Finite Group Databasebeta

← C2×#22623588 #33994227

Subgroups — C2×#22623588 #33994227

Order 18688.

11510 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×#41×D73C211yesmaximal, characteristic, complemented
3#22623588C2132yesmaximal, direct product factor
4C2×#17989259C211yesmaximal, characteristic, complemented
5C2×#17989258C213yesmaximal, complemented
6C2×#17989256C211yesmaximal, characteristic, complemented
7C2×#17989255C213yesmaximal, complemented
8C2×#17989248C211yesmaximal, characteristic, complemented
9C2×#17989247C213yesmaximal, complemented
10C2×#17989245C213yesmaximal, complemented
11C2×#17989155C213yesmaximal, complemented
12C2×#17989153C213yesmaximal, complemented
13C2×#17989100C213yesmaximal, complemented
14C2×#17989096C213yesmaximal, complemented
15C2×#17989063C211yesmaximal, characteristic, complemented
16C2×#548×C73C211yesmaximal, characteristic, complemented
17C2×#14556639—216no—
18C2×#14556639C22116yescomplemented
19C22×#11924029C2213yes—
20C22×#11924029C2211yescharacteristic
21C22×#11924029C2211yescharacteristic, complemented
22C22×#11924028C2213yes—
23C22×#11924028C2213yes—
24C22×#11924028C2213yescomplemented
25C22×#11924027C2213yes—
26C2×#41×D73—216no—
27C2×#41×D73C22116yescomplemented
28C22×Q8×D73C2211yescharacteristic
29C22×Q8×D73C2213yescomplemented
30C22×D4×D73C2213yes—
31C23×C4×D73C2213yes—
32#17989259C22116yescomplemented
33#17989258C22148yescomplemented
34#17989256C22116yescomplemented
35#17989255C22148yescomplemented
36#17989248C22116yescomplemented
37#17989247C22148yescomplemented
38#17989245C22148yescomplemented
39#17989155C22148yescomplemented
40#17989153C22148yescomplemented
41C2×#14556588C2213yescomplemented
42C2×#14556587C2216yescomplemented
43C2×#14556587C2213yescomplemented
44C2×#14556580C2213yescomplemented
45C2×#14556577C2216yescomplemented
46#17989100C22148yescomplemented
47#17989096C22148yescomplemented
48C2×#14556576C2213yes—
49C2×#14556573C2211yescharacteristic
50C2×#14556569C2213yescomplemented
51C2×#14556568C2213yescomplemented
52C2×#14556567C2213yescomplemented
53C2×#14556566C2213yescomplemented
54C2×#14556566C2213yescomplemented
55C2×#14556565C2213yescomplemented
56C2×#14556565C2213yescomplemented
57C2×#14556564C2216yescomplemented
58C2×#14556564C2216yescomplemented
59C2×#14556564C2213yescomplemented
60C2×#14556563C2213yescomplemented
61C2×#14556562C2213yescomplemented
62C2×#14556561C2216yes—
63C2×#14556561C2213yes—
64C2×#14556559C2213yes—
65#17989063C22116yescomplemented
66C2×Q8×Dic73C2211yescharacteristic, complemented
67C2×C4×Dic146C2213yescomplemented
68C2×#14556556C2213yescomplemented
69C2×C4×D292C2213yescomplemented
70C2×#14556553C2216yescomplemented
71C2×C4×C22⋊D73C2213yescomplemented
72C2×C4×C22⋊D73C2213yescomplemented
73C2×#14556551C2216yescomplemented
74C2×#14556549C2213yes—
75C2×#14556548C2213yes—
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×D73C2313yes—
85#14556639—2128no—
86C2×#11924029—224no—
87C2×#11924029—28no—
88C2×#11924029—28no—
89C2×#11924029C23124yes—
90C2×#11924029C2318yes—
91C2×#11924029C2318yescomplemented
92C2×#11924028—224no—
93C2×#11924028—224no—
94C2×#11924028—224no—
95C2×#11924028C23124yes—
96C2×#11924028C23124yes—
97C2×#11924028C23124yescomplemented
98C2×#11924027—224no—
99C2×#11924027C23124yes—
100#41×D73—2128no—
101C22×Dic146C2313yes—
102C22×Dic146C2313yes—
103C2×Q8×D73—224no—
104C2×Q8×D73D4116yescomplemented
105C2×Q8×D73C2318yes—
106C2×Q8×D73C23124yescomplemented
107C22×D292C2313yes—
108C22×D292C2313yes—
109C22×D292C2313yes—
110C22×D292C2316yes—
111C22×D292C2313yes—
112C22×C22⋊D73C2313yes—
113C22×C22⋊D73C2316yes—
114C22×C22⋊D73C2311yescharacteristic
115C22×C22⋊D73C2316yes—
116C22×C22⋊D73C2313yes—
117C22×C22⋊D73C2313yes—
118C2×D4×D73—224no—
119C2×D4×D73C23124yes—
120C23×Dic73C2313yes—
121C22×C4×D73—224no—
122C22×C4×D73C2311yescharacteristic
123C22×C4×D73C23124yes—
124C22×C4×D73C2313yes—
125C22×C4×D73C2313yes—
126C22×C4×D73C2313yes—
127C22×C4×D73C2316yes—
128C22×C4×D73C2313yes—
129#14556588C23124yescomplemented
130#14556587C23148yescomplemented
131#14556587C23124yescomplemented
132#14556580C23124yescomplemented
133#14556577C23148yescomplemented
134#14556576C23124yes—
135#14556573C2318yes—
136#14556569C23124yescomplemented
137#14556568C23124yescomplemented
138#14556567C23124yescomplemented
139#14556566C23124yescomplemented
140#14556566C23124yescomplemented
141#14556565C23124yescomplemented
142#14556565C23124yescomplemented
143#14556564C23148yescomplemented
144#14556564C23148yescomplemented
145#14556564C23124yescomplemented
146#14556563C23124yescomplemented
147#14556562C23124yescomplemented
148#14556561C23148yes—
149#14556561C23124yes—
150#14556559C23124yes—
151Q8×Dic73C2318yescomplemented
152C4×Dic146C23124yescomplemented
153#14556556C23124yescomplemented
154C4×D292C23124yescomplemented
155#14556553C23148yescomplemented
156C4×C22⋊D73C23124yescomplemented
157C4×C22⋊D73C23124yescomplemented
158#14556551C23148yescomplemented
159#14556549C23124yes—
160#14556548C23124yes—
161C2×C4⋊Dic73C2313yes—
162C2×C4⋊Dic73C2311yescharacteristic
163C2×#11924007C2313yes—
164C2×#11924007C2313yes—
165C2×#11924007C2313yes—
166C2×#11924007C2311yescharacteristic
167C2×C22⋊Dic73C2311yescharacteristic
168C2×C22⋊Dic73C2313yes—
169C2×#11924005C2311yescharacteristic
170C2×#11924005C2313yes—
171C2×#11924005C2313yes—
172C2×#11924005C2313yes—
173C2×#11924005C2313yes—
174C2×#11924005C2316yes—
175C2×#11924005C2313yes—
176C2×C4×Dic73C2313yes—
177C2×C4×Dic73C2316yes—
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—212no—
200C23×D73—46no—
201C23×D73—46no—
202C23×D73C2413yes—
203C23×D73C2413yes—
204C23×D73C2411yescharacteristic
205C23×D73C24112yes—
206#11924029—232no—
207#11924029—232no—
208#11924029—296no—
209#11924028—296no—
210#11924028—296no—
211#11924028—296no—
212#11924027—296no—
213C2×Dic146—212no—
214C2×Dic146C2×D4124yes—
215C2×Dic146C24112yes—
216C2×Dic146C24112yes—
217Q8×D73—296no—
218Q8×D73C2×D4164yescomplemented
219C2×D292—212no—
220C2×D292—212no—
221C2×D292—212no—
222C2×D292—412no—
223C2×D292—46no—
224C2×D292C24112yes—
225C2×D292C24112yes—
226C2×D292C24112yes—
227C2×D292C24124yes—
228C2×D292C24112yes—
229C2×C22⋊D73—24no—
230C2×C22⋊D73—224no—
231C2×C22⋊D73—212no—
232C2×C22⋊D73—412no—
233C2×C22⋊D73—46no—
234C2×C22⋊D73—46no—
235C2×C22⋊D73C2414yes—
236C2×C22⋊D73C24112yes—
237C2×C22⋊D73C24124yes—
238C2×C22⋊D73C24124yes—
239C2×C22⋊D73C24112yes—
240C2×C22⋊D73C24112yes—
241D4×D73—296no—
242C22×Dic73—212no—
243C22×Dic73C2411yescharacteristic
244C22×Dic73C2413yes—
245C22×Dic73C2411yescharacteristic
246C22×Dic73C2411yescharacteristic
247C22×Dic73C24112yes—
248C22×Dic73C2413yes—
249C2×C4×D73—24no—
250C2×C4×D73—212no—
251C2×C4×D73—212no—
252C2×C4×D73—212no—
253C2×C4×D73—224no—
254C2×C4×D73—296no—
255C2×C4×D73C2×D4124yes—
256C2×C4×D73C24124yes—
257C2×C4×D73C24112yes—
258C2×C4×D73C24112yes—
259C2×C4×D73C24112yes—
260C2×C4×D73C2414yes—
261C2×C4×D73C24112yes—
262C4⋊Dic73C24112yes—
263C4⋊Dic73C2414yes—
264#11924007C24112yes—
265#11924007C24112yes—
266#11924007C24112yes—
267#11924007C2414yes—
268C22⋊Dic73C2414yes—
269C22⋊Dic73C24112yes—
270#11924005C2414yes—
271#11924005C24112yes—
272#11924005C24112yes—
273#11924005C24112yes—
274#11924005C24112yes—
275#11924005C24124yes—
276#11924005C24112yes—
277C4×Dic73C24112yes—
278C4×Dic73C24124yes—
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—22no—
316C22×D73—22no—
317C22×D73—26no—
318C22×D73—26no—
319C22×D73—26no—
320C22×D73—26no—
321C22×D73—26no—
322C22×D73—26no—
323C22×D73—224no—
324C22×D73—412no—
325C22×D73—412no—
326C22×D73—448no—
327C22×D73C22×D414yes—
328C22×D73C2516yes—
329C22×D73C2516yes—
330C22×D73C2512yes—
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—28no—
348C22⋊D73—248no—
349C22⋊D73—224no—
350C22⋊D73—412no—
351C22⋊D73—424no—
352C22⋊D73—412no—
353C2×Dic73—22no—
354C2×Dic73—22no—
355C2×Dic73—22no—
356C2×Dic73—26no—
357C2×Dic73—224no—
358C2×Dic73C22×D4112yes—
359C2×Dic73C2512yes—
360C2×Dic73C2516yes—
361C2×Dic73C2512yes—
362C2×Dic73C2512yes—
363C2×Dic73C2516yes—
364D292—224no—
365D292—224no—
366D292—224no—
367D292—412no—
368D292—424no—
369C4×D73—28no—
370C4×D73—224no—
371C4×D73—224no—
372C4×D73—224no—
373C4×D73—248no—
374C4×D73C22×D4148yes—
375Dic146—224no—
376Dic146C22×D4148yes—
377C22×C73—26no—
378C22×C73—22no—
379C22×C73—22no—
380C22×C73—26no—
381C22×C73—26no—
382C22×C73—22no—
383C22×C73—412no—
384C22×C73—44no—
385C22×C73C23×D412yes—
386C22×C73#58512yes—
387C22×C73#58512yes—
388C22×C73C2611yescharacteristic
389C2×D73—22no—
390C2×D73—22no—
391C2×D73—28no—
392C2×D73—26no—
393C2×D73—26no—
394C2×D73—26no—
395C2×D73—26no—
396C2×D73—26no—
397C2×D73—26no—
398C2×D73—448no—
399C2×D73—412no—
400C2×D73—412no—
401C2×D73C23×D414yes—
402C4×C73—26no—
403C4×C73—22no—
404C4×C73—22no—
405C4×C73—26no—
406C4×C73C23×D4112yes—
407Dic73—22no—
408Dic73—22no—
409Dic73—22no—
410Dic73—26no—
411Dic73C23×D4112yes—
412C2×#3487—731nomaximal, Sylow
413C2×C73—46no—
414C2×C73—42no—
415C2×C73#348714yescomplemented
416C2×C73C24×D411yescharacteristic
417C2×C73C2×#58511yescharacteristic
418C2×C73C2×#58511yescharacteristic
419D73—24no—
420D73—46no—
421D73—46no—
422C22×2−1+4—731no—
423C23×#41—731no—
424#3487—7332no—
425C2×#550—731no—
426C2×#550—733no—
427C2×#550—731no—
428C2×#550—733no—
429C2×#548—731no—
430C2×#548—733no—
431C2×#548—733no—
432C2×#548D7311yescharacteristic, complemented
433C2×#535—733no—
434C2×#535—733no—
435C2×#525—733no—
436C2×#525—733no—
437C2×#519—731no—
438C73C2×#348711yescharacteristic, complemented, Sylow
439C2×2−1+4—7316no—
440C2×2−1+4—14616no—
441C22×#41—7316no—
442C22×#41—731no—
443C22×#41—733no—
444C22×#41—731no—
445C22×#41—733no—
446C22×#41—733no—
447C22×#41—733no—
448C22×#41—733no—
449C22×#41—14616no—
450C22×#41C2×D7311yescharacteristic
451C23×Q8—731no—
452C23×Q8—733no—
453C23×Q8C2×D7311yescharacteristic, complemented
454C23×D4—733no—
455C24×C4—733no—
456#550—7316no—
457#550—7348no—
458#550—7316no—
459#550—7348no—
460#548—7316no—
461#548—7348no—
462#548—7348no—
463#548C2×D73116yescomplemented
464#535—7348no—
465#535—7348no—
466C2×#127—733no—
467C2×#127—736no—
468C2×#127—733no—
469C2×#124—733no—
470C2×#124—736no—
471C2×#124C2×D7313yescomplemented
472#525—7348no—
473#525—7348no—
474C2×#123—733no—
475C2×#123—731no—
476C2×C22⋊Q8—733no—
477C2×C22⋊Q8—733no—
478C2×C22⋊Q8—733no—
479C2×C22⋊Q8C2×D7313yescomplemented
480C2×#121—733no—
481C2×#121—733no—
482C2×#121—733no—
483C2×#121—733no—
484C2×#121—733no—
485C2×#121—733no—
486C2×#121—733no—
487C2×#121—736no—
488C2×#121—736no—
489C2×#121C2×D7313yescomplemented
490C2×#120—733no—
491C2×#120—736no—
492C2×#120—733no—
493#519—7316no—
494C2×C4×Q8—731no—
495C2×C4×Q8—733no—
496C2×C4×Q8—733no—
497C2×C4×Q8C2×D7311yescharacteristic, complemented
498C2×C4×D4—733no—
499C2×C4×D4—733no—
500C2×C4×D4—736no—
501C2×C4×D4—736no—
502C2×C4×D4—733no—
503C2×C4×D4C2×D7313yescomplemented
504C2×#117—733no—
505C2×#117—733no—
506C25—733no—
5072−1+4—146128no—
508C2×#41—28no—
509C2×#41—7324no—
510C2×#41—738no—
511C2×#41—738no—
512C2×#41—7324no—
513C2×#41—7324no—
514C2×#41—7324no—
515C2×#41—7324no—
516C2×#41—14624no—
517C2×#41—14624no—
518C2×#41—14624no—
519C2×#41—14624no—
520C2×#41—14624no—
521C2×#41—146128no—
522C2×#41—1468no—
523C2×#41—1468no—
524C2×#41C22×D7318yes—
525C22×Q8—28no—
526C22×Q8—7316no—
527C22×Q8—738no—
528C22×Q8—7324no—
529C22×Q8—733no—
530C22×Q8—733no—
531C22×Q8—14624no—
532C22×Q8C22×D7313yes—
533C22×Q8C22×D7311yescharacteristic
534C22×Q8C22×D7318yescomplemented
535C22×D4—733no—
536C22×D4—733no—
537C22×D4—736no—
538C22×D4—731no—
539C22×D4—736no—
540C22×D4—733no—
541C22×D4—7324no—
542C22×D4—736no—
543C22×D4—733no—
544C22×D4—733no—
545C22×D4—733no—
546C22×D4—733no—
547C22×D4—14624no—
548C22×D4C22×D7313yes—
549C22×D4C22×D7313yes—
550C23×C4—733no—
551C23×C4—733no—
552C23×C4—736no—
553C23×C4—733no—
554C23×C4—733no—
555C23×C4—733no—
556C23×C4—731no—
557C23×C4—7324no—
558C23×C4—14624no—
559C23×C4C22×D7313yes—
560C23×C4C22×D7313yes—
561#127—7324no—
562#127—7348no—
563#127—7324no—
564#124—7324no—
565#124—7348no—
566#124C22×D73124yescomplemented
567#123—7324no—
568#123—738no—
569C22⋊Q8—7324no—
570C22⋊Q8—7324no—
571C22⋊Q8—7324no—
572C22⋊Q8C22×D73124yescomplemented
573#121—7324no—
574#121—7324no—
575#121—7324no—
576#121—7324no—
577#121—7324no—
578#121—7324no—
579#121—7324no—
580#121—7348no—
581#121—7348no—
582#121C22×D73124yescomplemented
583#120—7324no—
584#120—7348no—
585#120—7324no—
586C4×Q8—738no—
587C4×Q8—7324no—
588C4×Q8—7324no—
589C4×Q8C22×D7318yescomplemented
590C4×D4—7324no—
591C4×D4—7324no—
592C4×D4—7348no—
593C4×D4—7348no—
594C4×D4—7324no—
595C4×D4C22×D73124yescomplemented
596#117—7324no—
597#117—7324no—
598C2×C4⋊C4—733no—
599C2×C4⋊C4—733no—
600C2×C4⋊C4—733no—
601C2×C4⋊C4—731no—
602C2×C4⋊C4—733no—
603C2×C4⋊C4—731no—
604C2×C4⋊C4C22×D7313yes—
605C2×C4⋊C4C22×D7313yes—
606C2×C22⋊C4—731no—
607C2×C22⋊C4—733no—
608C2×C22⋊C4—733no—
609C2×C22⋊C4—731no—
610C2×C22⋊C4—733no—
611C2×C22⋊C4—733no—
612C2×C22⋊C4—733no—
613C2×C22⋊C4—736no—
614C2×C22⋊C4—733no—
615C2×C22⋊C4C22×D7316yes—
616C2×C22⋊C4C22×D7311yescharacteristic
617C2×C22⋊C4C22×D7313yes—
618C2×C42—736no—
619C2×C42—733no—
620C2×C42C22×D7313yes—
621C24—2926no—
622C24—2926no—
623C24—7312no—
624C24—731no—
625C24—733no—
626C24—733no—
627C24—14612no—
628C24C23×D7313yes—
629C24C23×D7311yescharacteristic
630#41—232no—
631#41—14696no—
632#41—14696no—
633#41—14696no—
634#41—14696no—
635#41—14696no—
636#41—14632no—
637#41—14632no—
638C2×Q8—232no—
639C2×Q8—212no—
640C2×Q8—7364no—
641C2×Q8—7324no—
642C2×Q8—7312no—
643C2×Q8—7312no—
644C2×Q8—14612no—
645C2×Q8—14696no—
646C2×Q8D4×D7318yes—
647C2×Q8C23×D73112yes—
648C2×Q8C23×D7314yes—
649C2×D4—212no—
650C2×D4—46no—
651C2×D4—29212no—
652C2×D4—2926no—
653C2×D4—2926no—
654C2×D4—2926no—
655C2×D4—29212no—
656C2×D4—7312no—
657C2×D4—7324no—
658C2×D4—7312no—
659C2×D4—734no—
660C2×D4—7324no—
661C2×D4—7312no—
662C2×D4—7324no—
663C2×D4—7312no—
664C2×D4—7312no—
665C2×D4—7312no—
666C2×D4—7312no—
667C2×D4—14612no—
668C2×D4—14696no—
669C2×D4—14624no—
670C2×D4—14612no—
671C2×D4—1464no—
672C2×D4—14612no—
673C2×D4—14612no—
674C2×D4C23×D73112yes—
675C2×D4C23×D73112yes—
676C22×C4—212no—
677C22×C4—212no—
678C22×C4—733no—
679C22×C4—7324no—
680C22×C4—7312no—
681C22×C4—7312no—
682C22×C4—731no—
683C22×C4—733no—
684C22×C4—731no—
685C22×C4—731no—
686C22×C4—7324no—
687C22×C4—7312no—
688C22×C4—7312no—
689C22×C4—7312no—
690C22×C4—734no—
691C22×C4—14612no—
692C22×C4—14696no—
693C22×C4—14624no—
694C22×C4—1464no—
695C22×C4—14612no—
696C22×C4—14612no—
697C22×C4—14612no—
698C22×C4C23×D73112yes—
699C22×C4C23×D73112yes—
700C22×C4C23×D7313yes—
701C22×C4C23×D7311yescharacteristic
702C22×C4C23×D7313yes—
703C22×C4C23×D7311yescharacteristic
704C22×C4C23×D7313yes—
705C4⋊C4—7312no—
706C4⋊C4—7312no—
707C4⋊C4—734no—
708C4⋊C4—7312no—
709C4⋊C4—7312no—
710C4⋊C4—734no—
711C4⋊C4C23×D73112yes—
712C4⋊C4C23×D73112yes—
713C22⋊C4—734no—
714C22⋊C4—7312no—
715C22⋊C4—7312no—
716C22⋊C4—734no—
717C22⋊C4—7312no—
718C22⋊C4—7312no—
719C22⋊C4—7312no—
720C22⋊C4—7324no—
721C22⋊C4—7312no—
722C22⋊C4C23×D73124yes—
723C22⋊C4C23×D7314yes—
724C22⋊C4C23×D73112yes—
725C42—7324no—
726C42—7312no—
727C42C23×D73112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—29212no—
735C23—29212no—
736C23—29248no—
737C23—734no—
738C23—732no—
739C23—736no—
740C23—736no—
741C23—14624no—
742C23—1466no—
743C23—1466no—
744C23—1466no—
745C23—1466no—
746C23—1466no—
747C23—1466no—
748C23—1462no—
749C23—1462no—
750C23C24×D7316yes—
751C23C24×D7312yes—
752C23C24×D7311yescharacteristic
753Q8—224no—
754Q8—7348no—
755Q8—14624no—
756Q8C2×D4×D73116yes—
757D4—224no—
758D4—412no—
759D4—29224no—
760D4—29212no—
761D4—29212no—
762D4—29212no—
763D4—29224no—
764D4—14624no—
765D4—14648no—
766D4—14624no—
767D4—1468no—
768D4—14624no—
769D4—14624no—
770C2×C4—22no—
771C2×C4—26no—
772C2×C4—26no—
773C2×C4—22no—
774C2×C4—224no—
775C2×C4—224no—
776C2×C4—7312no—
777C2×C4—736no—
778C2×C4—7348no—
779C2×C4—732no—
780C2×C4—736no—
781C2×C4—732no—
782C2×C4—732no—
783C2×C4—14624no—
784C2×C4—14648no—
785C2×C4—1468no—
786C2×C4—14624no—
787C2×C4—1462no—
788C2×C4—1462no—
789C2×C4—1462no—
790C2×C4—1466no—
791C2×C4—14624no—
792C2×C4—14624no—
793C2×C4C2×D4×D73112yes—
794C2×C4C24×D7316yes—
795C2×C4C24×D7312yes—
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—29248no—
808C22—29212no—
809C22—29212no—
810C22—734no—
811C22—1466no—
812C22—1466no—
813C22—1466no—
814C22—1466no—
815C22—1466no—
816C22—1466no—
817C22—1468no—
818C22—1462no—
819C22—1462no—
820C22C22×D4×D7312yes—
821C22#1798942312yes—
822C22#1798942412yes—
823C22C25×D7311yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—7312no—
829C4—1462no—
830C4—1462no—
831C4—1462no—
832C4—1466no—
833C4C22×D4×D73112yes—
834C2—46no—
835C2—42no—
836C2—2926no—
837C2—2926no—
838C2—1464no—
839C2#2262358814yesdirect 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×#3487
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×#41×D73C2semidirect
3. #22623588C2direct (N × H)
4. C2×#17989259C2semidirect
5. C2×#17989258C2semidirect
6. C2×#17989256C2semidirect
7. C2×#17989255C2semidirect
8. C2×#17989248C2semidirect
9. C2×#17989247C2semidirect
10. C2×#17989245C2semidirect
11. C2×#17989155C2semidirect
12. C2×#17989153C2semidirect
13. C2×#17989100C2semidirect
14. C2×#17989096C2semidirect
15. C2×#17989063C2semidirect
16. C2×#548×C73C2semidirect
18. C2×#14556639C22semidirect
21. C22×#11924029C22semidirect
24. C22×#11924028C22semidirect
27. C2×#41×D73C22semidirect
29. C22×Q8×D73C22semidirect
32. #17989259C22semidirect
33. #17989258C22semidirect
34. #17989256C22semidirect
35. #17989255C22semidirect
36. #17989248C22semidirect
37. #17989247C22semidirect
38. #17989245C22semidirect
39. #17989155C22semidirect
40. #17989153C22semidirect
41. C2×#14556588C22semidirect
42. C2×#14556587C22semidirect
43. C2×#14556587C22semidirect
44. C2×#14556580C22semidirect
45. C2×#14556577C22semidirect
46. #17989100C22semidirect
47. #17989096C22semidirect
50. C2×#14556569C22semidirect
51. C2×#14556568C22semidirect
52. C2×#14556567C22semidirect
53. C2×#14556566C22semidirect
54. C2×#14556566C22semidirect
55. C2×#14556565C22semidirect
56. C2×#14556565C22semidirect
57. C2×#14556564C22semidirect
58. C2×#14556564C22semidirect
59. C2×#14556564C22semidirect
60. C2×#14556563C22semidirect
61. C2×#14556562C22semidirect
65. #17989063C22semidirect
66. C2×Q8×Dic73C22semidirect
67. C2×C4×Dic146C22semidirect
68. C2×#14556556C22semidirect
69. C2×C4×D292C22semidirect
70. C2×#14556553C22semidirect
71. C2×C4×C22⋊D73C22semidirect
72. C2×C4×C22⋊D73C22semidirect
73. C2×#14556551C22semidirect
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
91. C2×#11924029C23semidirect
97. C2×#11924028C23semidirect
104. C2×Q8×D73D4semidirect
106. C2×Q8×D73C23semidirect
129. #14556588C23semidirect
130. #14556587C23semidirect
131. #14556587C23semidirect
132. #14556580C23semidirect
133. #14556577C23semidirect
136. #14556569C23semidirect
137. #14556568C23semidirect
138. #14556567C23semidirect
139. #14556566C23semidirect
140. #14556566C23semidirect
141. #14556565C23semidirect
142. #14556565C23semidirect
143. #14556564C23semidirect
144. #14556564C23semidirect
145. #14556564C23semidirect
146. #14556563C23semidirect
147. #14556562C23semidirect
151. Q8×Dic73C23semidirect
152. C4×Dic146C23semidirect
153. #14556556C23semidirect
154. C4×D292C23semidirect
155. #14556553C23semidirect
156. C4×C22⋊D73C23semidirect
157. C4×C22⋊D73C23semidirect
158. #14556551C23semidirect
183. C22×Q8×C73C23semidirect
188. #124×C73C23semidirect
189. C22⋊Q8×C73C23semidirect
190. #121×C73C23semidirect
191. C4×Q8×C73C23semidirect
192. C4×D4×C73C23semidirect
218. Q8×D73C2×D4semidirect
415. C2×C73#3487semidirect
432. C2×#548D73semidirect
438. C73C2×#3487semidirect
453. C23×Q8C2×D73semidirect
463. #548C2×D73semidirect
471. C2×#124C2×D73semidirect
479. C2×C22⋊Q8C2×D73semidirect
489. C2×#121C2×D73semidirect
497. C2×C4×Q8C2×D73semidirect
503. C2×C4×D4C2×D73semidirect
534. C22×Q8C22×D73semidirect
566. #124C22×D73semidirect
572. C22⋊Q8C22×D73semidirect
582. #121C22×D73semidirect
589. C4×Q8C22×D73semidirect
595. C4×D4C22×D73semidirect
839. C2#22623588direct (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×#41×D732
#226235882
C2×#179892592
C2×#179892582
C2×#179892562
C2×#179892552
C2×#179892482
C2×#179892472
C2×#179892452
C2×#179891552
C2×#179891532
C2×#179891002
C2×#179890962
C2×#179890632
C2×#548×C732
C2×#348773