Finite Group Databasebeta

← #30764277

Subgroups — #30764277

Order 17152.

790 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863151C211yesmaximal, characteristic
2C2×#16863150C211yesmaximal, characteristic
3C2×#16863150C211yesmaximal, characteristic
4C2×#16863150C211yesmaximal, characteristic
5C2×#16863150C211yesmaximal, characteristic
6C4×C67⋊#95C211yesmaximal, characteristic
7C2×#336×C67C211yesmaximal, characteristic
8C23×C67⋊C8C2211yescharacteristic
9C23×C67⋊C8C2211yescharacteristic
10C22×C4×Dic67C2211yescharacteristic
11C22×C4×Dic67C2211yescharacteristic
12C2×C67⋊#95C411yescharacteristic
13C2×C67⋊#95C411yescharacteristic
14C2×C67⋊#95C411yescharacteristic
15C2×C67⋊#95C411yescharacteristic
16#16863151—22no—
17#16863150—22no—
18#16863150—22no—
19#16863150—22no—
20#16863150—22no—
21C23×C8×C67C2211yescharacteristic
22C23×C8×C67C2211yescharacteristic
23C22×C42×C67C2211yescharacteristic
24#336×C67—22no—
25C23×Dic67C2×C411yescharacteristic
26C23×Dic67C2×C411yescharacteristic
27C23×Dic67C2×C411yescharacteristic
28C23×Dic67C2×C411yescharacteristic
29C22×C67⋊C8—21no—
30C22×C67⋊C8—21no—
31C22×C67⋊C8—21no—
32C22×C67⋊C8—21no—
33C22×C67⋊C8—21no—
34C22×C67⋊C8—21no—
35C22×C67⋊C8—21no—
36C22×C67⋊C8—21no—
37C22×C67⋊C8—21no—
38C22×C67⋊C8—21no—
39C22×C67⋊C8—21no—
40C22×C67⋊C8—21no—
41C22×C67⋊C8D412yes—
42C22×C67⋊C8Q812yes—
43C2×C4×Dic67—21no—
44C2×C4×Dic67—21no—
45C2×C4×Dic67—21no—
46C2×C4×Dic67—21no—
47C2×C4×Dic67—21no—
48C2×C4×Dic67—21no—
49C2×C4×Dic67—21no—
50C2×C4×Dic67—21no—
51C2×C4×Dic67—21no—
52C2×C4×Dic67—21no—
53C2×C4×Dic67—21no—
54C2×C4×Dic67—21no—
55C67⋊#95—22no—
56C67⋊#95—22no—
57C67⋊#95—22no—
58C67⋊#95C814yescomplemented
59C23×C4×C67C2×C411yescharacteristic
60C23×C4×C67C2×C411yescharacteristic
61C23×C4×C67C2311yescharacteristic
62C22×C8×C67—21no—
63C22×C8×C67—21no—
64C22×C8×C67—21no—
65C22×C8×C67—21no—
66C22×C8×C67—21no—
67C22×C8×C67—21no—
68C22×C8×C67—21no—
69C22×C8×C67—21no—
70C22×C8×C67—21no—
71C22×C8×C67—21no—
72C22×C8×C67—21no—
73C22×C8×C67—21no—
74C22×C8×C67D412yes—
75C22×C8×C67D412yes—
76C2×C42×C67—21no—
77C2×C42×C67—21no—
78C2×C42×C67—21no—
79C2×C42×C67—21no—
80C2×C42×C67—21no—
81C2×C42×C67—21no—
82C22×Dic67—21no—
83C22×Dic67—21no—
84C22×Dic67—21no—
85C22×Dic67—21no—
86C22×Dic67—21no—
87C22×Dic67—21no—
88C22×Dic67—21no—
89C22×Dic67—21no—
90C22×Dic67—21no—
91C22×Dic67—21no—
92C22×Dic67—21no—
93C22×Dic67—21no—
94C22×Dic67—21no—
95C22×Dic67—21no—
96C22×Dic67—21no—
97C22×Dic67—21no—
98C22×Dic67—21no—
99C22×Dic67—21no—
100C22×Dic67—21no—
101C22×Dic67—21no—
102C22×Dic67—21no—
103C22×Dic67—21no—
104C22×Dic67—21no—
105C22×Dic67—21no—
106C22×Dic67C2×C812yes—
107C22×Dic67C2×C812yes—
108C22×Dic67M1612yes—
109C22×Dic67M1612yes—
110C2×C67⋊C8—22no—
111C2×C67⋊C8—22no—
112C2×C67⋊C8—22no—
113C2×C67⋊C8—22no—
114C2×C67⋊C8—22no—
115C2×C67⋊C8—22no—
116C2×C67⋊C8—41no—
117C2×C67⋊C8—41no—
118C2×C67⋊C8—41no—
119C2×C67⋊C8—41no—
120C2×C67⋊C8—41no—
121C2×C67⋊C8—41no—
122C2×C67⋊C8—41no—
123C2×C67⋊C8—41no—
124C4×Dic67—41no—
125C4×Dic67—41no—
126C4×Dic67—41no—
127C4×Dic67—41no—
128C4×Dic67—41no—
129C4×Dic67—41no—
130C4×Dic67—41no—
131C4×Dic67—41no—
132C24×C67C22×C411yescharacteristic
133C22×C4×C67—21no—
134C22×C4×C67—21no—
135C22×C4×C67—21no—
136C22×C4×C67—21no—
137C22×C4×C67—21no—
138C22×C4×C67—21no—
139C22×C4×C67—21no—
140C22×C4×C67—21no—
141C22×C4×C67—21no—
142C22×C4×C67—21no—
143C22×C4×C67—21no—
144C22×C4×C67—21no—
145C22×C4×C67C2×C812yes—
146C22×C4×C67M1612yes—
147C22×C4×C67C2×D411yescharacteristic
148C22×C4×C67C2×D411yescharacteristic
149C22×C4×C67C2×D411yescharacteristic
150C22×C4×C67C2×Q811yescharacteristic
151C22×C4×C67#4111yescharacteristic
152C22×C4×C67#4111yescharacteristic
153C22×C4×C67#4111yescharacteristic
154C22×C4×C67#4111yescharacteristic
155C22×C4×C67#4111yescharacteristic
156C22×C4×C67#4111yescharacteristic
157C22×C4×C67#4111yescharacteristic
158C22×C4×C67#4111yescharacteristic
159C22×C4×C67#4111yescharacteristic
160C22×C4×C67#4111yescharacteristic
161C2×C8×C67—22no—
162C2×C8×C67—22no—
163C2×C8×C67—22no—
164C2×C8×C67—22no—
165C2×C8×C67—22no—
166C2×C8×C67—22no—
167C2×C8×C67—41no—
168C2×C8×C67—41no—
169C2×C8×C67—41no—
170C2×C8×C67—41no—
171C2×C8×C67—41no—
172C2×C8×C67—41no—
173C2×C8×C67—41no—
174C2×C8×C67—41no—
175C42×C67—41no—
176C42×C67—41no—
177C42×C67—41no—
178C42×C67—41no—
179C23×C67#11711yescharacteristic
180C23×C67#11711yescharacteristic
181C23×C67#11711yescharacteristic
182C23×C67C4×D411yescharacteristic
183C23×C67C4×D411yescharacteristic
184C23×C67C4×D411yescharacteristic
185C23×C67C4×Q811yescharacteristic
186C23×C67C22×C811yescharacteristic
187C23×C67C2×M1611yescharacteristic
188C23×C67C2×M1611yescharacteristic
189C23×C67C2×M1611yescharacteristic
190C23×C67#13111yescharacteristic
191C23×C67#13111yescharacteristic
192C23×C67#13111yescharacteristic
193C23×C67#13111yescharacteristic
194C2×C4×C67—22no—
195C2×C4×C67—22no—
196C2×C4×C67—22no—
197C2×C4×C67—22no—
198C2×C4×C67—22no—
199C2×C4×C67—22no—
200C2×C4×C67—41no—
201C2×C4×C67—41no—
202C2×C4×C67—41no—
203C2×C4×C67—41no—
204C2×C4×C67—41no—
205C2×C4×C67—41no—
206C2×C4×C67—41no—
207C2×C4×C67—41no—
208C2×C4×C67#12111yescharacteristic
209C2×C4×C67#12111yescharacteristic
210C2×C4×C67#12111yescharacteristic
211C2×C4×C67C22⋊Q811yescharacteristic
212C2×C4×C67C22⋊Q811yescharacteristic
213C2×C4×C67C22⋊Q811yescharacteristic
214C2×C4×C67#12311yescharacteristic
215C2×C4×C67#12311yescharacteristic
216C2×C4×C67#12311yescharacteristic
217C2×C4×C67#12311yescharacteristic
218C2×C4×C67#12311yescharacteristic
219C2×C4×C67#12311yescharacteristic
220C2×C4×C67#12411yescharacteristic
221C2×C4×C67#12411yescharacteristic
222C2×C4×C67#12411yescharacteristic
223C2×C4×C67#12511yescharacteristic
224C2×C4×C67#12511yescharacteristic
225C2×C4×C67#12511yescharacteristic
226C2×C4×C67#12611yescharacteristic
227C2×C4×C67#12611yescharacteristic
228C2×C4×C67#12611yescharacteristic
229C2×C4×C67#12611yescharacteristic
230C2×C4×C67#12611yescharacteristic
231C2×C4×C67#12611yescharacteristic
232C2×C4×C67#12611yescharacteristic
233C2×C4×C67#12611yescharacteristic
234C2×C4×C67#12611yescharacteristic
235C2×C4×C67#12611yescharacteristic
236C2×Dic67—22no—
237C2×Dic67—22no—
238C2×Dic67—22no—
239C2×Dic67—22no—
240C2×Dic67—22no—
241C2×Dic67—22no—
242C2×Dic67—22no—
243C2×Dic67—22no—
244C2×Dic67—22no—
245C2×Dic67—22no—
246C2×Dic67—22no—
247C2×Dic67—22no—
248C2×Dic67—41no—
249C2×Dic67—41no—
250C2×Dic67—41no—
251C2×Dic67—41no—
252C2×Dic67—41no—
253C2×Dic67—41no—
254C2×Dic67—41no—
255C2×Dic67—41no—
256C2×Dic67—41no—
257C2×Dic67—41no—
258C2×Dic67—41no—
259C2×Dic67—41no—
260C2×Dic67—41no—
261C2×Dic67—41no—
262C2×Dic67—41no—
263C2×Dic67—41no—
264C8×C67—42no—
265C8×C67—42no—
266C67⋊C8—42no—
267C67⋊C8—42no—
268C22×C67#38311yescharacteristic
269C22×C67#38711yescharacteristic
270C22×C67#38711yescharacteristic
271C22×C67#38711yescharacteristic
272C22×C67#38811yescharacteristic
273C22×C67#38811yescharacteristic
274C22×C67#38811yescharacteristic
275C22×C67#43111yescharacteristic
276C22×C67#43111yescharacteristic
277C22×C67#43111yescharacteristic
278C22×C67#43211yescharacteristic
279C22×C67#43211yescharacteristic
280C22×C67#43211yescharacteristic
281C22×C67#43311yescharacteristic
282C22×C67#43311yescharacteristic
283C22×C67#43311yescharacteristic
284C22×C67#43311yescharacteristic
285C22×C67#43311yescharacteristic
286C22×C67#43311yescharacteristic
287C22×C67C8×D411yescharacteristic
288C22×C67C8×D411yescharacteristic
289C22×C67C8×D411yescharacteristic
290C22×C67#43511yescharacteristic
291C22×C67#43511yescharacteristic
292C22×C67#43511yescharacteristic
293C22×C67#43511yescharacteristic
294C22×C67#43511yescharacteristic
295C22×C67#43511yescharacteristic
296C22×C67#43611yescharacteristic
297C22×C67#43611yescharacteristic
298C22×C67#43611yescharacteristic
299C22×C67C8×Q811yescharacteristic
300C22×C67#44611yescharacteristic
301C22×C67#44611yescharacteristic
302C22×C67#44611yescharacteristic
303C4×C67—42no—
304C4×C67—42no—
305C4×C67#39611yescharacteristic
306C4×C67#39711yescharacteristic
307C4×C67#39711yescharacteristic
308C4×C67#39711yescharacteristic
309C4×C67#40011yescharacteristic
310C4×C67#40011yescharacteristic
311C4×C67#40011yescharacteristic
312C4×C67#40111yescharacteristic
313Dic67—42no—
314Dic67—42no—
315Dic67—42no—
316Dic67—42no—
317#11298—671nomaximal, Sylow
318C2×C67#144311yescharacteristic
319C2×C67#183911yescharacteristic
320C2×C67#184011yescharacteristic
321C2×C67#191611yescharacteristic
322C2×C67#191611yescharacteristic
323C2×C67#191611yescharacteristic
324C2×C67#191711yescharacteristic
325C2×C67#191711yescharacteristic
326C2×C67#191711yescharacteristic
327C2×C67#192311yescharacteristic
328C2×C67#192311yescharacteristic
329C2×C67#192311yescharacteristic
330C2×C67#192411yescharacteristic
331C2×C67#192411yescharacteristic
332C2×C67#192411yescharacteristic
333C2×#336—671no—
334C2×#336—671no—
335C2×#336—671no—
336C2×#336—671no—
337C2×#336—671no—
338C2×#336D6711yescharacteristic
339C4×#95—671no—
340C67#1129811yescharacteristic, complemented, Sylow
341C23×C8—671no—
342C23×C8—671no—
343C23×C8C2×D6711yescharacteristic
344C23×C8C2×D6711yescharacteristic
345C22×C42—671no—
346C22×C42—671no—
347C22×C42C2×D6711yescharacteristic
348C2×#95—671no—
349C2×#95—671no—
350C2×#95—671no—
351C2×#95—671no—
352#336—22no—
353#336—1342no—
354#336—1342no—
355#336—1342no—
356#336—1342no—
357#336—1342no—
358C23×C4—671no—
359C23×C4—671no—
360C23×C4—671no—
361C23×C4—671no—
362C23×C4C4×D6711yescharacteristic
363C23×C4C4×D6711yescharacteristic
364C23×C4C22×D6711yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—672no—
378C22×C8—672no—
379C22×C8—1341no—
380C22×C8—1341no—
381C22×C8—1341no—
382C22×C8—1341no—
383C22×C8—1341no—
384C22×C8—1341no—
385C22×C8—1341no—
386C22×C8—1341no—
387C22×C8—1341no—
388C22×C8—1341no—
389C22×C8—1341no—
390C22×C8—1341no—
391C22×C8D26812yes—
392C22×C8C22⋊D6712yes—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—1341no—
400C2×C42—1341no—
401C2×C42—1341no—
402C2×C42—1341no—
403C2×C42—1341no—
404C2×C42—1341no—
405C2×C42—1341no—
406C2×C42—1341no—
407C2×C42—1341no—
408C2×C42—1341no—
409C2×C42—1341no—
410C2×C42—1341no—
411#95—674no—
412#95—1342no—
413#95—1342no—
414#95—1342no—
415C24C2×C4×D6711yescharacteristic
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—672no—
429C22×C4—672no—
430C22×C4—672no—
431C22×C4—672no—
432C22×C4—1341no—
433C22×C4—1341no—
434C22×C4—1341no—
435C22×C4—1341no—
436C22×C4—1341no—
437C22×C4—1341no—
438C22×C4—1341no—
439C22×C4—1341no—
440C22×C4—1341no—
441C22×C4—1341no—
442C22×C4—1341no—
443C22×C4—1341no—
444C22×C4—1341no—
445C22×C4—1341no—
446C22×C4—1341no—
447C22×C4—1341no—
448C22×C4—1341no—
449C22×C4—1341no—
450C22×C4—1341no—
451C22×C4—1341no—
452C22×C4—1341no—
453C22×C4—1341no—
454C22×C4—1341no—
455C22×C4—1341no—
456C22×C4C8×D6712yes—
457C22×C4#1176161112yes—
458C22×C4D4×D6711yescharacteristic
459C22×C4C2×C22⋊D6711yescharacteristic
460C22×C4C2×D26811yescharacteristic
461C22×C4Q8×D6711yescharacteristic
462C22×C4#1176162711yescharacteristic
463C22×C4#1176162711yescharacteristic
464C22×C4#1176162711yescharacteristic
465C22×C4#1176162711yescharacteristic
466C22×C4#1176162711yescharacteristic
467C22×C4#1176162811yescharacteristic
468C22×C4#1176162811yescharacteristic
469C22×C4#1176162811yescharacteristic
470C22×C4#1176162811yescharacteristic
471C22×C4#1176162911yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—2681no—
487C2×C8—2681no—
488C2×C8—2681no—
489C2×C8—2681no—
490C2×C8—2681no—
491C2×C8—2681no—
492C2×C8—2681no—
493C2×C8—2681no—
494C2×C8—1342no—
495C2×C8—1342no—
496C2×C8—1342no—
497C2×C8—1342no—
498C2×C8—1342no—
499C2×C8—1342no—
500C42—41no—
501C42—41no—
502C42—41no—
503C42—41no—
504C42—2681no—
505C42—2681no—
506C42—2681no—
507C42—2681no—
508C42—2681no—
509C42—2681no—
510C42—2681no—
511C42—2681no—
512C23#1452399911yescharacteristic
513C23#1452400011yescharacteristic
514C23#1452400111yescharacteristic
515C23(C22⋊D67)⋊C411yescharacteristic
516C23C4×C22⋊D6711yescharacteristic
517C23C4×D26811yescharacteristic
518C23#1452400811yescharacteristic
519C23C2×C8×D6711yescharacteristic
520C23M16×D6711yescharacteristic
521C23M16×D6711yescharacteristic
522C23C2×#1176161111yescharacteristic
523C23#1452404911yescharacteristic
524C23#1452404911yescharacteristic
525C23#1452405111yescharacteristic
526C23#1452405111yescharacteristic
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—2681no—
542C2×C4—2681no—
543C2×C4—2681no—
544C2×C4—2681no—
545C2×C4—2681no—
546C2×C4—2681no—
547C2×C4—2681no—
548C2×C4—2681no—
549C2×C4—2681no—
550C2×C4—2681no—
551C2×C4—2681no—
552C2×C4—2681no—
553C2×C4—2681no—
554C2×C4—2681no—
555C2×C4—2681no—
556C2×C4—2681no—
557C2×C4—1342no—
558C2×C4—1342no—
559C2×C4—1342no—
560C2×C4—1342no—
561C2×C4—1342no—
562C2×C4—1342no—
563C2×C4—1342no—
564C2×C4—1342no—
565C2×C4—1342no—
566C2×C4—1342no—
567C2×C4—1342no—
568C2×C4—1342no—
569C2×C4#1452401511yescharacteristic
570C2×C4#1452401711yescharacteristic
571C2×C4#1452401811yescharacteristic
572C2×C4#1452401911yescharacteristic
573C2×C4#1452402111yescharacteristic
574C2×C4#1452402311yescharacteristic
575C2×C4#1452402411yescharacteristic
576C2×C4#1452402511yescharacteristic
577C2×C4#1452402511yescharacteristic
578C2×C4#1452402611yescharacteristic
579C2×C4#1452402711yescharacteristic
580C2×C4#1452402711yescharacteristic
581C2×C4#1452402911yescharacteristic
582C2×C4#1452403011yescharacteristic
583C2×C4#1452403111yescharacteristic
584C2×C4#1452403311yescharacteristic
585C2×C4#1452403311yescharacteristic
586C2×C4#1452403311yescharacteristic
587C2×C4#1452403611yescharacteristic
588C2×C4#1452403611yescharacteristic
589C2×C4#1452403611yescharacteristic
590C2×C4#1452403611yescharacteristic
591C2×C4#1452403611yescharacteristic
592C2×C4#1452403711yescharacteristic
593C2×C4#1452403811yescharacteristic
594C2×C4#1452403811yescharacteristic
595C2×C4#1452403811yescharacteristic
596C2×C4#1452403811yescharacteristic
597C8—42no—
598C8—42no—
599C8—2682no—
600C8—2682no—
601C22#1686326311yescharacteristic
602C22#1686327711yescharacteristic
603C22#1686327811yescharacteristic
604C22#1686328111yescharacteristic
605C22#1686328711yescharacteristic
606C22#1686328811yescharacteristic
607C22#1686329011yescharacteristic
608C22#1686344611yescharacteristic
609C22#1686344711yescharacteristic
610C22#1686344811yescharacteristic
611C22#1686345011yescharacteristic
612C22#1686345111yescharacteristic
613C22#1686345211yescharacteristic
614C22#1686345411yescharacteristic
615C22#1686345411yescharacteristic
616C22#1686345511yescharacteristic
617C22#1686345611yescharacteristic
618C22#1686345611yescharacteristic
619C22#1686345811yescharacteristic
620C22(C22⋊D67)⋊C811yescharacteristic
621C22C8×C22⋊D6711yescharacteristic
622C22C8×D26811yescharacteristic
623C22#1686346411yescharacteristic
624C22#1686346511yescharacteristic
625C22#1686346711yescharacteristic
626C22#1686346911yescharacteristic
627C22#1686346911yescharacteristic
628C22#1686347011yescharacteristic
629C22#1686347111yescharacteristic
630C22#1686347211yescharacteristic
631C22#1686347511yescharacteristic
632C22#1686352011yescharacteristic
633C22#1686352311yescharacteristic
634C22#1686352511yescharacteristic
635C22#1686352511yescharacteristic
636C4—42no—
637C4—42no—
638C4—2682no—
639C4—2682no—
640C4—2682no—
641C4—2682no—
642C4#1686331811yescharacteristic
643C4#1686332111yescharacteristic
644C4#1686332311yescharacteristic
645C4#1686332411yescharacteristic
646C4#1686333411yescharacteristic
647C4#1686333611yescharacteristic
648C4#1686333711yescharacteristic
649C4C67⋊#40111yescharacteristic
650C2#2255846911yescharacteristic
651C2#2256035111yescharacteristic
652C2#2256035311yescharacteristic
653C2#2256076311yescharacteristic
654C2#2256076411yescharacteristic
655C2#2256076711yescharacteristic
656C2#2256077011yescharacteristic
657C2#2256077111yescharacteristic
658C2#2256077411yescharacteristic
659C2#2256081511yescharacteristic
660C2#2256081611yescharacteristic
661C2#2256081811yescharacteristic
662C2#2256082211yescharacteristic
663C2#2256082311yescharacteristic
664C2#2256082511yescharacteristic
subgroupG/H
center, FrattiniC23×C4C22×D67
commutatorC23×C67C22×C8
FittingC2×#336×C67C2
socle, prime radicalC24×C67C22×C4
cosocleC23×C4×C67C23
hypercenterC2×#336D67
hypocenterC67#11298
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
58. C67⋊#95C8semidirect
340. C67#11298semidirect

Maximal subgroups

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

subgroupindex
C2×#168631512
C2×#168631502
C4×C67⋊#952
C2×#336×C672
#1129867