C4—32no—
481C22×C4—92no—
482C22×C4—122no—
483C22×C4—122no—
484C22×C4C2×D3212yes—
485C4⋊C4—122no—
486C4⋊C4—362no—
487C22⋊C4—22no—
488C22⋊C4—62no—
489C22⋊C4—62no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—94no—
493C22⋊C4—94no—
494C22⋊C4—182no—
495C22⋊C4—362no—
496C22⋊C4—362no—
497C22⋊C4—362no—
498C22⋊C4—362no—
499C42—122no—
500C42—362no—
501C22×C3—24no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—24no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3#87214yes—
520C22×C3#89214yes—
521C22×C3C22×C4×D311yescharacteristic
522C22×C3C22×C4×D311yescharacteristic
523C22×C3C2×#23511yescharacteristic
524C22×C3C2×#23511yescharacteristic
525C22×C3C2×#23711yescharacteristic
526C22×C3#100412yes—
527C22×C3#100412yes—
528C22×C3C2×#23911yescharacteristic
529C22×C3#100912yes—
530C22×C3#100912yes—
531C2×D3—64no—
532C2×D3—64no—
533C2×D3—62no—
534C2×D3—62no—
535C2×D3—62no—
536C2×D3—62no—
537C2×D3—62no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—122no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—122no—
549C2×D3—1216no—
550C2×D3—1216no—
551C2×D3—124no—
552C2×D3—124no—
553C2×D3—124no—
554C2×D3—124no—
555C2×D3—1232no—
556C2×D3—122no—
557C2×D3—122no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—122no—
561C2×D3—122no—
562C2×D3—122no—
563C2×D3—122no—
564C3×C4—42no—
565C3×C4—42no—
566C3×C4—62no—
567C3×C4—62no—
568C3×C4—62no—
569C3×C4—62no—
570C3×C4—82no—
571C3×C4—122no—
572C3×C4—122no—
573Dic3—22no—
574Dic3—22no—
575Dic3—22no—
576Dic3—22no—
577Dic3—42no—
578Dic3—42no—
579Dic3—122no—
580Dic3—122no—
581Dic3—242no—
582C32#231211yescharacteristic, complemented, Sylow
583C23—22no—
584C23—22no—
585C23—92no—
586C23—92no—
587C23—181no—
588C23—181no—
589C23—182no—
590C23—182no—
591C23—182no—
592C23—182no—
593C23—181no—
594C23—181no—
595C23—188no—
596C23—364no—
597C23—364no—
598C23—368no—
599C23—368no—
600C23#379912yes—
601C23C4×D3212yes—
602C23#380412yes—
603C23C22×D3211yescharacteristic
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—32no—
608C2×C4—32no—
609C2×C4—32no—
610C2×C4—32no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—124no—
622C2×C4—124no—
623C2×C4—182no—
624C2×C4—182no—
625C2×C4—182no—
626C2×C3—24no—
627C2×C3—24no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—22no—
631C2×C3—22no—
632C2×C3—21no—
633C2×C3—44no—
634C2×C3C2×#87211yescharacteristic
635C2×C3#548611yescharacteristic
636C2×C3#548611yescharacteristic
637C2×C3C2×#89211yescharacteristic
638C2×C3#552111yescharacteristic
639C2×C3#552111yescharacteristic
640C2×C3#556012yes—
641C2×C3#556012yes—
642C2×C3#561712yes—
643C2×C3#564412yes—
644D3—124no—
645D3—124no—
646D3—122no—
647D3—122no—
648D3—122no—
649D3—122no—
650C22—22no—
651C22—22no—
652C22—24no—
653C22—24no—
654C22—182no—
655C22—182no—
656C22—182no—
657C22—182no—
658C22—182no—
659C22—182no—
660C22—3616no—
661C22—362no—
662C22—362no—
663C22—362no—
664C22—362no—
665C22#6383614yes—
666C22C2×#379911yescharacteristic
667C22C2×C4×D3211yescharacteristic
668C22#6431412yes—
669C22#6431412yes—
670C22C2×#380411yescharacteristic
671C4—42no—
672C4—62no—
673C4—62no—
674C4—62no—
675C4—62no—
676C4—122no—
677C4—122no—
678C4—362no—
679C3—21no—
680C3#7356711yescharacteristic, complemented
681C3#7400411yescharacteristic, complemented
682C2—24no—
683C2—362no—
684C2—362no—
685C2#1059418211yescharacteristic
686C2#1059418211yescharacteristic
687C2#1059424312yes—
688C2C2×#6383611yescharacteristic
689C2#1059522112yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4942C2semidirect
4. C3×Dic3×C22⋊C4C2semidirect
5. #10591716C2semidirect
7. Dic3×#217C2semidirect
8. #10591289C2semidirect
9. #10591259C2semidirect
10. #10591258C2semidirect
11. #10591194C2semidirect
23. C2×C3×Dic3⋊C4C22semidirect
24. C2×C3×C4×Dic3C22semidirect
25. C2×Dic3⋊Dic3C22semidirect
26. C2×#3722C4semidirect
33. C2×Dic32C22semidirect
34. C3×C3⋊#95C22semidirect
35. C3×C3⋊#95C22semidirect
36. #63579C22semidirect
37. #63579C22semidirect
52. #4942D3semidirect
54. Dic3×C22⋊C4D3semidirect
139. C2×Dic3⋊C4C2×D3semidirect
142. C2×C4×Dic3C2×D3semidirect
149. C3⋊#95C2×D3semidirect
150. C3⋊#95C2×D3semidirect
582. C32#2312semidirect
680. C3#73567semidirect
681. C3#74004semidirect

Maximal subgroups

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

subgroupindex
C22×#37222
#105926542
C3×#49422
C3×Dic3×C22⋊C42
#105917162
#105917142
Dic3×#2172
#105912892
#105912592
#105912582
#105911942
#740043
#735673