Finite Group Databasebeta

← #28748509

Subgroups — #28748509

Order 15104.

3232 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838064C211yesmaximal, characteristic
2C2×C4×#11745689C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
4#21427165C213yesmaximal, complemented
5#21427122C213yesmaximal, complemented
6#21427111C213yesmaximal, complemented
7#21427022C213yesmaximal, complemented
8#21426934C211yesmaximal, characteristic, complemented
9Q8×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
10#21426635C213yesmaximal, complemented
11#21426626C213yesmaximal, complemented
12#21426604C213yesmaximal, complemented
13C4×Q8×Dic59C211yesmaximal, characteristic, complemented
14C4×#14273689C213yesmaximal, complemented
15C59×#2351C211yesmaximal, characteristic, complemented
16C22×#11745689C2211yescharacteristic
17C22×Q8×D59C2211yescharacteristic
18#16838064C4116yescomplemented
19C2×#14273715C2213yes—
20C2×#14273707C2213yes—
21C2×#14273702C2213yes—
22C4×#11745689—28no—
23C2×Q8×Dic59C2211yescharacteristic
24C2×Q8×Dic59C2211yescharacteristic
25C2×C4×Dic118C2213yes—
26C2×#14273692C2213yes—
27C4×Q8×D59—28no—
28C2×C4×D236C2213yes—
29C2×C4×D236C2213yes—
30C2×#14273689C2213yes—
31C2×#14273689C2213yes—
32C2×#14273689C2213yes—
33C2×#14273685C2213yes—
34C2×C4⋊C4×D59C2213yes—
35C2×C42×D59C2213yes—
36C2×C42×D59C2213yes—
37#16837308C2213yes—
38#16837307C2213yes—
39#16837304C2213yes—
40#16837303C2213yes—
41#16837292C2216yes—
42#16837291C2216yes—
43#16837291C2216yes—
44#16837285C2216yes—
45#16837280C2216yes—
46#16837273C2216yes—
47#16837259C2213yes—
48#16837259C2213yes—
49C4⋊C4×Dic59C2213yes—
50C4⋊C4×Dic59C2213yes—
51C4⋊C4×Dic59C2213yes—
52C4⋊C4×Dic59C2213yes—
53C4×C4⋊Dic59C2213yes—
54C4×(C2×D59)⋊C4C2213yes—
55C4×(C2×D59)⋊C4C2213yes—
56#16837249C2211yescharacteristic
57#16837249C2213yes—
58#16837249C2213yes—
59#16837249C2213yes—
60#16837249C2216yes—
61C42×Dic59C2213yes—
62C2×C4×Q8×C59C2211yescharacteristic
63C2×C4×Q8×C59C2211yescharacteristic
64C2×C4×Q8×C59C2211yescharacteristic
65C59×#389C2213yes—
66C59×#389C2213yes—
67C59×#382C2213yes—
68C4×C4⋊C4×C59C2213yes—
69C2×#11745689—24no—
70C2×#11745689—24no—
71C2×#11745689C2×C418yescomplemented
72C22×Dic118C2313yes—
73C2×Q8×D59—24no—
74C2×Q8×D59—24no—
75C2×Q8×D59C2×C418yescomplemented
76C22×D236C2313yes—
77C22×D236C2313yes—
78C22×C4×D59C2313yes—
79C22×C4×D59C2313yes—
80C22×C4×D59C2313yes—
81C22×C4×D59C2313yes—
82C22×C4×D59C2313yes—
83C22×C4×D59C2311yescharacteristic
84#14273715C2×C4124yescomplemented
85#14273707C2×C4124yescomplemented
86#14273702C2×C4124yescomplemented
87Q8×Dic59—24no—
88Q8×Dic59D418yescomplemented
89C4×Dic118—212no—
90#14273692—212no—
91C4×D236—212no—
92C4×D236C2×C4124yescomplemented
93#14273689—212no—
94#14273689—212no—
95#14273689—212no—
96#14273685—212no—
97C2×C4⋊Dic59C2313yes—
98C2×C4⋊Dic59C2313yes—
99C2×C4⋊Dic59C2313yes—
100C2×Dic59⋊C4C2316yes—
101C4⋊C4×D59—212no—
102C2×(C2×D59)⋊C4C2313yes—
103C2×(C2×D59)⋊C4C2313yes—
104C2×(C2×D59)⋊C4C2313yes—
105C2×(C2×D59)⋊C4C2316yes—
106C2×(C2×D59)⋊C4C2316yes—
107C2×(C2×D59)⋊C4C2316yes—
108C2×(C2×D59)⋊C4C2313yes—
109C2×(C2×D59)⋊C4C2311yescharacteristic
110C2×(C2×D59)⋊C4C2311yescharacteristic
111C2×C4×Dic59C2311yescharacteristic
112C2×C4×Dic59C2313yes—
113C2×C4×Dic59C2313yes—
114C2×C4×Dic59C2313yes—
115C2×C4×Dic59C2313yes—
116C2×C4×Dic59C2311yescharacteristic
117C2×C4×Dic59C2313yes—
118C2×C4×Dic59C2313yes—
119C2×C4×Dic59C2313yes—
120C2×C4×Dic59C2313yes—
121C42×D59—212no—
122C42×D59—212no—
123C59⋊#95C2311yescharacteristic
124C59⋊#95C2313yes—
125C59⋊#95C2313yes—
126C59⋊#95C2313yes—
127C59⋊#95C2316yes—
128C59⋊#95C2316yes—
129C22×Q8×C59C2311yescharacteristic
130C4×Q8×C59—24no—
131C4×Q8×C59—24no—
132C4×Q8×C59C2×C418yescomplemented
133C2×C4⋊C4×C59C2313yes—
134C2×C4⋊C4×C59C2313yes—
135C2×C4⋊C4×C59C2313yes—
136C2×C4⋊C4×C59C2313yes—
137C2×C4⋊C4×C59C2313yes—
138C2×C42×C59C2313yes—
139C2×C42×C59C2313yes—
140C2×C42×C59C2313yes—
141#95×C59C2311yescharacteristic
142#95×C59C2313yes—
143#95×C59C2316yes—
144C23×D59C2413yes—
145C23×D59C2411yescharacteristic
146C2×Q8×C59C22×C414yes—
147C2×Q8×C59C2×D414yes—
148C2×Q8×C59#4114yes—
149C22×C4×C59C2413yes—
150C22×C4×C59C2413yes—
151C22×C4×C59C2411yescharacteristic
152C22×C4×C59C2413yes—
153C22×C4×C59C2411yescharacteristic
154C22×C4×C59C2411yescharacteristic
155C22×C4×C59C2413yes—
156C22×Dic59C2413yes—
157C22×Dic59C2411yescharacteristic
158C22×Dic59C2413yes—
159C22×Dic59C2413yes—
160C22×Dic59C2411yescharacteristic
161C22×Dic59C2411yescharacteristic
162#11745689—232no—
163Q8×D59—232no—
164C2×D236—26no—
165C2×D236—26no—
166C2×D236—26no—
167C2×D236—26no—
168C2×D236C22×C4112yes—
169C2×D236C22×C4112yes—
170C2×C4×D59—26no—
171C2×C4×D59—26no—
172C2×C4×D59—26no—
173C2×C4×D59—26no—
174C2×C4×D59—22no—
175C2×C4×D59—22no—
176C2×C4×D59—26no—
177C2×C4×D59—26no—
178C2×C4×D59—26no—
179C2×C4×D59—26no—
180C2×C4×D59—26no—
181C2×C4×D59—26no—
182C2×C4×D59—26no—
183C2×C4×D59—43no—
184C2×C4×D59—43no—
185C2×C4×D59C22×C4112yes—
186C2×C4×D59C22×C4112yes—
187C2×C4×D59#4114yescomplemented
188C2×Dic118—26no—
189C2×Dic118—26no—
190C2×Dic118C22×C4112yes—
191C4⋊C4×C59—26no—
192C4⋊C4×C59—26no—
193C4⋊C4×C59—26no—
194C4⋊C4×C59—26no—
195C4⋊C4×C59C22×C4112yes—
196C42×C59—26no—
197C42×C59—26no—
198C42×C59C22×C4112yes—
199(C2×D59)⋊C4—26no—
200(C2×D59)⋊C4—26no—
201(C2×D59)⋊C4—212no—
202(C2×D59)⋊C4—26no—
203(C2×D59)⋊C4—46no—
204(C2×D59)⋊C4C22×C414yes—
205(C2×D59)⋊C4C22×C4112yes—
206(C2×D59)⋊C4C22×C4124yes—
207(C2×D59)⋊C4#4114yescomplemented
208C4⋊Dic59—26no—
209C4⋊Dic59C22×C4112yes—
210C4⋊Dic59C2×D4112yes—
211Dic59⋊C4—212no—
212C4×Dic59—26no—
213C4×Dic59—22no—
214C4×Dic59—26no—
215C4×Dic59—26no—
216C4×Dic59—26no—
217C4×Dic59—26no—
218C4×Dic59—26no—
219C4×Dic59—22no—
220C4×Dic59—43no—
221C4×Dic59C2×D4112yes—
222C23×C59C2511yescharacteristic
223C22×D59—21no—
224C22×D59—21no—
225C22×D59—21no—
226C22×D59—21no—
227C22×D59—23no—
228C22×D59—23no—
229C22×D59—23no—
230C22×D59—23no—
231C22×D59—23no—
232C22×D59—23no—
233C22×D59C23×C416yes—
234C22×D59C23×C412yes—
235C22×D59C2×#4112yes—
236C22×D59C2×#4112yes—
237Q8×C59C4×D4116yescomplemented
238C2×C4×C59—21no—
239C2×C4×C59—21no—
240C2×C4×C59—23no—
241C2×C4×C59—23no—
242C2×C4×C59—21no—
243C2×C4×C59—21no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—23no—
247C2×C4×C59—23no—
248C2×C4×C59—23no—
249C2×C4×C59—23no—
250C2×C4×C59—23no—
251C2×C4×C59—23no—
252C2×C4×C59C23×C416yes—
253C2×C4×C59C23×C412yes—
254C2×C4×C59C23×C416yes—
255C2×C4×C59C22×D416yes—
256C2×C4×C59C2×#4112yes—
257C2×C4×C59C2×#4112yes—
258C2×C4×C59C2×#4116yes—
259C2×Dic59—21no—
260C2×Dic59—23no—
261C2×Dic59—21no—
262C2×Dic59—23no—
263C2×Dic59—23no—
264C2×Dic59—21no—
265C2×Dic59—21no—
266C2×Dic59—23no—
267C2×Dic59—23no—
268C2×Dic59—23no—
269C2×Dic59—23no—
270C2×Dic59C23×C412yes—
271C2×Dic59C23×C416yes—
272C2×Dic59C22×D416yes—
273C2×Dic59C22×D412yes—
274C2×Dic59C2×#4112yes—
275C2×Dic59C2×#4112yes—
276C2×Dic592−1+412yes—
277D236—224no—
278D236—224no—
279C4×D59—224no—
280C4×D59—224no—
281C4×D59—28no—
282C4×D59—412no—
283C4×D59—412no—
284C4×D59—412no—
285Dic118—224no—
286C4×#548—591nomaximal, Sylow
287C22×C59C24×C411yescharacteristic
288C22×C59C23×D411yescharacteristic
289C22×C59C22×#4111yescharacteristic
290C22×C59C22×#4111yescharacteristic
291C22×C59C22×#4111yescharacteristic
292C22×C59C2×2−1+411yescharacteristic
293C22×C59#58511yescharacteristic
294C2×D59—22no—
295C2×D59—22no—
296C2×D59—22no—
297C2×D59—22no—
298C2×D59—22no—
299C2×D59—22no—
300C2×D59—26no—
301C2×D59—26no—
302C2×D59—26no—
303C2×D59—43no—
304C2×D59—43no—
305C2×D59—43no—
306C2×D59—43no—
307C2×D59C4×#4114yescomplemented
308C4×C59—26no—
309C4×C59—22no—
310C4×C59—22no—
311C4×C59—22no—
312C4×C59—43no—
313C4×C59—43no—
314C4×C59C2×C4×D4112yes—
315Dic59—26no—
316Dic59—22no—
317Dic59—26no—
318Dic59—22no—
319Dic59—43no—
320Dic59#54814yescomplemented
321C2×#548—591no—
322C2×C4×#41—591no—
323C22×C4×Q8—591no—
324#2367—593no—
325#2362—593no—
326#2361—593no—
327#2352—593no—
328#2351D5911yescharacteristic, complemented
329#2341—591no—
330Q8×C22⋊C4—591no—
331C4×#124—593no—
332C4×C22⋊Q8—593no—
333C4×#121—593no—
334C42×Q8—591no—
335C42×D4—593no—
336C2×C59C22×C4×D411yescharacteristic
337C2×C59C2×C4×#4111yescharacteristic
338C2×C59C4×2−1+411yescharacteristic
339C2×C59C2×#54811yescharacteristic
340C2×C59D4×#4111yescharacteristic
341C2×C59#348011yescharacteristic
342C2×C59#348211yescharacteristic
343D59—24no—
344D59—46no—
345C22×#41—591no—
346C23×Q8—591no—
347#548—5916no—
348C2×#124—593no—
349C2×C22⋊Q8—593no—
350C2×#121—593no—
351C4×#41—1188no—
352C2×C4×Q8—591no—
353C2×C4×Q8—591no—
354C2×C4×Q8—593no—
355C2×C4×Q8—593no—
356C2×C4×Q8—1188no—
357C2×C4×Q8C2×D5911yescharacteristic
358C2×C4×Q8C2×D5911yescharacteristic
359C2×C4×Q8C2×D5911yescharacteristic
360C2×C4×D4—593no—
361C2×C4×D4—593no—
362C2×C4×D4—593no—
363C2×C4×D4—593no—
364C2×C4×D4—593no—
365C2×#117—593no—
366C22×C4⋊C4—593no—
367C22×C42—593no—
368C22×C42—593no—
369#391—593no—
370#391—593no—
371#390—593no—
372#390—593no—
373#389C2×D5913yes—
374#389C2×D5913yes—
375#388—596no—
376#388—596no—
377#388—596no—
378#387—596no—
379#386—596no—
380#385—596no—
381#382C2×D5913yes—
382#380—593no—
383#380—593no—
384C4×C4⋊C4—593no—
385C4×C4⋊C4—593no—
386C4×C4⋊C4—593no—
387C4×C4⋊C4—593no—
388C4×C4⋊C4—593no—
389C4×C4⋊C4C2×D5913yes—
390C4×C22⋊C4—593no—
391C4×C22⋊C4—593no—
392C4×C22⋊C4—593no—
393C4×C22⋊C4—593no—
394C4×C22⋊C4—591no—
395C4×C22⋊C4—593no—
396C4×C22⋊C4—596no—
397C43—593no—
398C59C4×#54811yescharacteristic, complemented, Sylow
399C2×#41—598no—
400C2×#41—1184no—
401C2×#41—1184no—
402C22×Q8—598no—
403C22×Q8—593no—
404C22×Q8—1184no—
405C22×Q8—1184no—
406C22×Q8C22×D5911yescharacteristic
407C22×D4—593no—
408C22×D4—593no—
409C23×C4—593no—
410C23×C4—593no—
411C23×C4—591no—
412C23×C4—593no—
413C23×C4—593no—
414C23×C4—593no—
415#124—5924no—
416C22⋊Q8—5924no—
417#121—5924no—
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—598no—
421C4×Q8—11812no—
422C4×Q8—11812no—
423C4×Q8—1184no—
424C4×Q8C4×D5918yescomplemented
425C4×D4—5924no—
426C4×D4—11812no—
427C4×D4—11812no—
428C4×D4—11812no—
429C4×D4—11812no—
430#117—11812no—
431C2×C4⋊C4—593no—
432C2×C4⋊C4—593no—
433C2×C4⋊C4—596no—
434C2×C4⋊C4—593no—
435C2×C4⋊C4—11812no—
436C2×C4⋊C4C22×D5913yes—
437C2×C4⋊C4C22×D5913yes—
438C2×C4⋊C4C22×D5913yes—
439C2×C4⋊C4C22×D5913yes—
440C2×C4⋊C4C22×D5913yes—
441C2×C22⋊C4—591no—
442C2×C22⋊C4—591no—
443C2×C22⋊C4—593no—
444C2×C22⋊C4—596no—
445C2×C22⋊C4—596no—
446C2×C22⋊C4—593no—
447C2×C22⋊C4—593no—
448C2×C22⋊C4—593no—
449C2×C22⋊C4—596no—
450C2×C42—593no—
451C2×C42—593no—
452C2×C42—593no—
453C2×C42—593no—
454C2×C42—593no—
455C2×C42—593no—
456C2×C42—593no—
457C2×C42—591no—
458C2×C42—591no—
459C2×C42—593no—
460C2×C42—11812no—
461C2×C42—11812no—
462C2×C42C22×D5913yes—
463C2×C42C22×D5913yes—
464C2×C42C22×D5913yes—
465#95—591no—
466#95—593no—
467#95—593no—
468#95—593no—
469#95—596no—
470#95—596no—
471#95C22×D5911yescharacteristic
472#95C22×D5913yes—
473#95C22×D5916yes—
474C24—591no—
475C24—593no—
476#41—11832no—
477C2×Q8—5912no—
478C2×Q8—11832no—
479C2×Q8—1186no—
480C2×Q8—1186no—
481C2×Q8C2×C4×D5914yes—
482C2×Q8D4×D5914yes—
483C2×Q8#1174568914yes—
484C2×D4—5912no—
485C2×D4—5912no—
486C2×D4—1186no—
487C2×D4—1186no—
488C2×D4—1186no—
489C2×D4—1186no—
490C22×C4—591no—
491C22×C4—591no—
492C22×C4—591no—
493C22×C4—593no—
494C22×C4—593no—
495C22×C4—5912no—
496C22×C4—5912no—
497C22×C4—594no—
498C22×C4—593no—
499C22×C4—1182no—
500C22×C4—1182no—
501C22×C4—1186no—
502C22×C4—1186no—
503C22×C4—1186no—
504C22×C4—1186no—
505C22×C4—1186no—
506C22×C4—1186no—
507C22×C4—1186no—
508C22×C4—1186no—
509C22×C4—1186no—
510C22×C4—1186no—
511C22×C4—1186no—
512C22×C4—2363no—
513C22×C4—2363no—
514C22×C4C23×D5913yes—
515C22×C4C23×D5913yes—
516C22×C4C23×D5913yes—
517C22×C4C23×D5911yescharacteristic
518C22×C4C23×D5911yescharacteristic
519C22×C4C23×D5911yescharacteristic
520C22×C4C23×D5913yes—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—26no—
524C4⋊C4—26no—
525C4⋊C4—5912no—
526C4⋊C4—5912no—
527C4⋊C4—11812no—
528C4⋊C4—1186no—
529C4⋊C4C2×C4×D59112yes—
530C22⋊C4—594no—
531C22⋊C4—5912no—
532C22⋊C4—5924no—
533C22⋊C4—594no—
534C22⋊C4—11812no—
535C22⋊C4—1186no—
536C22⋊C4—1186no—
537C22⋊C4—1186no—
538C22⋊C4—2366no—
539C42—26no—
540C42—26no—
541C42—5912no—
542C42—1182no—
543C42—1186no—
544C42—1186no—
545C42—1186no—
546C42—1186no—
547C42—1186no—
548C42—1182no—
549C42—1186no—
550C42—2363no—
551C42C2×C4×D59112yes—
552C23—592no—
553C23—592no—
554C23—592no—
555C23—596no—
556C23—1181no—
557C23—1181no—
558C23—1181no—
559C23—1181no—
560C23—1183no—
561C23—1183no—
562C23—1183no—
563C23—1183no—
564C23—1183no—
565C23—1183no—
566C23C24×D5911yescharacteristic
567Q8—11824no—
568Q8#14273689116yescomplemented
569D4—11824no—
570D4—11824no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—592no—
586C2×C4—592no—
587C2×C4—592no—
588C2×C4—596no—
589C2×C4—592no—
590C2×C4—596no—
591C2×C4—592no—
592C2×C4—1188no—
593C2×C4—1181no—
594C2×C4—1183no—
595C2×C4—1183no—
596C2×C4—1181no—
597C2×C4—1181no—
598C2×C4—1183no—
599C2×C4—1181no—
600C2×C4—1183no—
601C2×C4—11824no—
602C2×C4—11824no—
603C2×C4—1183no—
604C2×C4—1183no—
605C2×C4—1183no—
606C2×C4—23612no—
607C2×C4—23612no—
608C2×C4—23612no—
609C2×C4C22×C4×D5912yes—
610C2×C4C22×C4×D5916yes—
611C2×C4C22×C4×D5916yes—
612C2×C4C2×D4×D5916yes—
613C2×C4#41×D5912yes—
614C2×C4#41×D5912yes—
615C2×C4C2×#1174568916yes—
616C22—594no—
617C22—1182no—
618C22—1182no—
619C22—1182no—
620C22—1182no—
621C22—1182no—
622C22—1182no—
623C22—1186no—
624C22—1186no—
625C22—1186no—
626C22—2363no—
627C22—2363no—
628C22—2363no—
629C22—2363no—
630C22C23×C4×D5911yescharacteristic
631C22C22×D4×D5911yescharacteristic
632C22C2×#41×D5911yescharacteristic
633C22C2×#41×D5911yescharacteristic
634C22C22×#1174568911yescharacteristic
635C222−1+4×D5911yescharacteristic
636C22#1683823911yescharacteristic
637C4—26no—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—43no—
642C4—43no—
643C4—594no—
644C4—1182no—
645C4—1182no—
646C4—1186no—
647C4—1186no—
648C4—2363no—
649C4C2×#14273689112yes—
650C2—1184no—
651C2—2366no—
652C2C22×#1427368911yescharacteristic
653C2C4×#41×D5911yescharacteristic
654C2#2143730511yescharacteristic
655C2#548×D5911yescharacteristic
656C2#2143758511yescharacteristic
657C2#2143769611yescharacteristic
658C2#2143771611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2351C2
socle, cosocleC23×C59C25
prime radicalC2×#16838064C2
hypercenter#2351D59
hypocenterC59C4×#548
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745689C2semidirect
3. C2×C4×Q8×D59C2semidirect
4. #21427165C2semidirect
5. #21427122C2semidirect
6. #21427111C2semidirect
7. #21427022C2semidirect
8. #21426934C2semidirect
9. Q8×(C2×D59)⋊C4C2semidirect
10. #21426635C2semidirect
11. #21426626C2semidirect
12. #21426604C2semidirect
13. C4×Q8×Dic59C2semidirect
14. C4×#14273689C2semidirect
15. C59×#2351C2semidirect
18. #16838064C4semidirect
71. C2×#11745689C2×C4semidirect
75. C2×Q8×D59C2×C4semidirect
84. #14273715C2×C4semidirect
85. #14273707C2×C4semidirect
86. #14273702C2×C4semidirect
88. Q8×Dic59D4semidirect
92. C4×D236C2×C4semidirect
132. C4×Q8×C59C2×C4semidirect
187. C2×C4×D59#41semidirect
207. (C2×D59)⋊C4#41semidirect
237. Q8×C59C4×D4semidirect
307. C2×D59C4×#41semidirect
320. Dic59#548semidirect
328. #2351D59semidirect
398. C59C4×#548semidirect
424. C4×Q8C4×D59semidirect
568. Q8#14273689semidirect

Maximal subgroups

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

subgroupindex
C2×#168380642
C2×C4×#117456892
C2×C4×Q8×D592
#214271652
#214271222
#214271112
#214270222
#214269342
Q8×(C2×D59)⋊C42
#214266352
#214266262
#214266042
C4×Q8×Dic592
C4×#142736892
C59×#23512
C4×#54859