Finite Group Databasebeta

← #29685015

Subgroups — #29685015

Order 15616.

1414 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758222C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic, complemented
3C2×#16839714C211yesmaximal, characteristic, complemented
4#21446753C212yesmaximal, complemented
5#21446611C212yesmaximal, complemented
6#21446115C212yesmaximal, complemented
7#21446113C212yesmaximal, complemented
8#21445582C211yesmaximal, characteristic, complemented
9#21445582C211yesmaximal, characteristic, complemented
10#21445581C211yesmaximal, characteristic, complemented
11C61×#1749C211yesmaximal, characteristic, complemented
12C22×#11758222C411yescharacteristic
13C22×#11758189C2212yes—
14C4×#11758222—24no—
15C4×#11758222—24no—
16C2×C4×Dic122C411yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×D244C411yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×C22⋊D61C411yescharacteristic
21C2×C4×C22⋊D61C411yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24C2×#14519736C411yescharacteristic
25C2×#14519734C411yescharacteristic
26C2×#14519734C411yescharacteristic
27C2×C42×D61C2211yescharacteristic
28C2×C42×D61C2211yescharacteristic
29#16839817—24no—
30C2×#14519706C2212yes—
31C2×C22⋊#92418C2212yes—
32C2×#14519689C2212yes—
33C2×#14519689C2212yes—
34C2×#14519689C2212yes—
35#16839714—24no—
36C2×#14519688C2211yescharacteristic
37C2×#14519688C2211yescharacteristic
38C2×C8×Dic61C2212yes—
39#16839517C2212yes—
40#16839516C2212yes—
41#16839516C2212yes—
42C22×C42×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2212yes—
44C2×#97×C61C2211yescharacteristic
45C2×#97×C61C2211yescharacteristic
46C61×#336C2212yes—
47C2×#11758222—24no—
48C2×#11758222—24no—
49C2×#11758222—24no—
50C22×Dic122C2×C411yescharacteristic
51C22×D244C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758189—24no—
61C2×#11758189—24no—
62C2×#11758189—24no—
63C22×#92418C2312yes—
64C22×#92418C2312yes—
65C4×Dic122—24no—
66C4×Dic122—22no—
67C4×Dic122—22no—
68C4×D244—24no—
69C4×D244—22no—
70C4×D244—22no—
71C4×C22⋊D61—24no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—24no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77#14519736—24no—
78#14519734—24no—
79#14519734—24no—
80C2×C4⋊Dic61C2×C411yescharacteristic
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—22no—
99C42×D61—22no—
100C42×D61D414yes—
101C42×D61D414yes—
102#14519706—24no—
103C22⋊#92418—24no—
104#14519689—24no—
105#14519689—24no—
106#14519689—24no—
107#14519688—22no—
108#14519688—22no—
109C8×Dic61—24no—
110C23×C4×C61C2×C411yescharacteristic
111C23×C4×C61C2×C411yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C22×C8×C61C2312yes—
114C22×C8×C61C2312yes—
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117C2×C42×C61C2×C411yescharacteristic
118C2×C42×C61C2×C411yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C22⋊C8×C61—24no—
122#97×C61—22no—
123#97×C61—22no—
124C24×C61C22×C411yescharacteristic
125C23×D61C22×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—41no—
136C22×C4×C61—41no—
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C2411yescharacteristic
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61M1614yescomplemented
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155#11758222—232no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—41no—
172C2×C4×D61—41no—
173C2×C4×D61—41no—
174C2×C4×D61—41no—
175C2×C4×D61C22⋊C414yes—
176C2×C4×D61C22⋊C414yes—
177C2×C4×D61C2×D412yes—
178C2×C4×D61C2×D412yes—
179C2×Dic122—22no—
180C2×Dic122—22no—
181C2×Dic122M1614yescomplemented
182C2×C8×C61—22no—
183C2×C8×C61—22no—
184C2×C8×C61—22no—
185C2×C8×C61—22no—
186C2×C8×C61—22no—
187C2×C8×C61#4114yescomplemented
188C42×C61—22no—
189C42×C61—22no—
190C42×C61—21no—
191C42×C61—21no—
192C42×C61C2×D412yes—
193C42×C61C2×D412yes—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61C22⋊C414yes—
211C4×Dic61C22⋊C414yes—
212C4×Dic61C2×D412yes—
213C4×Dic61C2×D412yes—
214C2×#92418—22no—
215C2×#92418—22no—
216C2×#92418—22no—
217C2×#92418—22no—
218C2×#92418—22no—
219C2×#92418#4114yescomplemented
220#11758189—216no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61C2×M1612yes—
228C23×C61C23×C411yescharacteristic
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—21no—
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61C2×C22⋊C412yes—
242C22×D61C2×M1612yes—
243C2×C4×C61—28no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—44no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61C2×C22⋊C412yes—
260C2×C4×C61C2×C22⋊C412yes—
261C2×C4×C61C2×M1612yes—
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61C2×#4112yes—
265C2×C4×C61C2×#4112yes—
266C22⋊D61—28no—
267C22⋊D61—28no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61C2×C22⋊C412yes—
281C2×Dic61C2×C22⋊C412yes—
282C2×Dic61C2×C22⋊C412yes—
283C2×Dic61C2×M1612yes—
284C2×Dic61C2×M1612yes—
285C2×Dic61C2×M1612yes—
286D244—28no—
287C4×D61—28no—
288C4×D61—24no—
289C4×D61—24no—
290C4×D61—28no—
291C4×D61—44no—
292C4×D61—44no—
293C4×D61—42no—
294C4×D61—42no—
295Dic122—28no—
296C8×C61—24no—
297C8×C61—42no—
298#92418—24no—
299#92418—42no—
300#21380—611nomaximal, Sylow
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61C22×C22⋊C411yescharacteristic
309C22×C61C4×#4111yescharacteristic
310C22×C61C4×#4111yescharacteristic
311C22×C61C22×M1611yescharacteristic
312C22×C61C22×M1611yescharacteristic
313C22×C61#56811yescharacteristic
314C22×C61#56811yescharacteristic
315C2×D61—22no—
316C2×D61—22no—
317C2×D61—22no—
318C2×D61—22no—
319C2×D61—22no—
320C2×D61—22no—
321C2×D61—41no—
322C2×D61—41no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—41no—
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61#52512yes—
335C4×C61#53212yes—
336Dic61—22no—
337Dic61—22no—
338Dic61—22no—
339Dic61—41no—
340Dic61—41no—
341Dic61#40714yes—
342C2×C4×#41—611no—
343C2×#432—611no—
344C2×C4×M16—611no—
345#1984—612no—
346#1954—612no—
347#1870—612no—
348#1870—612no—
349#1749—611no—
350#1749—611no—
351#1749—611no—
352#1749D6111yescharacteristic, complemented
353C2×C61—42no—
354C2×C61#229711yescharacteristic
355C2×C61C2×#40711yescharacteristic
356C2×C61#287911yescharacteristic
357C2×C61#297011yescharacteristic
358C2×C61#297011yescharacteristic
359C2×C61#297111yescharacteristic
360C2×C61#297111yescharacteristic
361D61—42no—
362D61—42no—
363C22×#41—611no—
364C22×M16—612no—
365C4×#41—1224no—
366C4×#41—1224no—
367C2×C4×Q8—611no—
368C2×C4×Q8—611no—
369C2×C4×D4—611no—
370C2×C4×D4—611no—
371C2×C4×D4—611no—
372C2×C4×D4—611no—
373C2×C4×D4—611no—
374C2×C4×D4—611no—
375C2×#117—611no—
376C2×#117—611no—
377C2×#117—611no—
378C22×C42—611no—
379C22×C42—611no—
380C22×C42C2×D6111yescharacteristic
381#432—1224no—
382C2×C4⋊C8—612no—
383C2×C22⋊C8—612no—
384C2×C22⋊C8—612no—
385C2×C22⋊C8—612no—
386C2×C22⋊C8—612no—
387C2×C22⋊C8C2×D6112yes—
388C4×M16—1224no—
389C2×#97—611no—
390C2×#97—611no—
391C2×#97C2×D6111yescharacteristic
392C2×#97C2×D6111yescharacteristic
393C2×C4×C8—612no—
394#336—612no—
395#336—612no—
396#336—612no—
397#336C2×D6112yes—
398C61#2138011yescharacteristic, complemented, Sylow
399C2×#41—1224no—
400C2×#41—1224no—
401C2×#41—1224no—
402C22×Q8—611no—
403C22×D4—611no—
404C22×D4—611no—
405C22×D4—611no—
406C23×C4—611no—
407C23×C4—611no—
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4—611no—
412C23×C4C4×D6111yescharacteristic
413C23×C4C4×D6111yescharacteristic
414C23×C4C22×D6111yescharacteristic
415C2×M16—1224no—
416C2×M16—1224no—
417C2×M16—1224no—
418C22×C8—612no—
419C22×C8—612no—
420C22×C8C22×D6112yes—
421C22×C8C22×D6112yes—
422C4×Q8—1222no—
423C4×Q8—1222no—
424C4×Q8—1224no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1224no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1224no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1224no—
434#117—1224no—
435#117—1224no—
436#117—1224no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C22⋊C4—611no—
444C2×C22⋊C4—611no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4—611no—
447C2×C22⋊C4—611no—
448C2×C22⋊C4—611no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—614no—
455C2×C42—614no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—1222no—
460C2×C42—1222no—
461C2×C42C4×D6111yescharacteristic
462C2×C42C4×D6111yescharacteristic
463C2×C42C22×D6111yescharacteristic
464C2×C42C22×D6111yescharacteristic
465C4⋊C8—1224no—
466C22⋊C8—24no—
467C22⋊C8—1224no—
468C22⋊C8—1224no—
469C22⋊C8—1224no—
470C22⋊C8—1224no—
471#97—22no—
472#97—22no—
473#97—1222no—
474#97—1222no—
475C4×C8—1224no—
476C24—611no—
477C24—611no—
478C24C2×C4×D6111yescharacteristic
479#41—12232no—
480C2×Q8—614no—
481C2×Q8—1222no—
482C2×Q8—1222no—
483C2×D4—614no—
484C2×D4—1222no—
485C2×D4—1222no—
486C2×D4—1222no—
487C2×D4—1222no—
488C2×D4—1222no—
489C2×D4—1222no—
490C2×D4—1222no—
491C2×D4—1222no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—612no—
507C22×C4—612no—
508C22×C4—614no—
509C22×C4—614no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1222no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—2441no—
525C22×C4—2441no—
526C22×C4—2441no—
527C22×C4—2441no—
528C22×C4C2×C4×D6111yescharacteristic
529C22×C4C2×C4×D6111yescharacteristic
530C22×C4C2×C4×D6111yescharacteristic
531C22×C4C2×C4×D6111yescharacteristic
532C22×C4C2×C4×D6111yescharacteristic
533C22×C4C23×D6111yescharacteristic
534M16—12216no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—614no—
541C2×C8—1222no—
542C2×C8—1222no—
543C2×C8—1222no—
544C2×C8—1222no—
545C2×C8—1222no—
546C2×C8#1175822214yescomplemented
547C4⋊C4—1222no—
548C4⋊C4—1222no—
549C4⋊C4—1222no—
550C4⋊C4—1222no—
551C4⋊C4—1222no—
552C4⋊C4—1222no—
553C22⋊C4—1222no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—1222no—
558C22⋊C4—1222no—
559C42—21no—
560C42—21no—
561C42—22no—
562C42—22no—
563C42—612no—
564C42—612no—
565C42—614no—
566C42—614no—
567C42—1221no—
568C42—1221no—
569C42—1222no—
570C42—1222no—
571C42D4×D6112yes—
572C42D4×D6112yes—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—612no—
580C23—612no—
581C23—1221no—
582C23—1221no—
583C23—1221no—
584C23—1221no—
585C23—1221no—
586C23—1221no—
587C23—1221no—
588C23—1221no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23—1221no—
593C23M16×D6112yes—
594C23C22×C4×D6111yescharacteristic
595Q8—1228no—
596D4—1228no—
597D4—1228no—
598D4—1228no—
599C2×C4—28no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—44no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—612no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—612no—
620C2×C4—612no—
621C2×C4—1228no—
622C2×C4—1228no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1224no—
630C2×C4—1224no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—2444no—
638C2×C4—2444no—
639C2×C4—2442no—
640C2×C4—2442no—
641C2×C4C22⋊C4×D6112yes—
642C2×C4C22⋊C4×D6112yes—
643C2×C4M16×D6112yes—
644C2×C4C2×D4×D6111yescharacteristic
645C2×C4C2×D4×D6111yescharacteristic
646C2×C4#41×D6112yes—
647C2×C4C2×#1175822212yes—
648C8—24no—
649C8—42no—
650C8—1224no—
651C8—2442no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—1222no—
660C22—1222no—
661C22—1222no—
662C22—1222no—
663C22—1222no—
664C22—1222no—
665C22—2441no—
666C22—2441no—
667C22—2441no—
668C22—2441no—
669C22—2441no—
670C22—2441no—
671C22—2441no—
672C22—2441no—
673C22C2×C22⋊C4×D6111yescharacteristic
674C22#1684023011yescharacteristic
675C22C4×#1175822211yescharacteristic
676C22C2×M16×D6111yescharacteristic
677C22C2×M16×D6111yescharacteristic
678C22#1684052811yescharacteristic
679C22#1684052811yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—41no—
685C4—614no—
686C4—1222no—
687C4—1222no—
688C4—1222no—
689C4—2441no—
690C4—2441no—
691C4#1684027112yes—
692C4#1684030912yes—
693C2—42no—
694C2—2442no—
695C2—2442no—
696C2#2144830511yescharacteristic
697C2#407×D6111yescharacteristic
698C2#2145426211yescharacteristic
699C2#2145482811yescharacteristic
700C2#2145483011yescharacteristic
701C2#2145483611yescharacteristic
702C2#2145483711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1749C2
prime radicalC22×#11758222C4
cosocleC22×C4×C61C24
hypercenter#1749D61
hypocenterC61#21380
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#16839817C2semidirect
3. C2×#16839714C2semidirect
4. #21446753C2semidirect
5. #21446611C2semidirect
6. #21446115C2semidirect
7. #21446113C2semidirect
8. #21445582C2semidirect
9. #21445582C2semidirect
10. #21445581C2semidirect
11. C61×#1749C2semidirect
148. C2×C22⋊D61M16semidirect
181. C2×Dic122M16semidirect
187. C2×C8×C61#41semidirect
219. C2×#92418#41semidirect
352. #1749D61semidirect
398. C61#21380semidirect
546. C2×C8#11758222semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582222
C2×#168398172
C2×#168397142
#214467532
#214466112
#214461152
#214461132
#214455822
#214455812
C61×#17492
#2138061