Finite Group Databasebeta

← #33108491

Subgroups — #33108491

Order 18688.

892 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619382C211yesmaximal, characteristic
2C2×#17988701C211yesmaximal, characteristic, complemented
3#22618673C211yesmaximal, characteristic, complemented
4#22618497C211yesmaximal, characteristic, complemented
5#22610757C211yesmaximal, characteristic, complemented
6#22610703C211yesmaximal, characteristic, complemented
7#22610635C211yesmaximal, characteristic, complemented
8#22610632C211yesmaximal, characteristic, complemented
9#22610260C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22610206C211yesmaximal, characteristic, complemented
12#22610203C211yesmaximal, characteristic, complemented
13C4×#14556520C211yesmaximal, characteristic, complemented
14#104×Dic73C211yesmaximal, characteristic, complemented
15C2×#443×C73C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556599C2211yescharacteristic
18C2×#14556598C2211yescharacteristic
19#17989133C2211yescharacteristic
20#41×Dic73C2211yescharacteristic
21#17988811C411yescharacteristic, complemented
22#17988807C411yescharacteristic, complemented
23#17988804C411yescharacteristic, complemented
24#17988800C411yescharacteristic, complemented
25#17988795C411yescharacteristic, complemented
26#17988790C411yescharacteristic, complemented
27#17988785C411yescharacteristic, complemented
28#17988780C411yescharacteristic, complemented
29#17988701—24no—
30#17988663—21no—
31#17988658—21no—
32#17988656—21no—
33C8×C22⋊D73—21no—
34C2×#14556526C2211yescharacteristic
35#17988615—21no—
36#17988615C2211yescharacteristic
37#17988613—21no—
38#17988613C2211yescharacteristic
39#17988610—21no—
40#17988610C2211yescharacteristic
41C2×#14556520—21no—
42C2×#14556520C2211yescharacteristic
43C2×#14556520C2211yescharacteristic
44C2×#14556519C2211yescharacteristic
45C2×#14556518C2211yescharacteristic
46C2×#14556518C2211yescharacteristic
47C2×#14556517C2211yescharacteristic
48#17988584C2211yescharacteristic
49#17988583C2211yescharacteristic
50#17988554C2211yescharacteristic
51#17988553C2211yescharacteristic
52M16×Dic73C2211yescharacteristic
53C2×C4×#10596831C2211yescharacteristic
54C42×Dic73C2211yescharacteristic
55#17988352C2211yescharacteristic
56#17988351C2211yescharacteristic
57#17988348C2211yescharacteristic
58#17988347C2211yescharacteristic
59#17988341C2211yescharacteristic
60#17988341C2211yescharacteristic
61C2×#135×C73C2211yescharacteristic
62C2×#131×C73C2211yescharacteristic
63C2×#131×C73C2211yescharacteristic
64#443×C73—24no—
65C2×#108×C73C2211yescharacteristic
66C2×#104×C73C2211yescharacteristic
67C2×#104×C73C2211yescharacteristic
68C2×C4×C8×C73C2211yescharacteristic
69C2×#11924028C2311yescharacteristic
70#14556611—22no—
71#14556611—22no—
72C2×#11924018C2×C411yescharacteristic
73C2×#11924016C2×C411yescharacteristic
74C2×#11924015C2×C411yescharacteristic
75C2×#11924013C2×C411yescharacteristic
76#14556599—22no—
77#14556599—41no—
78#14556598—22no—
79#14556598—41no—
80C2×#11924012—21no—
81C2×#11924012C2311yescharacteristic
82C2×#11924012C2311yescharacteristic
83C2×#11924011—21no—
84C22×#10596831—21no—
85C22×#10596831C2311yescharacteristic
86C22×#10596831C2311yescharacteristic
87C2×C8×D73—21no—
88#14556589C2×C411yescharacteristic
89#14556587C2×C411yescharacteristic
90#14556580C2×C411yescharacteristic
91#14556578C2×C411yescharacteristic
92#14556563—21no—
93#14556563—21no—
94Q8×Dic73C2×C411yescharacteristic
95Q8×Dic73C2×C411yescharacteristic
96D4×Dic73—21no—
97D4×Dic73—21no—
98D4×Dic73C2×C411yescharacteristic
99D4×Dic73C2×C411yescharacteristic
100C4×C22⋊D73—21no—
101C4×C22⋊D73—21no—
102#14556550—21no—
103#14556550C2311yescharacteristic
104C2×C4×Dic73—21no—
105C2×C4×Dic73—21no—
106C2×C4×Dic73—21no—
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109#14556526—22no—
110#14556520—21no—
111#14556520—21no—
112#14556520—21no—
113#14556520—21no—
114#14556520—21no—
115#14556520—21no—
116#14556520C2×C411yescharacteristic
117#14556520C2×C411yescharacteristic
118#14556520C2×C411yescharacteristic
119#14556520C2×C411yescharacteristic
120#14556520D411yescharacteristic
121#14556520D411yescharacteristic
122#14556520D411yescharacteristic
123#14556520D411yescharacteristic
124#14556519—22no—
125#14556518—22no—
126#14556518—41no—
127#14556517—41no—
128#14556516C2×C411yescharacteristic
129#14556516C2×C411yescharacteristic
130#14556515C2×C411yescharacteristic
131#14556515C2×C411yescharacteristic
132#14556513C2×C411yescharacteristic
133#14556513C2×C411yescharacteristic
134#14556512C2×C411yescharacteristic
135#14556512C2×C411yescharacteristic
136C22⋊#10596831—21no—
137C22⋊#10596831—21no—
138#14556503—21no—
139#14556503—21no—
140#14556501—21no—
141C4×#10596831—22no—
142C8×Dic73—21no—
143C2×#41×C73C2311yescharacteristic
144C2×#41×C73C2311yescharacteristic
145#135×C73—22no—
146#135×C73—22no—
147C2×Q16×C73C2×C411yescharacteristic
148C2×SD16×C73C2×C411yescharacteristic
149C2×SD16×C73C2×C411yescharacteristic
150C2×D8×C73C2×C411yescharacteristic
151#131×C73—22no—
152#131×C73—22no—
153#131×C73—41no—
154#131×C73—41no—
155C2×M16×C73—21no—
156C2×M16×C73—21no—
157C2×M16×C73C2311yescharacteristic
158C2×M16×C73C2311yescharacteristic
159C22×C8×C73—21no—
160C22×C8×C73—21no—
161C22×C8×C73C2311yescharacteristic
162C22×C8×C73C2311yescharacteristic
163C2×C42×C73C2311yescharacteristic
164#108×C73—22no—
165#104×C73—22no—
166#104×C73D414yescomplemented
167C4×C8×C73—22no—
168#11924028—21no—
169#11924028—21no—
170#11924028—21no—
171#11924028—21no—
172C2×Dic146C22×C411yescharacteristic
173C2×D292C22×C411yescharacteristic
174C2×C22⋊D73—21no—
175C2×C22⋊D73—21no—
176C2×C22⋊D73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73#4111yescharacteristic
181C22×Dic73#4111yescharacteristic
182C2×C4×D73—21no—
183#11924018—22no—
184#11924016—22no—
185#11924015—22no—
186#11924013—22no—
187#11924012—21no—
188#11924012—21no—
189#11924012—21no—
190#11924012—21no—
191#11924012—42no—
192#11924011—42no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198C2×#10596831—21no—
199C2×#10596831—42no—
200C2×#10596831C22×C411yescharacteristic
201C2×#10596831C22×C411yescharacteristic
202C2×#10596831C2×D411yescharacteristic
203C2×#10596831C2×D411yescharacteristic
204C8×D73—42no—
205C4⋊Dic73—21no—
206C4⋊Dic73—21no—
207C4⋊Dic73C22×C411yescharacteristic
208C4⋊Dic73C22×C411yescharacteristic
209#11924007—21no—
210#11924007—21no—
211C22⋊Dic73—21no—
212C22⋊Dic73—21no—
213C22⋊Dic73—21no—
214C22⋊Dic73—21no—
215C22⋊Dic73—21no—
216#11924005—21no—
217#11924005—21no—
218C4×Dic73—24no—
219C4×Dic73—21no—
220C4×Dic73—21no—
221C4×Dic73—21no—
222C4×Dic73—21no—
223C4×Dic73—21no—
224C4×Dic73—42no—
225C4×Dic73C22×C411yescharacteristic
226C4×Dic73C22×C411yescharacteristic
227C4×Dic73C2×D411yescharacteristic
228C4×Dic73C2×D411yescharacteristic
229#41×C73—21no—
230#41×C73—21no—
231#41×C73—21no—
232#41×C73—21no—
233#41×C73—21no—
234#41×C73—21no—
235#41×C73C2×D412yes—
236#41×C73#4112yes—
237C2×Q8×C73C22×C411yescharacteristic
238C2×Q8×C73C22×C411yescharacteristic
239C2×D4×C73—21no—
240C2×D4×C73—21no—
241C2×D4×C73C22×C411yescharacteristic
242C2×D4×C73C22×C411yescharacteristic
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73C2411yescharacteristic
247Q16×C73—22no—
248SD16×C73—22no—
249SD16×C73—22no—
250D8×C73—22no—
251M16×C73—21no—
252M16×C73—21no—
253M16×C73—21no—
254M16×C73—42no—
255M16×C73—42no—
256M16×C73C2×D412yes—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—21no—
262C2×C8×C73—21no—
263C2×C8×C73—42no—
264C2×C8×C73—42no—
265C2×C8×C73C22×C411yescharacteristic
266C2×C8×C73C22×C411yescharacteristic
267C2×C8×C73C2×D411yescharacteristic
268C2×C8×C73C2×D411yescharacteristic
269C42×C73—21no—
270C42×C73C2×D412yes—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73C2×#4111yescharacteristic
274C22×D73—21no—
275Q8×C73—21no—
276Q8×C73—21no—
277Q8×C73—21no—
278Q8×C73C4×D412yes—
279D4×C73—22no—
280D4×C73—22no—
281D4×C73—21no—
282D4×C73—21no—
283D4×C73—21no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73C4×D412yes—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—21no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—21no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73C23×C411yescharacteristic
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C22×D411yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×C4×C732−1+411yescharacteristic
302C22⋊D73—41no—
303C22⋊D73—41no—
304C22⋊D73—42no—
305C22⋊D73—81no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—42no—
315C2×Dic73—81no—
316C2×Dic73C4×D411yescharacteristic
317C2×Dic73C4×D411yescharacteristic
318C2×Dic73C4×D411yescharacteristic
319C2×Dic73C4×D411yescharacteristic
320D292—21no—
321D292—21no—
322C4×D73—41no—
323C4×D73—41no—
324Dic146—21no—
325Dic146—21no—
326C8×C73—21no—
327C8×C73—21no—
328C8×C73—21no—
329C8×C73—21no—
330C8×C73—22no—
331C8×C73—41no—
332#10596831—21no—
333#10596831—21no—
334#10596831—21no—
335#10596831—21no—
336#10596831—41no—
337#10596831—41no—
338C22×C73—21no—
339C22×C73—21no—
340C22×C73—22no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73C2×C4×D411yescharacteristic
347C22×C73#54711yescharacteristic
348C22×C73#55311yescharacteristic
349C2×D73—41no—
350C2×D73—41no—
351C2×D73—41no—
352C4×C73—24no—
353C4×C73—22no—
354C4×C73—41no—
355C4×C73C2×C4×D411yescharacteristic
356C4×C73#52011yescharacteristic
357C4×C73D4211yescharacteristic
358C4×C73#54811yescharacteristic
359Dic73—21no—
360Dic73—21no—
361Dic73—21no—
362Dic73—42no—
363Dic73—41no—
364Dic73—41no—
365Dic73—41no—
366Dic73#44312yescomplemented
367#23015—731nomaximal, Sylow
368C2×C73—21no—
369C2×C73—21no—
370C2×C73—42no—
371C2×C73—81no—
372C2×C73#236111yescharacteristic
373C2×C73C2×#44311yescharacteristic
374C2×C73#295611yescharacteristic
375D73—81no—
376#3035—731no—
377C2×#443—731no—
378C2×#443D7311yescharacteristic, complemented
379#2935—731no—
380#2906—731no—
381#1962—731no—
382#1950—731no—
383#1937—731no—
384#1937—731no—
385#1876—731no—
386#1876—731no—
387#1866—731no—
388#1866—731no—
389C4×C4⋊C8—731no—
390C4×#104—731no—
391C73#2301511yescharacteristic, complemented, Sylow
392C2×#135—731no—
393C2×#135C2×D7311yescharacteristic
394C2×#131—731no—
395C2×#131—731no—
396C2×#131C2×D7311yescharacteristic
397C2×#131C2×D7311yescharacteristic
398#532—731no—
399C4×#41—731no—
400#464—731no—
401#464—731no—
402#463—731no—
403#463—731no—
404#462—731no—
405#461—731no—
406#460—731no—
407#459—731no—
408#443—24no—
409#443—1464no—
410#436—1461no—
411#435—1461no—
412#435—1461no—
413C8×D4—1461no—
414C2×#108—731no—
415C2×#108C2×D7311yescharacteristic
416#424—731no—
417#424—731no—
418#424—1461no—
419#424—1461no—
420#423—731no—
421#423—1461no—
422C2×C4⋊C8—731no—
423C2×C4⋊C8—731no—
424C2×C4⋊C8—1461no—
425C2×#104—731no—
426C2×#104—731no—
427C2×#104—731no—
428C2×#104—731no—
429C2×#104C2×D7311yescharacteristic
430C2×#104C2×D7311yescharacteristic
431#416—731no—
432#416—731no—
433#408—731no—
434#408—731no—
435C4×M16—731no—
436C2×C4×C8—731no—
437C2×C4×C8C2×D7311yescharacteristic
438C43—731no—
439#341—731no—
440#341—731no—
441#339—731no—
442#339—731no—
443#336—731no—
444#336—731no—
445C2×#41—731no—
446C2×#41C22×D7311yescharacteristic
447C2×#41C22×D7311yescharacteristic
448#135—22no—
449#135—22no—
450#135—1462no—
451#135—1462no—
452C2×Q16—731no—
453C2×Q16C4×D7311yescharacteristic
454C2×SD16—731no—
455C2×SD16—731no—
456C2×SD16C4×D7311yescharacteristic
457C2×SD16C4×D7311yescharacteristic
458C2×D8—731no—
459C2×D8C4×D7311yescharacteristic
460#131—22no—
461#131—22no—
462#131—41no—
463#131—41no—
464#131—2921no—
465#131—2921no—
466#131—1462no—
467#131—1462no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—731no—
471C2×M16—731no—
472C2×M16—1461no—
473C2×M16—1461no—
474C2×M16C22×D7311yescharacteristic
475C2×M16C22×D7311yescharacteristic
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—731no—
479C22×C8—731no—
480C22×C8—1461no—
481C22×C8—1461no—
482C22×C8C22×D7311yescharacteristic
483C22×C8C22×D7311yescharacteristic
484C4⋊Q8—731no—
485#127—731no—
486#124—731no—
487#124—731no—
488#121—1461no—
489#121—1461no—
490C4×Q8—731no—
491C4×Q8—731no—
492C4×D4—731no—
493C4×D4—731no—
494C4×D4—1461no—
495C4×D4—1461no—
496C4×D4—1461no—
497C4×D4—1461no—
498#117—731no—
499#117—1461no—
500C2×C42—731no—
501C2×C42—731no—
502C2×C42—1461no—
503C2×C42—1461no—
504C2×C42—1461no—
505C2×C42C22×D7311yescharacteristic
506#108—22no—
507#108—1462no—
508C4⋊C8—731no—
509C4⋊C8—731no—
510C4⋊C8—731no—
511C4⋊C8—731no—
512C4⋊C8—731no—
513C4⋊C8—731no—
514C4⋊C8—731no—
515C4⋊C8—731no—
516C4⋊C8—1461no—
517C4⋊C8—1461no—
518C4⋊C8—1461no—
519C4⋊C8—1461no—
520C4⋊C8—1461no—
521C4⋊C8—1461no—
522#104—22no—
523#104—2921no—
524#104—2921no—
525#104—1462no—
526#104—1462no—
527#104C22⋊D7314yescomplemented
528#103—731no—
529#103—731no—
530#103—731no—
531#103—731no—
532#102—731no—
533#102—731no—
534#102—731no—
535#102—731no—
536C22⋊C8—1461no—
537C22⋊C8—1461no—
538C22⋊C8—1461no—
539C22⋊C8—1461no—
540#97—1461no—
541C4×C8—22no—
542C4×C8—1461no—
543C4×C8—1462no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—1461no—
551#41—1461no—
552#41—1461no—
553#41—1461no—
554#41C2×C22⋊D7312yes—
555#41#1192402812yes—
556C2×Q8—731no—
557C2×Q8C2×C4×D7311yescharacteristic
558C2×Q8C2×C4×D7311yescharacteristic
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—731no—
562C2×D4—1461no—
563C2×D4—1461no—
564C2×D4—1461no—
565C2×D4C2×C4×D7311yescharacteristic
566C2×D4C2×C4×D7311yescharacteristic
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—731no—
571C22×C4—731no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1461no—
576C22×C4C23×D7311yescharacteristic
577Q16—22no—
578Q16—1462no—
579SD16—22no—
580SD16—22no—
581SD16—1462no—
582SD16—1462no—
583D8—22no—
584D8—1462no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—42no—
589M16—42no—
590M16—2922no—
591M16—2922no—
592M16—1461no—
593M16—1461no—
594M16—1461no—
595M16—1461no—
596M16C2×C22⋊D7312yes—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—42no—
604C2×C8—42no—
605C2×C8—2922no—
606C2×C8—2922no—
607C2×C8—731no—
608C2×C8—731no—
609C2×C8—731no—
610C2×C8—731no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8—1461no—
616C2×C8—1461no—
617C2×C8C2×C4×D7311yescharacteristic
618C2×C8C2×C4×D7311yescharacteristic
619C2×C8D4×D7311yescharacteristic
620C2×C8D4×D7311yescharacteristic
621C4⋊C4—731no—
622C4⋊C4—731no—
623C4⋊C4—1461no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4—1461no—
627C22⋊C4—1461no—
628C22⋊C4—1461no—
629C22⋊C4—1461no—
630C22⋊C4—1461no—
631C22⋊C4—1461no—
632C22⋊C4—1461no—
633C22⋊C4—1461no—
634C42—21no—
635C42—2922no—
636C42—731no—
637C42—731no—
638C42—731no—
639C42—731no—
640C42—1461no—
641C42—1461no—
642C42—1464no—
643C42—1461no—
644C42—1461no—
645C42—1461no—
646C42C2×C22⋊D7312yes—
647C23—21no—
648C23—21no—
649C23—1461no—
650C23#41×D7311yescharacteristic
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—1461no—
655Q8—1461no—
656Q8C4×C22⋊D7312yes—
657D4—22no—
658D4—22no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—41no—
663D4—41no—
664D4—2921no—
665D4—2921no—
666D4—2922no—
667D4—5841no—
668D4—1461no—
669D4—1461no—
670D4C4×C22⋊D7312yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—2921no—
681C2×C4—2921no—
682C2×C4—2922no—
683C2×C4—2921no—
684C2×C4—2921no—
685C2×C4—2921no—
686C2×C4—5841no—
687C2×C4—731no—
688C2×C4—731no—
689C2×C4—731no—
690C2×C4—731no—
691C2×C4—1462no—
692C2×C4—1461no—
693C2×C4—1461no—
694C2×C4—1461no—
695C2×C4—1462no—
696C2×C4C22×C4×D7311yescharacteristic
697C2×C4C2×D4×D7311yescharacteristic
698C2×C4C22×C22⋊D7311yescharacteristic
699C2×C4C2×#1192402811yescharacteristic
700C2×C4#1455663611yescharacteristic
701C2×C4#1455663811yescharacteristic
702C8—21no—
703C8—21no—
704C8—22no—
705C8—21no—
706C8—21no—
707C8—41no—
708C8—2921no—
709C8—2921no—
710C8—1461no—
711C8—1461no—
712C8—1461no—
713C8—1461no—
714C22—21no—
715C22—21no—
716C22—22no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—2921no—
723C22—2921no—
724C22—2921no—
725C22C4×D4×D7311yescharacteristic
726C22#1798923611yescharacteristic
727C22#1798928611yescharacteristic
728C4—24no—
729C4—22no—
730C4—41no—
731C4—2922no—
732C4—2921no—
733C4—2921no—
734C4—2921no—
735C4—732no—
736C4—1461no—
737C4—1461no—
738C4—1461no—
739C4C2×C4×C22⋊D7311yescharacteristic
740C4#1798906611yescharacteristic
741C4D4×C22⋊D7311yescharacteristic
742C4#1798924611yescharacteristic
743C2—21no—
744C2—21no—
745C2—42no—
746C2—81no—
747C2—5841no—
748C2#2261294811yescharacteristic
749C2#443×D7311yescharacteristic
750C2#2261883611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#443×C73C2
socleC22×C73C2×C4×D4
prime radical#22619382C2
cosocleC22×C4×C73C24
hypercenterC2×#443D73
hypocenterC73#23015
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#17988701C2semidirect
3. #22618673C2semidirect
4. #22618497C2semidirect
5. #22610757C2semidirect
6. #22610703C2semidirect
7. #22610635C2semidirect
8. #22610632C2semidirect
9. #22610260C2semidirect
10. #22610258C2semidirect
11. #22610206C2semidirect
12. #22610203C2semidirect
13. C4×#14556520C2semidirect
14. #104×Dic73C2semidirect
15. C2×#443×C73C2semidirect
21. #17988811C4semidirect
22. #17988807C4semidirect
23. #17988804C4semidirect
24. #17988800C4semidirect
25. #17988795C4semidirect
26. #17988790C4semidirect
27. #17988785C4semidirect
28. #17988780C4semidirect
166. #104×C73D4semidirect
366. Dic73#443semidirect
378. C2×#443D73semidirect
391. C73#23015semidirect
527. #104C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226193822
C2×#179887012
#226186732
#226184972
#226107572
#226107032
#226106352
#226106322
#226102602
#226102582
#226102062
#226102032
C4×#145565202
#104×Dic732
C2×#443×C732
#2301573