Finite Group Databasebeta

← #33101867

Subgroups — #33101867

Order 18688.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989385C211yesmaximal, characteristic
2C2×#17988707C211yesmaximal, characteristic, complemented
3C2×#17988702C211yesmaximal, characteristic, complemented
4#22618377C211yesmaximal, characteristic, complemented
5#22610823C211yesmaximal, characteristic, complemented
6#22610818C211yesmaximal, characteristic, complemented
7#22610261C211yesmaximal, characteristic, complemented
8#22610261C211yesmaximal, characteristic, complemented
9#22610258C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22609971C211yesmaximal, characteristic, complemented
12#22609875C211yesmaximal, characteristic, complemented
13#22609874C211yesmaximal, characteristic, complemented
14#22609717C211yesmaximal, characteristic, complemented
15C73×#2880C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17#17989385—24no—
18#17989385—24no—
19C2×#14556622C411yescharacteristic, complemented
20C2×#14556622C411yescharacteristic, complemented
21C2×#14556621C411yescharacteristic, complemented
22C2×#14556621C411yescharacteristic, complemented
23C2×#14556617C411yescharacteristic, complemented
24C2×#14556617C411yescharacteristic, complemented
25C2×#14556616C411yescharacteristic, complemented
26C2×#14556616C411yescharacteristic, complemented
27C2×#14556611C2211yescharacteristic
28C2×#14556611C2211yescharacteristic
29C2×#14556611C2211yescharacteristic
30C2×#14556611C2211yescharacteristic
31C2×#14556597C2211yescharacteristic, complemented
32C2×#14556597C2211yescharacteristic, complemented
33C22×#11924012C2211yescharacteristic
34#17988707—24no—
35#17988702—24no—
36C2×#14556526C2211yescharacteristic, complemented
37C2×#14556526C2211yescharacteristic, complemented
38C2×#14556518C2211yescharacteristic, complemented
39C2×#14556518C2211yescharacteristic, complemented
40C2×#14556518C2211yescharacteristic, complemented
41C2×#14556518C2211yescharacteristic, complemented
42C2×#14556517C2211yescharacteristic, complemented
43C2×#14556517C2211yescharacteristic, complemented
44C2×#14556517C2211yescharacteristic, complemented
45C2×#14556517C2211yescharacteristic, complemented
46#17988553C2211yescharacteristic, complemented
47#17988553C2211yescharacteristic, complemented
48#17988552—21no—
49#17988552—21no—
50#17988551C2211yescharacteristic
51#17988549—21no—
52C22⋊C8×D73—21no—
53C2×#14556501C2211yescharacteristic, complemented
54C2×C8×Dic73C2211yescharacteristic, complemented
55C4×C22⋊Dic73C2211yescharacteristic
56#17988351C2211yescharacteristic, complemented
57#17988351C2211yescharacteristic, complemented
58#17988341C2211yescharacteristic, complemented
59#17988341C2211yescharacteristic, complemented
60C22×#41×C73C2211yescharacteristic
61C2×#131×C73C2211yescharacteristic, complemented
62C2×#131×C73C2211yescharacteristic, complemented
63#408×C73—21no—
64#408×C73—21no—
65#408×C73C2211yescharacteristic, complemented
66#408×C73C2211yescharacteristic, complemented
67#407×C73—21no—
68#407×C73C2211yescharacteristic
69C2×C22⋊C8×C73—21no—
70C2×C22⋊C8×C73C2211yescharacteristic
71C2×#11924028—22no—
72C2×#11924028—22no—
73C2×#11924028—21no—
74C2×#11924028—21no—
75C2×#11924028—41no—
76C2×#11924028—41no—
77C2×#11924028C2×C411yescharacteristic
78C2×#11924028C2×C411yescharacteristic
79C2×#11924028C2311yescharacteristic
80C2×#11924028C2311yescharacteristic
81C22×Dic146C2×C411yescharacteristic
82C22×D292C2×C411yescharacteristic
83C22×C22⋊D73—21no—
84C22×C4×D73—21no—
85#14556622—24no—
86#14556622—24no—
87#14556621—24no—
88#14556621—24no—
89#14556617—24no—
90#14556617—24no—
91#14556616—24no—
92#14556616—24no—
93#14556611—22no—
94#14556611—22no—
95#14556611—22no—
96#14556611—22no—
97#14556611—22no—
98#14556611—22no—
99#14556611D414yes—
100#14556611D414yes—
101C2×#11924018C2×C411yescharacteristic
102C2×#11924018C2×C411yescharacteristic
103C2×#11924018C2×C411yescharacteristic
104C2×#11924018C2×C411yescharacteristic
105C2×#11924016C2×C411yescharacteristic
106C2×#11924016C2×C411yescharacteristic
107C2×#11924016C2×C411yescharacteristic
108C2×#11924016C2×C411yescharacteristic
109C2×#11924015C2×C411yescharacteristic
110C2×#11924015C2×C411yescharacteristic
111C2×#11924015C2×C411yescharacteristic
112C2×#11924015C2×C411yescharacteristic
113C2×#11924013C2×C411yescharacteristic
114C2×#11924013C2×C411yescharacteristic
115C2×#11924013C2×C411yescharacteristic
116C2×#11924013C2×C411yescharacteristic
117#14556597—22no—
118#14556597—22no—
119#14556597—41no—
120#14556597—41no—
121C2×#11924012—22no—
122C2×#11924012—22no—
123C2×#11924012C2×C411yescharacteristic
124C2×#11924012C2×C411yescharacteristic
125C2×#11924012C2×C411yescharacteristic
126C2×#11924012C2×C411yescharacteristic
127C2×#11924012C2311yescharacteristic
128C2×#11924012C2311yescharacteristic
129C2×#11924011—21no—
130C2×#11924011—21no—
131C22×#10596831C2311yescharacteristic
132C22×#10596831C2311yescharacteristic
133C2×C8×D73—21no—
134C2×C8×D73—21no—
135C2×C22⋊Dic73—21no—
136C2×C4×Dic73C2311yescharacteristic
137C2×C4×Dic73C2311yescharacteristic
138#14556526—22no—
139#14556526—22no—
140#14556518—22no—
141#14556518—22no—
142#14556518—41no—
143#14556518—41no—
144#14556517—22no—
145#14556517—22no—
146#14556517—41no—
147#14556517—41no—
148C22⋊#10596831—21no—
149C22⋊#10596831—21no—
150#14556503—21no—
151#14556503—21no—
152#14556503—21no—
153#14556503—21no—
154#14556501—22no—
155C8×Dic73—22no—
156#14556498—21no—
157C2×#41×C73—21no—
158C2×#41×C73—21no—
159C2×#41×C73—22no—
160C2×#41×C73—22no—
161C2×#41×C73—41no—
162C2×#41×C73—41no—
163C2×#41×C73C2×C411yescharacteristic
164C2×#41×C73C2×C411yescharacteristic
165C2×#41×C73C2311yescharacteristic
166C2×#41×C73C2311yescharacteristic
167C22×Q8×C73C2×C411yescharacteristic
168C22×D4×C73—21no—
169C22×D4×C73C2×C411yescharacteristic
170C23×C4×C73—21no—
171C23×C4×C73C2311yescharacteristic
172#131×C73—22no—
173#131×C73—22no—
174#131×C73—41no—
175#131×C73—41no—
176C2×M16×C73—21no—
177C2×M16×C73—21no—
178C2×M16×C73C2311yescharacteristic
179C2×M16×C73C2311yescharacteristic
180C22×C8×C73—21no—
181C22×C8×C73—21no—
182C22×C8×C73C2311yescharacteristic
183C22×C8×C73C2311yescharacteristic
184C22⋊C8×C73—21no—
185C22⋊C8×C73—21no—
186C22⋊C8×C73—21no—
187C22⋊C8×C73—21no—
188C22⋊C8×C73—21no—
189C22⋊C8×C73—21no—
190C22⋊C8×C73D411yescharacteristic
191C22⋊C8×C73D411yescharacteristic
192C22⋊C8×C73D411yescharacteristic
193C22⋊C8×C73D411yescharacteristic
194C23×D73—21no—
195#11924028—21no—
196#11924028—21no—
197#11924028—21no—
198#11924028—21no—
199#11924028—21no—
200#11924028—21no—
201#11924028—22no—
202#11924028—22no—
203#11924028—41no—
204#11924028—41no—
205#11924028—42no—
206#11924028—42no—
207#11924028—42no—
208#11924028—42no—
209#11924028C2×D412yes—
210#11924028C2×D412yes—
211C2×Dic146—22no—
212C2×Dic146—21no—
213C2×Dic146—41no—
214C2×Dic146C22×C411yescharacteristic
215C2×Dic146C22×C411yescharacteristic
216C2×D292—22no—
217C2×D292—21no—
218C2×D292—41no—
219C2×D292C22×C411yescharacteristic
220C2×D292C22×C411yescharacteristic
221C2×C22⋊D73—21no—
222C2×C22⋊D73—21no—
223C2×C22⋊D73—21no—
224C2×C22⋊D73—21no—
225C2×C22⋊D73—42no—
226C2×C22⋊D73—42no—
227C22×Dic73—21no—
228C22×Dic73—21no—
229C22×Dic73—21no—
230C2×C4×D73—21no—
231C2×C4×D73—21no—
232C2×C4×D73—21no—
233C2×C4×D73—21no—
234C2×C4×D73—42no—
235C2×C4×D73—42no—
236#11924018—22no—
237#11924018—22no—
238#11924018—22no—
239#11924018C22⋊C414yescomplemented
240#11924016—22no—
241#11924016—22no—
242#11924016—22no—
243#11924016C22⋊C414yescomplemented
244#11924015—22no—
245#11924015—22no—
246#11924015—22no—
247#11924015C22⋊C414yescomplemented
248#11924013—22no—
249#11924013—22no—
250#11924013—22no—
251#11924013C22⋊C414yescomplemented
252#11924012—22no—
253#11924012—22no—
254#11924012—22no—
255#11924012—22no—
256#11924012—21no—
257#11924012—21no—
258#11924012—21no—
259#11924012—21no—
260#11924011—42no—
261#11924011—42no—
262C2×#10596831—21no—
263C2×#10596831—21no—
264C2×#10596831—21no—
265C2×#10596831—21no—
266C2×#10596831C22×C411yescharacteristic
267C2×#10596831C22×C411yescharacteristic
268C2×#10596831C22×C411yescharacteristic
269C2×#10596831C22×C411yescharacteristic
270C2×#10596831C2×D412yes—
271C2×#10596831C2×D412yes—
272C8×D73—42no—
273C8×D73—42no—
274C22⋊Dic73—42no—
275C4×Dic73—21no—
276C4×Dic73—21no—
277C4×Dic73—21no—
278C4×Dic73—21no—
279C24×C73—21no—
280C24×C73#4111yescharacteristic
281#41×C73—21no—
282#41×C73—21no—
283#41×C73—22no—
284#41×C73—22no—
285#41×C73—21no—
286#41×C73—21no—
287#41×C73—21no—
288#41×C73—21no—
289#41×C73—42no—
290#41×C73—42no—
291#41×C73—41no—
292#41×C73—41no—
293#41×C73—42no—
294#41×C73—42no—
295#41×C73C2×D412yes—
296#41×C73C2×D412yes—
297C2×Q8×C73—21no—
298C2×Q8×C73—22no—
299C2×Q8×C73—41no—
300C2×Q8×C73C22×C411yescharacteristic
301C2×Q8×C73C22×C411yescharacteristic
302C2×D4×C73—21no—
303C2×D4×C73—22no—
304C2×D4×C73—21no—
305C2×D4×C73—21no—
306C2×D4×C73—21no—
307C2×D4×C73—21no—
308C2×D4×C73—41no—
309C2×D4×C73—42no—
310C2×D4×C73—42no—
311C2×D4×C73C22×C411yescharacteristic
312C2×D4×C73C22×C411yescharacteristic
313C22×C4×C73—21no—
314C22×C4×C73—21no—
315C22×C4×C73—21no—
316C22×C4×C73—21no—
317C22×C4×C73—21no—
318C22×C4×C73—21no—
319C22×C4×C73—21no—
320C22×C4×C73—21no—
321C22×C4×C73—21no—
322C22×C4×C73—42no—
323C22×C4×C73—42no—
324C22×C4×C73C22×C411yescharacteristic
325C22×C4×C73C22×C411yescharacteristic
326C22×C4×C73C2×D411yescharacteristic
327C22×C4×C73C2×D411yescharacteristic
328C22×C4×C73#4111yescharacteristic
329C22×C4×C73C2411yescharacteristic
330M16×C73—21no—
331M16×C73—21no—
332M16×C73—21no—
333M16×C73—21no—
334M16×C73—42no—
335M16×C73—42no—
336C2×C8×C73—21no—
337C2×C8×C73—21no—
338C2×C8×C73—21no—
339C2×C8×C73—21no—
340C2×C8×C73—21no—
341C2×C8×C73—21no—
342C2×C8×C73—42no—
343C2×C8×C73—42no—
344C2×C8×C73C2×D411yescharacteristic
345C2×C8×C73C2×D411yescharacteristic
346C2×C8×C73C2×D411yescharacteristic
347C2×C8×C73C2×D411yescharacteristic
348C23×C73—21no—
349C23×C73—21no—
350C23×C73—21no—
351C23×C73—21no—
352C23×C73—41no—
353C23×C73—41no—
354C23×C73—42no—
355C23×C73—42no—
356C23×C73—81no—
357C23×C73C4×D411yescharacteristic
358C23×C73C4×D411yescharacteristic
359C23×C73C2×#4111yescharacteristic
360C22×D73—21no—
361C22×D73—21no—
362C22×D73—42no—
363C22×D73—42no—
364C22×D73—81no—
365Q8×C73—21no—
366Q8×C73—21no—
367Q8×C73—21no—
368Q8×C73—42no—
369Q8×C73C2×C22⋊C412yes—
370D4×C73—22no—
371D4×C73—22no—
372D4×C73—21no—
373D4×C73—21no—
374D4×C73—21no—
375D4×C73—42no—
376D4×C73—42no—
377D4×C73—42no—
378D4×C73—41no—
379D4×C73—41no—
380D4×C73C2×C22⋊C412yes—
381C2×C4×C73—21no—
382C2×C4×C73—21no—
383C2×C4×C73—21no—
384C2×C4×C73—21no—
385C2×C4×C73—21no—
386C2×C4×C73—21no—
387C2×C4×C73—21no—
388C2×C4×C73—22no—
389C2×C4×C73—22no—
390C2×C4×C73—21no—
391C2×C4×C73—21no—
392C2×C4×C73—21no—
393C2×C4×C73—21no—
394C2×C4×C73—21no—
395C2×C4×C73—42no—
396C2×C4×C73—42no—
397C2×C4×C73—42no—
398C2×C4×C73—41no—
399C2×C4×C73—41no—
400C2×C4×C73C4×D411yescharacteristic
401C2×C4×C73C4×D411yescharacteristic
402C2×C4×C73C23×C411yescharacteristic
403C2×C4×C73C22×D411yescharacteristic
404C2×C4×C73C22×D411yescharacteristic
405C2×C4×C73C22×D411yescharacteristic
406C2×C4×C73H(5,𝔽2)11yescharacteristic
407C2×C4×C73H(5,𝔽2)11yescharacteristic
408C22⋊D73—22no—
409C22⋊D73—22no—
410C22⋊D73—42no—
411C22⋊D73—42no—
412C22⋊D73—41no—
413C22⋊D73—41no—
414C2×Dic73—21no—
415C2×Dic73—22no—
416C2×Dic73—21no—
417C2×Dic73—42no—
418C2×Dic73—41no—
419C2×Dic73—41no—
420C2×Dic73—41no—
421C2×Dic73—41no—
422C2×Dic73—41no—
423D292—21no—
424D292—21no—
425D292—21no—
426D292—42no—
427D292C2×C22⋊C412yes—
428C4×D73—22no—
429C4×D73—22no—
430C4×D73—42no—
431C4×D73—42no—
432C4×D73—41no—
433C4×D73—41no—
434Dic146—21no—
435Dic146—21no—
436Dic146—21no—
437Dic146—42no—
438Dic146C2×C22⋊C412yes—
439C8×C73—21no—
440C8×C73—21no—
441C8×C73—21no—
442C8×C73—21no—
443C8×C73—41no—
444C8×C73—41no—
445#10596831—21no—
446#10596831—21no—
447#10596831—41no—
448#10596831—41no—
449#10596831C2×C22⋊C412yes—
450#10596831C2×C22⋊C412yes—
451C22×C73—21no—
452C22×C73—21no—
453C22×C73—21no—
454C22×C73—21no—
455C22×C73—22no—
456C22×C73—21no—
457C22×C73—21no—
458C22×C73—21no—
459C22×C73—21no—
460C22×C73—41no—
461C22×C73—41no—
462C22×C73—41no—
463C22×C73—41no—
464C22×C73—41no—
465C22×C73—81no—
466C22×C73—81no—
467C22×C73—84no—
468C22×C73C2×C4×D411yescharacteristic
469C22×C73#54611yescharacteristic
470C22×C73#54611yescharacteristic
471C2×D73—22no—
472C2×D73—41no—
473C2×D73—41no—
474C2×D73—41no—
475C2×D73—41no—
476C2×D73—41no—
477C2×D73—84no—
478C4×C73—21no—
479C4×C73—21no—
480C4×C73—22no—
481C4×C73—41no—
482C4×C73C22×C22⋊C411yescharacteristic
483C4×C73#51811yescharacteristic
484C4×C73D4211yescharacteristic
485C4×C73D4211yescharacteristic
486Dic73—22no—
487Dic73—42no—
488Dic73—41no—
489Dic73—81no—
490#22453—731nomaximal, Sylow
491C2×C73—21no—
492C2×C73—21no—
493C2×C73—41no—
494C2×C73—41no—
495C2×C73—42no—
496C2×C73—81no—
497C2×C73D4×C22⋊C411yescharacteristic
498C2×C73#295511yescharacteristic
499C2×C73#295611yescharacteristic
500D73—42no—
501D73—81no—
502C2×#575—731no—
503C2×#444—731no—
504C2×#443—731no—
505#2880—731no—
506#2880D7311yescharacteristic, complemented
507#1975—731no—
508#1974—731no—
509#1876—731no—
510#1876—731no—
511#1876—731no—
512#1876—731no—
513#1811—731no—
514#1789—731no—
515#1789—731no—
516#1753—731no—
517C73#2245311yescharacteristic, complemented, Sylow
518C22×#41—731no—
519C22×#41C2×D7311yescharacteristic
520#575—1464no—
521#575—1464no—
522C2×#137—731no—
523C2×#137—731no—
524C2×#137—731no—
525C2×#137—731no—
526C2×AGL(1,ℤ/8)—731no—
527C2×AGL(1,ℤ/8)—731no—
528C2×AGL(1,ℤ/8)—731no—
529C2×AGL(1,ℤ/8)—731no—
530C2×#135—731no—
531C2×#135—731no—
532C2×#135—731no—
533C2×#135—731no—
534C2×#131—731no—
535C2×#131—731no—
536C2×#131C2×D7311yescharacteristic, complemented
537C2×#131C2×D7311yescharacteristic, complemented
538C22×M16—731no—
539#444—1464no—
540#443—1464no—
541C2×#108—731no—
542C2×#108—731no—
543C2×#104—731no—
544C2×#104—731no—
545C2×#104—731no—
546C2×#104—731no—
547C2×#104—731no—
548C2×#104—731no—
549C2×#104—731no—
550C2×#104—731no—
551#408—21no—
552#408—21no—
553#408—731no—
554#408—731no—
555#408—1461no—
556#408—1461no—
557#408C2×D7311yescharacteristic, complemented
558#408C2×D7311yescharacteristic, complemented
559#407—21no—
560#407—731no—
561#407—1461no—
562#407C2×D7311yescharacteristic
563C2×C22⋊C8—21no—
564C2×C22⋊C8—1461no—
565C2×C22⋊C8C2×D7311yescharacteristic
566C2×#97—731no—
567C2×C4×C8—731no—
568C4×C22⋊C4—731no—
569#341—731no—
570#341—731no—
571#336—731no—
572#336—731no—
573C2×#41—21no—
574C2×#41—21no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—41no—
578C2×#41—41no—
579C2×#41—2921no—
580C2×#41—2921no—
581C2×#41—731no—
582C2×#41—731no—
583C2×#41—731no—
584C2×#41—731no—
585C2×#41—1462no—
586C2×#41—1462no—
587C2×#41—1461no—
588C2×#41—1461no—
589C2×#41C4×D7311yescharacteristic
590C2×#41C4×D7311yescharacteristic
591C2×#41C22×D7311yescharacteristic
592C2×#41C22×D7311yescharacteristic
593C22×Q8—731no—
594C22×Q8C4×D7311yescharacteristic
595C22×D4—21no—
596C22×D4—731no—
597C22×D4—1461no—
598C22×D4C4×D7311yescharacteristic
599C23×C4—21no—
600C23×C4—1461no—
601C23×C4C22×D7311yescharacteristic
602#137—1464no—
603#137—1464no—
604#137—1464no—
605#137—1464no—
606AGL(1,ℤ/8)—1464no—
607AGL(1,ℤ/8)—1464no—
608AGL(1,ℤ/8)—1464no—
609AGL(1,ℤ/8)—1464no—
610#135—734no—
611#135—734no—
612#135—1462no—
613#135—1462no—
614#135—1462no—
615#135—1462no—
616#135—1462no—
617#135—1462no—
618C2×Q16—731no—
619C2×Q16—731no—
620C2×Q16—731no—
621C2×Q16—731no—
622C2×SD16—731no—
623C2×SD16—731no—
624C2×SD16—731no—
625C2×SD16—731no—
626C2×SD16—731no—
627C2×SD16—731no—
628C2×SD16—731no—
629C2×SD16—731no—
630C2×D8—731no—
631C2×D8—731no—
632C2×D8—731no—
633C2×D8—731no—
634#131—22no—
635#131—22no—
636#131—41no—
637#131—41no—
638#131—2921no—
639#131—2921no—
640#131—1462no—
641#131—1462no—
642C2×M16—21no—
643C2×M16—21no—
644C2×M16—731no—
645C2×M16—731no—
646C2×M16—731no—
647C2×M16—731no—
648C2×M16—731no—
649C2×M16—731no—
650C2×M16—1462no—
651C2×M16—1462no—
652C2×M16—1461no—
653C2×M16—1461no—
654C2×M16C22×D7311yescharacteristic
655C2×M16C22×D7311yescharacteristic
656C22×C8—21no—
657C22×C8—21no—
658C22×C8—731no—
659C22×C8—731no—
660C22×C8—1461no—
661C22×C8—1461no—
662C22×C8C22×D7311yescharacteristic
663C22×C8C22×D7311yescharacteristic
664C2×C22⋊C4—1461no—
665C2×C42—731no—
666C2×C42—731no—
667#108—1462no—
668#108—1462no—
669#104—2921no—
670#104—2921no—
671#104—2921no—
672#104—2921no—
673#104—1462no—
674#104—1462no—
675#104—1462no—
676#104—1462no—
677C22⋊C8—21no—
678C22⋊C8—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8—21no—
682C22⋊C8—21no—
683C22⋊C8—1461no—
684C22⋊C8—1461no—
685C22⋊C8—1461no—
686C22⋊C8—1461no—
687C22⋊C8—1461no—
688C22⋊C8—1461no—
689C22⋊C8C22⋊D7311yescharacteristic
690C22⋊C8C22⋊D7311yescharacteristic
691C22⋊C8C22⋊D7311yescharacteristic
692C22⋊C8C22⋊D7311yescharacteristic
693#97—1462no—
694C4×C8—1462no—
695#95—1461no—
696C24—21no—
697C24—1461no—
698C24#1192402811yescharacteristic
699#41—21no—
700#41—21no—
701#41—22no—
702#41—22no—
703#41—21no—
704#41—21no—
705#41—21no—
706#41—21no—
707#41—42no—
708#41—42no—
709#41—41no—
710#41—41no—
711#41—42no—
712#41—42no—
713#41—2922no—
714#41—2922no—
715#41—2921no—
716#41—2921no—
717#41—2922no—
718#41—2922no—
719#41—732no—
720#41—732no—
721#41—1462no—
722#41—1462no—
723#41—1461no—
724#41—1461no—
725#41—1461no—
726#41—1461no—
727#41—1461no—
728#41—1461no—
729#41D4×D7312yes—
730#41D4×D7312yes—
731C2×Q8—21no—
732C2×Q8—22no—
733C2×Q8—41no—
734C2×Q8—2921no—
735C2×Q8—731no—
736C2×Q8—731no—
737C2×Q8—1462no—
738C2×Q8—1461no—
739C2×Q8C2×C4×D7311yescharacteristic
740C2×Q8C2×C4×D7311yescharacteristic
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—41no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—2921no—
751C2×D4—2922no—
752C2×D4—2922no—
753C2×D4—731no—
754C2×D4—731no—
755C2×D4—1462no—
756C2×D4—1461no—
757C2×D4—1461no—
758C2×D4—1461no—
759C2×D4—1461no—
760C2×D4—1461no—
761C2×D4C2×C4×D7311yescharacteristic
762C2×D4C2×C4×D7311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—2922no—
775C22×C4—2922no—
776C22×C4—1461no—
777C22×C4—1461no—
778C22×C4—1461no—
779C22×C4—1461no—
780C22×C4—1461no—
781C22×C4—1461no—
782C22×C4—1461no—
783C22×C4C2×C4×D7311yescharacteristic
784C22×C4C2×C4×D7311yescharacteristic
785C22×C4C2×C22⋊D7311yescharacteristic
786C22×C4C2×C22⋊D7311yescharacteristic
787C22×C4#1192402811yescharacteristic
788C22×C4C23×D7311yescharacteristic
789Q16—734no—
790Q16—1462no—
791Q16—1462no—
792Q16—1462no—
793SD16—734no—
794SD16—734no—
795SD16—1462no—
796SD16—1462no—
797SD16—1462no—
798SD16—1462no—
799SD16—1462no—
800SD16—1462no—
801D8—734no—
802D8—1462no—
803D8—1462no—
804D8—1462no—
805M16—21no—
806M16—21no—
807M16—21no—
808M16—21no—
809M16—42no—
810M16—42no—
811M16—2922no—
812M16—2922no—
813M16—1461no—
814M16—1461no—
815M16—1461no—
816M16—1461no—
817M16—1462no—
818M16—1462no—
819M16—1462no—
820M16—1462no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—42no—
828C2×C8—42no—
829C2×C8—2922no—
830C2×C8—2922no—
831C2×C8—731no—
832C2×C8—731no—
833C2×C8—732no—
834C2×C8—732no—
835C2×C8—731no—
836C2×C8—731no—
837C2×C8—1461no—
838C2×C8—1461no—
839C2×C8—1461no—
840C2×C8—1461no—
841C2×C8C2×C22⋊D7311yescharacteristic
842C2×C8C2×C22⋊D7311yescharacteristic
843C2×C8C2×C22⋊D7311yescharacteristic
844C2×C8C2×C22⋊D7311yescharacteristic
845C22⋊C4—2922no—
846C42—1461no—
847C42—1461no—
848C42—1461no—
849C42—1461no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—81no—
859C23—2922no—
860C23—2922no—
861C23—5841no—
862C23—1461no—
863C23—1461no—
864C23C4×C22⋊D7311yescharacteristic
865C23C4×C22⋊D7311yescharacteristic
866C23C2×#1192402811yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—42no—
871Q8—2922no—
872Q8—732no—
873Q8—1461no—
874Q8—1461no—
875Q8—1461no—
876Q8C22⋊C4×D7312yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—41no—
886D4—41no—
887D4—2922no—
888D4—2922no—
889D4—2921no—
890D4—2921no—
891D4—2922no—
892D4—732no—
893D4—1462no—
894D4—1462no—
895D4—1461no—
896D4—1461no—
897D4—1461no—
898D4C22⋊C4×D7312yes—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—2922no—
919C2×C4—2922no—
920C2×C4—2921no—
921C2×C4—2921no—
922C2×C4—2922no—
923C2×C4—2921no—
924C2×C4—2921no—
925C2×C4—2921no—
926C2×C4—2921no—
927C2×C4—2921no—
928C2×C4—1462no—
929C2×C4—1461no—
930C2×C4—1461no—
931C2×C4—1462no—
932C2×C4—1462no—
933C2×C4C4×C22⋊D7311yescharacteristic
934C2×C4C4×C22⋊D7311yescharacteristic
935C2×C4C22×C4×D7311yescharacteristic
936C2×C4C2×D4×D7311yescharacteristic
937C2×C4C2×D4×D7311yescharacteristic
938C2×C4C22×C22⋊D7311yescharacteristic
939C2×C4#1455663611yescharacteristic
940C2×C4#1455663611yescharacteristic
941C8—21no—
942C8—21no—
943C8—21no—
944C8—21no—
945C8—41no—
946C8—41no—
947C8—2921no—
948C8—2921no—
949C8—732no—
950C8—732no—
951C8—1461no—
952C8—1461no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—22no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—81no—
968C22—81no—
969C22—84no—
970C22—2921no—
971C22—2921no—
972C22—2921no—
973C22—2921no—
974C22—2921no—
975C22—5844no—
976C22—1462no—
977C22C2×C4×C22⋊D7311yescharacteristic
978C22#1798922711yescharacteristic
979C22#1798922711yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—41no—
984C4—2922no—
985C4—2921no—
986C4—5841no—
987C4—1462no—
988C4C2×C22⋊C4×D7311yescharacteristic
989C4#1798906011yescharacteristic
990C4D4×C22⋊D7311yescharacteristic
991C4D4×C22⋊D7311yescharacteristic
992C2—21no—
993C2—21no—
994C2—41no—
995C2—41no—
996C2—42no—
997C2—81no—
998C2—2922no—
999C2—5841no—
1000C2C22⋊C4×C22⋊D7311yescharacteristic
1001C2#2261883211yescharacteristic
1002C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2880C2
socleC22×C73C2×C4×D4
prime radicalC2×#17989385C2
cosocleC22×C4×C73C24
hypercenter#2880D73
hypocenterC73#22453
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#17988707C2semidirect
3. C2×#17988702C2semidirect
4. #22618377C2semidirect
5. #22610823C2semidirect
6. #22610818C2semidirect
7. #22610261C2semidirect
8. #22610261C2semidirect
9. #22610258C2semidirect
10. #22610258C2semidirect
11. #22609971C2semidirect
12. #22609875C2semidirect
13. #22609874C2semidirect
14. #22609717C2semidirect
15. C73×#2880C2semidirect
19. C2×#14556622C4semidirect
20. C2×#14556622C4semidirect
21. C2×#14556621C4semidirect
22. C2×#14556621C4semidirect
23. C2×#14556617C4semidirect
24. C2×#14556617C4semidirect
25. C2×#14556616C4semidirect
26. C2×#14556616C4semidirect
31. C2×#14556597C22semidirect
32. C2×#14556597C22semidirect
36. C2×#14556526C22semidirect
37. C2×#14556526C22semidirect
38. C2×#14556518C22semidirect
39. C2×#14556518C22semidirect
40. C2×#14556518C22semidirect
41. C2×#14556518C22semidirect
42. C2×#14556517C22semidirect
43. C2×#14556517C22semidirect
44. C2×#14556517C22semidirect
45. C2×#14556517C22semidirect
46. #17988553C22semidirect
47. #17988553C22semidirect
53. C2×#14556501C22semidirect
54. C2×C8×Dic73C22semidirect
56. #17988351C22semidirect
57. #17988351C22semidirect
58. #17988341C22semidirect
59. #17988341C22semidirect
61. C2×#131×C73C22semidirect
62. C2×#131×C73C22semidirect
65. #408×C73C22semidirect
66. #408×C73C22semidirect
239. #11924018C22⋊C4semidirect
243. #11924016C22⋊C4semidirect
247. #11924015C22⋊C4semidirect
251. #11924013C22⋊C4semidirect
506. #2880D73semidirect
517. C73#22453semidirect
536. C2×#131C2×D73semidirect
537. C2×#131C2×D73semidirect
557. #408C2×D73semidirect
558. #408C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179893852
C2×#179887072
C2×#179887022
#226183772
#226108232
#226108182
#226102612
#226102582
#226099712
#226098752
#226098742
#226097172
C73×#28802
#2245373