Finite Group Databasebeta

← C2×#21428620 #28757935

Subgroups — C2×#21428620 #28757935

Order 15104.

2054 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
1#21428620C2116yesmaximal, direct product factor
2C2×#16837335C211yesmaximal, characteristic
3C2×#16837335C211yesmaximal, characteristic
4C2×#16837333C211yesmaximal, characteristic
5C2×#16837332C211yesmaximal, characteristic
6C2×#16837299C211yesmaximal, characteristic
7C2×#16837299C211yesmaximal, characteristic
8C2×#16837297C211yesmaximal, characteristic
9C2×#16837297C211yesmaximal, characteristic
10C2×#16837297C211yesmaximal, characteristic
11C2×#16837286C211yesmaximal, characteristic
12C2×#16837284C211yesmaximal, characteristic
13C2×#16837271C211yesmaximal, characteristic
14C2×C4×Dic59⋊C4C211yesmaximal, characteristic
15C2×#16837253C211yesmaximal, characteristic
16C2×C59×#389C211yesmaximal, characteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34C22×C4×Dic59C2211yescharacteristic
35#16837335C2218yes—
36#16837335C2218yes—
37#16837333C2218yes—
38#16837332C2218yes—
39#16837299C2218yes—
40#16837299C2218yes—
41#16837297C2218yes—
42#16837297C2218yes—
43#16837297C2218yes—
44#16837286C2218yes—
45#16837284C2218yes—
46#16837271C2218yes—
47C4×Dic59⋊C4C2218yes—
48#16837253C2218yes—
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C22×C4⋊C4×C59C2211yescharacteristic
60C22×C4⋊C4×C59C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C42×C59C2211yescharacteristic
64C59×#389C2218yes—
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C2×C4⋊Dic59—42no—
76C2×C4⋊Dic59—42no—
77C2×C4⋊Dic59C2314yes—
78C2×C4⋊Dic59C2314yes—
79C2×Dic59⋊C4—24no—
80C2×Dic59⋊C4—24no—
81C2×Dic59⋊C4—24no—
82C2×Dic59⋊C4—24no—
83C2×Dic59⋊C4—24no—
84C2×Dic59⋊C4—42no—
85C2×Dic59⋊C4—42no—
86C2×Dic59⋊C4—42no—
87C2×Dic59⋊C4—42no—
88C2×Dic59⋊C4—42no—
89C2×Dic59⋊C4Q818yes—
90C2×Dic59⋊C4Q818yes—
91C2×Dic59⋊C4C2314yes—
92C2×Dic59⋊C4C2314yes—
93C2×Dic59⋊C4C2314yes—
94C2×Dic59⋊C4C2314yes—
95C2×Dic59⋊C4C2314yes—
96C2×Dic59⋊C4C2314yes—
97C2×Dic59⋊C4C2314yes—
98C2×Dic59⋊C4C2314yes—
99C2×Dic59⋊C4C2314yes—
100C2×Dic59⋊C4C2314yes—
101C2×Dic59⋊C4C2314yes—
102C2×Dic59⋊C4C2314yes—
103C2×C4×Dic59—24no—
104C2×C4×Dic59—24no—
105C2×C4×Dic59—24no—
106C2×C4×Dic59—42no—
107C2×C4×Dic59C2314yes—
108C2×C4×Dic59C2314yes—
109C2×C4×Dic59C2314yes—
110C2×C4×Dic59C2314yes—
111C59⋊#95C2314yes—
112C59⋊#95C2314yes—
113C59⋊#95C2314yes—
114C59⋊#95C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C23×C4×C59C2311yescharacteristic
122C23×C4×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59—24no—
129C2×C4⋊C4×C59—42no—
130C2×C4⋊C4×C59—42no—
131C2×C4⋊C4×C59—42no—
132C2×C4⋊C4×C59C2314yes—
133C2×C4⋊C4×C59C2314yes—
134C2×C4⋊C4×C59C2314yes—
135C2×C4⋊C4×C59C2314yes—
136C2×C42×C59—42no—
137C2×C42×C59C2314yes—
138#95×C59C2314yes—
139#95×C59C2314yes—
140C24×C59C2411yescharacteristic
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59C2×Q814yes—
160C22×C4×C59C2×Q814yes—
161C22×C4×C59#4114yes—
162C22×C4×C59C2412yes—
163C22×C4×C59C2412yes—
164C22×C4×C59C2412yes—
165C22×C4×C59C2412yes—
166C22×C4×C59C2412yes—
167C22×C4×C59C2412yes—
168C22×C4×C59C2412yes—
169C22×Dic59—22no—
170C22×Dic59—22no—
171C22×Dic59—22no—
172C22×Dic59—22no—
173C22×Dic59—22no—
174C22×Dic59—22no—
175C22×Dic59—22no—
176C22×Dic59—22no—
177C22×Dic59—22no—
178C22×Dic59—22no—
179C22×Dic59—22no—
180C22×Dic59—22no—
181C22×Dic59—22no—
182C22×Dic59—22no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59C2×Q814yes—
188C22×Dic59C2×Q814yes—
189C22×Dic59C2×Q814yes—
190C22×Dic59C2×Q814yes—
191C22×Dic59#4114yes—
192C22×Dic59#4114yes—
193C22×Dic59C2412yes—
194C22×Dic59C2412yes—
195C22×Dic59C2412yes—
196C22×Dic59C2412yes—
197C22×Dic59C2412yes—
198C22×Dic59C2412yes—
199C22×Dic59C2412yes—
200C22×Dic59C2412yes—
201C4⋊C4×C59—28no—
202C4⋊C4×C59—44no—
203C4⋊C4×C59—44no—
204C4⋊C4×C59—44no—
205C42×C59—44no—
206C4⋊Dic59—44no—
207C4⋊Dic59—44no—
208Dic59⋊C4—28no—
209Dic59⋊C4—28no—
210Dic59⋊C4—28no—
211Dic59⋊C4—28no—
212Dic59⋊C4—28no—
213Dic59⋊C4—44no—
214Dic59⋊C4—44no—
215Dic59⋊C4—44no—
216Dic59⋊C4—44no—
217Dic59⋊C4—44no—
218Dic59⋊C4C2×Q8116yes—
219Dic59⋊C4C2×Q8116yes—
220C4×Dic59—28no—
221C4×Dic59—28no—
222C4×Dic59—28no—
223C4×Dic59—44no—
224C23×C59C22×Q812yes—
225C23×C59C22×Q812yes—
226C23×C59C2×#4112yes—
227C23×C59C2×#4112yes—
228C23×C59C2×#4112yes—
229C23×C59H(5,𝔽2)12yes—
230C23×C59H(5,𝔽2)12yes—
231C23×C59C2511yescharacteristic
232C2×C4×C59—28no—
233C2×C4×C59—28no—
234C2×C4×C59—28no—
235C2×C4×C59—22no—
236C2×C4×C59—22no—
237C2×C4×C59—22no—
238C2×C4×C59—22no—
239C2×C4×C59—22no—
240C2×C4×C59—22no—
241C2×C4×C59—22no—
242C2×C4×C59—22no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—22no—
246C2×C4×C59—22no—
247C2×C4×C59—22no—
248C2×C4×C59—22no—
249C2×C4×C59—22no—
250C2×C4×C59—22no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—44no—
254C2×C4×C59—44no—
255C2×C4×C59—44no—
256C2×C4×C59—44no—
257C2×C4×C59C22×Q814yes—
258C2×C4×C59C22×Q814yes—
259C2×C4×C59C2×#4114yes—
260C2×Dic59—28no—
261C2×Dic59—28no—
262C2×Dic59—28no—
263C2×Dic59—22no—
264C2×Dic59—22no—
265C2×Dic59—22no—
266C2×Dic59—22no—
267C2×Dic59—22no—
268C2×Dic59—22no—
269C2×Dic59—22no—
270C2×Dic59—22no—
271C2×Dic59—22no—
272C2×Dic59—22no—
273C2×Dic59—22no—
274C2×Dic59—22no—
275C2×Dic59—22no—
276C2×Dic59—22no—
277C2×Dic59—22no—
278C2×Dic59—22no—
279C2×Dic59—22no—
280C2×Dic59—22no—
281C2×Dic59—44no—
282C2×Dic59—44no—
283C2×Dic59—44no—
284C2×Dic59—44no—
285C2×Dic59#125116yes—
286C2×Dic59C22×Q814yes—
287C2×Dic59C22×Q814yes—
288C2×Dic59C22×Q814yes—
289C2×Dic59C22×Q814yes—
290C2×Dic59C2×#4114yes—
291C2×Dic59C2×#4114yes—
292C2×#2507—591nomaximal, Sylow
293C22×C59C2×#12514yes—
294C22×C59#53314yes—
295C22×C59#54014yes—
296C22×C59#55314yes—
297C22×C59#55414yes—
298C22×C59#55414yes—
299C22×C59Q8214yes—
300C22×C59C23×Q811yescharacteristic
301C22×C59C23×Q811yescharacteristic
302C22×C59C22×#4111yescharacteristic
303C22×C59C22×#4111yescharacteristic
304C22×C59C22×#4111yescharacteristic
305C22×C59C2×H(5,𝔽2)11yescharacteristic
306C22×C59C2×H(5,𝔽2)11yescharacteristic
307C4×C59—24no—
308C4×C59—24no—
309C4×C59—24no—
310C4×C59—42no—
311C4×C59—42no—
312C4×C59—42no—
313C4×C59—42no—
314Dic59—24no—
315Dic59—24no—
316Dic59—24no—
317Dic59—42no—
318Dic59—42no—
319Dic59—42no—
320Dic59—42no—
321Dic59C2×#12518yes—
322#2507—5916no—
323C2×#398—591no—
324C2×#398—591no—
325C2×#398—591no—
326C2×#398—591no—
327C2×#389—591no—
328C2×#389—591no—
329C2×#389—591no—
330C2×#389—591no—
331C2×#389—591no—
332C2×#389D5911yescharacteristic
333C2×#387—591no—
334C2×#387—591no—
335C2×#384—591no—
336C2×C4×C4⋊C4—591no—
337C2×C4×C4⋊C4—591no—
338C2×C59#250718yescomplemented
339C2×C59C22×#12511yescharacteristic
340C2×C59C2×#53311yescharacteristic
341C2×C59C2×#54011yescharacteristic
342C2×C59C2×#55311yescharacteristic
343C2×C59C2×#55411yescharacteristic
344C2×C59C2×#55411yescharacteristic
345C2×C59C2×Q8211yescharacteristic
346C22×C4⋊C4—591no—
347C22×C4⋊C4—591no—
348C22×C4⋊C4—591no—
349C22×C4⋊C4—591no—
350C22×C4⋊C4—591no—
351C22×C4⋊C4—591no—
352C22×C4⋊C4—591no—
353C22×C4⋊C4—591no—
354C22×C4⋊C4—591no—
355C22×C4⋊C4—591no—
356C22×C4⋊C4—591no—
357C22×C4⋊C4—591no—
358C22×C4⋊C4—591no—
359C22×C4⋊C4—591no—
360C22×C4⋊C4C2×D5911yescharacteristic
361C22×C4⋊C4C2×D5911yescharacteristic
362C22×C4⋊C4C2×D5911yescharacteristic
363C22×C4⋊C4C2×D5911yescharacteristic
364C22×C42—591no—
365C22×C42—591no—
366C22×C42—591no—
367C22×C42—591no—
368C22×C42C2×D5911yescharacteristic
369#398—598no—
370#398—598no—
371#398—598no—
372#398—598no—
373#389—598no—
374#389—598no—
375#389—598no—
376#389—598no—
377#389—598no—
378#389C2×D5918yes—
379#387—598no—
380#387—598no—
381#384—598no—
382C4×C4⋊C4—598no—
383C4×C4⋊C4—598no—
384C2×#95—591no—
385C2×#95—591no—
386C2×#95—591no—
387C2×#95—591no—
388C2×#95—591no—
389C2×#95—591no—
390C2×#95—591no—
391C2×#95—591no—
392C2×#95—591no—
393C2×#95—591no—
394C2×#95C2×D5911yescharacteristic
395C2×#95C2×D5911yescharacteristic
396C59C2×#250711yescharacteristic, complemented, Sylow
397C23×C4—591no—
398C23×C4—591no—
399C23×C4—591no—
400C23×C4—591no—
401C23×C4—591no—
402C23×C4—591no—
403C23×C4—591no—
404C23×C4—591no—
405C23×C4C22×D5911yescharacteristic
406C23×C4C22×D5911yescharacteristic
407C23×C4C22×D5911yescharacteristic
408C23×C4C22×D5911yescharacteristic
409C23×C4C22×D5911yescharacteristic
410C23×C4C22×D5911yescharacteristic
411C23×C4C22×D5911yescharacteristic
412C2×C4⋊C4—24no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—598no—
417C2×C4⋊C4—598no—
418C2×C4⋊C4—594no—
419C2×C4⋊C4—594no—
420C2×C4⋊C4—594no—
421C2×C4⋊C4—594no—
422C2×C4⋊C4—594no—
423C2×C4⋊C4—594no—
424C2×C4⋊C4—594no—
425C2×C4⋊C4—594no—
426C2×C4⋊C4—594no—
427C2×C4⋊C4—594no—
428C2×C4⋊C4—594no—
429C2×C4⋊C4—594no—
430C2×C4⋊C4—594no—
431C2×C4⋊C4—594no—
432C2×C4⋊C4—1184no—
433C2×C4⋊C4—1184no—
434C2×C4⋊C4—1184no—
435C2×C4⋊C4—1184no—
436C2×C4⋊C4—1184no—
437C2×C4⋊C4—2362no—
438C2×C4⋊C4—2362no—
439C2×C4⋊C4—2362no—
440C2×C4⋊C4—2362no—
441C2×C4⋊C4—2362no—
442C2×C4⋊C4—2362no—
443C2×C4⋊C4—2362no—
444C2×C4⋊C4C22×D5914yes—
445C2×C4⋊C4C22×D5914yes—
446C2×C4⋊C4C22×D5914yes—
447C2×C4⋊C4C22×D5914yes—
448C2×C42—42no—
449C2×C42—594no—
450C2×C42—594no—
451C2×C42—594no—
452C2×C42—594no—
453C2×C42—1184no—
454C2×C42—1184no—
455C2×C42—1184no—
456C2×C42—2362no—
457C2×C42C22×D5914yes—
458#95—594no—
459#95—594no—
460#95—594no—
461#95—594no—
462#95—594no—
463#95—594no—
464#95—594no—
465#95—594no—
466#95—594no—
467#95—594no—
468#95C22×D5914yes—
469#95C22×D5914yes—
470C24C23×D5911yescharacteristic
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—594no—
490C22×C4—594no—
491C22×C4—594no—
492C22×C4—592no—
493C22×C4—594no—
494C22×C4—594no—
495C22×C4—594no—
496C22×C4—592no—
497C22×C4—592no—
498C22×C4—592no—
499C22×C4—592no—
500C22×C4—592no—
501C22×C4—592no—
502C22×C4—592no—
503C22×C4—1182no—
504C22×C4—1182no—
505C22×C4—1182no—
506C22×C4—1182no—
507C22×C4—1182no—
508C22×C4—1182no—
509C22×C4—1182no—
510C22×C4—1182no—
511C22×C4—1182no—
512C22×C4—1182no—
513C22×C4—1182no—
514C22×C4—1182no—
515C22×C4—1182no—
516C22×C4—1182no—
517C22×C4—1182no—
518C22×C4—1182no—
519C22×C4—1182no—
520C22×C4—1182no—
521C22×C4#1174568514yes—
522C22×C4Q8×D5914yes—
523C22×C4Q8×D5914yes—
524C22×C4C23×D5912yes—
525C22×C4C23×D5912yes—
526C22×C4C23×D5912yes—
527C22×C4C23×D5912yes—
528C22×C4C23×D5912yes—
529C22×C4C23×D5912yes—
530C22×C4C23×D5912yes—
531C4⋊C4—28no—
532C4⋊C4—44no—
533C4⋊C4—44no—
534C4⋊C4—44no—
535C4⋊C4—5916no—
536C4⋊C4—5916no—
537C4⋊C4—1188no—
538C4⋊C4—1188no—
539C4⋊C4—1188no—
540C4⋊C4—1188no—
541C4⋊C4—1188no—
542C4⋊C4—2364no—
543C4⋊C4—2364no—
544C4⋊C4—2364no—
545C4⋊C4—2364no—
546C4⋊C4—2364no—
547C4⋊C4—2364no—
548C4⋊C4—2364no—
549C42—44no—
550C42—1188no—
551C42—1188no—
552C42—1188no—
553C42—2364no—
554C23C2×Q8×D5912yes—
555C23C2×Q8×D5912yes—
556C23#41×D5912yes—
557C23#41×D5912yes—
558C23C2×#1174568512yes—
559C23#1427377212yes—
560C23#1427377212yes—
561C23C24×D5911yescharacteristic
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—28no—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—5916no—
588C2×C4—594no—
589C2×C4—594no—
590C2×C4—594no—
591C2×C4—594no—
592C2×C4—594no—
593C2×C4—594no—
594C2×C4—1188no—
595C2×C4—1182no—
596C2×C4—1182no—
597C2×C4—1182no—
598C2×C4—1182no—
599C2×C4—1182no—
600C2×C4—1182no—
601C2×C4—1188no—
602C2×C4—1188no—
603C2×C4—1182no—
604C2×C4—1182no—
605C2×C4—1182no—
606C2×C4—1182no—
607C2×C4—1182no—
608C2×C4—1182no—
609C2×C4—1182no—
610C2×C4—1182no—
611C2×C4—1182no—
612C2×C4—1182no—
613C2×C4—1182no—
614C2×C4—1182no—
615C2×C4—2364no—
616C2×C4—2364no—
617C2×C4—2364no—
618C2×C4—2364no—
619C2×C4C2×Q8×D5914yes—
620C2×C4C2×Q8×D5914yes—
621C2×C4C2×#1174568514yes—
622C22#125×D5914yes—
623C22#1683795614yes—
624C22#1683800214yes—
625C22#1683810114yes—
626C22#1683810614yes—
627C22#1683810714yes—
628C22#1683813214yes—
629C22C22×Q8×D5911yescharacteristic
630C22C22×Q8×D5911yescharacteristic
631C22C2×#41×D5911yescharacteristic
632C22C2×#41×D5911yescharacteristic
633C22C22×#1174568511yescharacteristic
634C22C2×#1427377211yescharacteristic
635C22C2×#1427377211yescharacteristic
636C4—24no—
637C4—24no—
638C4—24no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—42no—
643C4—598no—
644C4—1184no—
645C4—1184no—
646C4—1184no—
647C4—2362no—
648C4—2362no—
649C4—2362no—
650C4—2362no—
651C2#2142862018yesdirect product factor
652C2C2×#125×D5911yescharacteristic
653C2C2×#1683795611yescharacteristic
654C2C2×#1683800211yescharacteristic
655C2C2×#1683810111yescharacteristic
656C2C2×#1683810611yescharacteristic
657C2C2×#1683810711yescharacteristic
658C2C2×#1683813211yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#389C2
socle, prime radicalC24×C59C24
hypercenterC2×#389D59
hypocenterC59C2×#2507
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. #21428620C2direct (N × H)
338. C2×C59#2507semidirect
396. C59C2×#2507semidirect
651. C2#21428620direct (N × H)

Maximal subgroups

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

subgroupindex
#214286202
C2×#168373352
C2×#168373332
C2×#168373322
C2×#168372992
C2×#168372972
C2×#168372862
C2×#168372842
C2×#168372712
C2×C4×Dic59⋊C42
C2×#168372532
C2×C59×#3892
C2×#250759