Finite Group Databasebeta

← C2×#22622339 #33964463

Subgroups — C2×#22622339 #33964463

Order 18688.

1918 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989308C211yesmaximal, characteristic, complemented
2C2×#17989301C211yesmaximal, characteristic
3#22622339C2116yesmaximal, direct product factor
4C2×#17988984C211yesmaximal, characteristic, complemented
5C2×#17988927C211yesmaximal, characteristic, complemented
6C2×#17988925C211yesmaximal, characteristic, complemented
7C2×#17988909C211yesmaximal, characteristic, complemented
8C2×#17988908C211yesmaximal, characteristic, complemented
9C2×#17988880C211yesmaximal, characteristic, complemented
10C2×#17988865C211yesmaximal, characteristic, complemented
11C2×#17988813C211yesmaximal, characteristic, complemented
12C2×SD16×Dic73C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D73C211yesmaximal, characteristic, complemented
14C2×#17988625C211yesmaximal, characteristic, complemented
15C2×#17988622C211yesmaximal, characteristic, complemented
16C2×#465×C73C211yesmaximal, characteristic, complemented
17C22×C8×D73C2211yescharacteristic
18#17989308—24no—
19#17989308C2218yescomplemented
20#17989301—24no—
21#17989301C2218yes—
22C2×#14556590C2211yescharacteristic
23C2×#14556590C2211yescharacteristic
24C2×#14556586—21no—
25C2×#14556584—21no—
26C2×#14556578—21no—
27C2×#14556577—21no—
28C2×#14556577—21no—
29C2×#14556567C2211yescharacteristic
30C2×#14556563—21no—
31C2×#14556562C2211yescharacteristic
32C2×Q8×Dic73C2211yescharacteristic
33C2×#14556556—21no—
34C2×D4×Dic73C2211yescharacteristic
35C2×C4×C22⋊D73C2211yescharacteristic
36C2×#14556550C2211yescharacteristic
37C2×#14556550C2211yescharacteristic
38C2×#14556549C2211yescharacteristic
39C2×#14556549C2211yescharacteristic
40C2×#14556547—21no—
41#17988984C2218yescomplemented
42#17988927C2218yescomplemented
43#17988925C2218yescomplemented
44#17988909C2218yescomplemented
45#17988908C2218yescomplemented
46#17988880C2218yescomplemented
47#17988865C2218yescomplemented
48#17988813C2218yescomplemented
49SD16×Dic73C2218yescomplemented
50C8×C22⋊D73C2218yescomplemented
51#17988625C2218yescomplemented
52#17988622C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556523C2211yescharacteristic
59C2×#14556522C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#465×C73C2218yescomplemented
74C2×#106×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×C22⋊D73—21no—
80C22×C22⋊D73D411yescharacteristic
81C23×Dic73—21no—
82C22×C4×D73C2311yescharacteristic
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85C2×C8×D73—24no—
86C2×C8×D73C2314yes—
87#14556590—22no—
88#14556590—22no—
89#14556590C2314yes—
90#14556590C2314yes—
91#14556586—28no—
92#14556584—28no—
93#14556578—28no—
94#14556577—28no—
95#14556577—28no—
96#14556567—22no—
97#14556567C2314yes—
98#14556563—28no—
99#14556562—22no—
100#14556562C2314yes—
101Q8×Dic73—22no—
102Q8×Dic73C2314yes—
103#14556556—28no—
104D4×Dic73—22no—
105D4×Dic73C2314yes—
106C4×C22⋊D73D414yes—
107C4×C22⋊D73C2314yes—
108#14556550—22no—
109#14556550—22no—
110#14556550C2314yes—
111#14556550C2314yes—
112#14556549—22no—
113#14556549—22no—
114#14556549C2314yes—
115#14556549C2314yes—
116#14556547—28no—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73C2311yescharacteristic
119C2×C4⋊Dic73C2311yescharacteristic
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×#11924007—21no—
123C2×#11924007—21no—
124C2×#11924007—21no—
125C2×#11924007D411yescharacteristic
126C2×C22⋊Dic73—21no—
127C2×C22⋊Dic73—21no—
128C2×C22⋊Dic73—21no—
129C2×C22⋊Dic73—21no—
130C2×C22⋊Dic73D411yescharacteristic
131C2×#11924005—21no—
132C2×#11924005—21no—
133C2×#11924005—21no—
134C2×#11924005D411yescharacteristic
135C2×C4×Dic73—21no—
136C2×C4×Dic73—21no—
137C2×C4×Dic73—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73C2311yescharacteristic
141#14556525C2314yes—
142#14556525C2314yes—
143#14556524C2314yes—
144#14556524C2314yes—
145#14556523C2314yes—
146#14556523C2314yes—
147#14556522C2314yes—
148#14556522C2314yes—
149#14556520C2314yes—
150#14556515C2314yes—
151#14556515C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154C22⋊#10596831C2314yes—
155#14556503C2314yes—
156C8×Dic73C2314yes—
157C22×Q8×C73C2311yescharacteristic
158C22×D4×C73—21no—
159C22×D4×C73C2311yescharacteristic
160C23×C4×C73C2311yescharacteristic
161C2×SD16×C73—24no—
162C2×SD16×C73C2314yes—
163C22×C8×C73—24no—
164C22×C8×C73C2311yescharacteristic
165C22×C8×C73C2314yes—
166C22×C8×C73C2311yescharacteristic
167C22⋊Q8×C73—22no—
168C22⋊Q8×C73C2314yes—
169#121×C73—22no—
170#121×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73—21no—
176#106×C73C2314yes—
177#103×C73C2314yes—
178#102×C73C2314yes—
179C23×D73C2×D411yescharacteristic
180C2×Dic146—24no—
181C2×Dic146—24no—
182C2×Dic146—44no—
183C2×Dic146—82no—
184C2×C22⋊D73—24no—
185C2×C22⋊D73—24no—
186C2×C22⋊D73—82no—
187C2×C22⋊D73C2×D414yes—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—24no—
193C22×Dic73—44no—
194C22×Dic73C2×D411yescharacteristic
195C22×Dic73C2×D411yescharacteristic
196C22×Dic73C2×D411yescharacteristic
197C2×C4×D73—22no—
198C2×C4×D73—22no—
199C2×C4×D73C2×D412yes—
200C2×C4×D73C2412yes—
201C2×#10596831—22no—
202C2×#10596831—22no—
203C2×#10596831C2412yes—
204C2×#10596831C2412yes—
205C8×D73—28no—
206C4⋊Dic73—21no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209C4⋊Dic73—21no—
210C4⋊Dic73—24no—
211C4⋊Dic73C2412yes—
212C4⋊Dic73C2412yes—
213C4⋊Dic73C2412yes—
214C4⋊Dic73C2412yes—
215#11924007—24no—
216#11924007—24no—
217#11924007—24no—
218#11924007C2×D414yes—
219C22⋊Dic73—24no—
220C22⋊Dic73—24no—
221C22⋊Dic73—24no—
222C22⋊Dic73—24no—
223C22⋊Dic73C2×D414yes—
224#11924005—24no—
225#11924005—24no—
226#11924005—24no—
227#11924005C2×D414yes—
228C4×Dic73—24no—
229C4×Dic73—24no—
230C4×Dic73—24no—
231C4×Dic73—24no—
232C4×Dic73—24no—
233C4×Dic73C2×D412yes—
234C4×Dic73C2412yes—
235C24×C73—21no—
236C24×C73C2×D411yescharacteristic
237C2×Q8×C73—21no—
238C2×Q8×C73—22no—
239C2×Q8×C73—22no—
240C2×Q8×C73C2412yes—
241C2×D4×C73—24no—
242C2×D4×C73—21no—
243C2×D4×C73—22no—
244C2×D4×C73—22no—
245C2×D4×C73—82no—
246C2×D4×C73C2412yes—
247C22×C4×C73—22no—
248C22×C4×C73—22no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2×D412yes—
254C22×C4×C73C2412yes—
255C22×C4×C73C2411yescharacteristic
256SD16×C73—28no—
257C2×C8×C73—22no—
258C2×C8×C73—28no—
259C2×C8×C73#4114yes—
260C2×C8×C73C2412yes—
261C2×C8×C73C2412yes—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73C2412yes—
266C4⋊C4×C73C2412yes—
267C22⋊C4×C73—24no—
268C22⋊C4×C73—24no—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—42no—
274C23×C73—42no—
275C23×C73—42no—
276C23×C73C22×D412yes—
277C23×C73C22×D411yescharacteristic
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73C22×D412yes—
282Q8×C73—22no—
283Q8×C73—22no—
284Q8×C73—42no—
285D4×C73—22no—
286D4×C73—22no—
287D4×C73—42no—
288D4×C73—84no—
289C2×C4×C73—22no—
290C2×C4×C73—24no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—42no—
297C2×C4×C73—42no—
298C2×C4×C73—42no—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4112yes—
302C2×C4×C732−1+412yes—
303C2×C4×C73C2511yescharacteristic
304C22⋊D73—28no—
305C22⋊D73—84no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—48no—
317C2×Dic73#13514yes—
318C2×Dic73C22×D412yes—
319C2×Dic73C22×D412yes—
320C2×Dic73C22×D412yes—
321C4×D73—24no—
322C4×D73—22no—
323C4×D73—22no—
324Dic146—48no—
325Dic146—84no—
326C8×C73—22no—
327C8×C73C2×#4114yes—
328#10596831—22no—
329#10596831—22no—
330C22×C73—22no—
331C22×C73—22no—
332C22×C73—22no—
333C22×C73—44no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—42no—
337C22×C73—84no—
338C22×C73#54712yes—
339C22×C73C2×#13512yes—
340C22×C73#57712yes—
341C22×C73C23×D411yescharacteristic
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—22no—
345C2×D73—44no—
346C4×C73—22no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73#54712yes—
351C4×C73C22×#4111yescharacteristic
352C4×C73C2×2−1+411yescharacteristic
353Dic73—22no—
354Dic73—22no—
355Dic73—42no—
356Dic73—42no—
357Dic73—42no—
358Dic73—42no—
359Dic73C2×#13514yes—
360C2×#3340—731nomaximal, Sylow
361C2×C73—42no—
362C2×C73—82no—
363C2×C73#334014yescomplemented
364C2×C73C2×#54711yescharacteristic
365C2×C73C22×#13511yescharacteristic
366C2×C73C2×#57711yescharacteristic
367D73—42no—
368C2×#556—731no—
369C2×#555—731no—
370#3340—7316no—
371C2×#498—731no—
372C2×#485—731no—
373C2×#485—731no—
374C2×#482—731no—
375C2×#482—731no—
376C2×#477—731no—
377C2×#474—731no—
378C2×#465—731no—
379C2×#465D7311yescharacteristic, complemented
380C2×C4×SD16—731no—
381C2×C8×D4—731no—
382C2×#427—731no—
383C2×#427—731no—
384C73C2×#334011yescharacteristic, complemented, Sylow
385C22×SD16C2×D7311yescharacteristic
386C23×C8—731no—
387C23×C8C2×D7311yescharacteristic
388#556—738no—
389#556—1464no—
390#555—738no—
391#555—1464no—
392C2×C4⋊Q8—731no—
393C2×C4⋊Q8—731no—
394C2×#126—1461no—
395C2×#126—1461no—
396C2×#124—1461no—
397C2×#124—1461no—
398C2×#124—1461no—
399C2×C22⋊Q8—731no—
400C2×C22⋊Q8C2×D7311yescharacteristic
401C2×#121—731no—
402C2×#121—1461no—
403C2×#121C2×D7311yescharacteristic
404C2×C4×Q8—731no—
405C2×C4×Q8—1461no—
406C2×C4×D4—731no—
407C2×C4×D4—731no—
408C2×#117—731no—
409C2×#117—731no—
410C2×#117—731no—
411C2×#117—731no—
412C2×#117—1461no—
413#498—738no—
414#485—738no—
415#485—738no—
416#482—738no—
417#482—738no—
418#477—738no—
419#474—738no—
420#465—738no—
421#465C2×D7318yescomplemented
422C4×SD16—738no—
423C8×D4—738no—
424#427—738no—
425#427—738no—
426C2×#107—731no—
427C2×#107—731no—
428C2×#107—731no—
429C2×#107—731no—
430C2×#106—731no—
431C2×#106—731no—
432C2×#106—731no—
433C2×#106—731no—
434C2×#106C2×D7311yescharacteristic
435C2×C4⋊C8—731no—
436C2×#103—731no—
437C2×#103—731no—
438C2×#103C2×D7311yescharacteristic
439C2×#102—731no—
440C2×#102—731no—
441C2×#102C2×D7311yescharacteristic
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C4×C8—731no—
445C22×Q8—1461no—
446C22×Q8—1461no—
447C22×Q8C22×D7311yescharacteristic
448C22×D4—21no—
449C22×D4—731no—
450C22×D4—1461no—
451C22×D4C22×D7311yescharacteristic
452C23×C4—731no—
453C23×C4—1461no—
454C23×C4C22×D7311yescharacteristic
455C2×SD16—24no—
456C2×SD16C22×D7314yes—
457C22×C8—24no—
458C22×C8—731no—
459C22×C8—731no—
460C22×C8—734no—
461C22×C8—1464no—
462C22×C8C22×D7311yescharacteristic
463C22×C8C22×D7314yes—
464C22×C8C22×D7311yescharacteristic
465C4⋊Q8—734no—
466C4⋊Q8—734no—
467C4⋊Q8—1462no—
468C4⋊Q8—1462no—
469#126—1468no—
470#126—1468no—
471#124—1468no—
472#124—1468no—
473#124—1468no—
474C22⋊Q8—22no—
475C22⋊Q8—734no—
476C22⋊Q8—1462no—
477C22⋊Q8C22×D7314yes—
478#121—22no—
479#121—734no—
480#121—1462no—
481#121—1468no—
482#121C22×D7314yes—
483C4×Q8—734no—
484C4×Q8—1462no—
485C4×Q8—1468no—
486C4×D4—734no—
487C4×D4—734no—
488C4×D4—734no—
489C4×D4—1462no—
490#117—734no—
491#117—734no—
492#117—734no—
493#117—734no—
494#117—1468no—
495#117—1462no—
496#117—1462no—
497#117—1462no—
498#117—1462no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—1461no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4C22×D7311yescharacteristic
510C2×C4⋊C4C22×D7311yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—731no—
514C2×C22⋊C4—731no—
515C2×C22⋊C4—1461no—
516C2×C22⋊C4—1461no—
517C2×C22⋊C4—1461no—
518C2×C22⋊C4—1461no—
519C2×C22⋊C4—1461no—
520C2×C22⋊C4—1461no—
521C2×C22⋊C4—1461no—
522C2×C42—731no—
523C2×C42—1461no—
524C2×C42—1461no—
525C2×C42—1461no—
526C2×C42—1461no—
527C2×C42—1461no—
528#107—734no—
529#107—734no—
530#107—734no—
531#107—734no—
532#106—734no—
533#106—734no—
534#106—734no—
535#106—734no—
536#106C22×D7314yes—
537C4⋊C8—734no—
538#103—734no—
539#103—734no—
540#103C22×D7314yes—
541#102—734no—
542#102—734no—
543#102C22×D7314yes—
544C22⋊C8—734no—
545C22⋊C8—734no—
546C4×C8—734no—
547C24—21no—
548C24—731no—
549C24D4×D7311yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—2924no—
554C2×Q8—5842no—
555C2×Q8—1464no—
556C2×Q8—1464no—
557C2×Q8C23×D7312yes—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—82no—
563C2×D4—5842no—
564C2×D4—734no—
565C2×D4—1464no—
566C2×D4—1464no—
567C2×D4C23×D7312yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—2924no—
574C22×C4—731no—
575C22×C4—731no—
576C22×C4—731no—
577C22×C4—732no—
578C22×C4—732no—
579C22×C4—1464no—
580C22×C4—1461no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1462no—
585C22×C4—1462no—
586C22×C4D4×D7312yes—
587C22×C4D4×D7311yescharacteristic
588C22×C4C23×D7312yes—
589C22×C4C23×D7311yescharacteristic
590SD16—28no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—732no—
594C2×C8—732no—
595C2×C8—1462no—
596C2×C8—1462no—
597C2×C8—1468no—
598C2×C8#1192402714yes—
599C2×C8C23×D7312yes—
600C2×C8C23×D7312yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—734no—
605C4⋊C4—732no—
606C4⋊C4—732no—
607C4⋊C4—732no—
608C4⋊C4—732no—
609C4⋊C4—1464no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
612C4⋊C4—1464no—
613C4⋊C4—1461no—
614C4⋊C4—1461no—
615C4⋊C4—1461no—
616C4⋊C4—1461no—
617C4⋊C4C23×D7312yes—
618C4⋊C4C23×D7312yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—734no—
622C22⋊C4—734no—
623C22⋊C4—1464no—
624C22⋊C4—1464no—
625C22⋊C4—1464no—
626C22⋊C4—1464no—
627C22⋊C4—1464no—
628C22⋊C4—1464no—
629C22⋊C4—1464no—
630C42—732no—
631C42—732no—
632C42—1464no—
633C42—1464no—
634C42—1464no—
635C42—1464no—
636C42—1464no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—732no—
645C23—1462no—
646C23—1462no—
647C23—1462no—
648C23C2×D4×D7312yes—
649C23C2×D4×D7311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—2928no—
654Q8—5844no—
655D4—22no—
656D4—22no—
657D4—42no—
658D4—84no—
659D4—5844no—
660D4—1468no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—2922no—
672C2×C4—2922no—
673C2×C4—2922no—
674C2×C4—2922no—
675C2×C4—2928no—
676C2×C4—732no—
677C2×C4—734no—
678C2×C4—732no—
679C2×C4—732no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1464no—
689C2×C4C2×D4×D7312yes—
690C2×C4C2×D4×D7311yescharacteristic
691C2×C4C2×#1192402712yes—
692C2×C4#1455663812yes—
693C2×C4C24×D7311yescharacteristic
694C8—22no—
695C8—1462no—
696C8—1462no—
697C8C2×#1192402714yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—2924no—
707C22—1462no—
708C22—1462no—
709C22—1462no—
710C22#1798923712yes—
711C22#135×D7312yes—
712C22#1798939312yes—
713C22C22×D4×D7311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—2922no—
719C4—2922no—
720C4—2922no—
721C4—2922no—
722C4—734no—
723C4—1462no—
724C4—1462no—
725C4#1798923712yes—
726C4C22×#1192402711yescharacteristic
727C4C2×#1455663811yescharacteristic
728C2—42no—
729C2—82no—
730C2—2922no—
731C2#2262233914yesdirect product factor
732C2C2×#1798923711yescharacteristic
733C2C2×#135×D7311yescharacteristic
734C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#465×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989301C2
hypercenterC2×#465D73
hypocenterC73C2×#3340
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#17989308C2semidirect
3. #22622339C2direct (N × H)
4. C2×#17988984C2semidirect
5. C2×#17988927C2semidirect
6. C2×#17988925C2semidirect
7. C2×#17988909C2semidirect
8. C2×#17988908C2semidirect
9. C2×#17988880C2semidirect
10. C2×#17988865C2semidirect
11. C2×#17988813C2semidirect
12. C2×SD16×Dic73C2semidirect
13. C2×C8×C22⋊D73C2semidirect
14. C2×#17988625C2semidirect
15. C2×#17988622C2semidirect
16. C2×#465×C73C2semidirect
19. #17989308C22semidirect
41. #17988984C22semidirect
42. #17988927C22semidirect
43. #17988925C22semidirect
44. #17988909C22semidirect
45. #17988908C22semidirect
46. #17988880C22semidirect
47. #17988865C22semidirect
48. #17988813C22semidirect
49. SD16×Dic73C22semidirect
50. C8×C22⋊D73C22semidirect
51. #17988625C22semidirect
52. #17988622C22semidirect
73. #465×C73C22semidirect
363. C2×C73#3340semidirect
379. C2×#465D73semidirect
384. C73C2×#3340semidirect
421. #465C2×D73semidirect
731. C2#22622339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893082
C2×#179893012
#226223392
C2×#179889842
C2×#179889272
C2×#179889252
C2×#179889092
C2×#179889082
C2×#179888802
C2×#179888652
C2×#179888132
C2×SD16×Dic732
C2×C8×C22⋊D732
C2×#179886252
C2×#179886222
C2×#465×C732
C2×#334073