Finite Group Databasebeta

← #13357991

Subgroups — #13357991

Order 1792.

860 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739763C211yesmaximal, characteristic
2C2×#89492C211yesmaximal, characteristic, complemented
3C2×#89491C211yesmaximal, characteristic, complemented
4C7×#1954C211yesmaximal, characteristic
5#11729369C211yesmaximal, characteristic
6#11728223C211yesmaximal, characteristic, complemented
7#11728196C211yesmaximal, characteristic, complemented
8#11727669C211yesmaximal, characteristic, complemented
9#11727669C211yesmaximal, characteristic, complemented
10#11727666C211yesmaximal, characteristic, complemented
11#11727666C211yesmaximal, characteristic, complemented
12#11727661C211yesmaximal, characteristic, complemented
13Dic7×C22⋊C8C211yesmaximal, characteristic, complemented
14#11727540C211yesmaximal, characteristic, complemented
15#11727503C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×#6489C2211yescharacteristic
18C22×C4×Dic7C2211yescharacteristic
19C2×C7×C4⋊C8C2211yescharacteristic
20C2×C7×C22⋊C8C2211yescharacteristic
21C2×C7×C22⋊C8C2211yescharacteristic
22C2×C7×C22⋊C8C2211yescharacteristic
23C2×C7×C22⋊C8C2211yescharacteristic
24C2×C4×C7×C8C2211yescharacteristic
25#89992C411yescharacteristic
26#89992C411yescharacteristic
27C4×C22⋊Dic7C2211yescharacteristic
28C4×C22⋊Dic7C2211yescharacteristic
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31C2×C22⋊(C7⋊C8)C2211yescharacteristic
32C2×C22⋊(C7⋊C8)C2211yescharacteristic
33C2×#6389C2211yescharacteristic
34C2×#6389C2211yescharacteristic
35C2×#6389C2211yescharacteristic
36C2×Dic7⋊C8C2211yescharacteristic
37C2×Dic7⋊C8C2211yescharacteristic
38C2×Dic7⋊C8C2211yescharacteristic
39C2×Dic7⋊C8C2211yescharacteristic
40C2×C8×Dic7C2211yescharacteristic
41C2×C8×Dic7C2211yescharacteristic
42C2×C8×Dic7C2211yescharacteristic
43#89753C411yescharacteristic
44#89753C411yescharacteristic
45#89723C411yescharacteristic
46#89723C411yescharacteristic
47#89722C411yescharacteristic
48#89722C411yescharacteristic
49C4×C4⋊Dic7C2211yescharacteristic
50#89704C2211yescharacteristic
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53#89492—24no—
54#89491—24no—
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89345C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89345C2211yescharacteristic
61#21273—71nomaximal, Sylow
62C22×C7×D4C2×C411yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2×C411yescharacteristic
66C23×Dic7C2×C411yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C22×C7×C8C2311yescharacteristic
71C4×C7×D4—22no—
72C4×C7×D4—22no—
73C2×C7×C4⋊C4C2×C411yescharacteristic
74C2×C7×C22⋊C4C2×C411yescharacteristic
75C2×C7×C22⋊C4C2×C411yescharacteristic
76C2×C42×C7C2311yescharacteristic
77C2×C22⋊Dic7C2×C411yescharacteristic
78C2×C22⋊Dic7C2×C411yescharacteristic
79C2×C22⋊Dic7C2×C411yescharacteristic
80C2×C22⋊Dic7C2×C411yescharacteristic
81C2×C22⋊Dic7C2×C411yescharacteristic
82C2×C22⋊Dic7C2×C411yescharacteristic
83#6489—22no—
84#6489—22no—
85C2×C4⋊Dic7C2×C411yescharacteristic
86C2×C4⋊Dic7C2×C411yescharacteristic
87C2×C4⋊Dic7C2×C411yescharacteristic
88C2×C4⋊Dic7C2×C411yescharacteristic
89C2×C4×Dic7—22no—
90C2×C4×Dic7—22no—
91C2×C4×Dic7C2×C411yescharacteristic
92C2×C4×Dic7C2×C411yescharacteristic
93C2×C4×Dic7C2311yescharacteristic
94C2×C4×Dic7C2311yescharacteristic
95C2×C4×Dic7C2311yescharacteristic
96C2×C4×Dic7C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C22×C7⋊C8C2311yescharacteristic
99C22×C7⋊C8C2311yescharacteristic
100C22×C7⋊C8C2311yescharacteristic
101C7×C4⋊C8—22no—
102C7×C22⋊C8—22no—
103C7×C22⋊C8—22no—
104C7×C22⋊C8—22no—
105C7×C22⋊C8—22no—
106C4×C7×C8—22no—
107C7⋊#95C2×C411yescharacteristic
108C7⋊#95C2×C411yescharacteristic
109C7⋊#95C2×C411yescharacteristic
110C7⋊#95C2×C411yescharacteristic
111C7⋊#95C2×C411yescharacteristic
112C7⋊#95C2×C411yescharacteristic
113C7⋊#95C2×C411yescharacteristic
114C7⋊#95C2×C411yescharacteristic
115C7⋊#95C2×C411yescharacteristic
116C7⋊#95C2×C411yescharacteristic
117C22⋊(C7⋊C8)—22no—
118C22⋊(C7⋊C8)—22no—
119C22⋊(C7⋊C8)—22no—
120C22⋊(C7⋊C8)—22no—
121#6389—22no—
122#6389—22no—
123#6389D414yescomplemented
124Dic7⋊C8—22no—
125Dic7⋊C8—22no—
126Dic7⋊C8—22no—
127Dic7⋊C8—22no—
128C8×Dic7—22no—
129C8×Dic7—22no—
130C8×Dic7—22no—
131C4⋊(C7⋊C8)—22no—
132#6377—22no—
133C2×#433—71no—
134C2×#432—71no—
135#2290—71no—
136#1955—71no—
137#1954D711yescharacteristic
138#1940—71no—
139#1939—71no—
140#1924—71no—
141#1924—71no—
142#1923—71no—
143#1923—71no—
144#1768—71no—
145#1750—71no—
146C4×C22⋊C8—71no—
147#1726—71no—
148C24×C7C22×C411yescharacteristic
149C24×C7C22×C411yescharacteristic
150C2×C7×D4—22no—
151C2×C7×D4—22no—
152C2×C7×D4—41no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7C22×C411yescharacteristic
166C22×C4×C7C22×C411yescharacteristic
167C22×C4×C7C22×C411yescharacteristic
168C22×C4×C7C22×C411yescharacteristic
169C22×C4×C7C2411yescharacteristic
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—41no—
175C22×Dic7—41no—
176C22×Dic7C22×C411yescharacteristic
177C22×Dic7C22×C411yescharacteristic
178C22×Dic7C22×C411yescharacteristic
179C22×Dic7C22×C411yescharacteristic
180C22×Dic7C22×C411yescharacteristic
181C22×Dic7C22×C411yescharacteristic
182C22×Dic7C22×C411yescharacteristic
183C22×Dic7C22×C411yescharacteristic
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8—21no—
192C2×C7×C8—21no—
193C2×C7×C8—21no—
194C2×C7×C8C2×D412yes—
195C2×C7×C8#4112yes—
196C7×C4⋊C4—22no—
197C7×C22⋊C4—22no—
198C7×C22⋊C4—22no—
199C42×C7#4112yes—
200C42×C7#4112yes—
201C22⋊Dic7—22no—
202C22⋊Dic7—22no—
203C22⋊Dic7—22no—
204C22⋊Dic7—22no—
205C22⋊Dic7—41no—
206C22⋊Dic7—41no—
207C4⋊Dic7—22no—
208C4⋊Dic7—22no—
209C4⋊Dic7—22no—
210C4⋊Dic7—41no—
211C4×Dic7—21no—
212C4×Dic7—21no—
213C4×Dic7—21no—
214C4×Dic7—21no—
215C4×Dic7—21no—
216C4×Dic7—21no—
217C4×Dic7—22no—
218C4×Dic7—22no—
219C4×Dic7C2×D412yes—
220C4×Dic7#4112yes—
221C2×C7⋊C8—21no—
222C2×C7⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8—21no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8C2×D412yes—
232C2×C7⋊C8#4112yes—
233C2×C4×D4C2×D711yescharacteristic
234C2×#117—71no—
235C22×C42—71no—
236#433—144no—
237#432—144no—
238C2×C4⋊C8—71no—
239C2×C4⋊C8—71no—
240C2×C4⋊C8—71no—
241C2×C4⋊C8—71no—
242C2×C4⋊C8—71no—
243C2×C4⋊C8C2×D711yescharacteristic
244C2×C22⋊C8—71no—
245C2×C22⋊C8—71no—
246C2×C22⋊C8—71no—
247C2×C22⋊C8—71no—
248C2×C22⋊C8C2×D711yescharacteristic
249C2×C22⋊C8C2×D711yescharacteristic
250C2×C22⋊C8C2×D711yescharacteristic
251C2×C22⋊C8C2×D711yescharacteristic
252C2×#97—71no—
253C2×#97—71no—
254C2×#97—71no—
255C2×#97—71no—
256C2×C4×C8—71no—
257C2×C4×C8—71no—
258C2×C4×C8—71no—
259C2×C4×C8C2×D711yescharacteristic
260#388—71no—
261#388—71no—
262#387—71no—
263#387—71no—
264#386—71no—
265#386—71no—
266#385—71no—
267#385—71no—
268C4×C4⋊C4—71no—
269C4×C22⋊C4—71no—
270C4×C22⋊C4—71no—
271#376—71no—
272#336—71no—
273#336—71no—
274#336—71no—
275#336—71no—
276#336—71no—
277#336—71no—
278C23×C7—21no—
279C23×C7—21no—
280C23×C7—21no—
281C23×C7—21no—
282C23×C7—21no—
283C23×C7—21no—
284C23×C7—21no—
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—21no—
288C23×C7—21no—
289C23×C7—21no—
290C23×C7—21no—
291C23×C7#13112yes—
292C23×C7C23×C411yescharacteristic
293C7×D4—44no—
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—21no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—41no—
312C2×C4×C7#11712yes—
313C2×C4×C7#11712yes—
314C2×C4×C7C22×D411yescharacteristic
315C2×C4×C7C2×#4111yescharacteristic
316C2×C4×C7C2×#4111yescharacteristic
317C2×C4×C7C2×#4111yescharacteristic
318C2×C4×C7C2×#4111yescharacteristic
319C2×C4×C7C2×#4111yescharacteristic
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7—21no—
323C2×Dic7—21no—
324C2×Dic7—21no—
325C2×Dic7—21no—
326C2×Dic7—21no—
327C2×Dic7—21no—
328C2×Dic7—21no—
329C2×Dic7—21no—
330C2×Dic7—21no—
331C2×Dic7—21no—
332C2×Dic7—21no—
333C2×Dic7—21no—
334C2×Dic7—21no—
335C2×Dic7—21no—
336C2×Dic7—21no—
337C2×Dic7—21no—
338C2×Dic7—21no—
339C2×Dic7—21no—
340C2×Dic7—21no—
341C2×Dic7—44no—
342C2×Dic7—44no—
343C2×Dic7C4×D412yes—
344C2×Dic7C4×D412yes—
345C2×Dic7#13112yes—
346C7×C8—22no—
347C7×C8—22no—
348C7×C8—41no—
349C7×C8—41no—
350C7⋊C8—22no—
351C7⋊C8—22no—
352C7⋊C8—41no—
353C7⋊C8—41no—
354C22×D4C4×D711yescharacteristic
355C23×C4—71no—
356C23×C4—71no—
357C23×C4C22×D711yescharacteristic
358C23×C4C22×D711yescharacteristic
359C22×C8—71no—
360C22×C8—71no—
361C22×C8—71no—
362C22×C8—71no—
363C22×C8C22×D711yescharacteristic
364C22×C8C22×D711yescharacteristic
365C22×C8C22×D711yescharacteristic
366C22×C8C22×D711yescharacteristic
367C4×D4—22no—
368C4×D4—22no—
369#117—142no—
370#117—142no—
371C2×C4⋊C4—71no—
372C2×C4⋊C4—71no—
373C2×C4⋊C4—71no—
374C2×C4⋊C4—71no—
375C2×C4⋊C4C4×D711yescharacteristic
376C2×C22⋊C4—71no—
377C2×C22⋊C4—71no—
378C2×C22⋊C4—71no—
379C2×C22⋊C4—71no—
380C2×C22⋊C4—71no—
381C2×C22⋊C4—71no—
382C2×C22⋊C4C4×D711yescharacteristic
383C2×C22⋊C4C4×D711yescharacteristic
384C2×C42—71no—
385C2×C42—71no—
386C2×C42—71no—
387C2×C42—71no—
388C2×C42—71no—
389C2×C42—71no—
390C2×C42—142no—
391C2×C42—142no—
392C2×C42C22×D711yescharacteristic
393C4⋊C8—22no—
394C4⋊C8—142no—
395C4⋊C8—142no—
396C4⋊C8—142no—
397C4⋊C8—142no—
398C4⋊C8—142no—
399C22⋊C8—22no—
400C22⋊C8—22no—
401C22⋊C8—22no—
402C22⋊C8—22no—
403C22⋊C8—142no—
404C22⋊C8—142no—
405C22⋊C8—142no—
406C22⋊C8—142no—
407#97—74no—
408#97—142no—
409#97—142no—
410#97—142no—
411C4×C8—22no—
412C4×C8—142no—
413C4×C8—142no—
414C4×C8—142no—
415#95—71no—
416#95—71no—
417#95—71no—
418#95—71no—
419#95—71no—
420#95—71no—
421#95—71no—
422#95—71no—
423#95—71no—
424#95—71no—
425C22×C7—22no—
426C22×C7—22no—
427C22×C7—22no—
428C22×C7—41no—
429C22×C7—41no—
430C22×C7—41no—
431C22×C7—41no—
432C22×C7—41no—
433C22×C7—41no—
434C22×C7—41no—
435C22×C7—41no—
436C22×C7—41no—
437C22×C7—41no—
438C22×C7—41no—
439C22×C7C2×#11711yescharacteristic
440C22×C7C2×C4×D411yescharacteristic
441C22×C7C4×#4111yescharacteristic
442C22×C7C2×#13111yescharacteristic
443C22×C7C2×#13111yescharacteristic
444C22×C7#56811yescharacteristic
445C22×C7#56811yescharacteristic
446C4×C7—22no—
447C4×C7—22no—
448C4×C7—41no—
449C4×C7—41no—
450C4×C7#52911yescharacteristic
451C4×C7#52911yescharacteristic
452C4×C7#53211yescharacteristic
453C4×C7#53211yescharacteristic
454Dic7—22no—
455Dic7—22no—
456Dic7—22no—
457Dic7—41no—
458Dic7—41no—
459Dic7—41no—
460Dic7—41no—
461Dic7—41no—
462C24C2×C4×D711yescharacteristic
463C24C2×C4×D711yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—41no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—71no—
480C22×C4—71no—
481C22×C4—71no—
482C22×C4—71no—
483C22×C4—71no—
484C22×C4—71no—
485C22×C4—71no—
486C22×C4—71no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4—142no—
491C22×C4—281no—
492C22×C4—281no—
493C22×C4C2×C4×D711yescharacteristic
494C22×C4C2×C4×D711yescharacteristic
495C22×C4C2×C4×D711yescharacteristic
496C22×C4C2×C4×D711yescharacteristic
497C22×C4C23×D711yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—72no—
509C2×C8—72no—
510C2×C8—141no—
511C2×C8—141no—
512C2×C8—141no—
513C2×C8—141no—
514C2×C8—141no—
515C2×C8—141no—
516C2×C8—141no—
517C2×C8—141no—
518C2×C8—141no—
519C2×C8—141no—
520C2×C8D4×D712yes—
521C2×C8#115912yes—
522C4⋊C4—22no—
523C4⋊C4—142no—
524C4⋊C4—142no—
525C4⋊C4—142no—
526C4⋊C4—281no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—142no—
530C22⋊C4—142no—
531C22⋊C4—142no—
532C22⋊C4—142no—
533C22⋊C4—281no—
534C22⋊C4—281no—
535C42—72no—
536C42—72no—
537C42—142no—
538C42—142no—
539C42—141no—
540C42—141no—
541C42—141no—
542C42—141no—
543C42—141no—
544C42—141no—
545C42#115912yes—
546C42#115912yes—
547C2×C7—42no—
548C2×C7—81no—
549C2×C7#229311yescharacteristic
550C2×C7#292411yescharacteristic
551C2×C7#292511yescharacteristic
552C2×C7#293311yescharacteristic
553C2×C7#293311yescharacteristic
554C2×C7#296611yescharacteristic
555C2×C7#296711yescharacteristic
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23#646412yes—
570C23C22×C4×D711yescharacteristic
571D4—44no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—72no—
591C2×C4—72no—
592C2×C4—72no—
593C2×C4—141no—
594C2×C4—141no—
595C2×C4—141no—
596C2×C4—141no—
597C2×C4—141no—
598C2×C4—141no—
599C2×C4—141no—
600C2×C4—141no—
601C2×C4—141no—
602C2×C4—141no—
603C2×C4—141no—
604C2×C4—141no—
605C2×C4—141no—
606C2×C4—141no—
607C2×C4—141no—
608C2×C4—141no—
609C2×C4—141no—
610C2×C4—141no—
611C2×C4—141no—
612C2×C4—141no—
613C2×C4—141no—
614C2×C4—284no—
615C2×C4—284no—
616C2×C4#644012yes—
617C2×C4#644012yes—
618C2×C4C2×D4×D711yescharacteristic
619C2×C4C2×#115911yescharacteristic
620C2×C4C2×#115911yescharacteristic
621C2×C4C2×#115911yescharacteristic
622C2×C4D7×#4111yescharacteristic
623C2×C4D7×#4111yescharacteristic
624C8—22no—
625C8—22no—
626C8—41no—
627C8—41no—
628C8—142no—
629C8—142no—
630C8—281no—
631C8—281no—
632C7#2127311yescharacteristic, complemented, Sylow
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#644011yescharacteristic
648C22C4×#115911yescharacteristic
649C22C4×D4×D711yescharacteristic
650C22C2×#646411yescharacteristic
651C22#9043611yescharacteristic
652C22D7×#13111yescharacteristic
653C22#9044111yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—142no—
659C4—142no—
660C4—142no—
661C4—281no—
662C4—281no—
663C4—281no—
664C4—281no—
665C4—281no—
666C4#9028711yescharacteristic
667C4#9029111yescharacteristic
668C4#9037111yescharacteristic
669C4#9040711yescharacteristic
670C2—42no—
671C2—81no—
672C2#1173373411yescharacteristic
673C2#1173602911yescharacteristic
674C2#1173609511yescharacteristic
675C2#1173684511yescharacteristic
676C2#1173686811yescharacteristic
677C2#1173696411yescharacteristic
678C2#1173698411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC7×#1954C2
prime radicalC22×C7×D4C2×C4
cosocleC22×C4×C7C24
hypercenter#1954D7
hypocenterC7#21273
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#89492C2semidirect
3. C2×#89491C2semidirect
6. #11728223C2semidirect
7. #11728196C2semidirect
8. #11727669C2semidirect
9. #11727669C2semidirect
10. #11727666C2semidirect
11. #11727666C2semidirect
12. #11727661C2semidirect
13. Dic7×C22⋊C8C2semidirect
14. #11727540C2semidirect
15. #11727503C2semidirect
123. #6389D4semidirect
632. C7#21273semidirect

Maximal subgroups

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

subgroupindex
#117397632
C2×#894922
C2×#894912
C7×#19542
#117293692
#117282232
#117281962
#117276692
#117276662
#117276612
Dic7×C22⋊C82
#117275402
#117275032
#212737