Finite Group Databasebeta

← #35196507

Subgroups — #35196507

Order 20224.

7094 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777496C214yesmaximal, complemented
2#23777485C214yesmaximal, complemented
3#23777393C218yesmaximal, complemented
4#23777265C216yesmaximal, complemented
5#23777210C211yesmaximal, characteristic, complemented
6#23777171C211yesmaximal, characteristic, complemented
7#23777109C216yesmaximal, complemented
8#23777051C212yesmaximal, complemented
9#23777017C218yesmaximal, complemented
10#23776995C214yesmaximal, complemented
11Q8×#11929624C214yesmaximal, complemented
12#23776833C216yesmaximal, complemented
13#23776696C216yesmaximal, complemented
14C4×#14579209C212yesmaximal, complemented
15C22×C4×Q8×C79C211yesmaximal, characteristic, complemented
16C2×#14579209C2212yes—
17#19099298C22112yescomplemented
18Q8×Dic158C2214yescomplemented
19#19099292C2214yescomplemented
20#19099291C22112yescomplemented
21#19099289C2218yescomplemented
22#19099286C22112yescomplemented
23#19099285C22124yescomplemented
24#19099273C22112yescomplemented
25#19099268C22124yes—
26#19099261C22124yes—
27#19099254C22124yescomplemented
28#19099248C22124yes—
29#19099235C2214yescomplemented
30Q8×D316C2214yescomplemented
31Q8×C22⋊D79C2218yes—
32Q8×C22⋊D79C2218yes—
33#19099225C2218yescomplemented
34#19099224C2218yes—
35#19099224C2218yes—
36#19099214C22124yes—
37#19099194C2216yes—
38#19099185C22124yescomplemented
39#19099171C22124yescomplemented
40#19099160C22124yes—
41#19099144C2216yes—
42#19099137C22112yes—
43#19099120C2216yes—
44#19099120C2216yes—
45#19099120C2216yes—
46#19099117C22124yescomplemented
47#19099113C2216yes—
48#19099113C2216yes—
49#19099113C2216yes—
50#19099100C22124yescomplemented
51#19099097C22112yes—
52#19099097C22112yes—
53#19099097C22112yes—
54#19099097C22112yes—
55#19099097C22112yes—
56#19099097C22112yes—
57#19099074C22112yes—
58#19099074C22112yes—
59#19099074C2214yes—
60#19099045C2218yescomplemented
61#19099044C22112yes—
62#19099041C2212yes—
63#19099039C2218yescomplemented
64C4×#11929625C2218yescomplemented
65C4×#11929624C22112yes—
66C4×#11929624C22112yes—
67C4×#11929624C22112yes—
68C4×Q8×D79C2218yescomplemented
69C23×Q8×C79C2211yescharacteristic
70C2×C4×Q8×C79C2213yes—
71C2×C4×Q8×C79C2211yescharacteristic
72C2×C4×Q8×C79C2214yes—
73C2×C4×Q8×C79C2211yescharacteristic
74C2×C4×Q8×C79C2214yes—
75C2×C4×Q8×C79C2214yes—
76C2×C4×Q8×C79C2213yes—
77C2×C4×Q8×C79C2214yes—
78C22×C4⋊C4×C79C2213yes—
79C22×C42×C79C2213yes—
80#14579209—216no—
81C2×#11929625C2318yes—
82C2×#11929624C23112yes—
83C2×#11929624C2314yes—
84C2×#11929624C23112yes—
85C2×Q8×D79C2318yes—
86#14579161C2316yes—
87#14579161C2316yes—
88#14579161C2316yes—
89#14579160C23124yes—
90#14579159C23124yes—
91#14579158C2316yes—
92#14579156C23148yes—
93#14579155C23124yes—
94#14579155C23124yes—
95#14579153C23112yes—
96#14579153C23112yes—
97#14579153C23112yes—
98#14579152C23124yes—
99#14579151C23148yes—
100#14579150C23124yes—
101#14579149C23112yes—
102#14579149C23112yes—
103#14579149C23112yes—
104#14579146C23148yes—
105#14579144C23124yes—
106#14579144C23124yes—
107#14579144C2318yes—
108#14579141C23124yes—
109#14579140C23112yes—
110#14579140C23112yes—
111#14579140C23112yes—
112#14579140C23112yes—
113#14579140C2314yes—
114#14579140C2314yes—
115#14579139C23148yes—
116#14579137C23124yes—
117#14579137C23124yes—
118#14579136C23124yes—
119#14579135C23112yes—
120#14579135C23112yes—
121#14579135C23112yes—
122#14579135C23112yes—
123#14579135C2314yes—
124#14579135C2314yes—
125#14579130C2318yes—
126Q8×Dic79C2318yes—
127Q8×Dic79C2318yes—
128C4×Dic158C23112yes—
129C4×Dic158C23112yes—
130C4×Dic158C23112yes—
131C4×Dic158C23112yes—
132C4×Dic158C23112yes—
133C4×Dic158C23112yes—
134#14579126C23124yes—
135C4×D316C23112yes—
136C4×D316C23112yes—
137C4×D316C23112yes—
138C4×D316C23112yes—
139C4×D316C23112yes—
140C4×D316C23112yes—
141#14579123C23124yes—
142C4×C22⋊D79C23124yes—
143C4×C22⋊D79C23124yes—
144C4×C22⋊D79C23124yes—
145C4×C22⋊D79C23124yes—
146C4×C22⋊D79C2318yes—
147C4×C22⋊D79C2318yes—
148#14579120C23112yes—
149#14579120C23112yes—
150#14579120C2314yes—
151#14579119C23124yes—
152#14579118C23124yes—
153#14579118C23124yes—
154#14579118C23124yes—
155C4⋊C4×D79C23124yes—
156C42×D79C23124yes—
157C22×Q8×C79—28no—
158C22×Q8×C79C2313yes—
159C22×Q8×C79C2314yes—
160C22×Q8×C79C2314yes—
161C22×Q8×C79C2311yescharacteristic
162C23×C4×C79C2311yescharacteristic
163C23×C4×C79C2313yes—
164C23×C4×C79C2313yes—
165C4×Q8×C79C23112yes—
166C4×Q8×C79C2314yes—
167C4×Q8×C79C2314yes—
168C4×Q8×C79C23112yes—
169C4×Q8×C79C23112yes—
170C4×Q8×C79C2314yes—
171C4×Q8×C79C2314yes—
172C4×Q8×C79C23112yes—
173C2×C4⋊C4×C79C2313yes—
174C2×C4⋊C4×C79C2316yes—
175C2×C4⋊C4×C79C23112yes—
176C2×C4⋊C4×C79C23112yes—
177C2×C4⋊C4×C79C2313yes—
178C2×C42×C79C2313yes—
179C2×C42×C79C2316yes—
180C2×C42×C79C2316yes—
181C2×C42×C79C2313yes—
182C2×C42×C79C2316yes—
183C2×C42×C79C2313yes—
184C2×C42×C79C2316yes—
185C2×C42×C79C2313yes—
186#11929625—232no—
187#11929624—248no—
188#11929624—216no—
189#11929624—424no—
190C2×Dic158C24112yes—
191C2×Dic158C2414yes—
192C2×Dic158C24112yes—
193Q8×D79—232no—
194C2×D316C24112yes—
195C2×D316C2414yes—
196C2×D316C24112yes—
197C2×C22⋊D79C2418yes—
198C2×C22⋊D79C2418yes—
199C2×C22⋊D79C2418yes—
200C2×C4×D79C24124yes—
201C2×C4×D79C2418yes—
202C2×C4×D79C24124yes—
203C4⋊Dic79C24112yes—
204C4⋊Dic79C24112yes—
205C4⋊Dic79C2414yes—
206C4⋊Dic79C2414yes—
207C4⋊Dic79C24112yes—
208C4⋊Dic79C24112yes—
209Dic79⋊C4C24124yes—
210Dic79⋊C4C2418yes—
211Dic79⋊C4C2418yes—
212Dic79⋊C4C24124yes—
213Dic79⋊C4C24124yes—
214Dic79⋊C4C24124yes—
215C22⋊Dic79C2418yes—
216C22⋊Dic79C2418yes—
217C22⋊Dic79C2418yes—
218(C2×D79)⋊C4C2418yes—
219(C2×D79)⋊C4C2418yes—
220(C2×D79)⋊C4C24124yes—
221(C2×D79)⋊C4C24124yes—
222(C2×D79)⋊C4C24124yes—
223(C2×D79)⋊C4C24124yes—
224C4×Dic79C2418yes—
225C4×Dic79C24124yes—
226C4×Dic79C24124yes—
227C24×C79C2411yescharacteristic
228C2×Q8×C79—216no—
229C2×Q8×C79—216no—
230C2×Q8×C79—212no—
231C2×Q8×C79#4118yescomplemented
232C2×Q8×C79C24112yes—
233C2×Q8×C79C2414yes—
234C22×C4×C79—212no—
235C22×C4×C79—24no—
236C22×C4×C79—46no—
237C22×C4×C79C2416yes—
238C22×C4×C79C2411yescharacteristic
239C22×C4×C79C2411yescharacteristic
240C22×C4×C79C2411yescharacteristic
241C22×C4×C79C2411yescharacteristic
242C22×C4×C79C2411yescharacteristic
243C22×C4×C79C2416yes—
244C22×C4×C79C2416yes—
245C22×C4×C79C2413yes—
246C22×C4×C79C2413yes—
247C22×C4×C79C2416yes—
248C22×C4×C79C2413yes—
249C22×C4×C79C2413yes—
250C22×C4×C79C2411yescharacteristic
251C4⋊C4×C79C24112yes—
252C4⋊C4×C79C24112yes—
253C4⋊C4×C79C24124yes—
254C42×C79C2416yes—
255C42×C79C2416yes—
256C42×C79C2416yes—
257C42×C79C2416yes—
258C42×C79C2416yes—
259C42×C79C2416yes—
260C42×C79C2416yes—
261C42×C79C2416yes—
262C23×C79—22no—
263C23×C79—22no—
264C23×C79—22no—
265C23×C79C2511yescharacteristic
266C23×C79C2511yescharacteristic
267C23×C79C2511yescharacteristic
268C22×D79C2518yes—
269Q8×C79—224no—
270Q8×C79C2×#41116yes—
271C2×C4×C79—26no—
272C2×C4×C79—22no—
273C2×C4×C79—212no—
274C2×C4×C79—212no—
275C2×C4×C79—212no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—43no—
281C2×C4×C79—46no—
282C2×C4×C79—43no—
283C2×C4×C79C2×#41112yes—
284C2×C4×C792−1+414yescomplemented
285C2×C4×C79C2516yes—
286C2×C4×C79C2511yescharacteristic
287C2×C4×C79C2511yescharacteristic
288C2×C4×C79C2516yes—
289C2×C4×C79C2516yes—
290C2×C4×C79C2516yes—
291C2×C4×C79C2511yescharacteristic
292C2×C4×C79C2511yescharacteristic
293C22⋊D79—216no—
294C22⋊D79—216no—
295C22⋊D79—216no—
296C2×Dic79C2518yes—
297C2×Dic79C2518yes—
298C2×Dic79C2518yes—
299D316—224no—
300D316—28no—
301D316—412no—
302C4×D79—248no—
303C4×D79—216no—
304C4×D79—424no—
305Dic158—224no—
306Dic158—28no—
307Dic158—412no—
308C22×C79—28no—
309C22×C79—21no—
310C22×C79—21no—
311C22×C79—21no—
312C22×C79—21no—
313C22×C79—21no—
314C22×C79—21no—
315C22×C79C22×#4112yes—
316C22×C79C2×2−1+412yes—
317C22×C79#58512yes—
318C22×C79C2611yescharacteristic
319C2×D79—28no—
320C2×D79—28no—
321C2×D79—28no—
322C4×C79—26no—
323C4×C79—21no—
324C4×C79—21no—
325C4×C79—26no—
326C4×C79—26no—
327C4×C79C22×#41112yes—
328C4×C79C2×2−1+412yes—
329C4×C79C2×2−1+412yes—
330Dic79—28no—
331Dic79—28no—
332Dic79—28no—
333#62788—791nomaximal, Sylow
334C2×C79—22no—
335C2×C79—22no—
336C2×C79—22no—
337C2×C79C23×#4111yescharacteristic
338C2×C79C22×2−1+411yescharacteristic
339C2×C79C2×#58511yescharacteristic
340D79—48no—
341#3523—794no—
342#3522—794no—
343#3516—798no—
344#3507—796no—
345#3502—791no—
346#3497—791no—
347#3492—796no—
348#3486—792no—
349#3482—798no—
350#3480—794no—
351Q8×#41—794no—
352#3461—796no—
353#3444—796no—
354C4×2−1+4—792no—
355C22×C4×Q8D7911yescharacteristic, complemented
356C79#6278811yescharacteristic, complemented, Sylow
357C2×2−1+4—792no—
358C23×Q8C2×D7911yescharacteristic
359#559—7912no—
360Q82—794no—
361#557—7912no—
362#557—794no—
363#557—798no—
364#556—7924no—
365#556—7912no—
366#554—7912no—
367#554—7924no—
368#553—7924no—
369#552—7924no—
370#552—7924no—
371#550—794no—
372D4×Q8—798no—
373D4×Q8—798no—
374D4×Q8—794no—
375#548—798no—
376#548—798no—
377#548—798no—
378#547—7924no—
379#544—796no—
380#542—7924no—
381#541—7924no—
382#539—7924no—
383#537—796no—
384#536—7912no—
385#533—7924no—
386#533—796no—
387#533—796no—
388#533—796no—
389#532—796no—
390#532—796no—
391#532—796no—
392#529—7924no—
393#529—7912no—
394#529—7912no—
395#529—7912no—
396#529—7912no—
397#529—7912no—
398#529—7912no—
399#525—794no—
400#525—7912no—
401#525—7912no—
402#520—798no—
403#520—7912no—
404#519—792no—
405#519—798no—
406C4×#41—798no—
407C4×#41—7912no—
408C4×#41—7912no—
409C4×#41—7912no—
410C2×C4×Q8—798no—
411C2×C4×Q8C2×D7911yescharacteristic
412C2×C4×Q8C2×D7913yes—
413C2×C4×Q8C2×D7914yes—
414C2×C4×Q8C2×D7914yes—
415C2×C4×Q8C2×D7911yescharacteristic
416C2×C4×Q8C2×D7913yes—
417C2×C4×Q8C2×D7914yes—
418C2×C4×Q8C2×D7914yes—
419C22×C4⋊C4C2×D7913yes—
420C22×C42C2×D7913yes—
4212−1+4—15816no—
422C2×#41—798no—
423C2×#41—7912no—
424C2×#41—794no—
425C2×#41—7912no—
426C22×Q8—28no—
427C22×Q8—798no—
428C22×Q8C22×D7913yes—
429C22×Q8C22×D7914yes—
430C22×Q8C22×D7914yes—
431C22×Q8C22×D7911yescharacteristic
432C23×C4C22×D7913yes—
433C23×C4C22×D7911yescharacteristic
434C23×C4C22×D7913yes—
435C4⋊Q8—7924no—
436C4⋊Q8—7924no—
437C4⋊Q8—796no—
438C4⋊Q8—796no—
439C4⋊Q8—796no—
440#127—796no—
441#126—7948no—
442#126—7924no—
443#126—7924no—
444#125—7924no—
445#125—7948no—
446#125—7912no—
447#125—7912no—
448#125—7912no—
449#124—7924no—
450#124—7912no—
451#124—7912no—
452#124—7912no—
453#123—798no—
454#123—7924no—
455#123—7924no—
456#123—7948no—
457C22⋊Q8—7924no—
458C22⋊Q8—7924no—
459C22⋊Q8—794no—
460C22⋊Q8—794no—
461C22⋊Q8—7912no—
462C22⋊Q8—7912no—
463C22⋊Q8—7912no—
464C22⋊Q8—7912no—
465C22⋊Q8—7924no—
466C22⋊Q8—7948no—
467#121—794no—
468#121—794no—
469#121—7912no—
470#121—7912no—
471#121—7912no—
472#121—7912no—
473#121—7924no—
474#120—798no—
475C4×Q8—798no—
476C4×Q8—798no—
477C4×Q8—7924no—
478C4×Q8—7912no—
479C4×Q8—7912no—
480C4×Q8—7912no—
481C4×Q8—7912no—
482C4×Q8—7912no—
483C4×Q8—7912no—
484C4×Q8C22×D7914yes—
485C4×Q8C22×D7914yes—
486C4×Q8C22×D79112yes—
487C4×Q8C22×D79112yes—
488C4×Q8C22×D7914yes—
489C4×Q8C22×D7914yes—
490C4×Q8C22×D79112yes—
491C4×Q8C22×D79112yes—
492C4×D4—798no—
493C4×D4—798no—
494C4×D4—7924no—
495C4×D4—7924no—
496C4×D4—7924no—
497C4×D4—7924no—
498C4×D4—7924no—
499C4×D4—7912no—
500C4×D4—7912no—
501C4×D4—7912no—
502C4×D4—7912no—
503C4×D4—7912no—
504C4×D4—7912no—
505#117—794no—
506#117—7912no—
507#117—7912no—
508#117—7924no—
509#117—7924no—
510#117—7924no—
511#117—7924no—
512C2×C4⋊C4—7924no—
513C2×C4⋊C4C22×D7913yes—
514C2×C4⋊C4C22×D7913yes—
515C2×C4⋊C4C22×D7916yes—
516C2×C4⋊C4C22×D79112yes—
517C2×C4⋊C4C22×D79112yes—
518C2×C42—7924no—
519C2×C42C22×D7913yes—
520C2×C42C22×D7916yes—
521C2×C42C22×D7916yes—
522C2×C42C22×D7916yes—
523C2×C42C22×D7913yes—
524C2×C42C22×D7913yes—
525C2×C42C22×D7916yes—
526C2×C42C22×D7913yes—
527C24C23×D7911yescharacteristic
528#41—31624no—
529#41—15832no—
530#41—15848no—
531#41—15816no—
532C2×Q8—216no—
533C2×Q8—216no—
534C2×Q8—212no—
535C2×Q8—7912no—
536C2×Q8—794no—
537C2×Q8—7912no—
538C2×Q8—15832no—
539C2×Q8#1192962418yescomplemented
540C2×Q8C23×D79112yes—
541C2×Q8C23×D7914yes—
542C2×D4—798no—
543C2×D4—798no—
544C2×D4—798no—
545C2×D4—7912no—
546C2×D4—794no—
547C2×D4—7912no—
548C22×C4—212no—
549C22×C4—24no—
550C22×C4—46no—
551C22×C4—7924no—
552C22×C4—7924no—
553C22×C4—798no—
554C22×C4C23×D7911yescharacteristic
555C22×C4C23×D7911yescharacteristic
556C22×C4C23×D7911yescharacteristic
557C22×C4C23×D7916yes—
558C22×C4C23×D7916yes—
559C22×C4C23×D7916yes—
560C22×C4C23×D7913yes—
561C22×C4C23×D7911yescharacteristic
562C22×C4C23×D7911yescharacteristic
563C22×C4C23×D7913yes—
564C22×C4C23×D7916yes—
565C22×C4C23×D7913yes—
566C22×C4C23×D7913yes—
567C22×C4C23×D7911yescharacteristic
568C4⋊C4—7924no—
569C4⋊C4—798no—
570C4⋊C4—798no—
571C4⋊C4—7924no—
572C4⋊C4—7924no—
573C4⋊C4—7924no—
574C4⋊C4—7912no—
575C4⋊C4—7912no—
576C4⋊C4—794no—
577C4⋊C4—794no—
578C4⋊C4—7912no—
579C4⋊C4—7912no—
580C4⋊C4C23×D79112yes—
581C4⋊C4C23×D79112yes—
582C4⋊C4C23×D79124yes—
583C22⋊C4—798no—
584C22⋊C4—798no—
585C22⋊C4—798no—
586C22⋊C4—7924no—
587C22⋊C4—798no—
588C22⋊C4—798no—
589C22⋊C4—7924no—
590C22⋊C4—7924no—
591C22⋊C4—7924no—
592C42—7924no—
593C42—7924no—
594C42—798no—
595C42C23×D7916yes—
596C42C23×D7916yes—
597C42C23×D7916yes—
598C42C23×D7916yes—
599C42C23×D7916yes—
600C42C23×D7916yes—
601C42C23×D7916yes—
602C42C23×D7916yes—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—798no—
607C23C24×D7911yescharacteristic
608C23C24×D7911yescharacteristic
609C23C24×D7911yescharacteristic
610Q8—224no—
611Q8—31612no—
612Q8—1588no—
613Q8—15824no—
614Q8C2×#11929624116yes—
615D4—31612no—
616D4—15816no—
617D4—15816no—
618D4—15816no—
619D4—1588no—
620D4—15824no—
621C2×C4—22no—
622C2×C4—212no—
623C2×C4—26no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—212no—
629C2×C4—212no—
630C2×C4—43no—
631C2×C4—46no—
632C2×C4—43no—
633C2×C4—31624no—
634C2×C4—798no—
635C2×C4—798no—
636C2×C4—798no—
637C2×C4—15816no—
638C2×C4—15848no—
639C2×C4C2×#11929624112yes—
640C2×C4#1457920914yescomplemented
641C2×C4C24×D7916yes—
642C2×C4C24×D7911yescharacteristic
643C2×C4C24×D7911yescharacteristic
644C2×C4C24×D7916yes—
645C2×C4C24×D7916yes—
646C2×C4C24×D7911yescharacteristic
647C2×C4C24×D7916yes—
648C2×C4C24×D7911yescharacteristic
649C22—28no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—1588no—
657C22—1588no—
658C22—1588no—
659C22C22×#1192962412yes—
660C22C2×#1457920912yes—
661C22#1909939912yes—
662C22C25×D7911yescharacteristic
663C4—26no—
664C4—21no—
665C4—21no—
666C4—26no—
667C4—26no—
668C4—1588no—
669C4—1588no—
670C4—1588no—
671C4C22×#11929624112yes—
672C4C2×#1457920912yes—
673C4C2×#1457920912yes—
674C2—22no—
675C2—22no—
676C2—22no—
677C2—3168no—
678C2C23×#1192962411yescharacteristic
679C2C22×#1457920911yescharacteristic
680C2C2×#1909939911yescharacteristic
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC22×C4×Q8×C79C2
hypercenterC22×C4×Q8D79
hypocenterC79#62788
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #23777496C2semidirect
2. #23777485C2semidirect
3. #23777393C2semidirect
4. #23777265C2semidirect
5. #23777210C2semidirect
6. #23777171C2semidirect
7. #23777109C2semidirect
8. #23777051C2semidirect
9. #23777017C2semidirect
10. #23776995C2semidirect
11. Q8×#11929624C2semidirect
12. #23776833C2semidirect
13. #23776696C2semidirect
14. C4×#14579209C2semidirect
15. C22×C4×Q8×C79C2semidirect
17. #19099298C22semidirect
18. Q8×Dic158C22semidirect
19. #19099292C22semidirect
20. #19099291C22semidirect
21. #19099289C22semidirect
22. #19099286C22semidirect
23. #19099285C22semidirect
24. #19099273C22semidirect
27. #19099254C22semidirect
29. #19099235C22semidirect
30. Q8×D316C22semidirect
33. #19099225C22semidirect
38. #19099185C22semidirect
39. #19099171C22semidirect
46. #19099117C22semidirect
50. #19099100C22semidirect
60. #19099045C22semidirect
63. #19099039C22semidirect
64. C4×#11929625C22semidirect
68. C4×Q8×D79C22semidirect
231. C2×Q8×C79#41semidirect
284. C2×C4×C792−1+4semidirect
355. C22×C4×Q8D79semidirect
356. C79#62788semidirect
539. C2×Q8#11929624semidirect
640. C2×C4#14579209semidirect

Maximal subgroups

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

subgroupindex
#237774962
#237774852
#237773932
#237772652
#237772102
#237771712
#237771092
#237770512
#237770172
#237769952
Q8×#119296242
#237768332
#237766962
C4×#145792092
C22×C4×Q8×C792
#6278879