Finite Group Databasebeta

← C2×#22623599 #33994296

Subgroups — C2×#22623599 #33994296

Order 18688.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556637C211yesmaximal, characteristic, complemented
2C22×#41×D73C211yesmaximal, characteristic, complemented
3#22623599C2132yesmaximal, direct product factor
4C2×#17989256C211yesmaximal, characteristic, complemented
5C2×#17989249C211yesmaximal, characteristic, complemented
6C2×#17989244C211yesmaximal, characteristic, complemented
7C2×#17989234C213yesmaximal, complemented
8C2×#17989233C213yesmaximal, complemented
9C2×#17989222C213yesmaximal, complemented
10C2×#17989221C213yesmaximal, complemented
11C2×#17989166C213yesmaximal, complemented
12C2×#17989150C213yesmaximal, complemented
13C2×#17989096C213yesmaximal, complemented
14C2×#121×D73C213yesmaximal, complemented
15C2×#17989069C211yesmaximal, characteristic, complemented
16C2×#550×C73C211yesmaximal, characteristic, complemented
17C2×#14556637—216no—
18C2×#14556637C22116yescomplemented
19C22×#11924029C2211yescharacteristic
20C22×#11924029C2211yescharacteristic, complemented
21C22×#11924028C2213yescomplemented
22C22×#11924028C2213yescomplemented
23C22×#11924027C2213yescomplemented
24C2×#41×D73—216no—
25C2×#41×D73C22116yescomplemented
26C22×Q8×D73C2211yescharacteristic, complemented
27C23×D292C2213yescomplemented
28C22×D4×D73C2213yescomplemented
29C22×D4×D73C2213yescomplemented
30C22×D4×D73C2213yescomplemented
31C22×D4×D73C2216yescomplemented
32C23×C4×D73C2213yescomplemented
33#17989256C22116yescomplemented
34#17989249C22116yescomplemented
35#17989244C22116yescomplemented
36#17989234C22148yescomplemented
37#17989233C22148yescomplemented
38#17989222C22148yescomplemented
39#17989221C22148yescomplemented
40#17989166C22148yescomplemented
41#17989150C22148yescomplemented
42C2×#14556587C2213yescomplemented
43C2×#14556579C2213yescomplemented
44C2×#14556578C2213yescomplemented
45#17989096C22148yescomplemented
46C2×#14556576C2213yescomplemented
47C2×#14556573C2213yescomplemented
48C2×#14556571C2213yescomplemented
49C2×#14556570C2213yescomplemented
50C2×#14556569C2211yescharacteristic, complemented
51C2×#14556568C2213yescomplemented
52C2×#14556566C2213yescomplemented
53C2×#14556565C2213yescomplemented
54C2×#14556564C2216yescomplemented
55C2×#14556564C2213yescomplemented
56C2×#14556563C2213yescomplemented
57C2×#14556563C2216yescomplemented
58C2×#14556562C2216yescomplemented
59C2×#14556562C2213yescomplemented
60C2×#14556562C2213yescomplemented
61#121×D73C22148yescomplemented
62C2×#14556561C2213yescomplemented
63C2×#14556559C2216yescomplemented
64C2×#14556559C2216yescomplemented
65C2×#14556559C2213yescomplemented
66#17989069C22116yescomplemented
67C2×Q8×Dic73C2211yescharacteristic, complemented
68C2×C4×D292C2213yescomplemented
69C2×C4×D292C2213yescomplemented
70C2×#14556553C2213yescomplemented
71C2×C4×C22⋊D73C2213yescomplemented
72C2×C4×C22⋊D73C2213yescomplemented
73C2×#14556548C2213yescomplemented
74C2×C4⋊C4×D73C2213yescomplemented
75C2×C22⋊C4×D73C2216yescomplemented
76C22×#41×C73C2211yescharacteristic, complemented
77C22×#41×C73C2211yescharacteristic, complemented
78#550×C73C22116yescomplemented
79C2×#127×C73C2213yescomplemented
80C2×#121×C73C2213yescomplemented
81C2×#121×C73C2213yescomplemented
82C2×C4×Q8×C73C2211yescharacteristic, complemented
83C2×C4×D4×C73C2213yescomplemented
84C24×D73C2313yes—
85C24×D73C2316yes—
86#14556637—2128no—
87C2×#11924029—28no—
88C2×#11924029D4116yescomplemented
89C2×#11924029C2318yes—
90C2×#11924029C2318yescomplemented
91C2×#11924028—224no—
92C2×#11924028—224no—
93C2×#11924028C23124yescomplemented
94C2×#11924028C23124yescomplemented
95C2×#11924027—224no—
96C2×#11924027C23124yescomplemented
97#41×D73—2128no—
98C22×Dic146C2313yes—
99C22×Dic146C2311yescharacteristic
100C2×Q8×D73—28no—
101C2×Q8×D73C2318yescomplemented
102C22×D292—224no—
103C22×D292C2313yes—
104C22×D292C2313yes—
105C22×D292C2313yes—
106C22×D292C2313yes—
107C22×D292C23124yescomplemented
108C22×C22⋊D73C2313yes—
109C22×C22⋊D73C2313yes—
110C22×C22⋊D73C2313yes—
111C22×C22⋊D73C2316yes—
112C22×C22⋊D73C2313yes—
113C22×C22⋊D73C2316yes—
114C2×D4×D73—224no—
115C2×D4×D73—224no—
116C2×D4×D73—224no—
117C2×D4×D73—424no—
118C2×D4×D73C23124yescomplemented
119C2×D4×D73C23124yescomplemented
120C2×D4×D73C23124yescomplemented
121C2×D4×D73C23148yescomplemented
122C23×Dic73C2313yes—
123C22×C4×D73—224no—
124C22×C4×D73C2311yescharacteristic
125C22×C4×D73C2313yes—
126C22×C4×D73C2313yes—
127C22×C4×D73C2313yes—
128C22×C4×D73C2316yes—
129C22×C4×D73C2313yes—
130C22×C4×D73C23124yescomplemented
131#14556587C23124yescomplemented
132#14556579C23124yescomplemented
133#14556578C23124yescomplemented
134#14556576C23124yescomplemented
135#14556573C23124yescomplemented
136#14556571C23124yescomplemented
137#14556570C23124yescomplemented
138#14556569C2318yescomplemented
139#14556568C23124yescomplemented
140#14556566C23124yescomplemented
141#14556565C23124yescomplemented
142#14556564C23148yescomplemented
143#14556564C23124yescomplemented
144#14556563C23124yescomplemented
145#14556563C23148yescomplemented
146#14556562C23148yescomplemented
147#14556562C23124yescomplemented
148#14556562C23124yescomplemented
149#14556561C23124yescomplemented
150#14556559C23148yescomplemented
151#14556559C23148yescomplemented
152#14556559C23124yescomplemented
153Q8×Dic73C2318yescomplemented
154C4×D292C23124yescomplemented
155C4×D292C23124yescomplemented
156#14556553C23124yescomplemented
157C4×C22⋊D73C23124yescomplemented
158C4×C22⋊D73C23124yescomplemented
159#14556548C23124yescomplemented
160C2×C4⋊Dic73C2313yes—
161C2×C4⋊Dic73C2313yes—
162C2×#11924007C2313yes—
163C2×#11924007C2311yescharacteristic
164C2×#11924007C2311yescharacteristic
165C2×#11924007C2313yes—
166C4⋊C4×D73C23124yescomplemented
167C2×C22⋊Dic73C2316yes—
168C2×C22⋊Dic73C2313yes—
169C2×C22⋊Dic73C2313yes—
170C2×#11924005C2313yes—
171C2×#11924005C2316yes—
172C2×#11924005C2313yes—
173C2×#11924005C2313yes—
174C2×#11924005C2311yescharacteristic
175C2×#11924005C2311yescharacteristic
176C2×#11924005C2313yes—
177C22⋊C4×D73C23148yescomplemented
178C2×C4×Dic73C2313yes—
179C2×#41×C73—28no—
180C2×#41×C73—28no—
181C2×#41×C73C2318yescomplemented
182C2×#41×C73C2318yescomplemented
183C22×Q8×C73C2311yescharacteristic
184C22×D4×C73C2313yes—
185C22×D4×C73C2313yes—
186C22×D4×C73C2316yes—
187C22×D4×C73C2313yes—
188C23×C4×C73C2313yes—
189C23×C4×C73C2313yes—
190#127×C73C23124yescomplemented
191#121×C73C23124yescomplemented
192#121×C73C23124yescomplemented
193C4×Q8×C73C2318yescomplemented
194C4×D4×C73C23124yescomplemented
195C2×C4⋊C4×C73C2311yescharacteristic
196C2×C4⋊C4×C73C2313yes—
197C2×C22⋊C4×C73C2313yes—
198C2×C22⋊C4×C73C2313yes—
199C2×C42×C73C2313yes—
200C23×D73—212no—
201C23×D73—212no—
202C23×D73—224no—
203C23×D73—46no—
204C23×D73—412no—
205C23×D73—412no—
206C23×D73C2413yes—
207C23×D73C24112yes—
208C23×D73C2413yes—
209C23×D73C2411yescharacteristic
210C23×D73C24124yes—
211#11924029—232no—
212#11924029C2×D4164yescomplemented
213#11924028—296no—
214#11924028—296no—
215#11924027—296no—
216C2×Dic146—212no—
217C2×Dic146—24no—
218C2×Dic146C2414yes—
219C2×Dic146C24112yes—
220Q8×D73—232no—
221C2×D292—212no—
222C2×D292—212no—
223C2×D292—212no—
224C2×D292—296no—
225C2×D292C2×D4124yescomplemented
226C2×D292C24112yes—
227C2×D292C24112yes—
228C2×D292C24112yes—
229C2×D292C24112yes—
230C2×C22⋊D73—212no—
231C2×C22⋊D73—224no—
232C2×C22⋊D73—212no—
233C2×C22⋊D73—212no—
234C2×C22⋊D73—412no—
235C2×C22⋊D73—46no—
236C2×C22⋊D73C24112yes—
237C2×C22⋊D73C24124yes—
238C2×C22⋊D73C24112yes—
239C2×C22⋊D73C24112yes—
240C2×C22⋊D73C24112yes—
241C2×C22⋊D73C24124yes—
242D4×D73—296no—
243D4×D73—296no—
244D4×D73—296no—
245D4×D73—496no—
246C22×Dic73—212no—
247C22×Dic73C2411yescharacteristic
248C22×Dic73C2413yes—
249C22×Dic73C2413yes—
250C22×Dic73C2411yescharacteristic
251C22×Dic73C24112yes—
252C22×Dic73C2411yescharacteristic
253C2×C4×D73—212no—
254C2×C4×D73—212no—
255C2×C4×D73—212no—
256C2×C4×D73—24no—
257C2×C4×D73—296no—
258C2×C4×D73—412no—
259C2×C4×D73C2×D4124yescomplemented
260C2×C4×D73C24112yes—
261C2×C4×D73C24112yes—
262C2×C4×D73C24112yes—
263C2×C4×D73C2414yes—
264C2×C4×D73C24124yes—
265C2×C4×D73C24112yes—
266C4⋊Dic73C24112yes—
267C4⋊Dic73C24112yes—
268#11924007C24112yes—
269#11924007C2414yes—
270#11924007C2414yes—
271#11924007C24112yes—
272C22⋊Dic73C24124yes—
273C22⋊Dic73C24112yes—
274C22⋊Dic73C24112yes—
275#11924005C24112yes—
276#11924005C24124yes—
277#11924005C24112yes—
278#11924005C24112yes—
279#11924005C2414yes—
280#11924005C2414yes—
281#11924005C24112yes—
282C4×Dic73C24112yes—
283C24×C73C2413yes—
284C24×C73C2413yes—
285#41×C73—232no—
286#41×C73—232no—
287C2×Q8×C73C2×D418yescomplemented
288C2×Q8×C73C2414yes—
289C2×D4×C73—212no—
290C2×D4×C73—212no—
291C2×D4×C73—46no—
292C2×D4×C73—412no—
293C2×D4×C73C24112yes—
294C2×D4×C73C24112yes—
295C2×D4×C73C24112yes—
296C2×D4×C73C24124yes—
297C22×C4×C73—212no—
298C22×C4×C73—212no—
299C22×C4×C73C2411yescharacteristic
300C22×C4×C73C2413yes—
301C22×C4×C73C2411yescharacteristic
302C22×C4×C73C2411yescharacteristic
303C22×C4×C73C24112yes—
304C22×C4×C73C24112yes—
305C22×C4×C73C2413yes—
306C4⋊C4×C73C2414yes—
307C4⋊C4×C73C24112yes—
308C22⋊C4×C73C24112yes—
309C22⋊C4×C73C24112yes—
310C42×C73C24112yes—
311C23×C73—26no—
312C23×C73—26no—
313C23×C73—26no—
314C23×C73—26no—
315C23×C73—26no—
316C23×C73—26no—
317C23×C73C2516yes—
318C23×C73C2516yes—
319C23×C73C2511yescharacteristic
320C22×D73—22no—
321C22×D73—26no—
322C22×D73—22no—
323C22×D73—26no—
324C22×D73—26no—
325C22×D73—26no—
326C22×D73—26no—
327C22×D73—224no—
328C22×D73—224no—
329C22×D73—248no—
330C22×D73—412no—
331C22×D73—448no—
332C22×D73—424no—
333C22×D73—424no—
334C22×D73—848no—
335C22×D73C22×D4112yes—
336C22×D73H(5,𝔽2)14yescomplemented
337C22×D73C2516yes—
338C22×D73C2516yes—
339C22×D73C2512yes—
340Q8×C73C22×D4116yescomplemented
341D4×C73—224no—
342D4×C73—224no—
343D4×C73—412no—
344D4×C73—424no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—26no—
348C2×C4×C73—22no—
349C2×C4×C73—224no—
350C2×C4×C73—224no—
351C2×C4×C73C22×D4112yes—
352C2×C4×C73C2512yes—
353C2×C4×C73C2516yes—
354C2×C4×C73C2512yes—
355C2×C4×C73C2512yes—
356C2×C4×C73C2516yes—
357C22⋊D73—224no—
358C22⋊D73—248no—
359C22⋊D73—224no—
360C22⋊D73—224no—
361C22⋊D73—424no—
362C22⋊D73—412no—
363C2×Dic73—22no—
364C2×Dic73—26no—
365C2×Dic73—26no—
366C2×Dic73—22no—
367C2×Dic73—224no—
368C2×Dic73C22×D414yes—
369C2×Dic73C2512yes—
370C2×Dic73C2516yes—
371C2×Dic73C2516yes—
372C2×Dic73C2512yes—
373C2×Dic73C2512yes—
374D292—224no—
375D292—224no—
376D292—224no—
377D292C22×D4148yescomplemented
378C4×D73—224no—
379C4×D73—224no—
380C4×D73—224no—
381C4×D73—28no—
382C4×D73—424no—
383C4×D73C22×D4148yescomplemented
384Dic146—224no—
385Dic146—28no—
386C22×C73—26no—
387C22×C73—26no—
388C22×C73—26no—
389C22×C73—26no—
390C22×C73—26no—
391C22×C73—26no—
392C22×C73—412no—
393C22×C73—412no—
394C22×C73C23×D412yes—
395C22×C73C2×H(5,𝔽2)12yes—
396C22×C73#58512yes—
397C22×C73C2611yescharacteristic
398C2×D73—22no—
399C2×D73—26no—
400C2×D73—22no—
401C2×D73—26no—
402C2×D73—28no—
403C2×D73—224no—
404C2×D73—26no—
405C2×D73—26no—
406C2×D73—26no—
407C2×D73—448no—
408C2×D73—412no—
409C2×D73—848no—
410C2×D73C23×D4112yes—
411C2×D73C2×H(5,𝔽2)14yescomplemented
412C4×C73—22no—
413C4×C73—22no—
414C4×C73—26no—
415C4×C73—22no—
416C4×C73C23×D4112yes—
417Dic73—26no—
418Dic73—22no—
419Dic73—26no—
420Dic73—22no—
421Dic73C23×D414yes—
422C2×#3488—731nomaximal, Sylow
423C2×C73—46no—
424C2×C73—46no—
425C2×C73#348814yescomplemented
426C2×C73C24×D411yescharacteristic
427C2×C73C22×H(5,𝔽2)11yescharacteristic
428C2×C73C2×#58511yescharacteristic
429D73—24no—
430D73—212no—
431D73—46no—
432C22×H(5,𝔽2)—731no—
433C23×#41—731no—
434#3488—7332no—
435C2×#550—731no—
436C2×#550D7311yescharacteristic, complemented
437C2×#548—731no—
438C2×#548—731no—
439C2×#546—733no—
440C2×#546—733no—
441C2×D42—733no—
442C2×D42—733no—
443C2×#537—733no—
444C2×#535—733no—
445C2×#525—733no—
446C22×#121—733no—
447C2×#520—731no—
448C73C2×#348811yescharacteristic, complemented, Sylow
449C2×H(5,𝔽2)—7316no—
450C2×H(5,𝔽2)—14616no—
451C22×#41—7316no—
452C22×#41—731no—
453C22×#41—731no—
454C22×#41—733no—
455C22×#41—733no—
456C22×#41—733no—
457C22×#41—14616no—
458C22×#41C2×D7311yescharacteristic, complemented
459C22×#41C2×D7311yescharacteristic, complemented
460C23×Q8—731no—
461C23×D4—736no—
462C23×D4—733no—
463C23×D4—733no—
464C23×D4—733no—
465C23×D4—733no—
466C24×C4—733no—
467#550—7316no—
468#550C2×D73116yescomplemented
469#548—7316no—
470#548—7316no—
471#546—7348no—
472#546—7348no—
473D42—7348no—
474D42—7348no—
475#537—7348no—
476#535—7348no—
477C2×#127—733no—
478C2×#127C2×D7313yescomplemented
479C2×#124—733no—
480C2×#124—733no—
481#525—7348no—
482C2×#123—733no—
483C2×#123—733no—
484C2×C22⋊Q8—733no—
485C2×C22⋊Q8—731no—
486C2×C22⋊Q8—733no—
487C2×C22⋊Q8—733no—
488C2×#121—736no—
489C2×#121—733no—
490C2×#121—733no—
491C2×#121—736no—
492C2×#121—733no—
493C2×#121—733no—
494C2×#121—7348no—
495C2×#121—733no—
496C2×#121—733no—
497C2×#121—736no—
498C2×#121C2×D7313yescomplemented
499C2×#121C2×D7313yescomplemented
500C2×#120—733no—
501C2×#120—736no—
502C2×#120—736no—
503C2×#120—733no—
504#520—7316no—
505C2×C4×Q8—731no—
506C2×C4×Q8C2×D7311yescharacteristic, complemented
507C2×C4×D4—733no—
508C2×C4×D4—733no—
509C2×C4×D4—733no—
510C2×C4×D4—733no—
511C2×C4×D4—733no—
512C2×C4×D4C2×D7313yescomplemented
513C2×#117—733no—
514C22×C4⋊C4—733no—
515C22×C22⋊C4—736no—
516C25—736no—
517C25—733no—
518H(5,𝔽2)—146128no—
519C2×#41—28no—
520C2×#41—28no—
521C2×#41—7316no—
522C2×#41—738no—
523C2×#41—738no—
524C2×#41—7324no—
525C2×#41—7324no—
526C2×#41—7324no—
527C2×#41—14624no—
528C2×#41—14624no—
529C2×#41—14624no—
530C2×#41—146128no—
531C2×#41—1468no—
532C2×#41C22×D7318yescomplemented
533C2×#41C22×D7318yescomplemented
534C22×Q8—738no—
535C22×Q8—731no—
536C22×Q8—733no—
537C22×Q8—1468no—
538C22×Q8C22×D7311yescharacteristic
539C22×D4—29224no—
540C22×D4—733no—
541C22×D4—736no—
542C22×D4—7348no—
543C22×D4—733no—
544C22×D4—736no—
545C22×D4—733no—
546C22×D4—733no—
547C22×D4—7324no—
548C22×D4—7324no—
549C22×D4—7324no—
550C22×D4—733no—
551C22×D4—733no—
552C22×D4—733no—
553C22×D4—733no—
554C22×D4—7324no—
555C22×D4—14624no—
556C22×D4—14624no—
557C22×D4—14624no—
558C22×D4—14624no—
559C22×D4C22×D7313yes—
560C22×D4C22×D7313yes—
561C22×D4C22×D7313yes—
562C22×D4C22×D7316yes—
563C23×C4—736no—
564C23×C4—733no—
565C23×C4—733no—
566C23×C4—733no—
567C23×C4—733no—
568C23×C4—733no—
569C23×C4—731no—
570C23×C4—7324no—
571C23×C4—14624no—
572C23×C4C22×D7313yes—
573C23×C4C22×D7313yes—
574#127—7324no—
575#127C22×D73124yescomplemented
576#124—7324no—
577#124—7324no—
578#123—7324no—
579#123—7324no—
580C22⋊Q8—7324no—
581C22⋊Q8—738no—
582C22⋊Q8—7324no—
583C22⋊Q8—7324no—
584#121—7348no—
585#121—7324no—
586#121—7324no—
587#121—7348no—
588#121—7324no—
589#121—7324no—
590#121—7324no—
591#121—7324no—
592#121—7348no—
593#121C22×D73124yescomplemented
594#121C22×D73124yescomplemented
595#120—7324no—
596#120—7348no—
597#120—7348no—
598#120—7324no—
599C4×Q8—738no—
600C4×Q8C22×D7318yescomplemented
601C4×D4—7324no—
602C4×D4—7324no—
603C4×D4—7324no—
604C4×D4—7324no—
605C4×D4—7324no—
606C4×D4C22×D73124yescomplemented
607#117—7324no—
608C2×C4⋊C4—733no—
609C2×C4⋊C4—733no—
610C2×C4⋊C4—731no—
611C2×C4⋊C4—731no—
612C2×C4⋊C4—733no—
613C2×C4⋊C4—733no—
614C2×C4⋊C4—7324no—
615C2×C4⋊C4C22×D7313yes—
616C2×C4⋊C4C22×D7311yescharacteristic
617C2×C22⋊C4—736no—
618C2×C22⋊C4—733no—
619C2×C22⋊C4—733no—
620C2×C22⋊C4—733no—
621C2×C22⋊C4—736no—
622C2×C22⋊C4—733no—
623C2×C22⋊C4—733no—
624C2×C22⋊C4—731no—
625C2×C22⋊C4—731no—
626C2×C22⋊C4—733no—
627C2×C22⋊C4—7348no—
628C2×C22⋊C4C22×D7313yes—
629C2×C22⋊C4C22×D7313yes—
630C2×C42—733no—
631C2×C42C22×D7313yes—
632C24—2926no—
633C24—29212no—
634C24—29212no—
635C24—7324no—
636C24—7312no—
637C24—733no—
638C24—731no—
639C24—733no—
640C24—14612no—
641C24—14612no—
642C24—14624no—
643C24C23×D7313yes—
644C24C23×D7313yes—
645#41—232no—
646#41—232no—
647#41—7364no—
648#41—14696no—
649#41—14696no—
650#41—14696no—
651#41—14632no—
652C2×Q8—734no—
653C2×Q8—7312no—
654C2×Q8—1464no—
655C2×Q8—14632no—
656C2×Q8—14612no—
657C2×Q8D4×D7318yescomplemented
658C2×Q8C23×D7314yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—412no—
662C2×D4—46no—
663C2×D4—29296no—
664C2×D4—29212no—
665C2×D4—2926no—
666C2×D4—7312no—
667C2×D4—7324no—
668C2×D4—7312no—
669C2×D4—7324no—
670C2×D4—7312no—
671C2×D4—7312no—
672C2×D4—7324no—
673C2×D4—7312no—
674C2×D4—7312no—
675C2×D4—7312no—
676C2×D4—7312no—
677C2×D4—14696no—
678C2×D4—14612no—
679C2×D4—14612no—
680C2×D4—14696no—
681C2×D4—14612no—
682C2×D4—14696no—
683C2×D4—14696no—
684C2×D4—14612no—
685C2×D4—14612no—
686C2×D4—14624no—
687C2×D4—14612no—
688C2×D4C23×D73112yes—
689C2×D4C23×D73112yes—
690C2×D4C23×D73112yes—
691C2×D4C23×D73124yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—29212no—
695C22×C4—7324no—
696C22×C4—731no—
697C22×C4—7324no—
698C22×C4—7312no—
699C22×C4—7312no—
700C22×C4—731no—
701C22×C4—733no—
702C22×C4—733no—
703C22×C4—731no—
704C22×C4—7312no—
705C22×C4—7312no—
706C22×C4—7312no—
707C22×C4—734no—
708C22×C4—1464no—
709C22×C4—14696no—
710C22×C4—14612no—
711C22×C4—14612no—
712C22×C4—14612no—
713C22×C4—14612no—
714C22×C4C23×D73112yes—
715C22×C4C23×D73112yes—
716C22×C4C23×D7311yescharacteristic
717C22×C4C23×D7313yes—
718C22×C4C23×D7311yescharacteristic
719C22×C4C23×D7311yescharacteristic
720C22×C4C23×D7313yes—
721C4⋊C4—7312no—
722C4⋊C4—734no—
723C4⋊C4—734no—
724C4⋊C4—7312no—
725C4⋊C4—7312no—
726C4⋊C4—7312no—
727C4⋊C4C23×D73112yes—
728C4⋊C4C23×D7314yes—
729C22⋊C4—7324no—
730C22⋊C4—7312no—
731C22⋊C4—7312no—
732C22⋊C4—7312no—
733C22⋊C4—7324no—
734C22⋊C4—7312no—
735C22⋊C4—7312no—
736C22⋊C4—734no—
737C22⋊C4—734no—
738C22⋊C4—7312no—
739C22⋊C4C23×D73112yes—
740C22⋊C4C23×D73112yes—
741C42—7312no—
742C42C23×D73112yes—
743C23—26no—
744C23—26no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—26no—
749C23—29212no—
750C23—29224no—
751C23—29224no—
752C23—29248no—
753C23—58448no—
754C23—7312no—
755C23—734no—
756C23—736no—
757C23—732no—
758C23—736no—
759C23—14624no—
760C23—14624no—
761C23—14648no—
762C23—1466no—
763C23—1466no—
764C23—1466no—
765C23—1462no—
766C23—1466no—
767C23—1462no—
768C23—1466no—
769C23C24×D7316yes—
770C23C24×D7316yes—
771C23C24×D7311yescharacteristic
772Q8—1468no—
773Q8—14624no—
774Q8C2×D4×D73116yescomplemented
775D4—224no—
776D4—224no—
777D4—424no—
778D4—412no—
779D4—29224no—
780D4—29212no—
781D4—7348no—
782D4—14624no—
783D4—14624no—
784D4—14624no—
785D4—14624no—
786D4—14624no—
787D4—14648no—
788D4—14624no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—29224no—
796C2×C4—734no—
797C2×C4—732no—
798C2×C4—7348no—
799C2×C4—732no—
800C2×C4—736no—
801C2×C4—736no—
802C2×C4—732no—
803C2×C4—1468no—
804C2×C4—14624no—
805C2×C4—14624no—
806C2×C4—1462no—
807C2×C4—1466no—
808C2×C4—1466no—
809C2×C4—1462no—
810C2×C4—14624no—
811C2×C4—14624no—
812C2×C4C2×D4×D73112yes—
813C2×C4C24×D7312yes—
814C2×C4C24×D7316yes—
815C2×C4C24×D7312yes—
816C2×C4C24×D7312yes—
817C2×C4C24×D7316yes—
818C22—26no—
819C22—26no—
820C22—26no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—412no—
826C22—29248no—
827C22—29212no—
828C22—58448no—
829C22—7312no—
830C22—734no—
831C22—1466no—
832C22—1466no—
833C22—1466no—
834C22—1468no—
835C22—14624no—
836C22—1462no—
837C22—1466no—
838C22—1462no—
839C22—1466no—
840C22C22×D4×D7312yes—
841C22H(5,𝔽2)×D7312yes—
842C22#1798942312yes—
843C22C25×D7311yescharacteristic
844C4—22no—
845C4—22no—
846C4—26no—
847C4—22no—
848C4—734no—
849C4—1462no—
850C4—1466no—
851C4—1466no—
852C4—1462no—
853C4C22×D4×D73112yes—
854C2—46no—
855C2—46no—
856C2—2926no—
857C2—1464no—
858C2—14612no—
859C2#2262359914yesdirect product factor
860C2C23×D4×D7311yescharacteristic
861C2C2×H(5,𝔽2)×D7311yescharacteristic
862C2C2×#1798942311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#550×C73C2
socleC23×C73C25
hypercenterC2×#550D73
hypocenterC73C2×#3488
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#14556637C2semidirect
2. C22×#41×D73C2semidirect
3. #22623599C2direct (N × H)
4. C2×#17989256C2semidirect
5. C2×#17989249C2semidirect
6. C2×#17989244C2semidirect
7. C2×#17989234C2semidirect
8. C2×#17989233C2semidirect
9. C2×#17989222C2semidirect
10. C2×#17989221C2semidirect
11. C2×#17989166C2semidirect
12. C2×#17989150C2semidirect
13. C2×#17989096C2semidirect
14. C2×#121×D73C2semidirect
15. C2×#17989069C2semidirect
16. C2×#550×C73C2semidirect
18. C2×#14556637C22semidirect
20. C22×#11924029C22semidirect
21. C22×#11924028C22semidirect
22. C22×#11924028C22semidirect
23. C22×#11924027C22semidirect
25. C2×#41×D73C22semidirect
26. C22×Q8×D73C22semidirect
27. C23×D292C22semidirect
28. C22×D4×D73C22semidirect
29. C22×D4×D73C22semidirect
30. C22×D4×D73C22semidirect
31. C22×D4×D73C22semidirect
32. C23×C4×D73C22semidirect
33. #17989256C22semidirect
34. #17989249C22semidirect
35. #17989244C22semidirect
36. #17989234C22semidirect
37. #17989233C22semidirect
38. #17989222C22semidirect
39. #17989221C22semidirect
40. #17989166C22semidirect
41. #17989150C22semidirect
42. C2×#14556587C22semidirect
43. C2×#14556579C22semidirect
44. C2×#14556578C22semidirect
45. #17989096C22semidirect
46. C2×#14556576C22semidirect
47. C2×#14556573C22semidirect
48. C2×#14556571C22semidirect
49. C2×#14556570C22semidirect
50. C2×#14556569C22semidirect
51. C2×#14556568C22semidirect
52. C2×#14556566C22semidirect
53. C2×#14556565C22semidirect
54. C2×#14556564C22semidirect
55. C2×#14556564C22semidirect
56. C2×#14556563C22semidirect
57. C2×#14556563C22semidirect
58. C2×#14556562C22semidirect
59. C2×#14556562C22semidirect
60. C2×#14556562C22semidirect
61. #121×D73C22semidirect
62. C2×#14556561C22semidirect
63. C2×#14556559C22semidirect
64. C2×#14556559C22semidirect
65. C2×#14556559C22semidirect
66. #17989069C22semidirect
67. C2×Q8×Dic73C22semidirect
68. C2×C4×D292C22semidirect
69. C2×C4×D292C22semidirect
70. C2×#14556553C22semidirect
71. C2×C4×C22⋊D73C22semidirect
72. C2×C4×C22⋊D73C22semidirect
73. C2×#14556548C22semidirect
74. C2×C4⋊C4×D73C22semidirect
75. C2×C22⋊C4×D73C22semidirect
76. C22×#41×C73C22semidirect
77. C22×#41×C73C22semidirect
78. #550×C73C22semidirect
79. C2×#127×C73C22semidirect
80. C2×#121×C73C22semidirect
81. C2×#121×C73C22semidirect
82. C2×C4×Q8×C73C22semidirect
83. C2×C4×D4×C73C22semidirect
88. C2×#11924029D4semidirect
90. C2×#11924029C23semidirect
93. C2×#11924028C23semidirect
94. C2×#11924028C23semidirect
96. C2×#11924027C23semidirect
101. C2×Q8×D73C23semidirect
107. C22×D292C23semidirect
118. C2×D4×D73C23semidirect
119. C2×D4×D73C23semidirect
120. C2×D4×D73C23semidirect
121. C2×D4×D73C23semidirect
130. C22×C4×D73C23semidirect
131. #14556587C23semidirect
132. #14556579C23semidirect
133. #14556578C23semidirect
134. #14556576C23semidirect
135. #14556573C23semidirect
136. #14556571C23semidirect
137. #14556570C23semidirect
138. #14556569C23semidirect
139. #14556568C23semidirect
140. #14556566C23semidirect
141. #14556565C23semidirect
142. #14556564C23semidirect
143. #14556564C23semidirect
144. #14556563C23semidirect
145. #14556563C23semidirect
146. #14556562C23semidirect
147. #14556562C23semidirect
148. #14556562C23semidirect
149. #14556561C23semidirect
150. #14556559C23semidirect
151. #14556559C23semidirect
152. #14556559C23semidirect
153. Q8×Dic73C23semidirect
154. C4×D292C23semidirect
155. C4×D292C23semidirect
156. #14556553C23semidirect
157. C4×C22⋊D73C23semidirect
158. C4×C22⋊D73C23semidirect
159. #14556548C23semidirect
166. C4⋊C4×D73C23semidirect
177. C22⋊C4×D73C23semidirect
181. C2×#41×C73C23semidirect
182. C2×#41×C73C23semidirect
190. #127×C73C23semidirect
191. #121×C73C23semidirect
192. #121×C73C23semidirect
193. C4×Q8×C73C23semidirect
194. C4×D4×C73C23semidirect
212. #11924029C2×D4semidirect
225. C2×D292C2×D4semidirect
259. C2×C4×D73C2×D4semidirect
287. C2×Q8×C73C2×D4semidirect
336. C22×D73H(5,𝔽2)semidirect
340. Q8×C73C22×D4semidirect
377. D292C22×D4semidirect
383. C4×D73C22×D4semidirect
411. C2×D73C2×H(5,𝔽2)semidirect
425. C2×C73#3488semidirect
436. C2×#550D73semidirect
448. C73C2×#3488semidirect
458. C22×#41C2×D73semidirect
459. C22×#41C2×D73semidirect
468. #550C2×D73semidirect
478. C2×#127C2×D73semidirect
498. C2×#121C2×D73semidirect
499. C2×#121C2×D73semidirect
506. C2×C4×Q8C2×D73semidirect
512. C2×C4×D4C2×D73semidirect
532. C2×#41C22×D73semidirect
533. C2×#41C22×D73semidirect
575. #127C22×D73semidirect
593. #121C22×D73semidirect
594. #121C22×D73semidirect
600. C4×Q8C22×D73semidirect
606. C4×D4C22×D73semidirect
657. C2×Q8D4×D73semidirect
774. Q8C2×D4×D73semidirect
859. C2#22623599direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566372
C22×#41×D732
#226235992
C2×#179892562
C2×#179892492
C2×#179892442
C2×#179892342
C2×#179892332
C2×#179892222
C2×#179892212
C2×#179891662
C2×#179891502
C2×#179890962
C2×#121×D732
C2×#179890692
C2×#550×C732
C2×#348873