Finite Group Databasebeta

← C107×#15139 #41041103

Subgroups — C107×#15139 #41041103

Order 27392.

1250 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C107C212yesmaximal
2C2×#389×C107C211yesmaximal, characteristic
3C2×#389×C107C211yesmaximal, characteristic
4C107×#1443C212yesmaximal
5C107×#1442C212yesmaximal
6C107×#1442C212yesmaximal
7C107×C4⋊#95C211yesmaximal, characteristic
8C107×C4⋊#95C211yesmaximal, characteristic
9C107×C4⋊#95C211yesmaximal, characteristic
10C107×C4⋊#95C211yesmaximal, characteristic
11C4×#95×C107C211yesmaximal, characteristic
12C22×C4⋊C4×C107C2211yescharacteristic
13C22×C4⋊C4×C107C2211yescharacteristic
14C22×C4⋊C4×C107C2212yes—
15C22×C4⋊C4×C107C2212yes—
16C22×C4⋊C4×C107C2211yescharacteristic
17C22×C4⋊C4×C107C2211yescharacteristic
18C22×C42×C107C2211yescharacteristic
19C22×C42×C107C2211yescharacteristic
20C22×C42×C107C2211yescharacteristic
21#400×C107—28no—
22#389×C107—24no—
23#389×C107—24no—
24C2×#95×C107C2212yes—
25C2×#95×C107C2212yes—
26C2×#95×C107C2212yes—
27C2×#95×C107C2212yes—
28C2×#95×C107C2211yescharacteristic
29C2×#95×C107C2211yescharacteristic
30C2×#95×C107C2211yescharacteristic
31C2×#95×C107C2212yes—
32C2×#95×C107C2212yes—
33C2×#95×C107C2212yes—
34C2×#95×C107C2212yes—
35C2×#95×C107C2212yes—
36C2×#95×C107C2212yes—
37C2×#95×C107C2211yescharacteristic
38C23×C4×C107C2312yes—
39C23×C4×C107C2312yes—
40C23×C4×C107C2311yescharacteristic
41C23×C4×C107C2311yescharacteristic
42C23×C4×C107C2311yescharacteristic
43C23×C4×C107C2312yes—
44C23×C4×C107C2312yes—
45C23×C4×C107C2311yescharacteristic
46C23×C4×C107C2311yescharacteristic
47C23×C4×C107C2311yescharacteristic
48C23×C4×C107C2311yescharacteristic
49C2×C4⋊C4×C107—22no—
50C2×C4⋊C4×C107—22no—
51C2×C4⋊C4×C107—22no—
52C2×C4⋊C4×C107—22no—
53C2×C4⋊C4×C107—24no—
54C2×C4⋊C4×C107—24no—
55C2×C4⋊C4×C107—22no—
56C2×C4⋊C4×C107—24no—
57C2×C4⋊C4×C107—24no—
58C2×C4⋊C4×C107—22no—
59C2×C4⋊C4×C107—22no—
60C2×C4⋊C4×C107—22no—
61C2×C4⋊C4×C107—22no—
62C2×C4⋊C4×C107—22no—
63C2×C4⋊C4×C107—42no—
64C2×C4⋊C4×C107—42no—
65C2×C4⋊C4×C107D414yes—
66C2×C4⋊C4×C107Q814yes—
67C2×C42×C107—22no—
68C2×C42×C107—22no—
69C2×C42×C107—22no—
70C2×C42×C107—22no—
71C2×C42×C107—22no—
72C2×C42×C107—22no—
73C2×C42×C107—22no—
74C2×C42×C107—22no—
75C2×C42×C107—22no—
76#95×C107—24no—
77#95×C107—24no—
78#95×C107—24no—
79#95×C107—24no—
80#95×C107—24no—
81#95×C107—24no—
82#95×C107—22no—
83#95×C107—22no—
84#95×C107—22no—
85#95×C107—24no—
86#95×C107—24no—
87#95×C107—24no—
88#95×C107—42no—
89#95×C107D414yes—
90C24×C107C2411yescharacteristic
91C22×C4×C107—21no—
92C22×C4×C107—21no—
93C22×C4×C107—22no—
94C22×C4×C107—22no—
95C22×C4×C107—22no—
96C22×C4×C107—21no—
97C22×C4×C107—21no—
98C22×C4×C107—21no—
99C22×C4×C107—21no—
100C22×C4×C107—21no—
101C22×C4×C107—21no—
102C22×C4×C107—21no—
103C22×C4×C107—21no—
104C22×C4×C107—22no—
105C22×C4×C107—22no—
106C22×C4×C107—21no—
107C22×C4×C107—21no—
108C22×C4×C107—21no—
109C22×C4×C107—21no—
110C22×C4×C107—21no—
111C22×C4×C107—21no—
112C22×C4×C107—21no—
113C22×C4×C107—21no—
114C22×C4×C107—21no—
115C22×C4×C107—21no—
116C22×C4×C107—21no—
117C22×C4×C107—21no—
118C22×C4×C107—21no—
119C22×C4×C107—21no—
120C22×C4×C107—22no—
121C22×C4×C107—22no—
122C22×C4×C107—22no—
123C22×C4×C107—21no—
124C22×C4×C107—22no—
125C22×C4×C107—21no—
126C22×C4×C107—22no—
127C22×C4×C107—21no—
128C22×C4×C107—21no—
129C22×C4×C107—21no—
130C22×C4×C107—21no—
131C22×C4×C107—22no—
132C22×C4×C107—21no—
133C22×C4×C107—21no—
134C22×C4×C107—21no—
135C22×C4×C107—22no—
136C22×C4×C107—21no—
137C22×C4×C107—21no—
138C22×C4×C107—21no—
139C22×C4×C107—22no—
140C22×C4×C107—22no—
141C22×C4×C107—22no—
142C22×C4×C107—22no—
143C22×C4×C107—22no—
144C22×C4×C107—22no—
145C22×C4×C107—22no—
146C22×C4×C107—22no—
147C22×C4×C107—22no—
148C22×C4×C107—22no—
149C22×C4×C107—22no—
150C22×C4×C107—22no—
151C22×C4×C107—22no—
152C22×C4×C107—22no—
153C22×C4×C107C2×D412yes—
154C22×C4×C107C2×D412yes—
155C22×C4×C107C2×D412yes—
156C22×C4×C107C2×D414yes—
157C22×C4×C107C2×D412yes—
158C22×C4×C107C2×Q814yes—
159C22×C4×C107C2×Q812yes—
160C22×C4×C107#4112yes—
161C22×C4×C107#4112yes—
162C22×C4×C107#4112yes—
163C22×C4×C107#4112yes—
164C22×C4×C107#4112yes—
165C22×C4×C107#4112yes—
166C22×C4×C107#4112yes—
167C22×C4×C107#4112yes—
168C4⋊C4×C107—28no—
169C4⋊C4×C107—28no—
170C4⋊C4×C107—48no—
171C4⋊C4×C107—48no—
172C4⋊C4×C107—44no—
173C4⋊C4×C107—44no—
174C42×C107—44no—
175C42×C107—44no—
176C42×C107—44no—
177C23×C107C22×D411yescharacteristic
178C23×C107C22×D411yescharacteristic
179C23×C107C22×Q811yescharacteristic
180C23×C107C2×#4111yescharacteristic
181C23×C107C2×#4111yescharacteristic
182C23×C107C2×#4111yescharacteristic
183C23×C107C2×#4111yescharacteristic
184C23×C107C2×#4111yescharacteristic
185C23×C107C2×#4111yescharacteristic
186C23×C107C2×#4111yescharacteristic
187C23×C107C2×#4111yescharacteristic
188C23×C107H(5,𝔽2)11yescharacteristic
189C23×C1072−1+411yescharacteristic
190C23×C1072−1+411yescharacteristic
191C23×C1072−1+411yescharacteristic
192C2×C4×C107—24no—
193C2×C4×C107—24no—
194C2×C4×C107—22no—
195C2×C4×C107—22no—
196C2×C4×C107—22no—
197C2×C4×C107—22no—
198C2×C4×C107—22no—
199C2×C4×C107—22no—
200C2×C4×C107—24no—
201C2×C4×C107—22no—
202C2×C4×C107—22no—
203C2×C4×C107—24no—
204C2×C4×C107—22no—
205C2×C4×C107—22no—
206C2×C4×C107—22no—
207C2×C4×C107—22no—
208C2×C4×C107—22no—
209C2×C4×C107—22no—
210C2×C4×C107—24no—
211C2×C4×C107—22no—
212C2×C4×C107—22no—
213C2×C4×C107—22no—
214C2×C4×C107—22no—
215C2×C4×C107—24no—
216C2×C4×C107—41no—
217C2×C4×C107—41no—
218C2×C4×C107—41no—
219C2×C4×C107—41no—
220C2×C4×C107—41no—
221C2×C4×C107—41no—
222C2×C4×C107—42no—
223C2×C4×C107—42no—
224C2×C4×C107—41no—
225C2×C4×C107—41no—
226C2×C4×C107—41no—
227C2×C4×C107—41no—
228C2×C4×C107—42no—
229C2×C4×C107—42no—
230C2×C4×C107—41no—
231C2×C4×C107—41no—
232C2×C4×C107—42no—
233C2×C4×C107—41no—
234C2×C4×C107—42no—
235C2×C4×C107—41no—
236C2×C4×C107—41no—
237C2×C4×C107—42no—
238C2×C4×C107—41no—
239C2×C4×C107—41no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—42no—
244C2×C4×C107—41no—
245C2×C4×C107—41no—
246C2×C4×C107—41no—
247C2×C4×C107—41no—
248C2×C4×C107—42no—
249C2×C4×C107—42no—
250C2×C4×C107—42no—
251C2×C4×C107—42no—
252C2×C4×C107—42no—
253C2×C4×C107—42no—
254C2×C4×C107—42no—
255C2×C4×C107—42no—
256C2×C4×C107—42no—
257C2×C4×C107—42no—
258C2×C4×C107—42no—
259C2×C4×C107—42no—
260C2×C4×C107—42no—
261C2×C4×C107—42no—
262C2×C4×C107C22⋊Q814yes—
263C2×C4×C107#12314yes—
264C2×C4×C107#12414yes—
265C2×C4×C107#12514yes—
266C2×C4×C107#12514yes—
267C2×C4×C107#12614yes—
268C2×C4×C107#12614yes—
269C22×C107C2×C22⋊Q811yescharacteristic
270C22×C107C2×#12311yescharacteristic
271C22×C107C2×#12411yescharacteristic
272C22×C107C2×#12511yescharacteristic
273C22×C107C2×#12511yescharacteristic
274C22×C107C2×#12611yescharacteristic
275C22×C107C2×#12611yescharacteristic
276C22×C107#52911yescharacteristic
277C22×C107#52911yescharacteristic
278C22×C107#52911yescharacteristic
279C22×C107#53211yescharacteristic
280C22×C107#53211yescharacteristic
281C22×C107#53211yescharacteristic
282C22×C107#54111yescharacteristic
283C22×C107#54111yescharacteristic
284C22×C107#54111yescharacteristic
285C22×C107#54211yescharacteristic
286C22×C107#54211yescharacteristic
287C22×C107#54211yescharacteristic
288C22×C107D4211yescharacteristic
289C22×C107#54711yescharacteristic
290C22×C107#54711yescharacteristic
291C22×C107#54711yescharacteristic
292C22×C107#54811yescharacteristic
293C22×C107#54811yescharacteristic
294C22×C107D4×Q811yescharacteristic
295C22×C107#55211yescharacteristic
296C22×C107#55211yescharacteristic
297C22×C107#55211yescharacteristic
298C22×C107#55311yescharacteristic
299C22×C107#55411yescharacteristic
300C22×C107#55511yescharacteristic
301C22×C107#55611yescharacteristic
302C22×C107#55711yescharacteristic
303C22×C107#55711yescharacteristic
304C4×C107—42no—
305C4×C107—44no—
306C4×C107—42no—
307C4×C107—44no—
308C4×C107—42no—
309C4×C107—42no—
310C4×C107—42no—
311C4×C107—42no—
312C4×C107—82no—
313C4×C107—82no—
314C4×C107#40018yescomplemented
315#15139C10711yesmaximal, characteristic, direct product factor, Sylow
316C2×C107C2×#40011yescharacteristic
317C2×C107#242111yescharacteristic
318C2×C107#242211yescharacteristic
319C2×C107#245211yescharacteristic
320C2×C107#245311yescharacteristic
321C2×C107#248911yescharacteristic
322C2×C107#249111yescharacteristic
323C2×C107#249511yescharacteristic
324C2×C107#249611yescharacteristic
325C2×C107#250611yescharacteristic
326C2×C107#250611yescharacteristic
327C2×C107#250811yescharacteristic
328C2×C107#250911yescharacteristic
329C2×C107#264511yescharacteristic
330C2×C107#286011yescharacteristic
331C2×#400C2×C10712yes—
332C2×#389C2×C10711yescharacteristic
333C2×#389C2×C10711yescharacteristic
334#1443C2×C10712yes—
335#1442C2×C10712yes—
336#1442C2×C10712yes—
337C4⋊#95C2×C10711yescharacteristic
338C4⋊#95C2×C10711yescharacteristic
339C4⋊#95C2×C10711yescharacteristic
340C4⋊#95C2×C10711yescharacteristic
341C4×#95C2×C10711yescharacteristic
342C107#1513911yescharacteristic, direct product factor, Sylow
343C22×C4⋊C4C22×C10711yescharacteristic
344C22×C4⋊C4C22×C10711yescharacteristic
345C22×C4⋊C4C22×C10712yes—
346C22×C4⋊C4C22×C10712yes—
347C22×C4⋊C4C22×C10711yescharacteristic
348C22×C4⋊C4C22×C10711yescharacteristic
349C22×C42C22×C10711yescharacteristic
350C22×C42C22×C10711yescharacteristic
351C22×C42C22×C10711yescharacteristic
352#400—28no—
353#389—24no—
354#389—24no—
355C2×#95C22×C10712yes—
356C2×#95C22×C10712yes—
357C2×#95C22×C10712yes—
358C2×#95C22×C10712yes—
359C2×#95C22×C10711yescharacteristic
360C2×#95C22×C10711yescharacteristic
361C2×#95C22×C10711yescharacteristic
362C2×#95C22×C10712yes—
363C2×#95C22×C10712yes—
364C2×#95C22×C10712yes—
365C2×#95C22×C10712yes—
366C2×#95C22×C10712yes—
367C2×#95C22×C10712yes—
368C2×#95C22×C10711yescharacteristic
369C23×C4C23×C10712yes—
370C23×C4C23×C10712yes—
371C23×C4C23×C10712yes—
372C23×C4C23×C10711yescharacteristic
373C23×C4C23×C10711yescharacteristic
374C23×C4C23×C10711yescharacteristic
375C23×C4C23×C10712yes—
376C23×C4C23×C10711yescharacteristic
377C23×C4C23×C10711yescharacteristic
378C23×C4C23×C10711yescharacteristic
379C23×C4C23×C10711yescharacteristic
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4D4×C10714yes—
397C2×C4⋊C4Q8×C10714yes—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—42no—
420#95D4×C10714yes—
421C24C24×C10711yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
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×C4C2×D4×C10712yes—
485C22×C4C2×D4×C10712yes—
486C22×C4C2×D4×C10712yes—
487C22×C4C2×D4×C10714yes—
488C22×C4C2×D4×C10712yes—
489C22×C4C2×Q8×C10714yes—
490C22×C4C2×Q8×C10712yes—
491C22×C4#41×C10712yes—
492C22×C4#41×C10712yes—
493C22×C4#41×C10712yes—
494C22×C4#41×C10712yes—
495C22×C4#41×C10712yes—
496C22×C4#41×C10712yes—
497C22×C4#41×C10712yes—
498C22×C4#41×C10712yes—
499C4⋊C4—28no—
500C4⋊C4—28no—
501C4⋊C4—48no—
502C4⋊C4—48no—
503C4⋊C4—44no—
504C4⋊C4—44no—
505C42—44no—
506C42—44no—
507C42—44no—
508C23C22×D4×C10711yescharacteristic
509C23C22×D4×C10711yescharacteristic
510C23C22×Q8×C10711yescharacteristic
511C23C2×#41×C10711yescharacteristic
512C23C2×#41×C10711yescharacteristic
513C23C2×#41×C10711yescharacteristic
514C23C2×#41×C10711yescharacteristic
515C23C2×#41×C10711yescharacteristic
516C23C2×#41×C10711yescharacteristic
517C23C2×#41×C10711yescharacteristic
518C23C2×#41×C10711yescharacteristic
519C23H(5,𝔽2)×C10711yescharacteristic
520C232−1+4×C10711yescharacteristic
521C232−1+4×C10711yescharacteristic
522C232−1+4×C10711yescharacteristic
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4C22⋊Q8×C10714yes—
594C2×C4#123×C10714yes—
595C2×C4#124×C10714yes—
596C2×C4#125×C10714yes—
597C2×C4#125×C10714yes—
598C2×C4#126×C10714yes—
599C2×C4#126×C10714yes—
600C22C2×C22⋊Q8×C10711yescharacteristic
601C22C2×#123×C10711yescharacteristic
602C22C2×#124×C10711yescharacteristic
603C22C2×#125×C10711yescharacteristic
604C22C2×#125×C10711yescharacteristic
605C22C2×#126×C10711yescharacteristic
606C22C2×#126×C10711yescharacteristic
607C22#529×C10711yescharacteristic
608C22#529×C10711yescharacteristic
609C22#529×C10711yescharacteristic
610C22#532×C10711yescharacteristic
611C22#532×C10711yescharacteristic
612C22#532×C10711yescharacteristic
613C22#541×C10711yescharacteristic
614C22#541×C10711yescharacteristic
615C22#541×C10711yescharacteristic
616C22#542×C10711yescharacteristic
617C22#542×C10711yescharacteristic
618C22#542×C10711yescharacteristic
619C22D42×C10711yescharacteristic
620C22#547×C10711yescharacteristic
621C22#547×C10711yescharacteristic
622C22#547×C10711yescharacteristic
623C22#548×C10711yescharacteristic
624C22#548×C10711yescharacteristic
625C22D4×Q8×C10711yescharacteristic
626C22#552×C10711yescharacteristic
627C22#552×C10711yescharacteristic
628C22#552×C10711yescharacteristic
629C22#553×C10711yescharacteristic
630C22#554×C10711yescharacteristic
631C22#555×C10711yescharacteristic
632C22#556×C10711yescharacteristic
633C22#557×C10711yescharacteristic
634C22#557×C10711yescharacteristic
635C4—42no—
636C4—44no—
637C4—42no—
638C4—44no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—42no—
643C4—82no—
644C4—82no—
645C4#400×C10718yescomplemented
646C2C2×#400×C10711yescharacteristic
647C2C107×#242111yescharacteristic
648C2C107×#242211yescharacteristic
649C2C107×#245211yescharacteristic
650C2C107×#245311yescharacteristic
651C2C107×#248911yescharacteristic
652C2C107×#249111yescharacteristic
653C2C107×#249511yescharacteristic
654C2C107×#249611yescharacteristic
655C2C107×#250611yescharacteristic
656C2C107×#250611yescharacteristic
657C2C107×#250811yescharacteristic
658C2C107×#250911yescharacteristic
659C2C107×#264511yescharacteristic
660C2C107×#286011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C107C24
commutator, Frattini, cosocleC24C24×C107
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C107 ◁ G

Complements

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

NH ≅ G/Ntype
314. C4×C107#400semidirect
315. #15139C107direct (N × H)
342. C107#15139direct (N × H)
645. C4#400×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#400×C1072
C2×#389×C1072
C107×#14432
C107×#14422
C107×C4⋊#952
C4×#95×C1072
#15139107