Finite Group Databasebeta

← #33247018

Subgroups — #33247018

Order 18688.

5050 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556639C211yesmaximal, characteristic
2C2×#17989063C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
4#22612771C213yesmaximal, complemented
5#22612769C211yesmaximal, characteristic, complemented
6#22612769C211yesmaximal, characteristic, complemented
7#22612768C213yesmaximal, complemented
8Q8×C22⋊Dic73C211yesmaximal, characteristic, complemented
9#22612765C213yesmaximal, complemented
10#22612765C213yesmaximal, complemented
11#22612522C213yesmaximal, complemented
12#22612520C213yesmaximal, complemented
13#22612420C213yesmaximal, complemented
14#22612417C213yesmaximal, complemented
15Q8×C22⋊C4×C73C211yesmaximal, characteristic, complemented
16C2×#14556639—28no—
17C2×#14556639—28no—
18C2×#14556639C4116yescomplemented
19C22×#11924029C2213yes—
20C22×#11924029C2211yescharacteristic
21C22×#11924028C2213yes—
22C22×#11924028C2213yes—
23C22×Q8×D73C2213yes—
24C22×Q8×D73C2211yescharacteristic
25#17989063—28no—
26C2×Q8×Dic73C2211yescharacteristic
27C2×Q8×Dic73C2211yescharacteristic
28C2×C4×Dic146C2213yes—
29C2×C4×Dic146C2213yes—
30C2×#14556556C2213yes—
31C2×#14556556C2213yes—
32C4×Q8×D73—28no—
33C2×#14556549C2213yes—
34C2×#14556548C2213yes—
35C2×C4⋊C4×D73C2213yes—
36C2×C42×D73C2213yes—
37#17988494C2213yes—
38#17988494C2213yes—
39#17988491C2216yes—
40#17988491C2213yes—
41#17988491C2213yes—
42#17988489C2213yes—
43#17988489C2213yes—
44#17988488C2213yes—
45#17988488C2213yes—
46#17988487C2213yes—
47#17988487C2216yes—
48#17988487C2213yes—
49#17988465C2216yes—
50#17988465C2213yes—
51#17988465C2213yes—
52#17988463C2213yes—
53#17988463C2211yescharacteristic
54#17988447C2213yes—
55#17988446C2216yes—
56#17988446C2216yes—
57#17988444C2213yes—
58#17988444C2213yes—
59C4×#11924005C2213yes—
60C4×#11924005C2213yes—
61C4×C22⋊Dic73C2213yes—
62#17988434C2216yes—
63#17988434C2216yes—
64C23×Q8×C73C2211yescharacteristic
65C2×C4×Q8×C73C2211yescharacteristic
66C2×C4×Q8×C73C2211yescharacteristic
67#391×C73C2213yes—
68#391×C73C2213yes—
69#380×C73C2213yes—
70C4×C22⋊C4×C73C2213yes—
71#14556639—2128no—
72C2×#11924029—212no—
73C2×#11924029—212no—
74C2×#11924029—24no—
75C2×#11924029—24no—
76C2×#11924029C2×C4124yes—
77C2×#11924029C2×C418yescomplemented
78C2×#11924028—212no—
79C2×#11924028—212no—
80C2×#11924028—212no—
81C2×#11924028—212no—
82C2×#11924028C2×C4124yes—
83C2×#11924028C2×C4124yescomplemented
84C22×Dic146C2313yes—
85C22×Dic146C2313yes—
86C2×Q8×D73—212no—
87C2×Q8×D73—212no—
88C2×Q8×D73C2×C418yes—
89C2×Q8×D73C2×C4124yescomplemented
90C2×Q8×D73D418yes—
91C2×Q8×D73D418yes—
92C22×D292C2313yes—
93C22×D292C2313yes—
94C22×C22⋊D73C2311yescharacteristic
95C22×C22⋊D73C2313yes—
96C22×C4×D73C2311yescharacteristic
97C22×C4×D73C2316yes—
98C22×C4×D73C2313yes—
99C22×C4×D73C2313yes—
100C22×C4×D73C2313yes—
101Q8×Dic73—24no—
102Q8×Dic73—24no—
103C4×Dic146—212no—
104C4×Dic146—212no—
105#14556556—212no—
106#14556556—212no—
107#14556549—212no—
108#14556548—212no—
109C2×C4⋊Dic73C2313yes—
110C2×C4⋊Dic73C2313yes—
111C2×#11924007C2316yes—
112C2×#11924007C2313yes—
113C2×#11924007C2313yes—
114C4⋊C4×D73—212no—
115C2×C22⋊Dic73C2311yescharacteristic
116C2×C22⋊Dic73C2313yes—
117C2×#11924005C2313yes—
118C2×#11924005C2313yes—
119C2×#11924005C2311yescharacteristic
120C2×#11924005C2313yes—
121C2×#11924005C2316yes—
122C2×#11924005C2316yes—
123C2×#11924005C2313yes—
124C2×#11924005C2313yes—
125C2×C4×Dic73C2313yes—
126C2×C4×Dic73C2313yes—
127C2×C4×Dic73C2316yes—
128C2×C4×Dic73C2313yes—
129C2×C4×Dic73C2313yes—
130C42×D73—212no—
131#14556498C2313yes—
132#14556498C2316yes—
133#14556498C2313yes—
134#14556498C2311yescharacteristic
135#14556498C2311yescharacteristic
136#14556498C2313yes—
137#14556498C2313yes—
138C22×Q8×C73—24no—
139C22×Q8×C73—24no—
140C22×Q8×C73C2×C418yescomplemented
141C22×Q8×C73C2313yes—
142C22×Q8×C73C2311yescharacteristic
143C23×C4×C73C2313yes—
144C4×Q8×C73—24no—
145C4×Q8×C73—24no—
146C2×C4⋊C4×C73C2313yes—
147C2×C4⋊C4×C73C2313yes—
148C2×C22⋊C4×C73C2311yescharacteristic
149C2×C22⋊C4×C73C2313yes—
150C2×C42×C73C2313yes—
151C2×C42×C73C2313yes—
152#95×C73C2313yes—
153#95×C73C2313yes—
154#95×C73C2316yes—
155C23×D73C2413yes—
156C23×D73C2411yescharacteristic
157#11924029—232no—
158#11924029—296no—
159#11924028—296no—
160#11924028—296no—
161C2×Dic146—26no—
162C2×Dic146—26no—
163C2×Dic146C22×C4112yes—
164C2×Dic146C22×C4112yes—
165C2×Dic146C2×D4112yes—
166C2×Dic146C2×D4112yes—
167Q8×D73—296no—
168Q8×D73C22⋊C4164yescomplemented
169C2×D292—26no—
170C2×D292—26no—
171C2×D292—26no—
172C2×D292—26no—
173C2×D292C22×C4112yes—
174C2×D292C22×C4112yes—
175C2×C22⋊D73—22no—
176C2×C22⋊D73—22no—
177C2×C22⋊D73—26no—
178C2×C22⋊D73—26no—
179C2×C22⋊D73C22×C414yes—
180C2×C22⋊D73C22×C4112yes—
181C22×Dic73C2411yescharacteristic
182C22×Dic73C2413yes—
183C22×Dic73C2413yes—
184C22×Dic73C2411yescharacteristic
185C22×Dic73C2411yescharacteristic
186C22×Dic73C2413yes—
187C2×C4×D73—22no—
188C2×C4×D73—26no—
189C2×C4×D73—26no—
190C2×C4×D73—22no—
191C2×C4×D73—212no—
192C2×C4×D73—212no—
193C2×C4×D73—22no—
194C2×C4×D73—26no—
195C2×C4×D73—43no—
196C2×C4×D73—43no—
197C2×C4×D73C22×C4112yes—
198C2×C4×D73C22×C4124yes—
199C2×C4×D73C22×C4112yes—
200C2×C4×D73C2×D4112yes—
201C2×C4×D73C2×D4112yes—
202C4⋊Dic73—26no—
203C4⋊Dic73—26no—
204#11924007—212no—
205#11924007—26no—
206#11924007—26no—
207C22⋊Dic73—22no—
208C22⋊Dic73—43no—
209#11924005—22no—
210#11924005—26no—
211#11924005—26no—
212#11924005—26no—
213#11924005—43no—
214#11924005—46no—
215#11924005—46no—
216#11924005—43no—
217C4×Dic73—26no—
218C4×Dic73—26no—
219C4×Dic73—26no—
220C4×Dic73—26no—
221C4×Dic73—212no—
222C24×C73C2411yescharacteristic
223C2×Q8×C73—232no—
224C2×Q8×C73—26no—
225C2×Q8×C73—26no—
226C2×Q8×C73C22×C4112yes—
227C2×Q8×C73C22×C414yes—
228C2×Q8×C73C2×D414yes—
229C2×Q8×C73C2×D414yes—
230C22×C4×C73—26no—
231C22×C4×C73—26no—
232C22×C4×C73C22×C4112yes—
233C22×C4×C73C2411yescharacteristic
234C22×C4×C73C2413yes—
235C22×C4×C73C2413yes—
236C22×C4×C73C2413yes—
237C22×C4×C73C2411yescharacteristic
238C22×C4×C73C2413yes—
239C4⋊C4×C73—26no—
240C4⋊C4×C73—26no—
241C22⋊C4×C73—22no—
242C22⋊C4×C73—43no—
243C42×C73—26no—
244C42×C73—26no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73C23×C412yes—
252C23×C73C2511yescharacteristic
253C22×D73—21no—
254C22×D73—21no—
255C22×D73—21no—
256C22×D73—21no—
257C22×D73—23no—
258C22×D73—23no—
259C22×D73—23no—
260C22×D73—23no—
261C22×D73—23no—
262C22×D73—23no—
263C22×D73C23×C416yes—
264C22×D73C23×C412yes—
265C22×D73C22×D412yes—
266C22×D73C22×D412yes—
267Q8×C73—224no—
268Q8×C73C2×C22⋊C4116yes—
269C2×C4×C73—21no—
270C2×C4×C73—23no—
271C2×C4×C73—23no—
272C2×C4×C73—21no—
273C2×C4×C73—224no—
274C2×C4×C73—21no—
275C2×C4×C73—23no—
276C2×C4×C73—23no—
277C2×C4×C73—21no—
278C2×C4×C73—23no—
279C2×C4×C73—23no—
280C2×C4×C73—23no—
281C2×C4×C73—21no—
282C2×C4×C73—23no—
283C2×C4×C73C23×C416yes—
284C2×C4×C73C23×C416yes—
285C2×C4×C73C22×D416yes—
286C2×C4×C73C22×D416yes—
287C2×C4×C732−1+412yescomplemented
288C22⋊D73—28no—
289C22⋊D73—224no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73—23no—
296C2×Dic73—23no—
297C2×Dic73—23no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—23no—
301C2×Dic73—23no—
302C2×Dic73—23no—
303C2×Dic73C23×C412yes—
304C2×Dic73C23×C416yes—
305C2×Dic73C22×D416yes—
306C2×Dic73C22×D416yes—
307C2×Dic732−1+412yescomplemented
308D292—224no—
309D292—224no—
310C4×D73—28no—
311C4×D73—224no—
312C4×D73—248no—
313C4×D73—412no—
314C4×D73C2×C22⋊C4148yes—
315Dic146—224no—
316Dic146C2×C22⋊C4148yes—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73C24×C411yescharacteristic
325C22×C73C23×D411yescharacteristic
326C22×C73C23×D411yescharacteristic
327C22×C73C2×2−1+411yescharacteristic
328C22×C73C2×2−1+411yescharacteristic
329C22×C73#58511yescharacteristic
330C22×C73#58511yescharacteristic
331C2×D73—22no—
332C2×D73—22no—
333C2×D73—22no—
334C2×D73—22no—
335C2×D73—22no—
336C2×D73—22no—
337C2×D73—26no—
338C2×D73—26no—
339C2×D73—26no—
340C2×D73—43no—
341C2×D73—43no—
342C2×D73—43no—
343C2×D73—43no—
344C2×D73C22×C22⋊C414yes—
345C4×C73—26no—
346C4×C73—22no—
347C4×C73—43no—
348C4×C73—43no—
349C4×C73—41no—
350C4×C73C22×C22⋊C4112yes—
351Dic73—22no—
352Dic73—22no—
353Dic73—43no—
354Dic73—41no—
355Dic73—43no—
356Dic73C22×C22⋊C4112yes—
357#34257—731nomaximal, Sylow
358C2×C73—42no—
359C2×C73C23×C22⋊C411yescharacteristic
360C2×C73C4×2−1+411yescharacteristic
361C2×C73C4×2−1+411yescharacteristic
362C2×C73#348611yescharacteristic
363C2×C73#348711yescharacteristic
364C2×C73#349711yescharacteristic
365C2×C73#349711yescharacteristic
366D73—24no—
367D73—46no—
368C22×2−1+4—731no—
369C2×#519—731no—
370C22×C4×Q8—731no—
371#2341—733no—
372#2341—733no—
373#2341—731no—
374#2341—731no—
375Q8×C22⋊C4—733no—
376Q8×C22⋊C4—733no—
377Q8×C22⋊C4—731no—
378Q8×C22⋊C4D7311yescharacteristic, complemented
379#2311—733no—
380#2311—733no—
381#2297—733no—
382#2297—733no—
383C73#3425711yescharacteristic, complemented, Sylow
384C2×2−1+4—7316no—
385C2×2−1+4—1468no—
386C2×2−1+4—1468no—
387C22×#41—733no—
388C22×#41—731no—
389C22×#41—733no—
390C22×#41—733no—
391C23×Q8—731no—
392C23×Q8—733no—
393C23×Q8C2×D7311yescharacteristic
394#519—1468no—
395C2×C4×Q8—731no—
396C2×C4×Q8—731no—
397C2×C4×Q8—733no—
398C2×C4×Q8—733no—
399C2×C4×Q8—733no—
400C2×C4×Q8—733no—
401C2×C4×Q8—1468no—
402C2×C4×Q8C2×D7311yescharacteristic
403C2×C4×Q8C2×D7311yescharacteristic
404C2×#117—733no—
405C2×#117—733no—
406C22×C4⋊C4—733no—
407C22×C42—733no—
408#391—733no—
409#391—733no—
410#391—736no—
411#391—733no—
412#391—733no—
413#391C2×D7313yes—
414#391C2×D7313yes—
415#390—733no—
416#390—733no—
417#390—736no—
418#390—733no—
419#390—733no—
420#390—733no—
421#390—733no—
422#386—733no—
423#386—731no—
424#386—736no—
425#386—733no—
426#386—733no—
427#380—733no—
428#380—733no—
429#380—733no—
430#380—736no—
431#380—736no—
432#380C2×D7313yes—
433C4×C22⋊C4—733no—
434C4×C22⋊C4—733no—
435C4×C22⋊C4—733no—
436C4×C22⋊C4—736no—
437C4×C22⋊C4—736no—
438C4×C22⋊C4C2×D7313yes—
4392−1+4—146128no—
440C2×#41—7324no—
441C2×#41—738no—
442C2×#41—7324no—
443C2×#41—7324no—
444C2×#41—14612no—
445C2×#41—14612no—
446C2×#41—14612no—
447C2×#41—14612no—
448C2×#41—14612no—
449C2×#41—14612no—
450C2×#41—1464no—
451C2×#41—1464no—
452C22×Q8—24no—
453C22×Q8—24no—
454C22×Q8—738no—
455C22×Q8—738no—
456C22×Q8—738no—
457C22×Q8—7324no—
458C22×Q8—733no—
459C22×Q8—733no—
460C22×Q8—14612no—
461C22×Q8—14612no—
462C22×Q8C4×D7318yescomplemented
463C22×Q8C22×D7313yes—
464C22×Q8C22×D7311yescharacteristic
465C22×D4—731no—
466C22×D4—733no—
467C22×D4—733no—
468C22×D4—733no—
469C23×C4—733no—
470C23×C4—733no—
471C23×C4—736no—
472C23×C4—733no—
473C23×C4—731no—
474C23×C4C22×D7313yes—
475C4×Q8—24no—
476C4×Q8—24no—
477C4×Q8—14612no—
478C4×Q8—14612no—
479C4×Q8—14612no—
480C4×Q8—14612no—
481C4×Q8—1464no—
482C4×Q8—1464no—
483#117—14612no—
484#117—14612no—
485C2×C4⋊C4—736no—
486C2×C4⋊C4—733no—
487C2×C4⋊C4—733no—
488C2×C4⋊C4—733no—
489C2×C4⋊C4—733no—
490C2×C4⋊C4—14612no—
491C2×C4⋊C4C22×D7313yes—
492C2×C4⋊C4C22×D7313yes—
493C2×C22⋊C4—733no—
494C2×C22⋊C4—733no—
495C2×C22⋊C4—736no—
496C2×C22⋊C4—736no—
497C2×C22⋊C4—733no—
498C2×C22⋊C4—731no—
499C2×C22⋊C4—733no—
500C2×C22⋊C4—731no—
501C2×C22⋊C4—733no—
502C2×C22⋊C4—733no—
503C2×C22⋊C4C22×D7311yescharacteristic
504C2×C22⋊C4C22×D7313yes—
505C2×C42—736no—
506C2×C42—733no—
507C2×C42—733no—
508C2×C42—733no—
509C2×C42—733no—
510C2×C42—14612no—
511C2×C42C22×D7313yes—
512C2×C42C22×D7313yes—
513#95—731no—
514#95—731no—
515#95—733no—
516#95—733no—
517#95—733no—
518#95—736no—
519#95—733no—
520#95C22×D7313yes—
521#95C22×D7316yes—
522#95C22×D7313yes—
523C24—731no—
524C24—733no—
525C24C23×D7311yescharacteristic
526#41—14696no—
527#41—14696no—
528#41—14696no—
529#41—14632no—
530C2×Q8—232no—
531C2×Q8—26no—
532C2×Q8—26no—
533C2×Q8—7364no—
534C2×Q8—7312no—
535C2×Q8—7312no—
536C2×Q8—7312no—
537C2×Q8—7312no—
538C2×Q8—1466no—
539C2×Q8—1466no—
540C2×Q8—14696no—
541C2×Q8C2×C4×D73112yes—
542C2×Q8C2×C4×D7314yes—
543C2×Q8D4×D7314yes—
544C2×Q8D4×D7314yes—
545C2×D4—7312no—
546C2×D4—734no—
547C2×D4—7312no—
548C2×D4—7312no—
549C2×D4—1466no—
550C2×D4—1466no—
551C2×D4—1466no—
552C2×D4—1466no—
553C2×D4—1462no—
554C2×D4—1462no—
555C2×D4—1466no—
556C2×D4—1466no—
557C22×C4—26no—
558C22×C4—26no—
559C22×C4—2923no—
560C22×C4—2923no—
561C22×C4—733no—
562C22×C4—7312no—
563C22×C4—7312no—
564C22×C4—7312no—
565C22×C4—731no—
566C22×C4—731no—
567C22×C4—7324no—
568C22×C4—7312no—
569C22×C4—731no—
570C22×C4—733no—
571C22×C4—733no—
572C22×C4—1466no—
573C22×C4—1462no—
574C22×C4—14612no—
575C22×C4—14612no—
576C22×C4—1462no—
577C22×C4—1466no—
578C22×C4—1466no—
579C22×C4—1462no—
580C22×C4C2×C4×D73112yes—
581C22×C4C23×D7313yes—
582C22×C4C23×D7313yes—
583C22×C4C23×D7311yescharacteristic
584C22×C4C23×D7313yes—
585C22×C4C23×D7311yescharacteristic
586C22×C4C23×D7313yes—
587C4⋊C4—26no—
588C4⋊C4—26no—
589C4⋊C4—14612no—
590C4⋊C4—1466no—
591C4⋊C4—1466no—
592C4⋊C4—1466no—
593C4⋊C4—1466no—
594C22⋊C4—22no—
595C22⋊C4—43no—
596C22⋊C4—2926no—
597C22⋊C4—2923no—
598C22⋊C4—2923no—
599C22⋊C4—2926no—
600C22⋊C4—2923no—
601C22⋊C4—1466no—
602C22⋊C4—1462no—
603C22⋊C4—1466no—
604C22⋊C4—1462no—
605C22⋊C4—1466no—
606C42—26no—
607C42—26no—
608C42—1466no—
609C42—1466no—
610C42—14612no—
611C42—1466no—
612C42—1466no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—732no—
620C23—732no—
621C23—732no—
622C23—736no—
623C23—1463no—
624C23—1463no—
625C23—1463no—
626C23—1463no—
627C23—1463no—
628C23—1463no—
629C23—1461no—
630C23—1461no—
631C23—1461no—
632C23—1461no—
633C23C22×C4×D7312yes—
634C23C24×D7311yescharacteristic
635Q8—224no—
636Q8—7348no—
637Q8—14624no—
638Q8C22⋊C4×D73116yes—
639D4—14624no—
640D4—14624no—
641D4—1468no—
642D4—14624no—
643C2×C4—21no—
644C2×C4—23no—
645C2×C4—23no—
646C2×C4—21no—
647C2×C4—224no—
648C2×C4—21no—
649C2×C4—23no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—23no—
655C2×C4—21no—
656C2×C4—23no—
657C2×C4—29212no—
658C2×C4—736no—
659C2×C4—736no—
660C2×C4—736no—
661C2×C4—7348no—
662C2×C4—732no—
663C2×C4—732no—
664C2×C4—14648no—
665C2×C4—1468no—
666C2×C4—1461no—
667C2×C4—1463no—
668C2×C4—1463no—
669C2×C4—1461no—
670C2×C4—1463no—
671C2×C4—1461no—
672C2×C4—1463no—
673C2×C4—1463no—
674C2×C4—1463no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4—1461no—
679C2×C4—14624no—
680C2×C4C22×C4×D7316yes—
681C2×C4C22×C4×D7316yes—
682C2×C4C2×D4×D7316yes—
683C2×C4C2×D4×D7316yes—
684C2×C4#1455663912yescomplemented
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—2923no—
693C22—2923no—
694C22—2923no—
695C22—2923no—
696C22—734no—
697C22—1466no—
698C22—1466no—
699C22—1466no—
700C22—1462no—
701C22—1462no—
702C22—1462no—
703C22—1462no—
704C22—1462no—
705C22—1462no—
706C22C23×C4×D7311yescharacteristic
707C22C22×D4×D7311yescharacteristic
708C22C22×D4×D7311yescharacteristic
709C222−1+4×D7311yescharacteristic
710C22C2×#1455663911yescharacteristic
711C22#1798942311yescharacteristic
712C22#1798942411yescharacteristic
713C4—22no—
714C4—26no—
715C4—43no—
716C4—43no—
717C4—41no—
718C4—2923no—
719C4—2921no—
720C4—2923no—
721C4—7312no—
722C4—1462no—
723C4—1462no—
724C4C2×C22⋊C4×D73112yes—
725C2—42no—
726C2—2926no—
727C2—1464no—
728C2C22×C22⋊C4×D7311yescharacteristic
729C2#2262314011yescharacteristic
730C2C4×#1455663911yescharacteristic
731C2#2262358111yescharacteristic
732C2#2262358811yescharacteristic
733C2#2262369911yescharacteristic
734C2#2262370111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingQ8×C22⋊C4×C73C2
socle, cosocleC23×C73C25
prime radicalC22×#14556639C2
hypercenterQ8×C22⋊C4D73
hypocenterC73#34257
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#17989063C2semidirect
3. C2×C4×Q8×D73C2semidirect
4. #22612771C2semidirect
5. #22612769C2semidirect
6. #22612769C2semidirect
7. #22612768C2semidirect
8. Q8×C22⋊Dic73C2semidirect
9. #22612765C2semidirect
10. #22612765C2semidirect
11. #22612522C2semidirect
12. #22612520C2semidirect
13. #22612420C2semidirect
14. #22612417C2semidirect
15. Q8×C22⋊C4×C73C2semidirect
18. C2×#14556639C4semidirect
77. C2×#11924029C2×C4semidirect
83. C2×#11924028C2×C4semidirect
89. C2×Q8×D73C2×C4semidirect
140. C22×Q8×C73C2×C4semidirect
168. Q8×D73C22⋊C4semidirect
287. C2×C4×C732−1+4semidirect
307. C2×Dic732−1+4semidirect
378. Q8×C22⋊C4D73semidirect
383. C73#34257semidirect
462. C22×Q8C4×D73semidirect
684. C2×C4#14556639semidirect

Maximal subgroups

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

subgroupindex
C22×#145566392
C2×#179890632
C2×C4×Q8×D732
#226127712
#226127692
#226127682
Q8×C22⋊Dic732
#226127652
#226125222
#226125202
#226124202
#226124172
Q8×C22⋊C4×C732
#3425773