Finite Group Databasebeta

← C2×#22623722 #33994452

Subgroups — C2×#22623722 #33994452

Order 18688.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556639C211yesmaximal, characteristic, complemented
2C22×#14556637C211yesmaximal, characteristic, complemented
3#22623722C2132yesmaximal, direct product factor
4C2×#17989249C211yesmaximal, characteristic, complemented
5C2×#17989248C211yesmaximal, characteristic, complemented
6C2×#17989244C211yesmaximal, characteristic, complemented
7C2×#17989234C213yesmaximal, complemented
8C2×#17989233C213yesmaximal, complemented
9C2×#17989230C213yesmaximal, complemented
10C2×#17989228C213yesmaximal, complemented
11C2×#17989160C213yesmaximal, complemented
12C2×#17989153C213yesmaximal, complemented
13C2×#17989134C213yesmaximal, complemented
14C2×#124×D73C213yesmaximal, complemented
15C2×C4×#11924029C211yesmaximal, characteristic, complemented
16C2×#548×C73C211yesmaximal, characteristic, complemented
17C2×#14556639—216no—
18C2×#14556639C22116yescomplemented
19C2×#14556637—216no—
20C2×#14556637C22116yescomplemented
21C22×#11924029C2211yescharacteristic
22C22×#11924029C2211yescharacteristic
23C22×#11924029C2213yescomplemented
24C22×#11924028C2213yes—
25C22×#11924028C2213yescomplemented
26C22×#11924028C2213yescomplemented
27C22×Q8×D73C2213yescomplemented
28C22×Q8×D73C2211yescharacteristic, complemented
29C23×D292C2213yes—
30C22×D4×D73C2213yes—
31C22×D4×D73C2213yes—
32#17989249C22116yescomplemented
33#17989248C22116yescomplemented
34#17989244C22116yescomplemented
35#17989234C22148yescomplemented
36#17989233C22148yescomplemented
37#17989230C22148yescomplemented
38#17989228C22148yescomplemented
39#17989160C22148yescomplemented
40#17989153C22148yescomplemented
41#17989134C22148yescomplemented
42C2×#14556590C2213yescomplemented
43C2×#14556587C2213yescomplemented
44C2×#14556580C2213yescomplemented
45C2×#14556579C2213yescomplemented
46C2×#14556578C2213yescomplemented
47C2×#14556577C2216yescomplemented
48C2×#14556577C2213yescomplemented
49C2×#14556577C2211yescharacteristic, complemented
50#124×D73C22148yescomplemented
51C2×#14556576C2216yescomplemented
52C2×#14556573C2216yescomplemented
53C2×#14556571C2213yescomplemented
54C2×#14556570C2213yescomplemented
55C2×#14556567C2213yescomplemented
56C2×#14556566C2213yescomplemented
57C2×#14556566C2213yescomplemented
58C2×#14556565C2213yescomplemented
59C2×#14556564C2213yescomplemented
60C2×#14556564C2213yescomplemented
61C2×#14556562C2213yescomplemented
62C2×#14556562C2213yescomplemented
63C2×#14556561C2216yescomplemented
64C2×#14556559C2216yescomplemented
65C4×#11924029C22116yescomplemented
66C2×Q8×Dic73C2211yescharacteristic, complemented
67C2×C4×D292C2213yescomplemented
68C2×C4×D292C2213yescomplemented
69C2×#14556553C2213yescomplemented
70C2×C4×C22⋊D73C2213yescomplemented
71C2×C4×C22⋊D73C2213yescomplemented
72C2×#14556549C2213yescomplemented
73C2×C22⋊C4×D73C2216yescomplemented
74C2×C22⋊C4×D73C2216yescomplemented
75C2×C42×D73C2213yescomplemented
76C22×#41×C73C2211yescharacteristic
77C23×Q8×C73C2211yescharacteristic, complemented
78#548×C73C22116yescomplemented
79C2×#124×C73C2213yescomplemented
80C2×C22⋊Q8×C73C2213yescomplemented
81C2×#121×C73C2213yescomplemented
82C2×C4×Q8×C73C2211yescharacteristic, complemented
83C2×C4×D4×C73C2213yescomplemented
84C24×D73C2316yes—
85#14556639—2128no—
86#14556637—2128no—
87C2×#11924029—224no—
88C2×#11924029—28no—
89C2×#11924029D4116yescomplemented
90C2×#11924029C2318yes—
91C2×#11924029C2318yes—
92C2×#11924029C23124yescomplemented
93C2×#11924028—224no—
94C2×#11924028—224no—
95C2×#11924028—224no—
96C2×#11924028C23124yes—
97C2×#11924028C23124yescomplemented
98C2×#11924028C23124yescomplemented
99C22×Dic146C2311yescharacteristic
100C22×Dic146C2313yes—
101C22×Dic146C2313yes—
102C2×Q8×D73—224no—
103C2×Q8×D73—28no—
104C2×Q8×D73C23124yescomplemented
105C2×Q8×D73C2318yescomplemented
106C22×D292—224no—
107C22×D292C2313yes—
108C22×D292C2313yes—
109C22×D292C23124yes—
110C22×D292C2313yes—
111C22×D292C2313yes—
112C22×D292C2313yes—
113C22×C22⋊D73C2311yescharacteristic
114C22×C22⋊D73C2313yes—
115C22×C22⋊D73C2313yes—
116C22×C22⋊D73C2313yes—
117C22×C22⋊D73C2313yes—
118C22×C22⋊D73C2313yes—
119C2×D4×D73—224no—
120C2×D4×D73—224no—
121C2×D4×D73C23124yes—
122C2×D4×D73C23124yes—
123C22×C4×D73C2313yes—
124C22×C4×D73C2316yes—
125C22×C4×D73C2313yes—
126C22×C4×D73C2313yes—
127C22×C4×D73C2313yes—
128C22×C4×D73C2313yes—
129#14556590C23124yescomplemented
130#14556587C23124yescomplemented
131#14556580C23124yescomplemented
132#14556579C23124yescomplemented
133#14556578C23124yescomplemented
134#14556577C2318yescomplemented
135#14556577C23124yescomplemented
136#14556577C23148yescomplemented
137#14556576C23148yescomplemented
138#14556573C23148yescomplemented
139#14556571C23124yescomplemented
140#14556570C23124yescomplemented
141#14556567C23124yescomplemented
142#14556566C23124yescomplemented
143#14556566C23124yescomplemented
144#14556565C23124yescomplemented
145#14556564C23124yescomplemented
146#14556564C23124yescomplemented
147#14556562C23124yescomplemented
148#14556562C23124yescomplemented
149#14556561C23148yescomplemented
150#14556559C23148yescomplemented
151Q8×Dic73C2318yescomplemented
152C4×D292C23124yescomplemented
153C4×D292C23124yescomplemented
154#14556553C23124yescomplemented
155C4×C22⋊D73C23124yescomplemented
156C4×C22⋊D73C23124yescomplemented
157#14556549C23124yescomplemented
158C2×C4⋊Dic73C2313yes—
159C2×C4⋊Dic73C2313yes—
160C2×#11924007C2313yes—
161C2×#11924007C2313yes—
162C2×C22⋊Dic73C2313yes—
163C2×C22⋊Dic73C2316yes—
164C2×C22⋊Dic73C2311yescharacteristic
165C2×#11924005C2313yes—
166C2×#11924005C2313yes—
167C2×#11924005C2316yes—
168C2×#11924005C2316yes—
169C2×#11924005C2316yes—
170C2×#11924005C2311yescharacteristic
171C2×#11924005C2311yescharacteristic
172C22⋊C4×D73C23148yescomplemented
173C22⋊C4×D73C23148yescomplemented
174C2×C4×Dic73C2313yes—
175C2×C4×Dic73C2311yescharacteristic
176C2×C4×Dic73C2313yes—
177C42×D73C23124yescomplemented
178C2×#41×C73—28no—
179C2×#41×C73C2318yes—
180C22×Q8×C73—28no—
181C22×Q8×C73C2313yes—
182C22×Q8×C73C2311yescharacteristic
183C22×Q8×C73C2318yescomplemented
184C22×D4×C73C2313yes—
185C22×D4×C73C2313yes—
186C23×C4×C73C2313yes—
187C23×C4×C73C2313yes—
188#124×C73C23124yescomplemented
189C22⋊Q8×C73C23124yescomplemented
190#121×C73C23124yescomplemented
191C4×Q8×C73C2318yescomplemented
192C4×D4×C73C23124yescomplemented
193C2×C4⋊C4×C73C2313yes—
194C2×C4⋊C4×C73C2313yes—
195C2×C22⋊C4×C73C2311yescharacteristic
196C2×C22⋊C4×C73C2313yes—
197C2×C22⋊C4×C73C2316yes—
198C2×C42×C73C2313yes—
199C23×D73—224no—
200C23×D73—412no—
201C23×D73—412no—
202C23×D73C2413yes—
203C23×D73C2411yescharacteristic
204C23×D73C2413yes—
205C23×D73C24124yes—
206#11924029—232no—
207#11924029—296no—
208#11924029C2×D4164yescomplemented
209#11924028—296no—
210#11924028—296no—
211#11924028—296no—
212C2×Dic146—212no—
213C2×Dic146—212no—
214C2×Dic146—24no—
215C2×Dic146C24112yes—
216C2×Dic146C24112yes—
217C2×Dic146C2414yes—
218Q8×D73—232no—
219Q8×D73—296no—
220C2×D292—212no—
221C2×D292—212no—
222C2×D292—212no—
223C2×D292—296no—
224C2×D292—46no—
225C2×D292C2×D4124yes—
226C2×D292C24112yes—
227C2×D292C24112yes—
228C2×D292C24112yes—
229C2×D292C24112yes—
230C2×D292C24112yes—
231C2×C22⋊D73—212no—
232C2×C22⋊D73—212no—
233C2×C22⋊D73—212no—
234C2×C22⋊D73—24no—
235C2×C22⋊D73—46no—
236C2×C22⋊D73—46no—
237C2×C22⋊D73C24112yes—
238C2×C22⋊D73C24112yes—
239C2×C22⋊D73C24112yes—
240C2×C22⋊D73C2414yes—
241C2×C22⋊D73C24112yes—
242C2×C22⋊D73C24112yes—
243D4×D73—296no—
244D4×D73—296no—
245C22×Dic73C2411yescharacteristic
246C22×Dic73C2413yes—
247C22×Dic73C2413yes—
248C22×Dic73C2411yescharacteristic
249C22×Dic73C2411yescharacteristic
250C2×C4×D73—224no—
251C2×C4×D73—212no—
252C2×C4×D73—212no—
253C2×C4×D73—46no—
254C2×C4×D73—46no—
255C2×C4×D73C2×D4124yes—
256C2×C4×D73C24124yes—
257C2×C4×D73C24112yes—
258C2×C4×D73C24112yes—
259C2×C4×D73C24112yes—
260C2×C4×D73C24112yes—
261C2×C4×D73C24112yes—
262C4⋊Dic73C24112yes—
263C4⋊Dic73C24112yes—
264#11924007C24112yes—
265#11924007C24112yes—
266C22⋊Dic73C24112yes—
267C22⋊Dic73C24124yes—
268C22⋊Dic73C2414yes—
269#11924005C24112yes—
270#11924005C24112yes—
271#11924005C24124yes—
272#11924005C24124yes—
273#11924005C24124yes—
274#11924005C2414yes—
275#11924005C2414yes—
276C4×Dic73C2414yes—
277C4×Dic73C24112yes—
278C4×Dic73C24112yes—
279C24×C73C2413yes—
280C24×C73C2411yescharacteristic
281#41×C73—232no—
282C2×Q8×C73—232no—
283C2×Q8×C73—212no—
284C2×Q8×C73C2×D418yes—
285C2×Q8×C73C24112yes—
286C2×Q8×C73C2414yes—
287C2×D4×C73—212no—
288C2×D4×C73—46no—
289C2×D4×C73C24112yes—
290C2×D4×C73C24112yes—
291C22×C4×C73—212no—
292C22×C4×C73—212no—
293C22×C4×C73C2411yescharacteristic
294C22×C4×C73C2413yes—
295C22×C4×C73C2413yes—
296C22×C4×C73C2411yescharacteristic
297C22×C4×C73C24112yes—
298C22×C4×C73C24112yes—
299C22×C4×C73C2413yes—
300C4⋊C4×C73C24112yes—
301C4⋊C4×C73C24112yes—
302C22⋊C4×C73C2414yes—
303C22⋊C4×C73C24112yes—
304C22⋊C4×C73C24124yes—
305C42×C73C24112yes—
306C23×C73—22no—
307C23×C73—26no—
308C23×C73—22no—
309C23×C73—26no—
310C23×C73—22no—
311C23×C73—26no—
312C23×C73C2516yes—
313C23×C73C2512yes—
314C23×C73C2511yescharacteristic
315C22×D73—26no—
316C22×D73—26no—
317C22×D73—22no—
318C22×D73—26no—
319C22×D73—22no—
320C22×D73—26no—
321C22×D73—22no—
322C22×D73—26no—
323C22×D73—248no—
324C22×D73—424no—
325C22×D73—424no—
326C22×D73—848no—
327C22×D73C22×D4112yes—
328C22×D73C2516yes—
329C22×D73C2512yes—
330C22×D73C2516yes—
331Q8×C73—224no—
332Q8×C73C22×D4116yes—
333D4×C73—224no—
334D4×C73—412no—
335C2×C4×C73—22no—
336C2×C4×C73—26no—
337C2×C4×C73—26no—
338C2×C4×C73—22no—
339C2×C4×C73—224no—
340C2×C4×C73—224no—
341C2×C4×C73C22×D4112yes—
342C2×C4×C73C2512yes—
343C2×C4×C73C2516yes—
344C2×C4×C73C2516yes—
345C2×C4×C73C2512yes—
346C2×C4×C73C2516yes—
347C22⋊D73—224no—
348C22⋊D73—224no—
349C22⋊D73—224no—
350C22⋊D73—28no—
351C22⋊D73—412no—
352C22⋊D73—412no—
353C2×Dic73—22no—
354C2×Dic73—26no—
355C2×Dic73—22no—
356C2×Dic73—26no—
357C2×Dic73C22×D414yes—
358C2×Dic73C2512yes—
359C2×Dic73C2516yes—
360C2×Dic73C2516yes—
361C2×Dic73C2512yes—
362C2×Dic73C2512yes—
363D292—224no—
364D292—224no—
365D292—224no—
366D292—412no—
367D292C22×D4148yes—
368C4×D73—248no—
369C4×D73—224no—
370C4×D73—224no—
371C4×D73—412no—
372C4×D73—412no—
373C4×D73C22×D4148yes—
374Dic146—224no—
375Dic146—224no—
376Dic146—28no—
377C22×C73—22no—
378C22×C73—26no—
379C22×C73—22no—
380C22×C73—26no—
381C22×C73—22no—
382C22×C73—26no—
383C22×C73—412no—
384C22×C73—44no—
385C22×C73C23×D412yes—
386C22×C73#58512yes—
387C22×C73#58512yes—
388C22×C73C2611yescharacteristic
389C2×D73—26no—
390C2×D73—26no—
391C2×D73—224no—
392C2×D73—22no—
393C2×D73—26no—
394C2×D73—22no—
395C2×D73—26no—
396C2×D73—22no—
397C2×D73—26no—
398C2×D73—44no—
399C2×D73—412no—
400C2×D73—848no—
401C2×D73C23×D4112yes—
402C4×C73—26no—
403C4×C73—22no—
404C4×C73—22no—
405C4×C73—26no—
406C4×C73C23×D4112yes—
407Dic73—26no—
408Dic73—22no—
409Dic73—22no—
410Dic73—26no—
411Dic73C23×D414yes—
412C2×#3500—731nomaximal, Sylow
413C2×C73—46no—
414C2×C73—42no—
415C2×C73#350014yescomplemented
416C2×C73C24×D411yescharacteristic
417C2×C73C2×#58511yescharacteristic
418C2×C73C2×#58511yescharacteristic
419D73—212no—
420D73—42no—
421D73—46no—
422C22×2−1+4—731no—
423C22×H(5,𝔽2)—731no—
424#3500—7332no—
425C2×#548—731no—
426C2×#548—731no—
427C2×#548—731no—
428C2×#548D7311yescharacteristic, complemented
429C2×#546—733no—
430C2×#546—733no—
431C2×#546—733no—
432C2×#546—733no—
433C2×#536—733no—
434C2×#535—733no—
435C2×#532—733no—
436C22×#124—733no—
437C2×C4×#41—731no—
438C73C2×#350011yescharacteristic, complemented, Sylow
439C2×2−1+4—7316no—
440C2×2−1+4—14616no—
441C2×H(5,𝔽2)—7316no—
442C2×H(5,𝔽2)—14616no—
443C22×#41—731no—
444C22×#41—731no—
445C22×#41—733no—
446C22×#41—733no—
447C22×#41—733no—
448C22×#41—733no—
449C22×#41C2×D7311yescharacteristic
450C23×Q8—733no—
451C23×Q8—731no—
452C23×Q8C2×D7311yescharacteristic, complemented
453C23×D4—733no—
454C23×D4—733no—
455C23×D4—733no—
456#548—7316no—
457#548—7316no—
458#548—7316no—
459#548C2×D73116yescomplemented
460#546—7348no—
461#546—7348no—
462#546—7348no—
463#546—7348no—
464#536—7348no—
465#535—7348no—
466#532—7348no—
467C2×C4⋊Q8—733no—
468C2×#127—733no—
469C2×#124—733no—
470C2×#124—733no—
471C2×#124—7348no—
472C2×#124—733no—
473C2×#124—736no—
474C2×#124—731no—
475C2×#124—733no—
476C2×#124C2×D7313yescomplemented
477C2×#123—736no—
478C2×#123—736no—
479C2×C22⋊Q8—733no—
480C2×C22⋊Q8—733no—
481C2×C22⋊Q8—733no—
482C2×C22⋊Q8C2×D7313yescomplemented
483C2×#121—733no—
484C2×#121—733no—
485C2×#121—733no—
486C2×#121—733no—
487C2×#121—733no—
488C2×#121—733no—
489C2×#121—733no—
490C2×#121C2×D7313yescomplemented
491C2×#120—736no—
492C2×#120—736no—
493C4×#41—7316no—
494C2×C4×Q8—731no—
495C2×C4×Q8C2×D7311yescharacteristic, complemented
496C2×C4×D4—733no—
497C2×C4×D4—733no—
498C2×C4×D4—733no—
499C2×C4×D4—733no—
500C2×C4×D4—733no—
501C2×C4×D4C2×D7313yescomplemented
502C2×#117—733no—
503C22×C22⋊C4—736no—
504C22×C22⋊C4—736no—
505C22×C42—733no—
506C25—736no—
5072−1+4—146128no—
508H(5,𝔽2)—146128no—
509C2×#41—28no—
510C2×#41—7316no—
511C2×#41—738no—
512C2×#41—7324no—
513C2×#41—738no—
514C2×#41—7324no—
515C2×#41—7324no—
516C2×#41—7324no—
517C2×#41—14624no—
518C2×#41—14624no—
519C2×#41—14624no—
520C2×#41—14624no—
521C2×#41—1468no—
522C2×#41C22×D7318yes—
523C22×Q8—28no—
524C22×Q8—7324no—
525C22×Q8—738no—
526C22×Q8—733no—
527C22×Q8—733no—
528C22×Q8—731no—
529C22×Q8—14624no—
530C22×Q8—1468no—
531C22×Q8C22×D7313yes—
532C22×Q8C22×D7311yescharacteristic
533C22×Q8C22×D7318yescomplemented
534C22×D4—733no—
535C22×D4—733no—
536C22×D4—733no—
537C22×D4—733no—
538C22×D4—733no—
539C22×D4—731no—
540C22×D4—7324no—
541C22×D4—7324no—
542C22×D4—733no—
543C22×D4—733no—
544C22×D4—733no—
545C22×D4—733no—
546C22×D4—733no—
547C22×D4—7324no—
548C22×D4—14624no—
549C22×D4—14624no—
550C22×D4—14624no—
551C22×D4C22×D7313yes—
552C22×D4C22×D7313yes—
553C23×C4—733no—
554C23×C4—733no—
555C23×C4—733no—
556C23×C4—736no—
557C23×C4—733no—
558C23×C4—733no—
559C23×C4C22×D7313yes—
560C23×C4C22×D7313yes—
561C4⋊Q8—7324no—
562#127—7324no—
563#124—7324no—
564#124—7324no—
565#124—7324no—
566#124—7348no—
567#124—738no—
568#124—7324no—
569#124C22×D73124yescomplemented
570#123—7348no—
571#123—7348no—
572C22⋊Q8—7324no—
573C22⋊Q8—7324no—
574C22⋊Q8—7324no—
575C22⋊Q8C22×D73124yescomplemented
576#121—7324no—
577#121—7324no—
578#121—7324no—
579#121—7324no—
580#121—7324no—
581#121—7324no—
582#121—7324no—
583#121C22×D73124yescomplemented
584#120—7348no—
585#120—7348no—
586C4×Q8—738no—
587C4×Q8C22×D7318yescomplemented
588C4×D4—7324no—
589C4×D4—7324no—
590C4×D4—7324no—
591C4×D4—7324no—
592C4×D4—7324no—
593C4×D4C22×D73124yescomplemented
594#117—7324no—
595C2×C4⋊C4—733no—
596C2×C4⋊C4—733no—
597C2×C4⋊C4—733no—
598C2×C4⋊C4—733no—
599C2×C4⋊C4C22×D7313yes—
600C2×C4⋊C4C22×D7313yes—
601C2×C22⋊C4—733no—
602C2×C22⋊C4—736no—
603C2×C22⋊C4—731no—
604C2×C22⋊C4—733no—
605C2×C22⋊C4—733no—
606C2×C22⋊C4—736no—
607C2×C22⋊C4—736no—
608C2×C22⋊C4—736no—
609C2×C22⋊C4—731no—
610C2×C22⋊C4—731no—
611C2×C22⋊C4—7348no—
612C2×C22⋊C4—7348no—
613C2×C22⋊C4C22×D7313yes—
614C2×C22⋊C4C22×D7316yes—
615C2×C22⋊C4C22×D7311yescharacteristic
616C2×C42—733no—
617C2×C42—733no—
618C2×C42—731no—
619C2×C42—7324no—
620C2×C42C22×D7313yes—
621C24—29212no—
622C24—29212no—
623C24—7324no—
624C24—733no—
625C24—733no—
626C24—731no—
627C24—14624no—
628C24C23×D7313yes—
629C24C23×D7311yescharacteristic
630#41—232no—
631#41—7364no—
632#41—14696no—
633#41—14696no—
634#41—14696no—
635#41—14696no—
636#41—14632no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—7312no—
640C2×Q8—7312no—
641C2×Q8—734no—
642C2×Q8—14612no—
643C2×Q8—1464no—
644C2×Q8—14696no—
645C2×Q8—14632no—
646C2×Q8—14612no—
647C2×Q8D4×D7318yes—
648C2×Q8C23×D73112yes—
649C2×Q8C23×D7314yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—2926no—
653C2×D4—2926no—
654C2×D4—2926no—
655C2×D4—7312no—
656C2×D4—7312no—
657C2×D4—7312no—
658C2×D4—7312no—
659C2×D4—7312no—
660C2×D4—734no—
661C2×D4—7324no—
662C2×D4—7312no—
663C2×D4—7312no—
664C2×D4—7312no—
665C2×D4—7312no—
666C2×D4—7312no—
667C2×D4—14696no—
668C2×D4—14612no—
669C2×D4—14612no—
670C2×D4—14696no—
671C2×D4—14612no—
672C2×D4—1464no—
673C2×D4—14696no—
674C2×D4—14612no—
675C2×D4—14612no—
676C2×D4—14612no—
677C2×D4C23×D73112yes—
678C2×D4C23×D73112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—2926no—
682C22×C4—2926no—
683C22×C4—7312no—
684C22×C4—7312no—
685C22×C4—731no—
686C22×C4—7324no—
687C22×C4—7312no—
688C22×C4—731no—
689C22×C4—733no—
690C22×C4—733no—
691C22×C4—731no—
692C22×C4—7324no—
693C22×C4—7312no—
694C22×C4—7312no—
695C22×C4—14624no—
696C22×C4—14612no—
697C22×C4—14612no—
698C22×C4C23×D73112yes—
699C22×C4C23×D73112yes—
700C22×C4C23×D7311yescharacteristic
701C22×C4C23×D7313yes—
702C22×C4C23×D7313yes—
703C22×C4C23×D7311yescharacteristic
704C22×C4C23×D7313yes—
705C4⋊C4—7312no—
706C4⋊C4—7312no—
707C4⋊C4—7312no—
708C4⋊C4—7312no—
709C4⋊C4C23×D73112yes—
710C4⋊C4C23×D73112yes—
711C22⋊C4—7312no—
712C22⋊C4—7324no—
713C22⋊C4—734no—
714C22⋊C4—7312no—
715C22⋊C4—7312no—
716C22⋊C4—7324no—
717C22⋊C4—7324no—
718C22⋊C4—7324no—
719C22⋊C4—734no—
720C22⋊C4—734no—
721C22⋊C4C23×D73112yes—
722C22⋊C4C23×D73124yes—
723C22⋊C4C23×D7314yes—
724C42—734no—
725C42—7312no—
726C42—7312no—
727C42C23×D73112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—29224no—
735C23—29224no—
736C23—58448no—
737C23—7312no—
738C23—736no—
739C23—736no—
740C23—732no—
741C23—14648no—
742C23—1462no—
743C23—1466no—
744C23—1462no—
745C23—1466no—
746C23—1462no—
747C23—1466no—
748C23—1466no—
749C23—1466no—
750C23C24×D7316yes—
751C23C24×D7312yes—
752C23C24×D7311yescharacteristic
753Q8—224no—
754Q8—14624no—
755Q8—1468no—
756Q8—14624no—
757Q8C2×D4×D73116yes—
758D4—224no—
759D4—412no—
760D4—29212no—
761D4—29212no—
762D4—29212no—
763D4—7348no—
764D4—14624no—
765D4—14624no—
766D4—14624no—
767D4—1468no—
768D4—14624no—
769D4—14624no—
770D4—14624no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—29212no—
778C2×C4—29212no—
779C2×C4—734no—
780C2×C4—732no—
781C2×C4—7348no—
782C2×C4—732no—
783C2×C4—736no—
784C2×C4—736no—
785C2×C4—732no—
786C2×C4—14648no—
787C2×C4—1462no—
788C2×C4—1466no—
789C2×C4—1462no—
790C2×C4—1466no—
791C2×C4—14624no—
792C2×C4—14624no—
793C2×C4C2×D4×D73112yes—
794C2×C4C24×D7312yes—
795C2×C4C24×D7316yes—
796C2×C4C24×D7316yes—
797C2×C4C24×D7312yes—
798C2×C4C24×D7316yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—29212no—
808C22—2924no—
809C22—58448no—
810C22—7312no—
811C22—1462no—
812C22—1466no—
813C22—1462no—
814C22—1466no—
815C22—1462no—
816C22—1466no—
817C22—1466no—
818C22—1466no—
819C22—14624no—
820C22C22×D4×D7312yes—
821C22#1798942312yes—
822C22#1798942412yes—
823C22C25×D7311yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—734no—
829C4—1462no—
830C4—1466no—
831C4—1462no—
832C4—1466no—
833C4C22×D4×D73112yes—
834C2—46no—
835C2—42no—
836C2—2926no—
837C2—2922no—
838C2—14612no—
839C2#2262372214yesdirect product factor
840C2C23×D4×D7311yescharacteristic
841C2C2×#1798942311yescharacteristic
842C2C2×#1798942411yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#548×C73C2
socleC23×C73C25
hypercenterC2×#548D73
hypocenterC73C2×#3500
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14556639C2semidirect
2. C22×#14556637C2semidirect
3. #22623722C2direct (N × H)
4. C2×#17989249C2semidirect
5. C2×#17989248C2semidirect
6. C2×#17989244C2semidirect
7. C2×#17989234C2semidirect
8. C2×#17989233C2semidirect
9. C2×#17989230C2semidirect
10. C2×#17989228C2semidirect
11. C2×#17989160C2semidirect
12. C2×#17989153C2semidirect
13. C2×#17989134C2semidirect
14. C2×#124×D73C2semidirect
15. C2×C4×#11924029C2semidirect
16. C2×#548×C73C2semidirect
18. C2×#14556639C22semidirect
20. C2×#14556637C22semidirect
23. C22×#11924029C22semidirect
25. C22×#11924028C22semidirect
26. C22×#11924028C22semidirect
27. C22×Q8×D73C22semidirect
28. C22×Q8×D73C22semidirect
32. #17989249C22semidirect
33. #17989248C22semidirect
34. #17989244C22semidirect
35. #17989234C22semidirect
36. #17989233C22semidirect
37. #17989230C22semidirect
38. #17989228C22semidirect
39. #17989160C22semidirect
40. #17989153C22semidirect
41. #17989134C22semidirect
42. C2×#14556590C22semidirect
43. C2×#14556587C22semidirect
44. C2×#14556580C22semidirect
45. C2×#14556579C22semidirect
46. C2×#14556578C22semidirect
47. C2×#14556577C22semidirect
48. C2×#14556577C22semidirect
49. C2×#14556577C22semidirect
50. #124×D73C22semidirect
51. C2×#14556576C22semidirect
52. C2×#14556573C22semidirect
53. C2×#14556571C22semidirect
54. C2×#14556570C22semidirect
55. C2×#14556567C22semidirect
56. C2×#14556566C22semidirect
57. C2×#14556566C22semidirect
58. C2×#14556565C22semidirect
59. C2×#14556564C22semidirect
60. C2×#14556564C22semidirect
61. C2×#14556562C22semidirect
62. C2×#14556562C22semidirect
63. C2×#14556561C22semidirect
64. C2×#14556559C22semidirect
65. C4×#11924029C22semidirect
66. C2×Q8×Dic73C22semidirect
67. C2×C4×D292C22semidirect
68. C2×C4×D292C22semidirect
69. C2×#14556553C22semidirect
70. C2×C4×C22⋊D73C22semidirect
71. C2×C4×C22⋊D73C22semidirect
72. C2×#14556549C22semidirect
73. C2×C22⋊C4×D73C22semidirect
74. C2×C22⋊C4×D73C22semidirect
75. C2×C42×D73C22semidirect
77. C23×Q8×C73C22semidirect
78. #548×C73C22semidirect
79. C2×#124×C73C22semidirect
80. C2×C22⋊Q8×C73C22semidirect
81. C2×#121×C73C22semidirect
82. C2×C4×Q8×C73C22semidirect
83. C2×C4×D4×C73C22semidirect
89. C2×#11924029D4semidirect
92. C2×#11924029C23semidirect
97. C2×#11924028C23semidirect
98. C2×#11924028C23semidirect
104. C2×Q8×D73C23semidirect
105. C2×Q8×D73C23semidirect
129. #14556590C23semidirect
130. #14556587C23semidirect
131. #14556580C23semidirect
132. #14556579C23semidirect
133. #14556578C23semidirect
134. #14556577C23semidirect
135. #14556577C23semidirect
136. #14556577C23semidirect
137. #14556576C23semidirect
138. #14556573C23semidirect
139. #14556571C23semidirect
140. #14556570C23semidirect
141. #14556567C23semidirect
142. #14556566C23semidirect
143. #14556566C23semidirect
144. #14556565C23semidirect
145. #14556564C23semidirect
146. #14556564C23semidirect
147. #14556562C23semidirect
148. #14556562C23semidirect
149. #14556561C23semidirect
150. #14556559C23semidirect
151. Q8×Dic73C23semidirect
152. C4×D292C23semidirect
153. C4×D292C23semidirect
154. #14556553C23semidirect
155. C4×C22⋊D73C23semidirect
156. C4×C22⋊D73C23semidirect
157. #14556549C23semidirect
172. C22⋊C4×D73C23semidirect
173. C22⋊C4×D73C23semidirect
177. C42×D73C23semidirect
183. C22×Q8×C73C23semidirect
188. #124×C73C23semidirect
189. C22⋊Q8×C73C23semidirect
190. #121×C73C23semidirect
191. C4×Q8×C73C23semidirect
192. C4×D4×C73C23semidirect
208. #11924029C2×D4semidirect
415. C2×C73#3500semidirect
428. C2×#548D73semidirect
438. C73C2×#3500semidirect
452. C23×Q8C2×D73semidirect
459. #548C2×D73semidirect
476. C2×#124C2×D73semidirect
482. C2×C22⋊Q8C2×D73semidirect
490. C2×#121C2×D73semidirect
495. C2×C4×Q8C2×D73semidirect
501. C2×C4×D4C2×D73semidirect
533. C22×Q8C22×D73semidirect
569. #124C22×D73semidirect
575. C22⋊Q8C22×D73semidirect
583. #121C22×D73semidirect
587. C4×Q8C22×D73semidirect
593. C4×D4C22×D73semidirect
839. C2#22623722direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566392
C22×#145566372
#226237222
C2×#179892492
C2×#179892482
C2×#179892442
C2×#179892342
C2×#179892332
C2×#179892302
C2×#179892282
C2×#179891602
C2×#179891532
C2×#179891342
C2×#124×D732
C2×C4×#119240292
C2×#548×C732
C2×#350073