Finite Group Databasebeta

← C2×#22621066 #33958041

Subgroups — C2×#22621066 #33958041

Order 18688.

2058 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989143C211yesmaximal, characteristic, complemented
2C2×#17989134C211yesmaximal, characteristic
3#22621066C2116yesmaximal, direct product factor
4C2×#17988991C211yesmaximal, characteristic, complemented
5C2×#17988984C211yesmaximal, characteristic, complemented
6C2×#17988932C211yesmaximal, characteristic, complemented
7C2×#17988932C211yesmaximal, characteristic, complemented
8C2×#17988914C211yesmaximal, characteristic, complemented
9C2×#17988913C211yesmaximal, characteristic, complemented
10C2×#17988910C211yesmaximal, characteristic, complemented
11C2×#17988909C211yesmaximal, characteristic, complemented
12C2×#17988888C211yesmaximal, characteristic, complemented
13C2×#17988887C211yesmaximal, characteristic, complemented
14C2×#17988884C211yesmaximal, characteristic, complemented
15C2×#17988639C211yesmaximal, characteristic, complemented
16C2×#478×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18#17989143—24no—
19#17989143C2218yescomplemented
20#17989134—24no—
21#17989134C2218yes—
22C2×#14556590C2211yescharacteristic
23C2×#14556590C2211yescharacteristic
24C2×#14556590C2211yescharacteristic
25C2×#14556587C2211yescharacteristic
26C2×#14556583C2211yescharacteristic
27C2×#14556577—21no—
28C2×#14556569—21no—
29C2×#14556569—21no—
30C2×#14556566C2211yescharacteristic
31C2×#14556564—21no—
32C2×#14556562C2211yescharacteristic
33C2×#14556556—21no—
34C2×#14556556—21no—
35C2×C4×D292C2211yescharacteristic
36C2×C4×C22⋊D73—21no—
37C2×#14556549C2211yescharacteristic
38C2×#14556549C2211yescharacteristic
39C2×C42×D73C2211yescharacteristic
40#17988991C2218yescomplemented
41#17988984C2218yescomplemented
42#17988932C2218yescomplemented
43#17988932C2218yescomplemented
44#17988914C2218yescomplemented
45#17988913C2218yescomplemented
46#17988910C2218yescomplemented
47#17988909C2218yescomplemented
48#17988888C2218yescomplemented
49#17988887C2218yescomplemented
50#17988884C2218yescomplemented
51#17988639C2218yescomplemented
52C2×#14556525C2211yescharacteristic
53C2×#14556524C2211yescharacteristic
54C2×#14556524C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556513C2211yescharacteristic
60C2×#14556513C2211yescharacteristic
61C2×#14556512C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556503C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×C8×Dic73C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×#125×C73C2211yescharacteristic
70C2×C4×D4×C73C2211yescharacteristic
71#478×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924028—28no—
78C2×#11924028—48no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146—21no—
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×C22⋊D73—21no—
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73D411yescharacteristic
89C22×C4×D73D411yescharacteristic
90C22×C4×D73C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93#14556590—22no—
94#14556590—22no—
95#14556590—22no—
96#14556590C2314yes—
97#14556590C2314yes—
98#14556590C2314yes—
99#14556587—22no—
100#14556587C2314yes—
101#14556583—22no—
102#14556583C2314yes—
103#14556577—28no—
104#14556569—28no—
105#14556569—28no—
106#14556566—22no—
107#14556566C2314yes—
108#14556564—28no—
109#14556562—22no—
110#14556562C2314yes—
111#14556556—28no—
112#14556556—28no—
113C4×D292—22no—
114C4×D292C2314yes—
115C4×C22⋊D73—28no—
116#14556549—22no—
117#14556549—22no—
118#14556549C2314yes—
119#14556549C2314yes—
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×#11924007—21no—
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×C22⋊Dic73—21no—
129C2×#11924005—21no—
130C2×#11924005—21no—
131C2×#11924005—21no—
132C2×#11924005—21no—
133C2×C4×Dic73—21no—
134C2×C4×Dic73—21no—
135C2×C4×Dic73D411yescharacteristic
136C2×C4×Dic73D411yescharacteristic
137C2×C4×Dic73C2311yescharacteristic
138C42×D73D414yes—
139C42×D73C2314yes—
140#14556525C2314yes—
141#14556524C2314yes—
142#14556524C2314yes—
143#14556523C2314yes—
144#14556522C2314yes—
145#14556522C2314yes—
146C4⋊#10596831C2314yes—
147#14556513C2314yes—
148#14556513C2314yes—
149#14556512C2314yes—
150#14556512C2314yes—
151#14556511C2314yes—
152#14556511C2314yes—
153#14556503C2314yes—
154#14556503C2314yes—
155C8×Dic73C2314yes—
156C8×Dic73C2314yes—
157C22×D4×C73C2311yescharacteristic
158C23×C4×C73—21no—
159C22×C8×C73C2311yescharacteristic
160C22×C8×C73C2311yescharacteristic
161#125×C73—22no—
162#125×C73C2314yes—
163C4×D4×C73—22no—
164C4×D4×C73C2314yes—
165C2×C4⋊C4×C73—21no—
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73C2311yescharacteristic
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C22⋊C4×C73—21no—
171C2×C42×C73C2311yescharacteristic
172#107×C73C2314yes—
173#106×C73C2314yes—
174C4⋊C8×C73C2314yes—
175#102×C73C2314yes—
176#102×C73C2314yes—
177C23×D73—21no—
178C23×D73C2×D411yescharacteristic
179#11924028—432no—
180C2×Dic146—24no—
181C2×Dic146—24no—
182C2×Dic146—24no—
183C2×Dic146—44no—
184C2×Dic146—44no—
185C2×Dic146—44no—
186C2×D292—22no—
187C2×D292—22no—
188C2×D292—24no—
189C2×D292—21no—
190C2×D292—44no—
191C2×D292C2412yes—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—24no—
195C2×C22⋊D73—44no—
196C2×C22⋊D73—44no—
197C2×C22⋊D73—44no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C2×C4×D73—22no—
205C2×C4×D73—22no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—24no—
209C2×C4×D73—44no—
210C2×C4×D73C2×D412yes—
211C2×C4×D73C2×D414yes—
212C2×C4×D73C2×D414yes—
213C2×C4×D73C2412yes—
214C2×#10596831—22no—
215C2×#10596831—22no—
216C2×#10596831C2412yes—
217C2×#10596831C2412yes—
218C4⋊Dic73—21no—
219C4⋊Dic73—21no—
220C4⋊Dic73—21no—
221C4⋊Dic73C2412yes—
222C4⋊Dic73C2412yes—
223C4⋊Dic73C2412yes—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229C22⋊Dic73—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234C4×Dic73—24no—
235C4×Dic73—24no—
236C4×Dic73C2×D412yes—
237C4×Dic73C2×D414yes—
238C4×Dic73C2×D414yes—
239C4×Dic73C2412yes—
240C24×C73—21no—
241C2×D4×C73—21no—
242C2×D4×C73—22no—
243C2×D4×C73—22no—
244C2×D4×C73C2412yes—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—24no—
249C22×C4×C73—44no—
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2411yescharacteristic
253C2×C8×C73—22no—
254C2×C8×C73—22no—
255C2×C8×C73C2412yes—
256C2×C8×C73C2412yes—
257C4⋊C4×C73—24no—
258C4⋊C4×C73—24no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73C2412yes—
263C4⋊C4×C73C2412yes—
264C4⋊C4×C73C2412yes—
265C22⋊C4×C73—24no—
266C42×C73C2×D412yes—
267C42×C73C2412yes—
268C23×C73—22no—
269C23×C73—42no—
270C23×C73—42no—
271C23×C73—42no—
272C23×C73C22×D411yescharacteristic
273C22×D73—22no—
274C22×D73—22no—
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—42no—
278C22×D73—42no—
279C22×D73—42no—
280C22×D73C22×D412yes—
281D4×C73—22no—
282D4×C73—22no—
283D4×C73—42no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—48no—
290C2×C4×C73—42no—
291C2×C4×C73—42no—
292C2×C4×C73—42no—
293C2×C4×C73C22×D412yes—
294C2×C4×C73C22×D412yes—
295C2×C4×C73C22×D411yescharacteristic
296C2×C4×C732−1+412yes—
297C2×C4×C732−1+412yes—
298C2×C4×C73C2511yescharacteristic
299C22⋊D73—48no—
300C22⋊D73—48no—
301C22⋊D73—48no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—42no—
307C2×Dic73—42no—
308C2×Dic73—42no—
309C2×Dic73#13514yes—
310C2×Dic73AGL(1,ℤ/8)14yes—
311C2×Dic73C22×D412yes—
312C2×Dic73C22×D412yes—
313C2×Dic73C22×D412yes—
314D292—22no—
315D292—22no—
316D292—48no—
317D292—42no—
318C4×D73—24no—
319C4×D73—22no—
320C4×D73—22no—
321C4×D73—28no—
322C4×D73—28no—
323C4×D73—48no—
324Dic146—48no—
325Dic146—48no—
326Dic146—48no—
327C8×C73—22no—
328C8×C73—22no—
329#10596831—22no—
330#10596831—22no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73—84no—
335C22×C73#53612yes—
336C22×C73C2×#13512yes—
337C22×C73C2×AGL(1,ℤ/8)12yes—
338C22×C73C23×D411yescharacteristic
339C2×D73—22no—
340C2×D73—22no—
341C2×D73—22no—
342C2×D73—44no—
343C2×D73—42no—
344C2×D73—42no—
345C2×D73—42no—
346C2×D73—84no—
347C4×C73—22no—
348C4×C73—22no—
349C4×C73—42no—
350C4×C73—42no—
351C4×C73—42no—
352C4×C73#53612yes—
353C4×C73C2×2−1+411yescharacteristic
354C4×C73C2×2−1+411yescharacteristic
355Dic73—22no—
356Dic73—42no—
357Dic73—42no—
358Dic73—42no—
359Dic73C2×#13514yes—
360Dic73C2×AGL(1,ℤ/8)14yes—
361C2×#3228—731nomaximal, Sylow
362C2×C73—82no—
363C2×C73#322814yescomplemented
364C2×C73C2×#53611yescharacteristic
365C2×C73C22×#13511yescharacteristic
366C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
367D73—42no—
368D73—82no—
369C2×#533—731no—
370C2×#532—731no—
371#3228—7316no—
372C2×#500—731no—
373C2×#498—731no—
374C2×#486—731no—
375C2×#486—731no—
376C2×#482—731no—
377C2×#482—731no—
378C2×#482—731no—
379C2×#482—731no—
380C2×#478—731no—
381C2×#478—731no—
382C2×#478—731no—
383C2×#478D7311yescharacteristic, complemented
384C2×#431—731no—
385C73C2×#322811yescharacteristic, complemented, Sylow
386C22×#41—1461no—
387#533—738no—
388#533—1464no—
389#532—738no—
390#532—1464no—
391C2×C4⋊Q8—731no—
392C2×C4⋊Q8—731no—
393C2×C4⋊Q8—731no—
394C2×#127—731no—
395C2×#125—731no—
396C2×#125C2×D7311yescharacteristic
397C2×#124—1461no—
398C2×C22⋊Q8—1461no—
399C2×C22⋊Q8—1461no—
400C2×#121—731no—
401C2×#121—731no—
402C2×#121—1461no—
403C2×C4×Q8—1461no—
404C2×C4×Q8—1461no—
405C2×C4×D4—731no—
406C2×C4×D4—1461no—
407C2×C4×D4C2×D7311yescharacteristic
408C2×#117—731no—
409C2×#117—731no—
410C22×C42—731no—
411#500—738no—
412#498—738no—
413#486—738no—
414#486—738no—
415#482—738no—
416#482—738no—
417#482—738no—
418#482—738no—
419#478—738no—
420#478—738no—
421#478—738no—
422#478C2×D7318yescomplemented
423#431—738no—
424C2×#107—731no—
425C2×#107—731no—
426C2×#107—731no—
427C2×#107C2×D7311yescharacteristic
428C2×#106—731no—
429C2×#106—731no—
430C2×#106—731no—
431C2×#106C2×D7311yescharacteristic
432C2×C4⋊C8—731no—
433C2×C4⋊C8C2×D7311yescharacteristic
434C2×#102—731no—
435C2×#102—731no—
436C2×#102—731no—
437C2×#102—731no—
438C2×#102—731no—
439C2×#102—731no—
440C2×#102C2×D7311yescharacteristic
441C2×#102C2×D7311yescharacteristic
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C4×C8—731no—
445C2×C4×C8—731no—
446C2×#41—2928no—
447C2×#41—1468no—
448C22×Q8—1461no—
449C22×Q8—1461no—
450C22×Q8—1461no—
451C22×D4—731no—
452C22×D4—1461no—
453C22×D4—1461no—
454C22×D4—1461no—
455C22×D4—1461no—
456C22×D4C22×D7311yescharacteristic
457C23×C4—21no—
458C23×C4—731no—
459C23×C4—731no—
460C23×C4—731no—
461C23×C4—1461no—
462C22×C8—731no—
463C22×C8—731no—
464C22×C8C22×D7311yescharacteristic
465C22×C8C22×D7311yescharacteristic
466C4⋊Q8—734no—
467C4⋊Q8—734no—
468C4⋊Q8—734no—
469C4⋊Q8—1462no—
470C4⋊Q8—1462no—
471C4⋊Q8—1462no—
472#127—734no—
473#127—1462no—
474#125—22no—
475#125—734no—
476#125—1462no—
477#125C22×D7314yes—
478#124—1468no—
479C22⋊Q8—1468no—
480C22⋊Q8—1468no—
481#121—734no—
482#121—734no—
483#121—1468no—
484#121—1462no—
485#121—1462no—
486C4×Q8—1468no—
487C4×Q8—1468no—
488C4×D4—22no—
489C4×D4—734no—
490C4×D4—1468no—
491C4×D4—1462no—
492C4×D4C22×D7314yes—
493#117—734no—
494#117—734no—
495#117—1462no—
496#117—1462no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1461no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4C22×D7311yescharacteristic
508C2×C4⋊C4C22×D7311yescharacteristic
509C2×C4⋊C4C22×D7311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C22⋊C4—1461no—
515C2×C22⋊C4—1461no—
516C2×C42—731no—
517C2×C42—731no—
518C2×C42—731no—
519C2×C42—734no—
520C2×C42—734no—
521C2×C42—1461no—
522C2×C42—1461no—
523C2×C42C22×D7311yescharacteristic
524#107—734no—
525#107—734no—
526#107—734no—
527#107C22×D7314yes—
528#106—734no—
529#106—734no—
530#106—734no—
531#106C22×D7314yes—
532C4⋊C8—734no—
533C4⋊C8C22×D7314yes—
534#102—734no—
535#102—734no—
536#102—734no—
537#102—734no—
538#102—734no—
539#102—734no—
540#102C22×D7314yes—
541#102C22×D7314yes—
542C22⋊C8—734no—
543C22⋊C8—734no—
544C4×C8—734no—
545C4×C8—734no—
546C24—21no—
547C24—731no—
548C24—1461no—
549#41—29232no—
550C2×Q8—2924no—
551C2×Q8—2924no—
552C2×Q8—2924no—
553C2×Q8—1464no—
554C2×Q8—1464no—
555C2×Q8—1464no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—2924no—
560C2×D4—2924no—
561C2×D4—2924no—
562C2×D4—2924no—
563C2×D4—732no—
564C2×D4—1464no—
565C2×D4—1464no—
566C2×D4—1464no—
567C2×D4—1464no—
568C2×D4—1461no—
569C2×D4—1462no—
570C2×D4—1462no—
571C2×D4C23×D7312yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—44no—
577C22×C4—2924no—
578C22×C4—731no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—732no—
582C22×C4—734no—
583C22×C4—734no—
584C22×C4—732no—
585C22×C4—1464no—
586C22×C4—1464no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1464no—
591C22×C4—1462no—
592C22×C4—1462no—
593C22×C4D4×D7311yescharacteristic
594C22×C4D4×D7311yescharacteristic
595C22×C4C23×D7311yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—732no—
599C2×C8—732no—
600C2×C8—1462no—
601C2×C8—1462no—
602C2×C8C23×D7312yes—
603C2×C8C23×D7312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—732no—
610C4⋊C4—732no—
611C4⋊C4—732no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1464no—
615C4⋊C4—1464no—
616C4⋊C4—1464no—
617C4⋊C4—1461no—
618C4⋊C4—1461no—
619C4⋊C4—1461no—
620C4⋊C4C23×D7312yes—
621C4⋊C4C23×D7312yes—
622C4⋊C4C23×D7312yes—
623C22⋊C4—24no—
624C22⋊C4—1464no—
625C22⋊C4—1464no—
626C22⋊C4—1464no—
627C22⋊C4—1464no—
628C22⋊C4—1464no—
629C42—734no—
630C42—734no—
631C42—732no—
632C42—732no—
633C42—1464no—
634C42—1464no—
635C42D4×D7312yes—
636C42C23×D7312yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—2922no—
642C23—2922no—
643C23—2922no—
644C23—732no—
645C23—1462no—
646C23—1462no—
647C23—1462no—
648C23—1462no—
649C23C2×D4×D7311yescharacteristic
650Q8—2928no—
651Q8—2928no—
652Q8—2928no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—2928no—
657D4—2928no—
658D4—2928no—
659D4—2928no—
660D4—2922no—
661D4—1462no—
662D4—1462no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—48no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—2928no—
673C2×C4—2922no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—732no—
677C2×C4—732no—
678C2×C4—734no—
679C2×C4—734no—
680C2×C4—732no—
681C2×C4—1468no—
682C2×C4—1468no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1464no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4C2×D4×D7312yes—
691C2×C4C2×D4×D7312yes—
692C2×C4C2×D4×D7311yescharacteristic
693C2×C4#1455663812yes—
694C2×C4#1455663912yes—
695C2×C4C24×D7311yescharacteristic
696C8—22no—
697C8—22no—
698C8—1462no—
699C8—1462no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—2924no—
705C22—2922no—
706C22—2922no—
707C22—2922no—
708C22—5844no—
709C22—1462no—
710C22—1462no—
711C22—1462no—
712C22#1798916012yes—
713C22#135×D7312yes—
714C22AGL(1,ℤ/8)×D7312yes—
715C22C22×D4×D7311yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—2922no—
722C4—2922no—
723C4—2922no—
724C4—734no—
725C4—734no—
726C4—1462no—
727C4#1798916012yes—
728C4C2×#1455663811yescharacteristic
729C4C2×#1455663911yescharacteristic
730C2—82no—
731C2—2922no—
732C2—5842no—
733C2#2262106614yesdirect product factor
734C2C2×#1798916011yescharacteristic
735C2C2×#135×D7311yescharacteristic
736C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#478×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989134C2
hypercenterC2×#478D73
hypocenterC73C2×#3228
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#17989143C2semidirect
3. #22621066C2direct (N × H)
4. C2×#17988991C2semidirect
5. C2×#17988984C2semidirect
6. C2×#17988932C2semidirect
7. C2×#17988932C2semidirect
8. C2×#17988914C2semidirect
9. C2×#17988913C2semidirect
10. C2×#17988910C2semidirect
11. C2×#17988909C2semidirect
12. C2×#17988888C2semidirect
13. C2×#17988887C2semidirect
14. C2×#17988884C2semidirect
15. C2×#17988639C2semidirect
16. C2×#478×C73C2semidirect
19. #17989143C22semidirect
40. #17988991C22semidirect
41. #17988984C22semidirect
42. #17988932C22semidirect
43. #17988932C22semidirect
44. #17988914C22semidirect
45. #17988913C22semidirect
46. #17988910C22semidirect
47. #17988909C22semidirect
48. #17988888C22semidirect
49. #17988887C22semidirect
50. #17988884C22semidirect
51. #17988639C22semidirect
71. #478×C73C22semidirect
363. C2×C73#3228semidirect
383. C2×#478D73semidirect
385. C73C2×#3228semidirect
422. #478C2×D73semidirect
733. C2#22621066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891432
C2×#179891342
#226210662
C2×#179889912
C2×#179889842
C2×#179889322
C2×#179889142
C2×#179889132
C2×#179889102
C2×#179889092
C2×#179888882
C2×#179888872
C2×#179888842
C2×#179886392
C2×#478×C732
C2×#322873