Finite Group Databasebeta

← #33248657

Subgroups — #33248657

Order 18688.

2106 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989123C211yesmaximal, characteristic
2#22613122C212yesmaximal, complemented
3#22613121C212yesmaximal, complemented
4#22613114C212yesmaximal, complemented
5#22613103C212yesmaximal, complemented
6#22613097C211yesmaximal, characteristic, complemented
7#22613090C211yesmaximal, characteristic
8#22613085C211yesmaximal, characteristic
9#22613077C212yesmaximal, complemented
10#22613077C212yesmaximal, complemented
11#22612423C212yesmaximal, complemented
12#22612412C212yesmaximal, complemented
13#22612406C212yesmaximal, complemented
14#22612391C212yesmaximal, complemented
15#22612373C212yesmaximal, complemented
16#22612369C212yesmaximal, complemented
17#22612333C211yesmaximal, characteristic, complemented
18#22612322C211yesmaximal, characteristic, complemented
19C73×#2378C211yesmaximal, characteristic, complemented
20#17989123C4116yescomplemented
21C2×#14556586C2212yes—
22C2×#14556582C2211yescharacteristic
23C2×#14556580C2211yescharacteristic
24C2×#14556575C2212yes—
25C2×#14556565C2211yescharacteristic
26C2×Q8×Dic73C2211yescharacteristic
27C2×#14556553C2211yescharacteristic
28C2×#14556551C2212yes—
29C2×#14556549C2212yes—
30C2×#14556549C2212yes—
31C2×#14556547C2211yescharacteristic
32C2×#14556547C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C2×C42×D73C2212yes—
35#17988494C2212yes—
36#17988487C2212yes—
37#17988487C2212yes—
38#17988486C2212yes—
39#17988485C2212yes—
40#17988485C2212yes—
41#17988484C2212yes—
42#17988483C2212yes—
43#17988483C2212yes—
44#17988482C2212yes—
45#17988480C2212yes—
46#17988480C2212yes—
47#17988479C2212yes—
48#17988478C2212yes—
49#17988478C2212yes—
50#17988478C2212yes—
51#17988477C2212yes—
52#17988476C2212yes—
53#17988476C2212yes—
54#17988476C2212yes—
55#17988473C2212yes—
56#17988473C2212yes—
57#17988472C2212yes—
58#17988472C2212yes—
59#17988472C2212yes—
60#17988471C2212yes—
61#17988470C2212yes—
62#17988470C2212yes—
63#17988470C2212yes—
64#17988469C2212yes—
65#17988465C2212yes—
66#17988465C2212yes—
67#17988463C2212yes—
68#17988463C2212yes—
69#17988461C2212yes—
70#17988461C2212yes—
71#17988461C2212yes—
72#17988461C2212yes—
73#17988458C2212yes—
74#17988458C2212yes—
75#17988458C2212yes—
76#17988458C2212yes—
77#17988456C2212yes—
78#17988454C2211yescharacteristic
79#17988454C2211yescharacteristic
80#17988451C2212yes—
81#17988451C2212yes—
82#17988450C2211yescharacteristic
83#17988447C2211yescharacteristic
84#17988445C2212yes—
85#17988445C2211yescharacteristic
86#17988445C2211yescharacteristic
87C4⋊C4×Dic73C2212yes—
88C4⋊C4×Dic73C2212yes—
89#17988438C2211yescharacteristic
90#17988438C2211yescharacteristic
91#17988438C2212yes—
92#17988438C2212yes—
93C22⋊C4×Dic73C2212yes—
94#17988434C2212yes—
95#17988434C2212yes—
96#17988432C2212yes—
97#17988432C2212yes—
98C42×Dic73C2212yes—
99C2×C22⋊Q8×C73C2211yescharacteristic
100#391×C73C2212yes—
101#389×C73C2212yes—
102#388×C73C2212yes—
103#388×C73C2212yes—
104#387×C73C2212yes—
105#387×C73C2212yes—
106#381×C73C2211yescharacteristic
107#380×C73C2211yescharacteristic
108C22×D292C2311yescharacteristic
109C22×C22⋊D73C2312yes—
110C23×Dic73C2311yescharacteristic
111C23×Dic73C2311yescharacteristic
112C22×C4×D73C2312yes—
113C22×C4×D73C2312yes—
114C22×C4×D73C2312yes—
115#14556586C2×C4116yescomplemented
116#14556582C2×C418yescomplemented
117#14556580C2×C418yes—
118#14556575C2×C4116yescomplemented
119#14556565C2×C418yes—
120Q8×Dic73C2×C418yescomplemented
121#14556553C2×C418yes—
122#14556551C2×C4116yescomplemented
123#14556549—44no—
124#14556549C2×C4116yescomplemented
125#14556547—42no—
126#14556547—42no—
127C2×C4⋊Dic73C2312yes—
128C2×C4⋊Dic73C2312yes—
129C2×C4⋊Dic73C2312yes—
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2312yes—
132C2×C4⋊Dic73C2312yes—
133C2×#11924007C2312yes—
134C2×#11924007C2312yes—
135C2×#11924007C2312yes—
136C2×#11924007C2312yes—
137C2×#11924007C2312yes—
138C2×#11924007C2312yes—
139C2×#11924007C2312yes—
140C2×#11924007C2312yes—
141C2×#11924007C2312yes—
142C2×C22⋊Dic73C2312yes—
143C2×C22⋊Dic73C2311yescharacteristic
144C2×C22⋊Dic73C2311yescharacteristic
145C2×#11924005C2312yes—
146C2×#11924005C2312yes—
147C2×#11924005C2312yes—
148C2×#11924005C2312yes—
149C2×#11924005C2312yes—
150C2×#11924005C2312yes—
151C2×#11924005C2312yes—
152C2×#11924005C2312yes—
153C2×#11924005C2312yes—
154C2×#11924005C2312yes—
155C2×C4×Dic73C2×C418yescomplemented
156C2×C4×Dic73C2312yes—
157C2×C4×Dic73C2312yes—
158C2×C4×Dic73C2312yes—
159C2×C4×Dic73C2312yes—
160C2×C4×Dic73C2312yes—
161C2×C4×Dic73C2312yes—
162C2×C4×Dic73C2312yes—
163C2×C4×Dic73C2312yes—
164C2×C4×Dic73C2312yes—
165C2×C4×Dic73C2311yescharacteristic
166C2×C4×Dic73C2311yescharacteristic
167C2×C4×Dic73C2311yescharacteristic
168C2×C4×Dic73C2311yescharacteristic
169C42×D73—44no—
170#14556498C2312yes—
171#14556498C2312yes—
172#14556498C2312yes—
173#14556498C2312yes—
174#14556498C2312yes—
175#14556498C2312yes—
176#14556498C2312yes—
177#14556498C2312yes—
178#14556498C2312yes—
179#14556498C2312yes—
180#14556498C2312yes—
181#14556498C2311yescharacteristic
182#14556498C2311yescharacteristic
183#14556498C2312yes—
184#14556498C2312yes—
185#14556498C2312yes—
186#14556498C2312yes—
187#14556498C2312yes—
188C22×Q8×C73C2311yescharacteristic
189C23×C4×C73C2311yescharacteristic
190C22⋊Q8×C73C2×C418yescomplemented
191C2×C4⋊C4×C73C2312yes—
192C2×C4⋊C4×C73C2312yes—
193C2×C4⋊C4×C73C2312yes—
194C2×C4⋊C4×C73C2311yescharacteristic
195C2×C4⋊C4×C73C2312yes—
196C2×C22⋊C4×C73C2311yescharacteristic
197C2×C22⋊C4×C73C2311yescharacteristic
198C2×C22⋊C4×C73C2312yes—
199C2×C22⋊C4×C73C2312yes—
200C2×C42×C73C2312yes—
201C2×C42×C73C2312yes—
202#95×C73C2312yes—
203#95×C73C2311yescharacteristic
204#95×C73C2312yes—
205#95×C73C2311yescharacteristic
206#95×C73C2312yes—
207#95×C73C2312yes—
208#95×C73C2312yes—
209#95×C73C2312yes—
210C23×D73C2412yes—
211C2×D292—42no—
212C2×D292C22×C414yes—
213C2×C22⋊D73—42no—
214C2×C22⋊D73—42no—
215C2×C22⋊D73C22×C418yes—
216C22×Dic73—22no—
217C22×Dic73—22no—
218C22×Dic73—42no—
219C22×Dic73C22×C414yes—
220C22×Dic73C22×C414yes—
221C22×Dic73C2412yes—
222C22×Dic73C2412yes—
223C22×Dic73C2412yes—
224C22×Dic73C2412yes—
225C22×Dic73C2412yes—
226C22×Dic73C2411yescharacteristic
227C22×Dic73C2411yescharacteristic
228C22×Dic73C2411yescharacteristic
229C22×Dic73C2411yescharacteristic
230C2×C4×D73—24no—
231C2×C4×D73—24no—
232C2×C4×D73—42no—
233C2×C4×D73—42no—
234C2×C4×D73—42no—
235C2×C4×D73—42no—
236C2×C4×D73—42no—
237C2×C4×D73—42no—
238C2×C4×D73C22×C418yes—
239C4⋊Dic73—42no—
240C4⋊Dic73—42no—
241C4⋊Dic73—42no—
242C4⋊Dic73C22×C418yes—
243C4⋊Dic73C22×C414yes—
244C4⋊Dic73C22×C418yes—
245#11924007—42no—
246#11924007—42no—
247#11924007—42no—
248#11924007—42no—
249#11924007—42no—
250#11924007—42no—
251#11924007—42no—
252#11924007—42no—
253#11924007C22×C418yes—
254C22⋊Dic73—42no—
255C22⋊Dic73—41no—
256C22⋊Dic73—41no—
257#11924005—42no—
258#11924005—42no—
259#11924005—42no—
260#11924005—42no—
261#11924005—42no—
262#11924005—42no—
263#11924005C22×C418yes—
264#11924005C22×C418yes—
265#11924005C22×C418yes—
266#11924005C22×C418yes—
267C4×Dic73—24no—
268C4×Dic73—24no—
269C4×Dic73—24no—
270C4×Dic73—24no—
271C4×Dic73—42no—
272C4×Dic73—42no—
273C4×Dic73—42no—
274C4×Dic73—42no—
275C4×Dic73C22×C414yes—
276C4×Dic73C22×C414yes—
277C4×Dic73C22×C414yes—
278C4×Dic73C22×C414yes—
279C4×Dic73C22×C418yes—
280C24×C73C2411yescharacteristic
281C2×Q8×C73—42no—
282C2×Q8×C73C22×C414yes—
283C22×C4×C73—42no—
284C22×C4×C73C22×C414yes—
285C22×C4×C73C2412yes—
286C22×C4×C73C2412yes—
287C22×C4×C73C2412yes—
288C22×C4×C73C2412yes—
289C22×C4×C73C2411yescharacteristic
290C22×C4×C73C2412yes—
291C22×C4×C73C2412yes—
292C22×C4×C73C2411yescharacteristic
293C4⋊C4×C73—42no—
294C4⋊C4×C73—42no—
295C4⋊C4×C73—42no—
296C4⋊C4×C73C22×C418yes—
297C4⋊C4×C73C22×C414yes—
298C22⋊C4×C73—42no—
299C22⋊C4×C73—41no—
300C22⋊C4×C73—41no—
301C22⋊C4×C73C22×C418yes—
302C42×C73—42no—
303C42×C73—42no—
304C23×C73—21no—
305C23×C73—21no—
306C23×C73—22no—
307C23×C73—22no—
308C23×C73C23×C412yes—
309C23×C73C2511yescharacteristic
310C22×D73—22no—
311C22×D73—22no—
312C22×D73—22no—
313C22×D73—22no—
314C22×D73—22no—
315C22×D73—22no—
316C22×D73C23×C414yes—
317Q8×C73—44no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—44no—
337C2×C4×C73C23×C414yes—
338C2×C4×C73C23×C414yes—
339C2×C4×C73C23×C412yes—
340C2×C4×C73C23×C412yes—
341C22⋊D73—48no—
342C2×Dic73—21no—
343C2×Dic73—21no—
344C2×Dic73—22no—
345C2×Dic73—22no—
346C2×Dic73—22no—
347C2×Dic73—22no—
348C2×Dic73—28no—
349C2×Dic73—22no—
350C2×Dic73—22no—
351C2×Dic73—22no—
352C2×Dic73—22no—
353C2×Dic73—22no—
354C2×Dic73—22no—
355C2×Dic73—22no—
356C2×Dic73—22no—
357C2×Dic73—22no—
358C2×Dic73—22no—
359C2×Dic73—22no—
360C2×Dic73—22no—
361C2×Dic73—44no—
362C2×Dic73C23×C412yes—
363C2×Dic73C23×C412yes—
364C2×Dic73C23×C412yes—
365C2×Dic73C23×C414yes—
366C2×Dic73C23×C412yes—
367C2×Dic73H(5,𝔽2)12yes—
368C2×Dic732−1+412yes—
369D292—44no—
370C4×D73—216no—
371C4×D73—48no—
372C4×D73—48no—
373C22×C73—22no—
374C22×C73—22no—
375C22×C73—22no—
376C22×C73—42no—
377C22×C73—42no—
378C22×C73C24×C411yescharacteristic
379C22×C73C2×H(5,𝔽2)11yescharacteristic
380C22×C73C2×2−1+411yescharacteristic
381C22×C73#58512yes—
382C22×C73#58512yes—
383C2×D73—24no—
384C2×D73—24no—
385C2×D73—24no—
386C2×D73—42no—
387C2×D73—42no—
388C2×D73—42no—
389C2×D73—42no—
390C4×C73—24no—
391C4×C73—22no—
392C4×C73—22no—
393C4×C73—24no—
394C4×C73—42no—
395C4×C73—42no—
396C4×C73—42no—
397C4×C73—42no—
398Dic73—22no—
399Dic73—22no—
400Dic73—22no—
401Dic73—24no—
402Dic73—42no—
403Dic73—42no—
404Dic73—42no—
405Dic73—42no—
406Dic73#52014yes—
407#34350—731nomaximal, Sylow
408C2×C73—42no—
409C2×C73C2×#52011yescharacteristic
410C2×C73#342811yescharacteristic
411C2×C73#342811yescharacteristic
412C2×C73#352912yes—
413C2×C73#353112yes—
414D73—44no—
415C2×#529—731no—
416#2383—732no—
417#2383—732no—
418#2382—732no—
419#2379—732no—
420#2378—731no—
421#2378D7311yescharacteristic, complemented
422#2377—731no—
423#2377—731no—
424#2376—732no—
425#2376—732no—
426#2298—732no—
427#2296—732no—
428#2295—732no—
429#2293—732no—
430#2290—732no—
431#2290—732no—
432#2285—731no—
433#2283—731no—
434C73#3435011yescharacteristic, complemented, Sylow
435#529—7316no—
436C2×#126—732no—
437C2×#125—731no—
438C2×#124—731no—
439C2×#123—732no—
440C2×C22⋊Q8C2×D7311yescharacteristic
441C2×#121—731no—
442C2×C4×Q8—731no—
443C2×C4×D4—731no—
444C2×C4×D4—732no—
445C2×#117—732no—
446C2×#117—732no—
447C2×#117—731no—
448C2×#117—731no—
449C22×C42—732no—
450C22×C42—731no—
451#391—732no—
452#391C2×D7312yes—
453#390—732no—
454#390—732no—
455#389—732no—
456#389—732no—
457#389—732no—
458#389—732no—
459#389—732no—
460#389—732no—
461#389—732no—
462#389C2×D7312yes—
463#388—732no—
464#388—732no—
465#388—732no—
466#388—732no—
467#388—732no—
468#388—732no—
469#388—732no—
470#388—732no—
471#388—732no—
472#388—732no—
473#388C2×D7312yes—
474#388C2×D7312yes—
475#387—732no—
476#387—732no—
477#387—732no—
478#387—732no—
479#387—732no—
480#387—732no—
481#387—732no—
482#387—732no—
483#387—732no—
484#387—732no—
485#387C2×D7312yes—
486#387C2×D7312yes—
487#386—732no—
488#386—732no—
489#386—732no—
490#386—732no—
491#385—732no—
492#385—732no—
493#385—732no—
494#385—732no—
495#385—732no—
496#385—732no—
497#385—732no—
498#385—732no—
499#384—732no—
500#383—731no—
501#383—731no—
502#382—732no—
503#382—732no—
504#381—731no—
505#381C2×D7311yescharacteristic
506#380—731no—
507#380—732no—
508#380—731no—
509#380—731no—
510#380C2×D7311yescharacteristic
511C4×C4⋊C4—732no—
512C4×C4⋊C4—732no—
513C4×C4⋊C4—731no—
514C4×C4⋊C4—731no—
515C4×C4⋊C4—732no—
516C4×C4⋊C4—732no—
517C4×C22⋊C4—732no—
518C4×C22⋊C4—732no—
519C4×C22⋊C4—732no—
520#376—732no—
521#376—732no—
522C43—732no—
523C22×Q8C22×D7311yescharacteristic
524C22×D4—732no—
525C22×D4—731no—
526C23×C4—732no—
527C23×C4—732no—
528C23×C4—731no—
529C23×C4—731no—
530C23×C4—732no—
531C23×C4C22×D7311yescharacteristic
532#126—7316no—
533#125—738no—
534#124—738no—
535#123—7316no—
536C22⋊Q8C4×D7318yescomplemented
537#121—738no—
538C4×Q8—738no—
539C4×D4—738no—
540C4×D4—7316no—
541#117—2922no—
542#117—2922no—
543#117—2924no—
544#117—7316no—
545C2×C4⋊C4—732no—
546C2×C4⋊C4—732no—
547C2×C4⋊C4—732no—
548C2×C4⋊C4—732no—
549C2×C4⋊C4—732no—
550C2×C4⋊C4—732no—
551C2×C4⋊C4—732no—
552C2×C4⋊C4—732no—
553C2×C4⋊C4—732no—
554C2×C4⋊C4—732no—
555C2×C4⋊C4—732no—
556C2×C4⋊C4—732no—
557C2×C4⋊C4—732no—
558C2×C4⋊C4—731no—
559C2×C4⋊C4—732no—
560C2×C4⋊C4C22×D7312yes—
561C2×C4⋊C4C22×D7312yes—
562C2×C4⋊C4C22×D7312yes—
563C2×C4⋊C4C22×D7312yes—
564C2×C4⋊C4C22×D7311yescharacteristic
565C2×C22⋊C4—731no—
566C2×C22⋊C4—731no—
567C2×C22⋊C4—732no—
568C2×C22⋊C4—732no—
569C2×C22⋊C4—732no—
570C2×C22⋊C4—732no—
571C2×C22⋊C4—732no—
572C2×C22⋊C4—732no—
573C2×C22⋊C4—732no—
574C2×C22⋊C4—732no—
575C2×C22⋊C4—732no—
576C2×C22⋊C4—732no—
577C2×C22⋊C4—732no—
578C2×C22⋊C4C22×D7311yescharacteristic
579C2×C22⋊C4C22×D7311yescharacteristic
580C2×C22⋊C4C22×D7312yes—
581C2×C22⋊C4C22×D7312yes—
582C2×C42—2924no—
583C2×C42—732no—
584C2×C42—732no—
585C2×C42—732no—
586C2×C42—732no—
587C2×C42—738no—
588C2×C42—731no—
589C2×C42—732no—
590C2×C42—731no—
591C2×C42—731no—
592C2×C42—731no—
593C2×C42—732no—
594C2×C42—732no—
595C2×C42—732no—
596C2×C42—732no—
597C2×C42C22×D7312yes—
598C2×C42C22×D7312yes—
599#95—732no—
600#95—732no—
601#95—732no—
602#95—732no—
603#95—732no—
604#95—732no—
605#95—732no—
606#95—732no—
607#95—732no—
608#95—732no—
609#95—732no—
610#95—732no—
611#95—732no—
612#95—731no—
613#95—731no—
614#95—732no—
615#95—732no—
616#95—732no—
617#95C22×D7312yes—
618#95C22×D7312yes—
619#95C22×D7312yes—
620#95C22×D7312yes—
621#95C22×D7312yes—
622#95C22×D7311yescharacteristic
623#95C22×D7311yescharacteristic
624#95C22×D7312yes—
625C24—732no—
626C24C23×D7311yescharacteristic
627C2×Q8—42no—
628C2×Q8C2×C4×D7314yes—
629C2×D4—2922no—
630C2×D4—2922no—
631C2×D4—2922no—
632C2×D4—738no—
633C2×D4—734no—
634C22×C4—42no—
635C22×C4—2922no—
636C22×C4—2922no—
637C22×C4—2922no—
638C22×C4—2922no—
639C22×C4—2922no—
640C22×C4—2922no—
641C22×C4—2922no—
642C22×C4—734no—
643C22×C4—731no—
644C22×C4—734no—
645C22×C4—732no—
646C22×C4—731no—
647C22×C4—731no—
648C22×C4—731no—
649C22×C4—738no—
650C22×C4—732no—
651C22×C4—732no—
652C22×C4—732no—
653C22×C4—732no—
654C22×C4—1464no—
655C22×C4—1464no—
656C22×C4—1462no—
657C22×C4—1462no—
658C22×C4C2×C4×D7314yes—
659C22×C4C23×D7312yes—
660C22×C4C23×D7312yes—
661C22×C4C23×D7312yes—
662C22×C4C23×D7312yes—
663C22×C4C23×D7311yescharacteristic
664C22×C4C23×D7312yes—
665C22×C4C23×D7311yescharacteristic
666C22×C4C23×D7312yes—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—2922no—
671C4⋊C4—2922no—
672C4⋊C4—2922no—
673C4⋊C4—2922no—
674C4⋊C4—2922no—
675C4⋊C4—2922no—
676C4⋊C4—2922no—
677C4⋊C4—2922no—
678C4⋊C4—2922no—
679C4⋊C4—2922no—
680C4⋊C4—2922no—
681C4⋊C4—738no—
682C4⋊C4—738no—
683C4⋊C4—734no—
684C4⋊C4—738no—
685C4⋊C4C2×C4×D7318yes—
686C4⋊C4C2×C4×D7314yes—
687C22⋊C4—42no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—2922no—
691C22⋊C4—2922no—
692C22⋊C4—2922no—
693C22⋊C4—2922no—
694C22⋊C4—2922no—
695C22⋊C4—2922no—
696C22⋊C4—2922no—
697C22⋊C4—2921no—
698C22⋊C4—2921no—
699C22⋊C4—738no—
700C22⋊C4—738no—
701C22⋊C4—738no—
702C22⋊C4—738no—
703C22⋊C4C2×C4×D7318yes—
704C42—42no—
705C42—42no—
706C42—2922no—
707C42—2922no—
708C42—2922no—
709C42—2922no—
710C42—734no—
711C42—734no—
712C42—734no—
713C42—734no—
714C42—738no—
715C42—1464no—
716C42—1464no—
717C42—1464no—
718C42—1464no—
719C23—21no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—734no—
724C23—1462no—
725C23—1462no—
726C23—1462no—
727C23—1462no—
728C23—1462no—
729C23—1462no—
730C23C22×C4×D7312yes—
731C23C24×D7311yescharacteristic
732Q8—44no—
733D4—2924no—
734D4—2928no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—44no—
754C2×C4—2928no—
755C2×C4—2928no—
756C2×C4—2924no—
757C2×C4—732no—
758C2×C4—732no—
759C2×C4—732no—
760C2×C4—732no—
761C2×C4—732no—
762C2×C4—732no—
763C2×C4—734no—
764C2×C4—14616no—
765C2×C4—1462no—
766C2×C4—1462no—
767C2×C4—1462no—
768C2×C4—1462no—
769C2×C4—1462no—
770C2×C4—1462no—
771C2×C4—1462no—
772C2×C4—1462no—
773C2×C4—1462no—
774C2×C4—1462no—
775C2×C4—1462no—
776C2×C4—1462no—
777C2×C4—1468no—
778C2×C4—1461no—
779C2×C4—1461no—
780C2×C4—1462no—
781C2×C4—1462no—
782C2×C4—1462no—
783C2×C4—1462no—
784C2×C4C22×C4×D7312yes—
785C2×C4C22×C4×D7312yes—
786C2×C4C22×C4×D7314yes—
787C2×C4C22×C4×D7314yes—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—42no—
792C22—42no—
793C22—2922no—
794C22—2922no—
795C22—2922no—
796C22—2922no—
797C22—1464no—
798C22—1464no—
799C22—1464no—
800C22C23×C4×D7311yescharacteristic
801C22H(5,𝔽2)×D7311yescharacteristic
802C222−1+4×D7311yescharacteristic
803C22#1798942212yes—
804C22#1798942412yes—
805C4—24no—
806C4—22no—
807C4—22no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—2922no—
814C4—2922no—
815C4—2922no—
816C4—2922no—
817C4—734no—
818C4—1462no—
819C4—1462no—
820C4—1462no—
821C4—1464no—
822C2—42no—
823C2—2924no—
824C2#520×D7311yescharacteristic
825C2#2262312911yescharacteristic
826C2#2262313311yescharacteristic
827C2#2262406812yes—
828C2#2262407712yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2378C2
socle, cosocleC23×C73C25
prime radicalC2×#14556565C22
hypercenter#2378D73
hypocenterC73#34350
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2378

Complements

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

NH ≅ G/Ntype
2. #22613122C2semidirect
3. #22613121C2semidirect
4. #22613114C2semidirect
5. #22613103C2semidirect
6. #22613097C2semidirect
9. #22613077C2semidirect
10. #22613077C2semidirect
11. #22612423C2semidirect
12. #22612412C2semidirect
13. #22612406C2semidirect
14. #22612391C2semidirect
15. #22612373C2semidirect
16. #22612369C2semidirect
17. #22612333C2semidirect
18. #22612322C2semidirect
19. C73×#2378C2semidirect
20. #17989123C4semidirect
115. #14556586C2×C4semidirect
116. #14556582C2×C4semidirect
118. #14556575C2×C4semidirect
120. Q8×Dic73C2×C4semidirect
122. #14556551C2×C4semidirect
124. #14556549C2×C4semidirect
155. C2×C4×Dic73C2×C4semidirect
190. C22⋊Q8×C73C2×C4semidirect
421. #2378D73semidirect
434. C73#34350semidirect
536. C22⋊Q8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891232
#226131222
#226131212
#226131142
#226131032
#226130972
#226130902
#226130852
#226130772
#226124232
#226124122
#226124062
#226123912
#226123732
#226123692
#226123332
#226123222
C73×#23782
#3435073