Finite Group Databasebeta

← #33108515

Subgroups — #33108515

Order 18688.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619382C211yesmaximal, characteristic
2C2×#17988706C211yesmaximal, characteristic, complemented
3#22618673C211yesmaximal, characteristic, complemented
4#22618497C211yesmaximal, characteristic, complemented
5#22610761C211yesmaximal, characteristic, complemented
6#22610703C211yesmaximal, characteristic, complemented
7#22610639C211yesmaximal, characteristic, complemented
8#22610635C211yesmaximal, characteristic, complemented
9#22610260C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22610206C211yesmaximal, characteristic, complemented
12#22610203C211yesmaximal, characteristic, complemented
13#22609789C211yesmaximal, characteristic, complemented
14#22609743C211yesmaximal, 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#17988706—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×#14556502C2211yescharacteristic
54#17988433C2211yescharacteristic
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×Dic73C2311yescharacteristic
106C2×C4×Dic73C2311yescharacteristic
107#14556526—22no—
108#14556520—21no—
109#14556520—21no—
110#14556520—21no—
111#14556520—21no—
112#14556520—21no—
113#14556520—21no—
114#14556520C2×C411yescharacteristic
115#14556520C2×C411yescharacteristic
116#14556520C2×C411yescharacteristic
117#14556520C2×C411yescharacteristic
118#14556520D411yescharacteristic
119#14556520D411yescharacteristic
120#14556520D411yescharacteristic
121#14556520D411yescharacteristic
122#14556519—22no—
123#14556518—22no—
124#14556518—41no—
125#14556517—41no—
126#14556516C2×C411yescharacteristic
127#14556516C2×C411yescharacteristic
128#14556515C2×C411yescharacteristic
129#14556515C2×C411yescharacteristic
130#14556513C2×C411yescharacteristic
131#14556513C2×C411yescharacteristic
132#14556512C2×C411yescharacteristic
133#14556512C2×C411yescharacteristic
134C22⋊#10596831—21no—
135C22⋊#10596831—21no—
136#14556503—21no—
137#14556503—21no—
138#14556502—22no—
139#14556501—21no—
140C8×Dic73—21no—
141#14556498—21no—
142#14556498—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—21no—
219C4×Dic73—21no—
220C4×Dic73—21no—
221C4×Dic73—21no—
222C4×Dic73—21no—
223C4×Dic73C22×C411yescharacteristic
224C4×Dic73C22×C411yescharacteristic
225C4×Dic73C2×D411yescharacteristic
226C4×Dic73C2×D411yescharacteristic
227#41×C73—21no—
228#41×C73—21no—
229#41×C73—21no—
230#41×C73—21no—
231#41×C73—21no—
232#41×C73—21no—
233#41×C73C2×D412yes—
234#41×C73#4112yes—
235C2×Q8×C73C22×C411yescharacteristic
236C2×Q8×C73C22×C411yescharacteristic
237C2×D4×C73—21no—
238C2×D4×C73—21no—
239C2×D4×C73C22×C411yescharacteristic
240C2×D4×C73C22×C411yescharacteristic
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73C2411yescharacteristic
245Q16×C73—22no—
246SD16×C73—22no—
247SD16×C73—22no—
248D8×C73—22no—
249M16×C73—21no—
250M16×C73—21no—
251M16×C73—21no—
252M16×C73—42no—
253M16×C73—42no—
254M16×C73C2×D412yes—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—42no—
262C2×C8×C73—42no—
263C2×C8×C73C22×C411yescharacteristic
264C2×C8×C73C22×C411yescharacteristic
265C2×C8×C73C2×D411yescharacteristic
266C2×C8×C73C2×D411yescharacteristic
267C42×C73—21no—
268C42×C73C2×D412yes—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73C2×#4111yescharacteristic
272C22×D73—21no—
273Q8×C73—21no—
274Q8×C73—21no—
275Q8×C73—21no—
276Q8×C73C4×D412yes—
277D4×C73—22no—
278D4×C73—22no—
279D4×C73—21no—
280D4×C73—21no—
281D4×C73—21no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73C4×D412yes—
285C2×C4×C73—21no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—21no—
289C2×C4×C73—22no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73C23×C411yescharacteristic
295C2×C4×C73C22×D411yescharacteristic
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C732−1+411yescharacteristic
300C22⋊D73—42no—
301C22⋊D73—41no—
302C22⋊D73—41no—
303C22⋊D73—81no—
304C2×Dic73—21no—
305C2×Dic73—21no—
306C2×Dic73—21no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—42no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—81no—
314C2×Dic73C4×D411yescharacteristic
315C2×Dic73C4×D411yescharacteristic
316C2×Dic73C4×D411yescharacteristic
317C2×Dic73C4×D411yescharacteristic
318D292—21no—
319D292—21no—
320C4×D73—41no—
321C4×D73—41no—
322Dic146—21no—
323Dic146—21no—
324C8×C73—21no—
325C8×C73—21no—
326C8×C73—21no—
327C8×C73—21no—
328C8×C73—22no—
329C8×C73—41no—
330#10596831—21no—
331#10596831—21no—
332#10596831—21no—
333#10596831—21no—
334#10596831—41no—
335#10596831—41no—
336C22×C73—21no—
337C22×C73—21no—
338C22×C73—22no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73C2×C4×D411yescharacteristic
345C22×C73#54711yescharacteristic
346C22×C73#55311yescharacteristic
347C2×D73—41no—
348C2×D73—41no—
349C2×D73—41no—
350C4×C73—22no—
351C4×C73—42no—
352C4×C73—41no—
353C4×C73C2×C4×D411yescharacteristic
354C4×C73#52011yescharacteristic
355C4×C73D4211yescharacteristic
356C4×C73#54811yescharacteristic
357Dic73—21no—
358Dic73—21no—
359Dic73—21no—
360Dic73—21no—
361Dic73—41no—
362Dic73—41no—
363Dic73—41no—
364Dic73—81no—
365#23017—731nomaximal, Sylow
366C2×C73—21no—
367C2×C73—21no—
368C2×C73—42no—
369C2×C73—81no—
370C2×C73#236111yescharacteristic
371C2×C73#295511yescharacteristic
372C2×C73#295711yescharacteristic
373D73—81no—
374#3035—731no—
375C2×#444—731no—
376C2×#443D7311yescharacteristic, complemented
377#2935—731no—
378#2906—731no—
379#1963—731no—
380#1950—731no—
381#1938—731no—
382#1937—731no—
383#1876—731no—
384#1876—731no—
385#1866—731no—
386#1866—731no—
387#1768—731no—
388#1759—731no—
389C73#2301711yescharacteristic, complemented, Sylow
390C2×#135—731no—
391C2×#135C2×D7311yescharacteristic
392C2×#131—731no—
393C2×#131—731no—
394C2×#131C2×D7311yescharacteristic
395C2×#131C2×D7311yescharacteristic
396#532—731no—
397C4×#41—731no—
398#464—731no—
399#464—731no—
400#463—731no—
401#463—731no—
402#462—731no—
403#461—731no—
404#460—731no—
405#459—731no—
406#444—1464no—
407#443—24no—
408#436—1461no—
409#435—1461no—
410#435—1461no—
411C8×D4—1461no—
412C2×#108—731no—
413C2×#108C2×D7311yescharacteristic
414#424—731no—
415#424—731no—
416#424—1461no—
417#424—1461no—
418#423—731no—
419#423—1461no—
420C2×C4⋊C8—731no—
421C2×C4⋊C8—731no—
422C2×C4⋊C8—1461no—
423C2×#104—731no—
424C2×#104—731no—
425C2×#104—731no—
426C2×#104—731no—
427C2×#104C2×D7311yescharacteristic
428C2×#104C2×D7311yescharacteristic
429#416—731no—
430#416—731no—
431#408—731no—
432#408—731no—
433C4×M16—731no—
434C2×#97—731no—
435C2×C4×C8C2×D7311yescharacteristic
436#376—731no—
437#341—731no—
438#341—731no—
439#339—731no—
440#339—731no—
441#336—731no—
442#336—731no—
443C2×#41—731no—
444C2×#41C22×D7311yescharacteristic
445C2×#41C22×D7311yescharacteristic
446#135—22no—
447#135—22no—
448#135—1462no—
449#135—1462no—
450C2×Q16—731no—
451C2×Q16C4×D7311yescharacteristic
452C2×SD16—731no—
453C2×SD16—731no—
454C2×SD16C4×D7311yescharacteristic
455C2×SD16C4×D7311yescharacteristic
456C2×D8—731no—
457C2×D8C4×D7311yescharacteristic
458#131—22no—
459#131—22no—
460#131—41no—
461#131—41no—
462#131—2921no—
463#131—2921no—
464#131—1462no—
465#131—1462no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—731no—
469C2×M16—731no—
470C2×M16—1461no—
471C2×M16—1461no—
472C2×M16C22×D7311yescharacteristic
473C2×M16C22×D7311yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—1461no—
479C22×C8—1461no—
480C22×C8C22×D7311yescharacteristic
481C22×C8C22×D7311yescharacteristic
482C4⋊Q8—731no—
483#127—731no—
484#124—731no—
485#124—731no—
486#121—1461no—
487#121—1461no—
488C4×Q8—731no—
489C4×Q8—731no—
490C4×D4—731no—
491C4×D4—731no—
492C4×D4—1461no—
493C4×D4—1461no—
494C4×D4—1461no—
495C4×D4—1461no—
496#117—731no—
497#117—1461no—
498C2×C42—731no—
499C2×C42—731no—
500C2×C42—1461no—
501C2×C42C22×D7311yescharacteristic
502#108—22no—
503#108—1462no—
504C4⋊C8—731no—
505C4⋊C8—731no—
506C4⋊C8—731no—
507C4⋊C8—731no—
508C4⋊C8—731no—
509C4⋊C8—731no—
510C4⋊C8—731no—
511C4⋊C8—731no—
512C4⋊C8—1461no—
513C4⋊C8—1461no—
514C4⋊C8—1461no—
515C4⋊C8—1461no—
516C4⋊C8—1461no—
517C4⋊C8—1461no—
518#104—22no—
519#104—2921no—
520#104—2921no—
521#104—1462no—
522#104—1462no—
523#104C22⋊D7314yescomplemented
524#103—731no—
525#103—731no—
526#103—731no—
527#103—731no—
528#102—731no—
529#102—731no—
530#102—731no—
531#102—731no—
532C22⋊C8—1461no—
533C22⋊C8—1461no—
534C22⋊C8—1461no—
535C22⋊C8—1461no—
536#97—1461no—
537#97—1462no—
538C4×C8—22no—
539C4×C8—1461no—
540#95—1461no—
541#95—1461no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—1461no—
549#41—1461no—
550#41—1461no—
551#41—1461no—
552#41C2×C22⋊D7312yes—
553#41#1192402812yes—
554C2×Q8—731no—
555C2×Q8C2×C4×D7311yescharacteristic
556C2×Q8C2×C4×D7311yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—731no—
560C2×D4—1461no—
561C2×D4—1461no—
562C2×D4—1461no—
563C2×D4C2×C4×D7311yescharacteristic
564C2×D4C2×C4×D7311yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—731no—
569C22×C4—731no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4C23×D7311yescharacteristic
575Q16—22no—
576Q16—1462no—
577SD16—22no—
578SD16—22no—
579SD16—1462no—
580SD16—1462no—
581D8—22no—
582D8—1462no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—42no—
587M16—42no—
588M16—2922no—
589M16—2922no—
590M16—1461no—
591M16—1461no—
592M16—1461no—
593M16—1461no—
594M16C2×C22⋊D7312yes—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—2922no—
604C2×C8—2922no—
605C2×C8—731no—
606C2×C8—731no—
607C2×C8—731no—
608C2×C8—731no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8C2×C4×D7311yescharacteristic
616C2×C8C2×C4×D7311yescharacteristic
617C2×C8D4×D7311yescharacteristic
618C2×C8D4×D7311yescharacteristic
619C4⋊C4—731no—
620C4⋊C4—731no—
621C4⋊C4—1461no—
622C4⋊C4—1461no—
623C4⋊C4—1461no—
624C4⋊C4—1461no—
625C22⋊C4—1461no—
626C22⋊C4—1461no—
627C22⋊C4—1461no—
628C22⋊C4—1461no—
629C22⋊C4—1461no—
630C22⋊C4—1461no—
631C22⋊C4—1461no—
632C42—21no—
633C42—731no—
634C42—731no—
635C42—731no—
636C42—731no—
637C42—1461no—
638C42—1461no—
639C42—1461no—
640C42—1461no—
641C42—1461no—
642C42C2×C22⋊D7312yes—
643C23—21no—
644C23—21no—
645C23—1461no—
646C23#41×D7311yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—1461no—
651Q8—1461no—
652Q8C4×C22⋊D7312yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—41no—
659D4—41no—
660D4—2921no—
661D4—2921no—
662D4—2922no—
663D4—5841no—
664D4—1461no—
665D4—1461no—
666D4C4×C22⋊D7312yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—2922no—
677C2×C4—2921no—
678C2×C4—2921no—
679C2×C4—2921no—
680C2×C4—2921no—
681C2×C4—2921no—
682C2×C4—2921no—
683C2×C4—2921no—
684C2×C4—5841no—
685C2×C4—731no—
686C2×C4—731no—
687C2×C4—731no—
688C2×C4—731no—
689C2×C4—1461no—
690C2×C4—1461no—
691C2×C4—1461no—
692C2×C4C22×C4×D7311yescharacteristic
693C2×C4C2×D4×D7311yescharacteristic
694C2×C4C22×C22⋊D7311yescharacteristic
695C2×C4C2×#1192402811yescharacteristic
696C2×C4#1455663611yescharacteristic
697C2×C4#1455663811yescharacteristic
698C8—21no—
699C8—21no—
700C8—22no—
701C8—21no—
702C8—21no—
703C8—41no—
704C8—2921no—
705C8—2921no—
706C8—1461no—
707C8—1461no—
708C8—1461no—
709C8—1461no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—2921no—
719C22—2921no—
720C22—2921no—
721C22C4×D4×D7311yescharacteristic
722C22#1798923611yescharacteristic
723C22#1798928611yescharacteristic
724C4—22no—
725C4—42no—
726C4—41no—
727C4—2921no—
728C4—2921no—
729C4—2921no—
730C4—5841no—
731C4—1461no—
732C4—1461no—
733C4—1461no—
734C4—1461no—
735C4C2×C4×C22⋊D7311yescharacteristic
736C4#1798906611yescharacteristic
737C4D4×C22⋊D7311yescharacteristic
738C4#1798924611yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—81no—
743C2—5841no—
744C2#2261294811yescharacteristic
745C2#2261882911yescharacteristic
746C2#2261884311yescharacteristic
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#23017
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×#17988706C2semidirect
3. #22618673C2semidirect
4. #22618497C2semidirect
5. #22610761C2semidirect
6. #22610703C2semidirect
7. #22610639C2semidirect
8. #22610635C2semidirect
9. #22610260C2semidirect
10. #22610258C2semidirect
11. #22610206C2semidirect
12. #22610203C2semidirect
13. #22609789C2semidirect
14. #22609743C2semidirect
15. C2×#443×C73C2semidirect
21. #17988811C4semidirect
22. #17988807C4semidirect
23. #17988804C4semidirect
24. #17988800C4semidirect
25. #17988795C4semidirect
26. #17988790C4semidirect
27. #17988785C4semidirect
28. #17988780C4semidirect
166. #104×C73D4semidirect
376. C2×#443D73semidirect
389. C73#23017semidirect
523. #104C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226193822
C2×#179887062
#226186732
#226184972
#226107612
#226107032
#226106392
#226106352
#226102602
#226102582
#226102062
#226102032
#226097892
#226097432
C2×#443×C732
#2301773