Finite Group Databasebeta

← #13321578

Subgroups — #13321578

Order 1792.

1074 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742855C211yesmaximal, characteristic
2C7×#2973C211yesmaximal, characteristic, complemented
3#11739778C211yesmaximal, characteristic, complemented
4#11728588C212yesmaximal, complemented
5#11728587C212yesmaximal, complemented
6#11727733C212yesmaximal, complemented
7#11727730C212yesmaximal, complemented
8#11727700C211yesmaximal, characteristic, complemented
9C2×#89262C211yesmaximal, characteristic, complemented
10#11727698C211yesmaximal, characteristic, complemented
11C2×#89265C211yesmaximal, characteristic, complemented
12C2×C4×C7×D4C2211yescharacteristic
13#90495—21no—
14C2×D4×Dic7—21no—
15#90482C2212yes—
16C2×#6493C2211yescharacteristic
17C2×#6487C2211yescharacteristic
18#90256C412yescomplemented
19#90247—22no—
20#90243C412yescomplemented
21#90241C412yescomplemented
22#90232C412yescomplemented
23#90231—22no—
24#90206—21no—
25#90185—21no—
26#90177—21no—
27#90170C2212yes—
28C7×#435—22no—
29C7×#435—22no—
30C7×#432C2212yescomplemented
31C7×#407C2212yescomplemented
32C2×C7×C22⋊C8C2211yescharacteristic
33C2×C7×C22⋊C8C2211yescharacteristic
34#89984C2211yescharacteristic
35#89984C2211yescharacteristic, complemented
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic, complemented
38#89757—21no—
39#89722—21no—
40#89722—21no—
41#89708C2211yescharacteristic, complemented
42C4×C4⋊Dic7C2211yescharacteristic, complemented
43#89265C2212yes—
44#89265C2212yes—
45#89265C2212yes—
46#89265C2212yes—
47#89262C2212yescomplemented
48#89262C2212yescomplemented
49#89262C2212yescomplemented
50#89262C2212yescomplemented
51#17622—71nomaximal, Sylow
52C22×C7×D4D411yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C22×C22⋊D7—21no—
56C23×Dic7—21no—
57C23×Dic7—21no—
58C2×#1157C2×C412yescomplemented
59C22×D28C2×C411yescharacteristic, complemented
60C22×Dic14C2×C411yescharacteristic, complemented
61C2×C7×M16—22no—
62C22×C7×C8—21no—
63C22×C7×C8—21no—
64C4×C7×D4C2×C412yes—
65C4×C7×D4C2×C412yes—
66C4×C7×D4D412yes—
67C4×C7×D4D412yes—
68C2×C7×C4⋊C4D411yescharacteristic
69C2×C7×C22⋊C4D411yescharacteristic
70C2×C7×C22⋊C4D411yescharacteristic
71C2×C42×C7C2311yescharacteristic
72#6516—22no—
73C2×C22⋊Dic7—21no—
74C2×C22⋊Dic7—21no—
75C2×C22⋊Dic7—21no—
76#6502—22no—
77#6502—22no—
78#6500—22no—
79#6498—22no—
80D4×Dic7—44no—
81#6493—21no—
82#6493—21no—
83#6493C2×C412yescomplemented
84#6493C2×C412yescomplemented
85#6493C2312yes—
86#6492—22no—
87#6492—22no—
88C4×C22⋊D7—22no—
89C4×C22⋊D7—22no—
90C4×C22⋊D7—22no—
91C2×(C2×D7)⋊C4—21no—
92#6489C2×C412yescomplemented
93C2×C4⋊Dic7—21no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7C2×C411yescharacteristic, complemented
98C2×C4⋊Dic7C2×C411yescharacteristic, complemented
99#6487—21no—
100#6487—21no—
101#6487C2×C412yescomplemented
102#6487C2×C412yescomplemented
103#6487C2312yes—
104C2×Dic7⋊C4—21no—
105C2×C4×Dic7—21no—
106#6461—22no—
107#6459—22no—
108#6457—22no—
109#6452—22no—
110#6448—22no—
111#6447—22no—
112#6446—22no—
113(C22⋊D7)⋊C4—22no—
114(C22⋊D7)⋊C4—22no—
115D7×C22⋊C4—22no—
116#6442—22no—
117#6440—22no—
118#6439—22no—
119#6438C2×C412yescomplemented
120C4×D28C2×C412yescomplemented
121#6435—22no—
122#6433C2×C412yescomplemented
123C4×Dic14C2×C412yescomplemented
124C7×C4⋊C8—22no—
125C7×C22⋊C8—21no—
126C7×C22⋊C8—21no—
127C7×C22⋊C8—22no—
128C7×C22⋊C8C2312yes—
129C7×C22⋊C8C2312yes—
130C7×#97—22no—
131C7⋊#95—21no—
132C7⋊#95—21no—
133C7⋊#95—21no—
134C7⋊#95C2311yescharacteristic
135C7⋊#95C2311yescharacteristic
136C7⋊#95C2311yescharacteristic
137C7⋊#95C2311yescharacteristic
138#3505—71no—
139#2973D711yescharacteristic, complemented
140#2349—71no—
141#1520—71no—
142#1519—71no—
143#1513—72no—
144#1512—72no—
145#1509—72no—
146#1504—72no—
147C2×#328—71no—
148C2×#327—71no—
149C24×C7C2×D411yescharacteristic
150C24×C7C2×D411yescharacteristic
151C23×D7—21no—
152C2×C7×D4—22no—
153C2×C7×D4—22no—
154C2×C7×D4C22⋊C412yes—
155C2×C7×D4C22⋊C412yes—
156C22×C4×C7—81no—
157C22×C4×C7—81no—
158C22×C4×C7C22×C411yescharacteristic
159C22×C4×C7C22×C412yes—
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2411yescharacteristic
169C2×C22⋊D7—22no—
170C2×C22⋊D7—22no—
171C2×C22⋊D7—22no—
172C2×C22⋊D7—22no—
173C2×C22⋊D7—42no—
174C2×C22⋊D7—42no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—42no—
183C22×Dic7—42no—
184C22×Dic7—42no—
185C22×Dic7—42no—
186C22×Dic7—81no—
187C22×Dic7—81no—
188#1157—82no—
189C2×D28—21no—
190C2×D28—81no—
191C2×D28C22×C412yes—
192C2×C4×D7—22no—
193C2×C4×D7—22no—
194C2×Dic14—21no—
195C2×Dic14—81no—
196C2×Dic14C22×C412yes—
197C7×M16—82no—
198C2×C7×C8—22no—
199C2×C7×C8—22no—
200C2×C7×C8—81no—
201C2×C7×C8—81no—
202C7×C4⋊C4C22⋊C412yes—
203C7×C4⋊C4C22⋊C412yes—
204C7×C22⋊C4C22⋊C412yes—
205C7×C22⋊C4C22⋊C412yes—
206C7×C22⋊C4C22⋊C412yes—
207C7×C22⋊C4C22⋊C412yes—
208C42×C7C22×C412yes—
209C42×C7C2×D412yes—
210C22⋊Dic7—22no—
211C22⋊Dic7—22no—
212C22⋊Dic7—22no—
213C22⋊Dic7—22no—
214C22⋊Dic7—42no—
215C22⋊Dic7—42no—
216(C2×D7)⋊C4—22no—
217(C2×D7)⋊C4—22no—
218(C2×D7)⋊C4—22no—
219(C2×D7)⋊C4—22no—
220(C2×D7)⋊C4—22no—
221(C2×D7)⋊C4—22no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7—42no—
225C4⋊Dic7—42no—
226C4⋊Dic7—81no—
227C4⋊Dic7—81no—
228C4⋊Dic7C22×C412yes—
229C4⋊Dic7C22×C412yes—
230Dic7⋊C4—22no—
231Dic7⋊C4—22no—
232Dic7⋊C4—22no—
233Dic7⋊C4—22no—
234Dic7⋊C4—22no—
235Dic7⋊C4—22no—
236C4×Dic7—22no—
237C4×Dic7—22no—
238C4×Dic7—42no—
239#553—72no—
240#553—142no—
241#552—72no—
242#551—142no—
243#548—72no—
244#546—72no—
245#539—141no—
246#538—141no—
247#534—141no—
248#529—72no—
249#525—72no—
250C2×C22⋊Q8—71no—
251C2×#121—71no—
252#518—141no—
253C2×C4×D4—141no—
254C2×C4×D4C2×D711yescharacteristic
255#435—22no—
256#435—22no—
257#432C2×D712yescomplemented
258#407C2×D712yescomplemented
259C2×C22⋊C8C2×D711yescharacteristic
260C2×C22⋊C8C2×D711yescharacteristic
261#389—141no—
262#385—141no—
263#385—141no—
264#382—71no—
265#380—71no—
266#380—71no—
267C4×C4⋊C4—71no—
268C2×#95—71no—
269C2×#95—71no—
270#328—72no—
271#328—72no—
272#328—72no—
273#328—72no—
274#327—72no—
275#327—72no—
276#327—72no—
277#327—72no—
278C23×C7—21no—
279C23×C7—21no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7C2×C22⋊C412yes—
285C23×C7C2×C22⋊C411yescharacteristic
286C23×C7C2×C22⋊C411yescharacteristic
287C23×C7AGL(1,ℤ/8)12yes—
288C23×C7#13712yes—
289C23×C7C22×D411yescharacteristic
290C22×D7—22no—
291C22×D7—42no—
292C22×D7—81no—
293C22×D7—81no—
294C7×D4—24no—
295C7×D4—24no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—42no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7—42no—
307C2×C4×C7—41no—
308C2×C4×C7C2×C22⋊C412yes—
309C2×C4×C7C2×C22⋊C412yes—
310C2×C4×C7C2×C22⋊C411yescharacteristic
311C2×C4×C7C2×C22⋊C412yes—
312C2×C4×C7C2×C22⋊C411yescharacteristic
313C2×C4×C7C23×C411yescharacteristic
314C2×C4×C7C22×D411yescharacteristic
315C22⋊D7—42no—
316C22⋊D7—42no—
317C22⋊D7—44no—
318C22⋊D7—82no—
319C22⋊D7—82no—
320C2×Dic7—22no—
321C2×Dic7—22no—
322C2×Dic7—22no—
323C2×Dic7—22no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—42no—
327C2×Dic7—41no—
328C2×Dic7—41no—
329C2×Dic7—41no—
330C2×Dic7—41no—
331C2×Dic7—41no—
332C2×Dic7—41no—
333C2×Dic7—41no—
334C2×Dic7—41no—
335C2×Dic7—41no—
336C2×Dic7—81no—
337C2×Dic7—81no—
338C2×Dic7—84no—
339C2×Dic7—84no—
340D28—42no—
341D28—81no—
342C4×D7—82no—
343C4×D7—82no—
344Dic14—42no—
345Dic14—81no—
346C7×C8—42no—
347C7×C8—42no—
348C2×#41—72no—
349C22×Q8—71no—
350C22×D4—71no—
351C22×D4—141no—
352C22×D4D2811yescharacteristic
353C23×C4—141no—
354C23×C4—141no—
355C23×C4C22×D711yescharacteristic
356C23×C4C22×D711yescharacteristic
357C2×M16—22no—
358C22×C8—21no—
359C22×C8—21no—
360#126—142no—
361#126—142no—
362#126—142no—
363#125—72no—
364#125—142no—
365#124—72no—
366#124—142no—
367#123—142no—
368#123—142no—
369#123—142no—
370#123—142no—
371#123—142no—
372C22⋊Q8—72no—
373C22⋊Q8—72no—
374C22⋊Q8—72no—
375C22⋊Q8—141no—
376C22⋊Q8—141no—
377C22⋊Q8—142no—
378#121—72no—
379#121—72no—
380#121—72no—
381#121—142no—
382#121—142no—
383#121—141no—
384#121—141no—
385#121—142no—
386#120—142no—
387#120—142no—
388C4×Q8—72no—
389C4×D4—72no—
390C4×D4—142no—
391C4×D4—142no—
392C4×D4—142no—
393C4×D4—142no—
394C4×D4—142no—
395C4×D4—284no—
396C4×D4C4×D712yes—
397C4×D4C4×D712yes—
398C4×D4C22⋊D712yes—
399C4×D4C22⋊D712yes—
400#117—72no—
401#117—142no—
402#117—142no—
403C2×C4⋊C4—71no—
404C2×C4⋊C4—71no—
405C2×C4⋊C4—141no—
406C2×C4⋊C4—141no—
407C2×C4⋊C4—141no—
408C2×C4⋊C4—141no—
409C2×C4⋊C4—141no—
410C2×C4⋊C4D2811yescharacteristic
411C2×C22⋊C4—141no—
412C2×C22⋊C4—141no—
413C2×C22⋊C4—142no—
414C2×C22⋊C4—141no—
415C2×C22⋊C4—141no—
416C2×C22⋊C4D2811yescharacteristic
417C2×C22⋊C4D2811yescharacteristic
418C2×C42—141no—
419C2×C42C22×D711yescharacteristic
420C4⋊C8—22no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—22no—
424C22⋊C8C22×D712yes—
425C22⋊C8C22×D712yes—
426#97—22no—
427#95—71no—
428#95—71no—
429#95—71no—
430#95—71no—
431#95—141no—
432#95—141no—
433#95—141no—
434C22×C7—21no—
435C22×C7—21no—
436C22×C7—21no—
437C22×C7—21no—
438C22×C7—21no—
439C22×C7—21no—
440C22×C7—22no—
441C22×C7—22no—
442C22×C7—22no—
443C22×C7—42no—
444C22×C7—42no—
445C22×C7—42no—
446C22×C7—42no—
447C22×C7#41712yes—
448C22×C7#41712yes—
449C22×C7C22×C22⋊C411yescharacteristic
450C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C7C2×#13711yescharacteristic
452C2×D7—42no—
453C2×D7—42no—
454C2×D7—42no—
455C2×D7—162no—
456C4×C7—21no—
457C4×C7—21no—
458C4×C7—21no—
459C4×C7—22no—
460C4×C7—21no—
461C4×C7—22no—
462C4×C7—22no—
463Dic7—42no—
464Dic7—42no—
465Dic7—42no—
466Dic7—42no—
467Dic7—81no—
468Dic7—81no—
469Dic7—81no—
470C24—141no—
471C24C2×D2811yescharacteristic
472C24C2×D2811yescharacteristic
473#41—562no—
474C2×Q8—72no—
475C2×Q8—141no—
476C2×Q8—561no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—72no—
480C2×D4—142no—
481C2×D4—142no—
482C2×D4—142no—
483C2×D4—142no—
484C2×D4—141no—
485C2×D4—282no—
486C2×D4—282no—
487C2×D4—561no—
488C2×D4(C2×D7)⋊C412yes—
489C2×D4(C2×D7)⋊C412yes—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4—141no—
493C22×C4—141no—
494C22×C4—141no—
495C22×C4—141no—
496C22×C4—142no—
497C22×C4—142no—
498C22×C4—141no—
499C22×C4—141no—
500C22×C4—141no—
501C22×C4—282no—
502C22×C4—282no—
503C22×C4—282no—
504C22×C4—282no—
505C22×C4—561no—
506C22×C4—561no—
507C22×C4C2×C4×D711yescharacteristic
508C22×C4C2×C4×D711yescharacteristic
509C22×C4C2×C4×D712yes—
510C22×C4C2×D2811yescharacteristic
511C22×C4C2×D2811yescharacteristic
512C22×C4C2×D2811yescharacteristic
513C22×C4C2×D2811yescharacteristic
514C22×C4C2×C22⋊D711yescharacteristic
515C22×C4C2×C22⋊D711yescharacteristic
516C22×C4C2×C22⋊D712yes—
517C22×C4C23×D711yescharacteristic
518M16—82no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—81no—
522C2×C8—81no—
523C4⋊C4—72no—
524C4⋊C4—72no—
525C4⋊C4—142no—
526C4⋊C4—142no—
527C4⋊C4—142no—
528C4⋊C4—142no—
529C4⋊C4—142no—
530C4⋊C4—141no—
531C4⋊C4—141no—
532C4⋊C4—142no—
533C4⋊C4—282no—
534C4⋊C4—282no—
535C4⋊C4—561no—
536C4⋊C4—561no—
537C4⋊C4(C2×D7)⋊C412yes—
538C4⋊C4(C2×D7)⋊C412yes—
539C22⋊C4—142no—
540C22⋊C4—142no—
541C22⋊C4—142no—
542C22⋊C4—142no—
543C22⋊C4—142no—
544C22⋊C4—142no—
545C22⋊C4—142no—
546C22⋊C4—142no—
547C22⋊C4—142no—
548C22⋊C4—142no—
549C22⋊C4—282no—
550C22⋊C4—282no—
551C22⋊C4(C2×D7)⋊C412yes—
552C22⋊C4(C2×D7)⋊C412yes—
553C22⋊C4(C2×D7)⋊C412yes—
554C22⋊C4(C2×D7)⋊C412yes—
555C42—142no—
556C42—142no—
557C42—282no—
558C42C2×C4×D712yes—
559C42C2×C22⋊D712yes—
560C2×C7—21no—
561C2×C7—22no—
562C2×C7—21no—
563C2×C7—22no—
564C2×C7—42no—
565C2×C7#288311yescharacteristic
566C2×C7C2×#41711yescharacteristic
567C2×C7#290111yescharacteristic
568D7—82no—
569C23—21no—
570C23—21no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—142no—
576C23—282no—
577C23—561no—
578C23—561no—
579C23#647112yes—
580C23#647212yes—
581C23C2×(C2×D7)⋊C412yes—
582C23C2×(C2×D7)⋊C411yescharacteristic
583C23C2×(C2×D7)⋊C411yescharacteristic
584C23C22×D2811yescharacteristic
585Q8—282no—
586Q8—561no—
587D4—24no—
588D4—24no—
589D4—282no—
590D4—284no—
591D4—282no—
592D4—282no—
593D4—561no—
594D4—562no—
595D4—562no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—142no—
609C2×C4—142no—
610C2×C4—142no—
611C2×C4—142no—
612C2×C4—281no—
613C2×C4—282no—
614C2×C4—281no—
615C2×C4—281no—
616C2×C4—281no—
617C2×C4—281no—
618C2×C4—281no—
619C2×C4—281no—
620C2×C4—281no—
621C2×C4—281no—
622C2×C4—281no—
623C2×C4—281no—
624C2×C4—562no—
625C2×C4—562no—
626C2×C4—561no—
627C2×C4—561no—
628C2×C4—564no—
629C2×C4—564no—
630C2×C4C2×(C2×D7)⋊C412yes—
631C2×C4C2×(C2×D7)⋊C412yes—
632C2×C4C2×(C2×D7)⋊C412yes—
633C2×C4C2×(C2×D7)⋊C411yescharacteristic
634C2×C4C2×(C2×D7)⋊C411yescharacteristic
635C2×C4C22×C4×D711yescharacteristic
636C2×C4C22×C22⋊D711yescharacteristic
637C8—42no—
638C8—42no—
639C7#1762211yescharacteristic, complemented, Sylow
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—282no—
654C22—282no—
655C22—282no—
656C22—1122no—
657C22#8990512yes—
658C22#8990512yes—
659C22C2×#647111yescharacteristic
660C22C2×#647211yescharacteristic
661C22C22×(C2×D7)⋊C411yescharacteristic
662C4—22no—
663C4—22no—
664C4—21no—
665C4—21no—
666C4—22no—
667C4—21no—
668C4—21no—
669C4—282no—
670C4—282no—
671C4—282no—
672C4—282no—
673C4—561no—
674C4—561no—
675C4—561no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—22no—
680C2—42no—
681C2—562no—
682C2#1173999111yescharacteristic
683C2C2×#8990511yescharacteristic
684C2#1174126211yescharacteristic
subgroupG/H
centerC22C22×(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2973C2
socleC22×C7C22×C22⋊C4
prime radical#11742855C2
cosocleC22×C4×C7C24
hypercenter#2973D7
hypocenterC7#17622
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. C7×#2973C2semidirect
3. #11739778C2semidirect
4. #11728588C2semidirect
5. #11728587C2semidirect
6. #11727733C2semidirect
7. #11727730C2semidirect
8. #11727700C2semidirect
9. C2×#89262C2semidirect
10. #11727698C2semidirect
11. C2×#89265C2semidirect
18. #90256C4semidirect
20. #90243C4semidirect
21. #90241C4semidirect
22. #90232C4semidirect
30. C7×#432C22semidirect
31. C7×#407C22semidirect
35. #89984C22semidirect
37. C2×C7⋊#95C22semidirect
41. #89708C22semidirect
42. C4×C4⋊Dic7C22semidirect
47. #89262C22semidirect
48. #89262C22semidirect
49. #89262C22semidirect
50. #89262C22semidirect
58. C2×#1157C2×C4semidirect
59. C22×D28C2×C4semidirect
60. C22×Dic14C2×C4semidirect
83. #6493C2×C4semidirect
84. #6493C2×C4semidirect
92. #6489C2×C4semidirect
97. C2×C4⋊Dic7C2×C4semidirect
98. C2×C4⋊Dic7C2×C4semidirect
101. #6487C2×C4semidirect
102. #6487C2×C4semidirect
119. #6438C2×C4semidirect
120. C4×D28C2×C4semidirect
122. #6433C2×C4semidirect
123. C4×Dic14C2×C4semidirect
139. #2973D7semidirect
257. #432C2×D7semidirect
258. #407C2×D7semidirect
639. C7#17622semidirect

Maximal subgroups

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

subgroupindex
#117428552
C7×#29732
#117397782
#117285882
#117285872
#117277332
#117277302
#117277002
C2×#892622
#117276982
C2×#892652
#176227