Finite Group Databasebeta

← #33994534

Subgroups — #33994534

Order 18688.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989423C212yesmaximal, complemented
2#22623723C214yesmaximal, complemented
3#22623720C214yesmaximal, complemented
4#22623713C214yesmaximal, complemented
5#22623706C214yesmaximal, complemented
6#22623700C214yesmaximal, complemented
7#22623694C214yesmaximal, complemented
8#22623692C218yesmaximal, complemented
9#22623414C2116yesmaximal, complemented
10#22623264C211yesmaximal, characteristic, complemented
11#22623258C214yesmaximal, complemented
12C2×#17989133C212yesmaximal, complemented
13#532×D73C214yesmaximal, complemented
14C2×#17989055C211yesmaximal, characteristic, complemented
15C73×#3449C211yesmaximal, characteristic, complemented
16#17989423—232no—
17C2×#14556639C2214yescomplemented
18C2×#14556638C2214yescomplemented
19C2×#14556638C2214yescomplemented
20C2×#14556637C2214yescomplemented
21C2×#14556637C2214yescomplemented
22C2×#14556636C2218yescomplemented
23C2×#14556636C2214yescomplemented
24C22×#11924028C2211yescharacteristic
25C22×#11924028C2212yescomplemented
26C22×#11924028C2218yescomplemented
27C2×#41×D73C2218yescomplemented
28C2×#41×D73C2218yescomplemented
29#17989255C22116yescomplemented
30#17989250C22116yescomplemented
31#17989247C22116yescomplemented
32#17989243C22116yescomplemented
33#17989239C22116yescomplemented
34#17989235C22132yescomplemented
35#17989234C22116yescomplemented
36#17989229C22132yescomplemented
37#17989228C22116yescomplemented
38#17989224C22132yescomplemented
39#17989221C22116yescomplemented
40#17989219C22132yescomplemented
41#17989168C2214yescomplemented
42#17989164C22116yescomplemented
43#17989163C2214yescomplemented
44#17989162C2218yescomplemented
45#17989157C2218yescomplemented
46#17989156C2214yescomplemented
47#17989155C2218yescomplemented
48#17989150C2218yescomplemented
49#17989149C2214yescomplemented
50#17989145C22116yescomplemented
51#17989138C2214yescomplemented
52#17989137C2214yescomplemented
53#17989136C2218yescomplemented
54#17989135C2214yescomplemented
55#17989134C22116yescomplemented
56#17989133C2214yescomplemented
57#17989133C2218yescomplemented
58#17989133C2218yescomplemented
59#17989133C2214yescomplemented
60#17989133C2214yescomplemented
61#17989133C2214yescomplemented
62#17989132C22116yescomplemented
63C2×#14556589C2212yescomplemented
64C4⋊Q8×D73C2214yescomplemented
65C2×#14556587C2212yescomplemented
66#127×D73C2214yescomplemented
67C2×#14556580C2212yescomplemented
68C2×#14556578C2212yescomplemented
69#124×D73C2218yescomplemented
70#17989099C2218yescomplemented
71#17989096C22132yescomplemented
72C2×#14556563C2218yescomplemented
73#121×D73C22116yescomplemented
74#17989055C2218yescomplemented
75#17989055C2214yescomplemented
76#17989055C2214yescomplemented
77C2×#14556556C2212yescomplemented
78C2×#14556553C2212yescomplemented
79C2×C4×C22⋊D73C2218yescomplemented
80C2×#14556551C2214yescomplemented
81C4×D4×D73C22116yescomplemented
82C2×#14556548C2212yescomplemented
83C22×C4×Dic73C2211yescharacteristic, complemented
84C2×C42×D73C2212yescomplemented
85C22×#41×C73C2212yescomplemented
86#537×C73C2214yescomplemented
87#536×C73C2214yescomplemented
88#535×C73C2214yescomplemented
89#534×C73C2214yescomplemented
90#532×C73C2214yescomplemented
91#525×C73C2218yescomplemented
92C2×#117×C73C2211yescharacteristic, complemented
93#14556639—232no—
94#14556638—232no—
95#14556638—232no—
96#14556637—232no—
97#14556637—232no—
98#14556636—232no—
99#14556636—264no—
100C2×#11924029C2318yes—
101C2×#11924029C2318yes—
102C2×#11924028—264no—
103C2×#11924028—216no—
104C2×#11924028D4116yescomplemented
105C2×#11924028C2314yes—
106C2×#11924028C2314yes—
107C2×#11924028C2314yes—
108C2×#11924028C2314yes—
109C2×#11924028C23116yes—
110C2×#11924028C23116yes—
111C2×#11924028C2318yes—
112C2×#11924028C2318yes—
113C2×#11924028C2314yes—
114C2×#11924028C2314yes—
115C2×#11924027C23116yes—
116C2×#11924027C2318yes—
117C2×#11924027C23116yes—
118C2×#11924027C2318yes—
119#41×D73—264no—
120#41×D73—264no—
121C22×Dic146C2312yes—
122C22×Dic146C2318yes—
123C22×Dic146C2311yescharacteristic
124C2×Q8×D73C2318yes—
125C2×Q8×D73C2318yes—
126C22×D292C2312yes—
127C22×D292C2318yes—
128C22×D292C2311yescharacteristic
129C22×C22⋊D73C2314yes—
130C22×C22⋊D73C23116yes—
131C22×C22⋊D73C2318yes—
132C22×C22⋊D73C2312yes—
133C2×D4×D73C2318yes—
134C2×D4×D73C23116yes—
135C2×D4×D73C23116yes—
136C2×D4×D73C2318yes—
137C2×D4×D73C23116yes—
138C23×Dic73C2312yes—
139C22×C4×D73C23116yes—
140C22×C4×D73C2314yes—
141C22×C4×D73C2314yes—
142C22×C4×D73C2312yes—
143#14556591C2314yes—
144#14556590C23116yes—
145#14556589C2314yes—
146#14556589C2314yes—
147#14556589C2318yes—
148#14556588C2314yes—
149#14556587C2314yes—
150#14556587C23116yes—
151#14556587C2314yes—
152#14556587C2318yes—
153#14556580C2314yes—
154#14556580C2314yes—
155#14556580C2318yes—
156#14556579C2318yes—
157#14556578C2314yes—
158#14556578C2314yes—
159#14556578C2318yes—
160#14556577C23132yes—
161#14556576C23132yes—
162#14556575C23116yes—
163#14556573C23132yes—
164#14556571C23116yes—
165#14556569C23132yes—
166#14556568C23132yes—
167#14556566C23116yes—
168#14556566C23116yes—
169#14556565C23116yes—
170#14556564C23132yes—
171#14556564C23132yes—
172#14556563C23116yes—
173#14556563C23116yes—
174#14556563C23116yes—
175#14556563C23116yes—
176#14556563C23132yes—
177#14556562C23116yes—
178#14556561C23132yes—
179#14556561C23116yes—
180#14556559C23132yes—
181#14556556C2318yes—
182#14556556C2318yes—
183C4×D292C23116yes—
184D4×Dic73C23116yes—
185#14556553C23116yes—
186#14556553C2318yes—
187#14556553C2318yes—
188C4×C22⋊D73C23116yes—
189C4×C22⋊D73C23116yes—
190C4×C22⋊D73C23116yes—
191C4×C22⋊D73C23116yes—
192#14556551C23132yes—
193#14556551C23116yes—
194#14556551C23116yes—
195#14556548C2318yes—
196#14556548C2318yes—
197C2×#11924007C2318yes—
198C2×#11924007C2314yes—
199C4⋊C4×D73C23116yes—
200C2×C22⋊Dic73C2318yes—
201C2×#11924005C2314yes—
202C2×#11924005C2318yes—
203C22⋊C4×D73C23132yes—
204C2×C4×Dic73C2312yes—
205C2×C4×Dic73C2314yes—
206C2×C4×Dic73C2311yescharacteristic
207C2×C4×Dic73C2311yescharacteristic
208C2×C4×Dic73C2312yes—
209C2×C4×Dic73C2314yes—
210C2×C4×Dic73C2312yes—
211C42×D73C2314yes—
212C42×D73C2318yes—
213C42×D73C2314yes—
214C2×#41×C73—216no—
215C2×#41×C73C2314yes—
216C2×#41×C73C2314yes—
217C2×#41×C73C2314yes—
218C2×#41×C73C2314yes—
219C22×Q8×C73C2312yes—
220C22×D4×C73C2312yes—
221C22×D4×C73C2314yes—
222C23×C4×C73C2314yes—
223C23×C4×C73C2311yescharacteristic
224C4⋊Q8×C73C2314yes—
225#127×C73C2314yes—
226#124×C73C2318yes—
227#123×C73C23116yes—
228C22⋊Q8×C73C23116yes—
229#121×C73C23116yes—
230#121×C73C23116yes—
231#120×C73C23116yes—
232C4×D4×C73C23116yes—
233#117×C73C2314yes—
234#117×C73C2314yes—
235C2×C4⋊C4×C73C2312yes—
236C2×C22⋊C4×C73C2312yes—
237C2×C42×C73C2312yes—
238C23×D73C24116yes—
239C23×D73C2414yes—
240C23×D73C2412yes—
241#11924029—232no—
242#11924029—232no—
243#11924028—216no—
244#11924028—216no—
245#11924028—216no—
246#11924028—216no—
247#11924028—264no—
248#11924028—232no—
249#11924028—264no—
250#11924028—232no—
251#11924028C2×D4132yescomplemented
252#11924028C2×D4132yescomplemented
253#11924027—264no—
254#11924027—264no—
255#11924027—232no—
256#11924027—232no—
257C2×Dic146—28no—
258C2×Dic146—232no—
259C2×Dic146C2×D418yescomplemented
260C2×Dic146C24116yes—
261C2×Dic146C2414yes—
262C2×Dic146C2414yes—
263C2×Dic146C2414yes—
264Q8×D73—232no—
265Q8×D73—232no—
266C2×D292—28no—
267C2×D292—232no—
268C2×D292C2×D418yescomplemented
269C2×D292C24116yes—
270C2×D292C2414yes—
271C2×D292C2414yes—
272C2×D292C24116yes—
273C2×D292C2414yes—
274C2×C22⋊D73—216no—
275C2×C22⋊D73—264no—
276C2×C22⋊D73—416no—
277C2×C22⋊D73C2×D4116yescomplemented
278C2×C22⋊D73C24116yes—
279C2×C22⋊D73C24116yes—
280C2×C22⋊D73C2418yes—
281C2×C22⋊D73C2418yes—
282C2×C22⋊D73C24116yes—
283C2×C22⋊D73C24116yes—
284C2×C22⋊D73C2418yes—
285D4×D73—264no—
286D4×D73—264no—
287D4×D73—232no—
288D4×D73—232no—
289D4×D73—432no—
290C22×Dic73—44no—
291C22×Dic73C2412yes—
292C22×Dic73C2414yes—
293C22×Dic73C2414yes—
294C22×Dic73C24116yes—
295C22×Dic73C2414yes—
296C22×Dic73C2412yes—
297C22×Dic73C2412yes—
298C2×C4×D73—216no—
299C2×C4×D73—264no—
300C2×C4×D73—48no—
301C2×C4×D73C2×D4116yescomplemented
302C2×C4×D73C2418yes—
303C2×C4×D73C24116yes—
304C2×C4×D73C24116yes—
305C2×C4×D73C2418yes—
306C2×C4×D73C2418yes—
307C2×C4×D73C2418yes—
308C2×C4×D73C2414yes—
309C2×C4×D73C2414yes—
310C4⋊Dic73C24116yes—
311#11924007C24116yes—
312#11924007C24116yes—
313#11924007C24116yes—
314C22⋊Dic73C24116yes—
315C22⋊Dic73C24116yes—
316#11924005C24116yes—
317#11924005C24132yes—
318#11924005C24116yes—
319#11924005C24116yes—
320C4×Dic73C2412yes—
321C4×Dic73C2411yescharacteristic
322C4×Dic73C2411yescharacteristic
323C4×Dic73C2418yes—
324C4×Dic73C2418yes—
325C4×Dic73C2412yes—
326C4×Dic73C2412yes—
327C4×Dic73C2414yes—
328C4×Dic73C2414yes—
329C24×C73C2414yes—
330C24×C73C2411yescharacteristic
331#41×C73—216no—
332#41×C73—216no—
333#41×C73—216no—
334#41×C73—216no—
335C2×Q8×C73—28no—
336C2×Q8×C73C2414yes—
337C2×Q8×C73C2414yes—
338C2×D4×C73—216no—
339C2×D4×C73—28no—
340C2×D4×C73C2418yes—
341C2×D4×C73C2418yes—
342C2×D4×C73C2414yes—
343C2×D4×C73C2414yes—
344C2×D4×C73C24116yes—
345C22×C4×C73—216no—
346C22×C4×C73C2×D418yescomplemented
347C22×C4×C73C2418yes—
348C22×C4×C73C2418yes—
349C22×C4×C73C2414yes—
350C22×C4×C73C2414yes—
351C22×C4×C73C2411yescharacteristic
352C22×C4×C73C2411yescharacteristic
353C22×C4×C73C2412yes—
354C22×C4×C73C2412yes—
355C4⋊C4×C73C2418yes—
356C4⋊C4×C73C24116yes—
357C22⋊C4×C73C2418yes—
358C22⋊C4×C73C24132yes—
359C42×C73C2414yes—
360C42×C73C2414yes—
361C23×C73—28no—
362C23×C73—42no—
363C23×C73—48no—
364C23×C73C22×D414yes—
365C23×C73C2518yes—
366C23×C73C2512yes—
367C23×C73C2511yescharacteristic
368C22×D73—28no—
369C22×D73—232no—
370C22×D73—44no—
371C22×D73—432no—
372C22×D73—48no—
373C22×D73C22×D418yes—
374C22×D73C2518yes—
375C22×D73C2514yes—
376Q8×C73—28no—
377Q8×C73—28no—
378D4×C73—216no—
379D4×C73—216no—
380D4×C73—28no—
381D4×C73—28no—
382D4×C73—416no—
383C2×C4×C73—28no—
384C2×C4×C73—216no—
385C2×C4×C73—216no—
386C2×C4×C73—44no—
387C2×C4×C73C22×D418yes—
388C2×C4×C73C22×D418yes—
389C2×C4×C73C22×D414yes—
390C2×C4×C73C22×D414yes—
391C2×C4×C73C2518yes—
392C2×C4×C73C2518yes—
393C2×C4×C73C2511yescharacteristic
394C2×C4×C73C2512yes—
395C2×C4×C73C2511yescharacteristic
396C22⋊D73—216no—
397C22⋊D73—216no—
398C22⋊D73—232no—
399C22⋊D73—232no—
400C22⋊D73—232no—
401C22⋊D73—416no—
402C22⋊D73C22×D4132yes—
403C2×Dic73—28no—
404C2×Dic73—232no—
405C2×Dic73—24no—
406C2×Dic73—28no—
407C2×Dic73—44no—
408C2×Dic73—42no—
409C2×Dic73C22×D418yes—
410C2×Dic73C2512yes—
411C2×Dic73C2514yes—
412C2×Dic73C2518yes—
413C2×Dic73C2514yes—
414C2×Dic73C2512yes—
415D292—232no—
416D292—28no—
417D292—28no—
418D292—416no—
419D292C22×D4116yes—
420C4×D73—232no—
421C4×D73—216no—
422C4×D73—216no—
423C4×D73—232no—
424C4×D73—216no—
425C4×D73—48no—
426C4×D73C22×D4116yes—
427C4×D73C22×D4116yes—
428Dic146—28no—
429Dic146—28no—
430Dic146—232no—
431Dic146C22×D4116yes—
432C22×C73—22no—
433C22×C73—24no—
434C22×C73—28no—
435C22×C73—216no—
436C22×C73—44no—
437C22×C73—88no—
438C22×C73C23×D414yes—
439C22×C73C23×D412yes—
440C22×C73C2611yescharacteristic
441C2×D73—28no—
442C2×D73—28no—
443C2×D73—216no—
444C2×D73—48no—
445C2×D73—832no—
446C2×D73—88no—
447C2×D73C23×D418yes—
448C4×C73—28no—
449C4×C73—28no—
450C4×C73C23×D412yes—
451C4×C73C23×D414yes—
452C4×C73C23×D412yes—
453Dic73—28no—
454Dic73—22no—
455Dic73—24no—
456Dic73C23×D418yes—
457Dic73#58514yescomplemented
458#62812—731nomaximal, Sylow
459C2×C73—22no—
460C2×C73—24no—
461C2×C73—48no—
462C2×C73C24×D411yescharacteristic
463C2×C73C2×#58512yes—
464D73—28no—
465D73—48no—
466C2×#585—732no—
467#3500—734no—
468#3500—734no—
469#3499—734no—
470#3498—734no—
471#3497—734no—
472#3496—734no—
473#3496—738no—
474D4×#41—7316no—
475#3449—734no—
476#3449—731no—
477#3449D7311yescharacteristic, complemented
478C2×#532—732no—
479C2×#532—734no—
480C2×C4×#41—731no—
481C73#6281211yescharacteristic, complemented, Sylow
482#585—14632no—
483C2×2−1+4—734no—
484C2×2−1+4—734no—
485C2×2−1+4—734no—
486C2×H(5,𝔽2)—734no—
487C2×H(5,𝔽2)—734no—
488C2×H(5,𝔽2)—738no—
489C2×H(5,𝔽2)—734no—
490C22×#41—738no—
491C22×#41—738no—
492C22×#41—731no—
493C22×#41—732no—
494C22×#41—738no—
495C22×#41C2×D7312yescomplemented
496#550—7316no—
497D4×Q8—7316no—
498#548—7316no—
499#548—7316no—
500#547—7332no—
501#547—7316no—
502#546—7332no—
503#546—7316no—
504#546—7316no—
505#546—7332no—
506D42—7316no—
507D42—7332no—
508#537—7316no—
509#537—734no—
510#537C2×D7314yescomplemented
511#536—738no—
512#536—738no—
513#536—734no—
514#536C2×D7314yescomplemented
515#535—738no—
516#535—738no—
517#535—734no—
518#535C2×D7314yescomplemented
519#534—7316no—
520#534—734no—
521#534C2×D7314yescomplemented
522#532—734no—
523#532—734no—
524#532—738no—
525#532—738no—
526#532—734no—
527#532—734no—
528#532—734no—
529#532—734no—
530#532—738no—
531#532—7316no—
532#532—7316no—
533#532—734no—
534#532C2×D7314yescomplemented
535C2×C4⋊Q8—732no—
536C2×C4⋊Q8—734no—
537C2×#127—732no—
538C2×#127—734no—
539C2×#124—732no—
540C2×#124—732no—
541C2×#124—738no—
542#525—7332no—
543#525—738no—
544#525C2×D7318yescomplemented
545C2×#121—738no—
546C2×#121—7316no—
547C4×#41—738no—
548C4×#41—734no—
549C4×#41—734no—
550C2×C4×Q8—732no—
551C2×C4×D4—738no—
552C2×C4×D4—7316no—
553C2×C4×D4—732no—
554C2×C4×D4—734no—
555C2×#117—732no—
556C2×#117C2×D7311yescharacteristic, complemented
557C22×C42—731no—
558C22×C42—732no—
5592−1+4—14632no—
5602−1+4—14632no—
5612−1+4—14632no—
562H(5,𝔽2)—14664no—
563H(5,𝔽2)—14632no—
564H(5,𝔽2)—14632no—
565H(5,𝔽2)—14632no—
566C2×#41—216no—
567C2×#41—738no—
568C2×#41—738no—
569C2×#41—738no—
570C2×#41—7316no—
571C2×#41—7316no—
572C2×#41—738no—
573C2×#41—7316no—
574C2×#41—734no—
575C2×#41—734no—
576C2×#41—7316no—
577C2×#41—734no—
578C2×#41—734no—
579C2×#41—734no—
580C2×#41—734no—
581C2×#41—738no—
582C2×#41—7316no—
583C2×#41—738no—
584C2×#41—14664no—
585C2×#41—14664no—
586C2×#41—14664no—
587C2×#41—14616no—
588C2×#41C22×D7314yes—
589C2×#41C22×D7314yes—
590C2×#41C22×D7314yes—
591C2×#41C22×D7314yes—
592C22×Q8—738no—
593C22×Q8—738no—
594C22×Q8—731no—
595C22×Q8—732no—
596C22×Q8—738no—
597C22×Q8C22×D7312yes—
598C22×D4—738no—
599C22×D4—7316no—
600C22×D4—732no—
601C22×D4—734no—
602C22×D4—7316no—
603C22×D4—7316no—
604C22×D4—738no—
605C22×D4—7316no—
606C22×D4—738no—
607C22×D4—731no—
608C22×D4—732no—
609C22×D4—738no—
610C22×D4C22×D7314yes—
611C22×D4C22×D7312yes—
612C23×C4—732no—
613C23×C4—734no—
614C23×C4—732no—
615C23×C4—7316no—
616C23×C4—734no—
617C23×C4C22×D7314yes—
618C23×C4C22×D7311yescharacteristic
619C4⋊Q8—734no—
620C4⋊Q8—734no—
621C4⋊Q8—738no—
622C4⋊Q8—7316no—
623C4⋊Q8—734no—
624C4⋊Q8C22×D7314yes—
625#127—734no—
626#127—734no—
627#127—738no—
628#127—7316no—
629#127—734no—
630#127C22×D7314yes—
631#124—734no—
632#124—734no—
633#124—738no—
634#124—734no—
635#124—734no—
636#124—738no—
637#124—7332no—
638#124—738no—
639#124C22×D7318yes—
640#123—7332no—
641#123—7332no—
642#123—7316no—
643#123C22×D73116yes—
644C22⋊Q8—7332no—
645C22⋊Q8—7316no—
646C22⋊Q8—7332no—
647C22⋊Q8C22×D73116yes—
648#121—7316no—
649#121—7316no—
650#121—7316no—
651#121—7316no—
652#121—7316no—
653#121—7332no—
654#121—7316no—
655#121—7316no—
656#121—7316no—
657#121—7332no—
658#121—7332no—
659#121C22×D73116yes—
660#121C22×D73116yes—
661#120—7332no—
662#120—7332no—
663#120—7316no—
664#120C22×D73116yes—
665C4×Q8—738no—
666C4×Q8—738no—
667C4×D4—7316no—
668C4×D4—7316no—
669C4×D4—7316no—
670C4×D4—7316no—
671C4×D4—7316no—
672C4×D4—738no—
673C4×D4—738no—
674C4×D4—7316no—
675C4×D4—7316no—
676C4×D4—7316no—
677C4×D4—7332no—
678C4×D4—7316no—
679C4×D4C22×D73116yes—
680#117—738no—
681#117—738no—
682#117C22×D7314yes—
683#117C22×D7314yes—
684C2×C4⋊C4—734no—
685C2×C4⋊C4—738no—
686C2×C4⋊C4—7316no—
687C2×C4⋊C4C22×D7312yes—
688C2×C22⋊C4—738no—
689C2×C22⋊C4—734no—
690C2×C22⋊C4—738no—
691C2×C22⋊C4—7332no—
692C2×C22⋊C4C22×D7312yes—
693C2×C42—731no—
694C2×C42—734no—
695C2×C42—732no—
696C2×C42—734no—
697C2×C42—732no—
698C2×C42—732no—
699C2×C42—731no—
700C2×C42—738no—
701C2×C42—734no—
702C2×C42—734no—
703C2×C42C22×D7312yes—
704C24—732no—
705C24—7316no—
706C24—734no—
707C24C23×D7314yes—
708C24C23×D7311yescharacteristic
709#41—216no—
710#41—216no—
711#41—216no—
712#41—216no—
713#41—7332no—
714#41—7332no—
715#41—14664no—
716#41—14664no—
717#41—14632no—
718#41—14632no—
719#41—14664no—
720#41—14632no—
721#41—14632no—
722#41—14664no—
723#41—14632no—
724#41—14632no—
725#41—14616no—
726#41—14616no—
727#41—14616no—
728#41—14616no—
729C2×Q8—28no—
730C2×Q8—738no—
731C2×Q8—734no—
732C2×Q8—7316no—
733C2×Q8—734no—
734C2×Q8—734no—
735C2×Q8—14632no—
736C2×Q8—14632no—
737C2×Q8—14632no—
738C2×Q8—1468no—
739C2×Q8C23×D7314yes—
740C2×Q8C23×D7314yes—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—29232no—
744C2×D4—29216no—
745C2×D4—7316no—
746C2×D4—7316no—
747C2×D4—738no—
748C2×D4—7316no—
749C2×D4—7316no—
750C2×D4—738no—
751C2×D4—738no—
752C2×D4—7316no—
753C2×D4—738no—
754C2×D4—7316no—
755C2×D4—734no—
756C2×D4—7316no—
757C2×D4—734no—
758C2×D4—734no—
759C2×D4—14632no—
760C2×D4—14632no—
761C2×D4—14664no—
762C2×D4—14632no—
763C2×D4—14664no—
764C2×D4—14664no—
765C2×D4—14616no—
766C2×D4—1468no—
767C2×D4C23×D7318yes—
768C2×D4C23×D7318yes—
769C2×D4C23×D7314yes—
770C2×D4C23×D7314yes—
771C2×D4C23×D73116yes—
772C22×C4—216no—
773C22×C4—2928no—
774C22×C4—2924no—
775C22×C4—734no—
776C22×C4—732no—
777C22×C4—738no—
778C22×C4—732no—
779C22×C4—7316no—
780C22×C4—734no—
781C22×C4—734no—
782C22×C4—732no—
783C22×C4—734no—
784C22×C4—734no—
785C22×C4—7316no—
786C22×C4—738no—
787C22×C4—7316no—
788C22×C4—7316no—
789C22×C4—738no—
790C22×C4—738no—
791C22×C4—14664no—
792C22×C4—14616no—
793C22×C4D4×D7318yescomplemented
794C22×C4C23×D7314yes—
795C22×C4C23×D7318yes—
796C22×C4C23×D7318yes—
797C22×C4C23×D7314yes—
798C22×C4C23×D7311yescharacteristic
799C22×C4C23×D7312yes—
800C22×C4C23×D7311yescharacteristic
801C22×C4C23×D7312yes—
802C4⋊C4—7316no—
803C4⋊C4—7316no—
804C4⋊C4—7316no—
805C4⋊C4—7316no—
806C4⋊C4C23×D73116yes—
807C4⋊C4C23×D7318yes—
808C22⋊C4—7316no—
809C22⋊C4—7316no—
810C22⋊C4—7316no—
811C22⋊C4—7316no—
812C22⋊C4—7316no—
813C22⋊C4—7332no—
814C22⋊C4C23×D73132yes—
815C22⋊C4C23×D7318yes—
816C42—731no—
817C42—731no—
818C42—732no—
819C42—738no—
820C42—734no—
821C42—738no—
822C42—734no—
823C42—732no—
824C42—732no—
825C42C23×D7314yes—
826C42C23×D7314yes—
827C23—28no—
828C23—42no—
829C23—48no—
830C23—2924no—
831C23—2928no—
832C23—29232no—
833C23—738no—
834C23—734no—
835C23—738no—
836C23—14632no—
837C23—1468no—
838C23C2×D4×D7314yes—
839C23C24×D7318yes—
840C23C24×D7312yes—
841C23C24×D7311yescharacteristic
842Q8—28no—
843Q8—28no—
844Q8—7316no—
845Q8—14632no—
846Q8—1468no—
847Q8—1468no—
848D4—216no—
849D4—216no—
850D4—28no—
851D4—28no—
852D4—416no—
853D4—29216no—
854D4—29216no—
855D4—7332no—
856D4—7316no—
857D4—14632no—
858D4—14632no—
859D4—14632no—
860D4—14632no—
861D4—14616no—
862D4—14616no—
863D4—1468no—
864D4—1468no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—216no—
868C2×C4—44no—
869C2×C4—2928no—
870C2×C4—2924no—
871C2×C4—2922no—
872C2×C4—738no—
873C2×C4—732no—
874C2×C4—734no—
875C2×C4—7316no—
876C2×C4—7316no—
877C2×C4—732no—
878C2×C4—734no—
879C2×C4—738no—
880C2×C4—14616no—
881C2×C4—14632no—
882C2×C4—14632no—
883C2×C4—1464no—
884C2×C4—1468no—
885C2×C4—14632no—
886C2×C4—1468no—
887C2×C4—14616no—
888C2×C4—14616no—
889C2×C4C2×D4×D7318yes—
890C2×C4C2×D4×D7314yes—
891C2×C4C2×D4×D7318yes—
892C2×C4C2×D4×D7314yes—
893C2×C4C24×D7318yes—
894C2×C4C24×D7318yes—
895C2×C4C24×D7311yescharacteristic
896C2×C4C24×D7312yes—
897C2×C4C24×D7311yescharacteristic
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—88no—
904C22—2928no—
905C22—5848no—
906C22—58432no—
907C22—738no—
908C22—1468no—
909C22—14616no—
910C22—1468no—
911C22C22×D4×D7314yes—
912C22C22×D4×D7312yes—
913C22C25×D7311yescharacteristic
914C4—28no—
915C4—28no—
916C4—738no—
917C4—734no—
918C4—1468no—
919C4—1462no—
920C4—1464no—
921C4C22×D4×D7312yes—
922C4C22×D4×D7314yes—
923C4C22×D4×D7312yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—2928no—
928C2—1468no—
929C2C23×D4×D7311yescharacteristic
930C2#585×D7312yes—
subgroupG/H
centerC2×C4C24×D73
commutator, socle, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC73×#3449C2
hypercenter#3449D73
hypocenterC73#62812
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#17989423C2semidirect
2. #22623723C2semidirect
3. #22623720C2semidirect
4. #22623713C2semidirect
5. #22623706C2semidirect
6. #22623700C2semidirect
7. #22623694C2semidirect
8. #22623692C2semidirect
9. #22623414C2semidirect
10. #22623264C2semidirect
11. #22623258C2semidirect
12. C2×#17989133C2semidirect
13. #532×D73C2semidirect
14. C2×#17989055C2semidirect
15. C73×#3449C2semidirect
17. C2×#14556639C22semidirect
18. C2×#14556638C22semidirect
19. C2×#14556638C22semidirect
20. C2×#14556637C22semidirect
21. C2×#14556637C22semidirect
22. C2×#14556636C22semidirect
23. C2×#14556636C22semidirect
25. C22×#11924028C22semidirect
26. C22×#11924028C22semidirect
27. C2×#41×D73C22semidirect
28. C2×#41×D73C22semidirect
29. #17989255C22semidirect
30. #17989250C22semidirect
31. #17989247C22semidirect
32. #17989243C22semidirect
33. #17989239C22semidirect
34. #17989235C22semidirect
35. #17989234C22semidirect
36. #17989229C22semidirect
37. #17989228C22semidirect
38. #17989224C22semidirect
39. #17989221C22semidirect
40. #17989219C22semidirect
41. #17989168C22semidirect
42. #17989164C22semidirect
43. #17989163C22semidirect
44. #17989162C22semidirect
45. #17989157C22semidirect
46. #17989156C22semidirect
47. #17989155C22semidirect
48. #17989150C22semidirect
49. #17989149C22semidirect
50. #17989145C22semidirect
51. #17989138C22semidirect
52. #17989137C22semidirect
53. #17989136C22semidirect
54. #17989135C22semidirect
55. #17989134C22semidirect
56. #17989133C22semidirect
57. #17989133C22semidirect
58. #17989133C22semidirect
59. #17989133C22semidirect
60. #17989133C22semidirect
61. #17989133C22semidirect
62. #17989132C22semidirect
63. C2×#14556589C22semidirect
64. C4⋊Q8×D73C22semidirect
65. C2×#14556587C22semidirect
66. #127×D73C22semidirect
67. C2×#14556580C22semidirect
68. C2×#14556578C22semidirect
69. #124×D73C22semidirect
70. #17989099C22semidirect
71. #17989096C22semidirect
72. C2×#14556563C22semidirect
73. #121×D73C22semidirect
74. #17989055C22semidirect
75. #17989055C22semidirect
76. #17989055C22semidirect
77. C2×#14556556C22semidirect
78. C2×#14556553C22semidirect
79. C2×C4×C22⋊D73C22semidirect
80. C2×#14556551C22semidirect
81. C4×D4×D73C22semidirect
82. C2×#14556548C22semidirect
83. C22×C4×Dic73C22semidirect
84. C2×C42×D73C22semidirect
85. C22×#41×C73C22semidirect
86. #537×C73C22semidirect
87. #536×C73C22semidirect
88. #535×C73C22semidirect
89. #534×C73C22semidirect
90. #532×C73C22semidirect
91. #525×C73C22semidirect
92. C2×#117×C73C22semidirect
104. C2×#11924028D4semidirect
251. #11924028C2×D4semidirect
252. #11924028C2×D4semidirect
259. C2×Dic146C2×D4semidirect
268. C2×D292C2×D4semidirect
277. C2×C22⋊D73C2×D4semidirect
301. C2×C4×D73C2×D4semidirect
346. C22×C4×C73C2×D4semidirect
457. Dic73#585semidirect
477. #3449D73semidirect
481. C73#62812semidirect
495. C22×#41C2×D73semidirect
510. #537C2×D73semidirect
514. #536C2×D73semidirect
518. #535C2×D73semidirect
521. #534C2×D73semidirect
534. #532C2×D73semidirect
544. #525C2×D73semidirect
556. C2×#117C2×D73semidirect
793. C22×C4D4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179894232
#226237232
#226237202
#226237132
#226237062
#226237002
#226236942
#226236922
#226234142
#226232642
#226232582
C2×#179891332
#532×D732
C2×#179890552
C73×#34492
#6281273