Finite Group Databasebeta

← C2×#22621126 #33958124

Subgroups — C2×#22621126 #33958124

Order 18688.

2038 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×#17989140C211yesmaximal, characteristic, complemented
2C2×#17989132C211yesmaximal, characteristic
3#22621126C2116yesmaximal, direct product factor
4C2×#17988995C211yesmaximal, characteristic, complemented
5C2×#17988994C211yesmaximal, characteristic, complemented
6C2×#17988950C211yesmaximal, characteristic, complemented
7C2×#17988950C211yesmaximal, characteristic, complemented
8C2×#17988912C211yesmaximal, characteristic, complemented
9C2×#17988911C211yesmaximal, characteristic, complemented
10C2×#17988908C211yesmaximal, characteristic, complemented
11C2×#17988876C211yesmaximal, characteristic, complemented
12C2×#17988875C211yesmaximal, characteristic, complemented
13C2×#17988866C211yesmaximal, characteristic, complemented
14C2×#17988865C211yesmaximal, characteristic, complemented
15C2×#17988641C211yesmaximal, characteristic, complemented
16C2×#482×C73C211yesmaximal, characteristic, complemented
17C22×#11924027—21no—
18#17989140—24no—
19#17989140C2218yescomplemented
20#17989132—24no—
21#17989132C2218yes—
22C2×#14556590C2211yescharacteristic
23C2×#14556590C2211yescharacteristic
24C2×#14556590C2211yescharacteristic
25C2×#14556587C2211yescharacteristic
26C2×#14556582C2211yescharacteristic
27C2×#14556582C2211yescharacteristic
28C2×#14556577—21no—
29C2×#14556568—21no—
30C2×#14556568—21no—
31C2×#14556565C2211yescharacteristic
32C2×#14556563—21no—
33C2×C4×Dic146—21no—
34C2×C4×Dic146—21no—
35C2×D4×Dic73C2211yescharacteristic
36C2×#14556553C2211yescharacteristic
37C2×#14556551—21no—
38C2×#14556550C2211yescharacteristic
39C22×C4×Dic73C2211yescharacteristic
40#17988995C2218yescomplemented
41#17988994C2218yescomplemented
42#17988950C2218yescomplemented
43#17988950C2218yescomplemented
44#17988912C2218yescomplemented
45#17988911C2218yescomplemented
46#17988908C2218yescomplemented
47#17988876C2218yescomplemented
48#17988875C2218yescomplemented
49#17988866C2218yescomplemented
50#17988865C2218yescomplemented
51#17988641C2218yescomplemented
52C2×#14556525C2211yescharacteristic
53C2×#14556524C2211yescharacteristic
54C2×#14556524C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556513C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C2×#121×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71#482×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C2×#11924027—28no—
78C2×#11924027—48no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146—21no—
82C22×D292C2311yescharacteristic
83C22×C22⋊D73—21no—
84C22×C22⋊D73—21no—
85C22×C22⋊D73—21no—
86C23×Dic73—21no—
87C23×Dic73D411yescharacteristic
88C23×Dic73D411yescharacteristic
89C22×C4×D73—21no—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92#14556590—22no—
93#14556590—22no—
94#14556590—22no—
95#14556590C2314yes—
96#14556590C2314yes—
97#14556590C2314yes—
98#14556587—22no—
99#14556587C2314yes—
100#14556582—22no—
101#14556582—22no—
102#14556582C2314yes—
103#14556582C2314yes—
104#14556577—28no—
105#14556568—28no—
106#14556568—28no—
107#14556565—22no—
108#14556565C2314yes—
109#14556563—28no—
110C4×Dic146—28no—
111C4×Dic146—28no—
112D4×Dic73—22no—
113D4×Dic73C2314yes—
114#14556553—22no—
115#14556553C2314yes—
116#14556551—28no—
117#14556550—22no—
118#14556550C2314yes—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×C22⋊Dic73—21no—
130C2×C22⋊Dic73—21no—
131C2×#11924005—21no—
132C2×#11924005—21no—
133C2×C4×Dic73—21no—
134C2×C4×Dic73D414yes—
135C2×C4×Dic73D411yescharacteristic
136C2×C4×Dic73D411yescharacteristic
137C2×C4×Dic73C2311yescharacteristic
138C2×C4×Dic73C2311yescharacteristic
139C2×C4×Dic73C2314yes—
140#14556525C2314yes—
141#14556524C2314yes—
142#14556524C2314yes—
143#14556523C2314yes—
144#14556522C2314yes—
145#14556522C2314yes—
146#14556520C2314yes—
147#14556520C2314yes—
148#14556513C2314yes—
149#14556513C2314yes—
150#14556512C2314yes—
151#14556512C2314yes—
152#14556511C2314yes—
153#14556511C2314yes—
154C22⋊#10596831C2314yes—
155#14556501C2314yes—
156#14556501C2314yes—
157C22×D4×C73—21no—
158C22×D4×C73C2311yescharacteristic
159C23×C4×C73C2311yescharacteristic
160C22×C8×C73C2311yescharacteristic
161C22×C8×C73C2311yescharacteristic
162#121×C73—22no—
163#121×C73C2314yes—
164#117×C73—22no—
165#117×C73C2314yes—
166C2×C4⋊C4×C73C2311yescharacteristic
167C2×C4⋊C4×C73C2311yescharacteristic
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C22⋊C4×C73—21no—
170C2×C22⋊C4×C73—21no—
171C2×C42×C73—21no—
172#107×C73C2314yes—
173#106×C73C2314yes—
174#102×C73C2314yes—
175#102×C73C2314yes—
176C22⋊C8×C73C2314yes—
177C23×D73—21no—
178#11924027—432no—
179C2×Dic146—24no—
180C2×Dic146—24no—
181C2×Dic146—24no—
182C2×Dic146—44no—
183C2×Dic146—44no—
184C2×Dic146—44no—
185C2×D292—22no—
186C2×D292—22no—
187C2×D292—21no—
188C2×D292C2412yes—
189C2×C22⋊D73—24no—
190C2×C22⋊D73—24no—
191C2×C22⋊D73—24no—
192C2×C22⋊D73—44no—
193C2×C22⋊D73—44no—
194C2×C22⋊D73—44no—
195C22×Dic73—24no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—24no—
200C22×Dic73—42no—
201C22×Dic73—44no—
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D414yes—
206C22×Dic73C2×D414yes—
207C22×Dic73C2×D411yescharacteristic
208C2×C4×D73—24no—
209C2×C4×D73—44no—
210C2×#10596831—22no—
211C2×#10596831—22no—
212C2×#10596831C2412yes—
213C2×#10596831C2412yes—
214C4⋊Dic73—21no—
215C4⋊Dic73—21no—
216C4⋊Dic73—21no—
217C4⋊Dic73—24no—
218C4⋊Dic73—24no—
219C4⋊Dic73C2412yes—
220C4⋊Dic73C2412yes—
221C4⋊Dic73C2412yes—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227C22⋊Dic73—24no—
228C22⋊Dic73—24no—
229#11924005—24no—
230#11924005—24no—
231C4×Dic73—24no—
232C4×Dic73C2×D414yes—
233C4×Dic73C2×D412yes—
234C4×Dic73C2×D414yes—
235C4×Dic73C2×D412yes—
236C4×Dic73C2412yes—
237C4×Dic73C2412yes—
238C24×C73—21no—
239C24×C73C2×D411yescharacteristic
240C2×D4×C73—24no—
241C2×D4×C73—21no—
242C2×D4×C73—22no—
243C2×D4×C73—22no—
244C2×D4×C73—44no—
245C2×D4×C73C2412yes—
246C22×C4×C73—22no—
247C22×C4×C73—22no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D412yes—
253C22×C4×C73C2412yes—
254C22×C4×C73C2411yescharacteristic
255C2×C8×C73—22no—
256C2×C8×C73—22no—
257C2×C8×C73C2412yes—
258C2×C8×C73C2412yes—
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—
266C22⋊C4×C73—24no—
267C42×C73—24no—
268C23×C73—22no—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73—22no—
272C23×C73—42no—
273C23×C73—42no—
274C23×C73—42no—
275C23×C73C22×D412yes—
276C23×C73C22×D411yescharacteristic
277C22×D73—22no—
278C22×D73—42no—
279C22×D73—42no—
280C22×D73—42no—
281D4×C73—22no—
282D4×C73—22no—
283D4×C73—48no—
284D4×C73—42no—
285C2×C4×C73—22no—
286C2×C4×C73—24no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C732−1+412yes—
298C2×C4×C732−1+412yes—
299C2×C4×C73C2511yescharacteristic
300C22⋊D73—48no—
301C22⋊D73—48no—
302C22⋊D73—48no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—28no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—44no—
311C2×Dic73—42no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—48no—
315C2×Dic73AGL(1,ℤ/8)14yes—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319C2×Dic73C22×D412yes—
320D292—22no—
321D292—22no—
322D292—42no—
323C4×D73—48no—
324Dic146—48no—
325Dic146—48no—
326Dic146—48no—
327C8×C73—22no—
328C8×C73—22no—
329#10596831—22no—
330#10596831—22no—
331C22×C73—22no—
332C22×C73—22no—
333C22×C73—22no—
334C22×C73—44no—
335C22×C73—42no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—84no—
339C22×C73#53612yes—
340C22×C73C2×AGL(1,ℤ/8)12yes—
341C22×C73#57512yes—
342C22×C73C23×D411yescharacteristic
343C2×D73—42no—
344C2×D73—42no—
345C2×D73—42no—
346C2×D73—84no—
347C4×C73—22no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73—42no—
351C4×C73#53612yes—
352C4×C73C2×2−1+411yescharacteristic
353C4×C73C2×2−1+411yescharacteristic
354Dic73—22no—
355Dic73—22no—
356Dic73—22no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360Dic73C2×AGL(1,ℤ/8)14yes—
361C2×#3235—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73—82no—
364C2×C73#323514yescomplemented
365C2×C73C2×#53611yescharacteristic
366C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
367C2×C73C2×#57511yescharacteristic
368D73—82no—
369C2×#533—731no—
370C2×#532—731no—
371#3235—7316no—
372C2×#501—731no—
373C2×#501—731no—
374C2×#490—731no—
375C2×#490—731no—
376C2×#482—731no—
377C2×#482—731no—
378C2×#482—731no—
379C2×#482D7311yescharacteristic, complemented
380C2×#476—731no—
381C2×#476—731no—
382C2×#474—731no—
383C2×#474—731no—
384C2×#432—731no—
385C73C2×#323511yescharacteristic, 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×#125—731no—
397C2×#124—1461no—
398C2×C22⋊Q8—1461no—
399C2×C22⋊Q8—1461no—
400C2×#121—731no—
401C2×#121—1461no—
402C2×#121C2×D7311yescharacteristic
403C2×C4×Q8—1461no—
404C2×C4×Q8—1461no—
405C2×C4×D4—731no—
406C2×C4×D4—731no—
407C2×C4×D4—1461no—
408C2×#117—731no—
409C2×#117C2×D7311yescharacteristic
410C22×C42—731no—
411#501—738no—
412#501—738no—
413#490—738no—
414#490—738no—
415#482—738no—
416#482—738no—
417#482—738no—
418#482C2×D7318yescomplemented
419#476—738no—
420#476—738no—
421#474—738no—
422#474—738no—
423#432—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⋊C8—731no—
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⋊C8C2×D7311yescharacteristic
444C2×#97—731no—
445C2×#97—731no—
446C2×#41—2928no—
447C2×#41—1468no—
448C22×Q8—1461no—
449C22×Q8—1461no—
450C22×Q8—1461no—
451C22×D4—21no—
452C22×D4—731no—
453C22×D4—1461no—
454C22×D4—1461no—
455C22×D4—1461no—
456C22×D4C22×D7311yescharacteristic
457C23×C4—731no—
458C23×C4—731no—
459C23×C4—1461no—
460C23×C4—1461no—
461C23×C4C22×D7311yescharacteristic
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—734no—
475#125—734no—
476#125—1462no—
477#125—1462no—
478#124—1468no—
479C22⋊Q8—1468no—
480C22⋊Q8—1468no—
481#121—22no—
482#121—734no—
483#121—1468no—
484#121—1462no—
485#121C22×D7314yes—
486C4×Q8—1468no—
487C4×Q8—1468no—
488C4×D4—734no—
489C4×D4—734no—
490C4×D4—1468no—
491C4×D4—1462no—
492C4×D4—1462no—
493#117—22no—
494#117—734no—
495#117—1462no—
496#117C22×D7314yes—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
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—21no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C22⋊C4—1461no—
515C2×C22⋊C4—1461no—
516C2×C42—21no—
517C2×C42—731no—
518C2×C42—731no—
519C2×C42—734no—
520C2×C42—731no—
521C2×C42—731no—
522C2×C42—734no—
523C2×C42—1461no—
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⋊C8—734no—
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⋊C8C22×D7314yes—
544#97—734no—
545#97—734no—
546C24—21no—
547C24—1461no—
548C24D4×D7311yescharacteristic
549#41—29232no—
550C2×Q8—2924no—
551C2×Q8—2924no—
552C2×Q8—2924no—
553C2×Q8—1464no—
554C2×Q8—1464no—
555C2×Q8—1464no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—44no—
561C2×D4—2924no—
562C2×D4—2924no—
563C2×D4—2924no—
564C2×D4—732no—
565C2×D4—1464no—
566C2×D4—1464no—
567C2×D4—1464no—
568C2×D4—1461no—
569C2×D4—1462no—
570C2×D4—1462no—
571C2×D4C23×D7312yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—2924no—
578C22×C4—2924no—
579C22×C4—2922no—
580C22×C4—734no—
581C22×C4—731no—
582C22×C4—734no—
583C22×C4—731no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—1464no—
587C22×C4—1464no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1464no—
592C22×C4D4×D7312yes—
593C22×C4D4×D7311yescharacteristic
594C22×C4C23×D7312yes—
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—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—732no—
608C4⋊C4—732no—
609C4⋊C4—732no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
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—24no—
625C22⋊C4—1464no—
626C22⋊C4—1464no—
627C22⋊C4—1464no—
628C22⋊C4—1464no—
629C42—24no—
630C42—734no—
631C42—732no—
632C42—734no—
633C42—732no—
634C42—732no—
635C42—732no—
636C42—1464no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—2922no—
645C23—2922no—
646C23—2922no—
647C23—1462no—
648C23C2×D4×D7312yes—
649C23C2×D4×D7311yescharacteristic
650Q8—2928no—
651Q8—2928no—
652Q8—2928no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—2928no—
658D4—2928no—
659D4—2928no—
660D4—2922no—
661D4—1462no—
662D4—1462no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—2928no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—2922no—
677C2×C4—2928no—
678C2×C4—2924no—
679C2×C4—732no—
680C2×C4—734no—
681C2×C4—732no—
682C2×C4—732no—
683C2×C4—732no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1468no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4C2×D4×D7312yes—
692C2×C4C2×D4×D7311yescharacteristic
693C2×C4#1455663812yes—
694C2×C4#1455663812yes—
695C2×C4C24×D7311yescharacteristic
696C8—22no—
697C8—22no—
698C8—1462no—
699C8—1462no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22—2922no—
709C22—2922no—
710C22—2922no—
711C22—5844no—
712C22#1798915912yes—
713C22AGL(1,ℤ/8)×D7312yes—
714C22#1798938412yes—
715C22C22×D4×D7311yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—2922no—
721C4—2922no—
722C4—2922no—
723C4—734no—
724C4—1462no—
725C4—1462no—
726C4—1462no—
727C4#1798915912yes—
728C4C2×#1455663811yescharacteristic
729C4C2×#1455663811yescharacteristic
730C2—42no—
731C2—82no—
732C2—5842no—
733C2#2262112614yesdirect product factor
734C2C2×#1798915911yescharacteristic
735C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
736C2C2×#1798938411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#482×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989132C2
hypercenterC2×#482D73
hypocenterC73C2×#3235
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#17989140C2semidirect
3. #22621126C2direct (N × H)
4. C2×#17988995C2semidirect
5. C2×#17988994C2semidirect
6. C2×#17988950C2semidirect
7. C2×#17988950C2semidirect
8. C2×#17988912C2semidirect
9. C2×#17988911C2semidirect
10. C2×#17988908C2semidirect
11. C2×#17988876C2semidirect
12. C2×#17988875C2semidirect
13. C2×#17988866C2semidirect
14. C2×#17988865C2semidirect
15. C2×#17988641C2semidirect
16. C2×#482×C73C2semidirect
19. #17989140C22semidirect
40. #17988995C22semidirect
41. #17988994C22semidirect
42. #17988950C22semidirect
43. #17988950C22semidirect
44. #17988912C22semidirect
45. #17988911C22semidirect
46. #17988908C22semidirect
47. #17988876C22semidirect
48. #17988875C22semidirect
49. #17988866C22semidirect
50. #17988865C22semidirect
51. #17988641C22semidirect
71. #482×C73C22semidirect
364. C2×C73#3235semidirect
379. C2×#482D73semidirect
385. C73C2×#3235semidirect
418. #482C2×D73semidirect
733. C2#22621126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891402
C2×#179891322
#226211262
C2×#179889952
C2×#179889942
C2×#179889502
C2×#179889122
C2×#179889112
C2×#179889082
C2×#179888762
C2×#179888752
C2×#179888662
C2×#179888652
C2×#179886412
C2×#482×C732
C2×#323573