Finite Group Databasebeta

← C2×#22620600 #33955853

Subgroups — C2×#22620600 #33955853

Order 18688.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989210C211yesmaximal, characteristic
2C2×#17989197C211yesmaximal, characteristic, complemented
3#22620600C2116yesmaximal, direct product factor
4C2×#17988994C211yesmaximal, characteristic, complemented
5C2×#17988980C211yesmaximal, characteristic, complemented
6C2×#17988943C211yesmaximal, characteristic, complemented
7C2×#17988936C211yesmaximal, characteristic, complemented
8C2×#17988833C211yesmaximal, characteristic
9C2×#17988826C211yesmaximal, characteristic, complemented
10C2×#17988818C211yesmaximal, characteristic
11C2×#17988691C211yesmaximal, characteristic, complemented
12C2×#17988690C211yesmaximal, characteristic, complemented
13C2×Q16×Dic73C211yesmaximal, characteristic, complemented
14C2×#17988674C211yesmaximal, characteristic, complemented
15C2×#17988545C211yesmaximal, characteristic, complemented
16C2×#470×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20C23×#10596831C2211yescharacteristic
21#17989210—24no—
22#17989210C2218yes—
23#17989197—24no—
24#17989197C2218yescomplemented
25C2×#14556590C2211yescharacteristic
26C2×#14556589C2211yescharacteristic
27C2×#14556586—21no—
28C2×#14556584—21no—
29C2×#14556584—21no—
30C2×#14556582—21no—
31C2×#14556582C2211yescharacteristic
32C2×#14556581—21no—
33C2×#14556580C2211yescharacteristic
34C2×#14556577—21no—
35C2×#14556573—21no—
36C2×#14556571—21no—
37C2×#14556570C2211yescharacteristic
38C2×#14556565C2211yescharacteristic
39C2×Q8×Dic73C2211yescharacteristic
40C2×Q8×Dic73C2211yescharacteristic
41C2×#14556556C2211yescharacteristic
42C2×#14556553C2211yescharacteristic
43C2×#14556550C2211yescharacteristic
44#17988994C2218yescomplemented
45#17988980C2218yescomplemented
46#17988943C2218yescomplemented
47#17988936C2218yescomplemented
48#17988833C2218yes—
49#17988826C2218yescomplemented
50#17988818C2218yes—
51#17988691C2218yescomplemented
52#17988690C2218yescomplemented
53Q16×Dic73C2218yescomplemented
54#17988674C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64#17988545C2218yescomplemented
65C2×#14556501C2211yescharacteristic
66C2×#14556501C2211yescharacteristic
67C2×C8×Dic73C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×C22⋊Q8×C73C2211yescharacteristic
73#470×C73C2218yescomplemented
74C2×#106×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C22×C4×D73—21no—
82C2×#11924018—24no—
83C2×#11924018C2314yes—
84C2×#11924017—24no—
85C2×#11924017C2314yes—
86C2×#11924015—24no—
87C2×#11924015C2314yes—
88C22×#10596831—24no—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2314yes—
91C22×#10596831C2311yescharacteristic
92#14556590—22no—
93#14556590C2314yes—
94#14556589—22no—
95#14556589C2314yes—
96#14556586—28no—
97#14556584—28no—
98#14556584—28no—
99#14556582—28no—
100#14556582—22no—
101#14556582C2314yes—
102#14556581—28no—
103#14556580—22no—
104#14556580C2314yes—
105#14556577—28no—
106#14556573—28no—
107#14556571—28no—
108#14556570—22no—
109#14556570C2314yes—
110#14556565—22no—
111#14556565C2314yes—
112Q8×Dic73—22no—
113Q8×Dic73—22no—
114Q8×Dic73C2314yes—
115Q8×Dic73C2314yes—
116#14556556—22no—
117#14556556C2314yes—
118#14556553—22no—
119#14556553C2314yes—
120#14556550D414yes—
121#14556550C2314yes—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73D411yescharacteristic
126C2×C4⋊Dic73D411yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73D411yescharacteristic
137C2×C22⋊Dic73D411yescharacteristic
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73C2311yescharacteristic
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556524C2314yes—
149#14556522C2314yes—
150#14556516C2314yes—
151#14556515C2314yes—
152#14556515C2314yes—
153#14556514C2314yes—
154#14556513C2314yes—
155#14556511C2314yes—
156#14556501C2314yes—
157#14556501C2314yes—
158C8×Dic73C2314yes—
159C8×Dic73C2314yes—
160C22×Q8×C73C2311yescharacteristic
161C22×Q8×C73C2311yescharacteristic
162C23×C4×C73C2311yescharacteristic
163C2×Q16×C73—24no—
164C2×Q16×C73C2314yes—
165C2×M16×C73—24no—
166C2×M16×C73C2314yes—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C22⋊Q8×C73—22no—
170C22⋊Q8×C73—22no—
171C22⋊Q8×C73C2314yes—
172C22⋊Q8×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73—21no—
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179#106×C73C2314yes—
180#103×C73C2314yes—
181#103×C73C2314yes—
182C23×D73—21no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—24no—
187C2×Dic146—82no—
188C2×Dic146C2412yes—
189C2×D292—22no—
190C2×D292—22no—
191C2×D292—21no—
192C2×D292C2412yes—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—82no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73C2×D411yescharacteristic
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C22×Dic73C2×D411yescharacteristic
202C2×C4×D73—24no—
203C2×C4×D73—82no—
204#11924018—28no—
205#11924017—28no—
206#11924015—28no—
207C2×#10596831—22no—
208C2×#10596831—28no—
209C2×#10596831#4114yes—
210C2×#10596831C2412yes—
211C2×#10596831C2412yes—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73—24no—
215C4⋊Dic73—24no—
216C4⋊Dic73—24no—
217C4⋊Dic73C2×D414yes—
218C4⋊Dic73C2×D414yes—
219C4⋊Dic73C2412yes—
220C4⋊Dic73C2412yes—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227C22⋊Dic73—24no—
228C22⋊Dic73C2×D414yes—
229C22⋊Dic73C2×D414yes—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234C4×Dic73—24no—
235C4×Dic73—24no—
236C4×Dic73—24no—
237C4×Dic73C2×D412yes—
238C4×Dic73C2×D412yes—
239C4×Dic73C2412yes—
240C4×Dic73C2412yes—
241C24×C73C2×D411yescharacteristic
242C2×Q8×C73—21no—
243C2×Q8×C73—21no—
244C2×Q8×C73—22no—
245C2×Q8×C73—22no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73C2412yes—
249C2×Q8×C73C2412yes—
250C22×C4×C73—22no—
251C22×C4×C73—22no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D412yes—
258C22×C4×C73C2412yes—
259C22×C4×C73C2411yescharacteristic
260Q16×C73—28no—
261M16×C73—28no—
262C2×C8×C73—22no—
263C2×C8×C73#4114yes—
264C2×C8×C73C2412yes—
265C2×C8×C73C2412yes—
266C4⋊C4×C73—24no—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C2412yes—
271C4⋊C4×C73C2412yes—
272C22⋊C4×C73—24no—
273C22⋊C4×C73—24no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73C22×D412yes—
278C23×C73C22×D411yescharacteristic
279C22×D73—22no—
280C22×D73—42no—
281C22×D73—42no—
282C22×D73—42no—
283Q8×C73—22no—
284Q8×C73—22no—
285Q8×C73—22no—
286Q8×C73—22no—
287Q8×C73—42no—
288Q8×C73—42no—
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—22no—
297C2×C4×C73—42no—
298C2×C4×C73—42no—
299C2×C4×C73—42no—
300C2×C4×C73—42no—
301C2×C4×C73C22×D412yes—
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C2×#4112yes—
304C2×C4×C73C2×#4112yes—
305C2×C4×C73C2511yescharacteristic
306C22⋊D73—84no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319C2×Dic73C22×D412yes—
320C2×Dic73C22×D412yes—
321D292—22no—
322D292—22no—
323D292—42no—
324C4×D73—84no—
325Dic146—22no—
326Dic146—22no—
327Dic146—42no—
328Dic146—84no—
329C8×C73—22no—
330C8×C73C2×#4114yes—
331#10596831—22no—
332#10596831C2×#4114yes—
333C22×C73—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—44no—
337C22×C73#53212yes—
338C22×C73#57712yes—
339C22×C73#57812yes—
340C22×C73C23×D411yescharacteristic
341C2×D73—42no—
342C2×D73—42no—
343C2×D73—42no—
344C2×D73—84no—
345C4×C73—22no—
346C4×C73—42no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73#53212yes—
351C4×C73C22×#4111yescharacteristic
352C4×C73C22×#4111yescharacteristic
353Dic73—22no—
354Dic73—22no—
355Dic73—22no—
356Dic73—22no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360C2×#3178—731nomaximal, Sylow
361C2×C73—42no—
362C2×C73#317814yescomplemented
363C2×C73C2×#53211yescharacteristic
364C2×C73C2×#57711yescharacteristic
365C2×C73C2×#57811yescharacteristic
366D73—82no—
367C2×#542—731no—
368C2×#541—731no—
369#3178—7316no—
370C2×#501—731no—
371C2×#497—731no—
372C2×#488—731no—
373C2×#487—731no—
374C2×#470D7311yescharacteristic, complemented
375C2×#468—731no—
376C2×#467—731no—
377C2×#465—731no—
378C2×#441—731no—
379C2×#440—731no—
380C2×C4×Q16—731no—
381C2×C4×SD16—731no—
382C2×#405—731no—
383C73C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16—731no—
385C22×Q16C2×D7311yescharacteristic
386C22×SD16—731no—
387C22×SD16—731no—
388C22×M16C2×D7311yescharacteristic
389C23×C8—731no—
390#542—738no—
391#542—1464no—
392#541—738no—
393#541—1464no—
394C2×C4⋊Q8—731no—
395C2×C4⋊Q8—731no—
396C2×#126—1461no—
397C2×#126—1461no—
398C2×#126—1461no—
399C2×#125—731no—
400C2×#125—1461no—
401C2×#125—1461no—
402C2×#124—731no—
403C2×#124—1461no—
404C2×#123—1461no—
405C2×C22⋊Q8—731no—
406C2×C22⋊Q8—1461no—
407C2×C22⋊Q8C2×D7311yescharacteristic
408C2×C22⋊Q8C2×D7311yescharacteristic
409C2×#121—731no—
410C2×C4×Q8—731no—
411C2×C4×Q8—731no—
412C2×C4×Q8—731no—
413C2×C4×D4—731no—
414C2×#117—731no—
415#501—738no—
416#497—738no—
417#488—738no—
418#487—738no—
419#470C2×D7318yescomplemented
420#468—738no—
421#467—738no—
422#465—738no—
423#441—738no—
424#440—738no—
425C4×Q16—738no—
426C4×SD16—738no—
427C2×#107—731no—
428C2×#107—731no—
429C2×#106—731no—
430C2×#106C2×D7311yescharacteristic
431C2×#103—731no—
432C2×#103—731no—
433C2×#103—731no—
434C2×#103—731no—
435C2×#103C2×D7311yescharacteristic
436C2×#103C2×D7311yescharacteristic
437C2×#102—731no—
438C2×#102—731no—
439#405—738no—
440C2×#97—731no—
441C2×#97—731no—
442C2×C4×C8—731no—
443C2×C4×C8—731no—
444C22×Q8—731no—
445C22×Q8—1461no—
446C22×Q8C22×D7311yescharacteristic
447C22×Q8C22×D7311yescharacteristic
448C22×D4—731no—
449C22×D4—1461no—
450C23×C4—1461no—
451C23×C4C22×D7311yescharacteristic
452C2×Q16—24no—
453C2×Q16—734no—
454C2×Q16—1464no—
455C2×Q16C22×D7314yes—
456C2×SD16—734no—
457C2×SD16—734no—
458C2×SD16—1464no—
459C2×SD16—1464no—
460C2×M16—24no—
461C2×M16C22×D7314yes—
462C22×C8—731no—
463C22×C8—731no—
464C22×C8—734no—
465C22×C8—1464no—
466C22×C8C22×D7311yescharacteristic
467C22×C8C22×D7311yescharacteristic
468C4⋊Q8—734no—
469C4⋊Q8—734no—
470C4⋊Q8—1462no—
471C4⋊Q8—1462no—
472#126—1468no—
473#126—1468no—
474#126—1468no—
475#125—734no—
476#125—1462no—
477#125—1468no—
478#125—1468no—
479#124—734no—
480#124—1462no—
481#124—1468no—
482#123—1468no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—734no—
486C22⋊Q8—1468no—
487C22⋊Q8—1462no—
488C22⋊Q8C22×D7314yes—
489C22⋊Q8C22×D7314yes—
490#121—734no—
491#121—1462no—
492C4×Q8—734no—
493C4×Q8—734no—
494C4×Q8—734no—
495C4×Q8—1462no—
496C4×Q8—1462no—
497C4×Q8—1462no—
498C4×D4—734no—
499C4×D4—1462no—
500#117—734no—
501#117—734no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4C22×D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—731no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C42—731no—
529C2×C42—731no—
530C2×C42—1461no—
531C2×C42—1461no—
532C2×C42—1461no—
533#107—734no—
534#107—734no—
535#106—734no—
536#106C22×D7314yes—
537#103—734no—
538#103—734no—
539#103—734no—
540#103—734no—
541#103C22×D7314yes—
542#103C22×D7314yes—
543#102—734no—
544#102—734no—
545#97—734no—
546#97—734no—
547C4×C8—734no—
548C4×C8—734no—
549C24—1461no—
550C24D4×D7311yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—5842no—
558C2×Q8—732no—
559C2×Q8—1464no—
560C2×Q8—1462no—
561C2×Q8—1462no—
562C2×Q8—1461no—
563C2×Q8C23×D7312yes—
564C2×Q8C23×D7312yes—
565C2×D4—5842no—
566C2×D4—732no—
567C2×D4—1464no—
568C2×D4—1461no—
569C2×D4—1462no—
570C2×D4—1462no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—5842no—
578C22×C4—731no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—1464no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4D4×D7312yes—
587C22×C4D4×D7311yescharacteristic
588C22×C4C23×D7312yes—
589C22×C4C23×D7311yescharacteristic
590Q16—28no—
591Q16—1468no—
592SD16—1468no—
593SD16—1468no—
594M16—28no—
595C2×C8—22no—
596C2×C8—734no—
597C2×C8—732no—
598C2×C8—732no—
599C2×C8—1468no—
600C2×C8—1462no—
601C2×C8#1192402714yes—
602C2×C8C23×D7312yes—
603C2×C8C23×D7312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—734no—
609C4⋊C4—734no—
610C4⋊C4—732no—
611C4⋊C4—732no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1464no—
615C4⋊C4—1464no—
616C4⋊C4—1464no—
617C4⋊C4—1464no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1461no—
622C4⋊C4—1461no—
623C4⋊C4C23×D7312yes—
624C4⋊C4C23×D7312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—734no—
628C22⋊C4—734no—
629C22⋊C4—1464no—
630C22⋊C4—1464no—
631C22⋊C4—1464no—
632C22⋊C4—1464no—
633C22⋊C4—1464no—
634C42—732no—
635C42—732no—
636C42—732no—
637C42—732no—
638C42—1464no—
639C42—1464no—
640C42—1464no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—2922no—
645C23—2922no—
646C23—2922no—
647C23—1462no—
648C23C2×D4×D7312yes—
649C23C2×D4×D7311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—2922no—
657Q8—5844no—
658Q8—1462no—
659Q8—1462no—
660D4—2922no—
661D4—5844no—
662D4—1462no—
663D4—1462no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—2922no—
677C2×C4—2922no—
678C2×C4—2922no—
679C2×C4—5844no—
680C2×C4—732no—
681C2×C4—732no—
682C2×C4—732no—
683C2×C4—732no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4C2×D4×D7312yes—
692C2×C4C2×D4×D7311yescharacteristic
693C2×C4#41×D7312yes—
694C2×C4C2×#1192402712yes—
695C2×C4C24×D7311yescharacteristic
696C8—22no—
697C8—734no—
698C8—1462no—
699C8C2×#1192402714yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—2922no—
705C22—2922no—
706C22—2922no—
707C22—5844no—
708C22#1798913212yes—
709C22#1798939612yes—
710C22#1798940312yes—
711C22C22×D4×D7311yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—2922no—
718C4—2922no—
719C4—2922no—
720C4—1462no—
721C4—1462no—
722C4—1462no—
723C4—1462no—
724C4#1798913212yes—
725C4C2×#41×D7311yescharacteristic
726C4C22×#1192402711yescharacteristic
727C2—42no—
728C2—5842no—
729C2#2262060014yesdirect product factor
730C2C2×#1798913211yescharacteristic
731C2C2×#1798939611yescharacteristic
732C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#470×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenterC2×#470D73
hypocenterC73C2×#3178
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×#17989197C2semidirect
3. #22620600C2direct (N × H)
4. C2×#17988994C2semidirect
5. C2×#17988980C2semidirect
6. C2×#17988943C2semidirect
7. C2×#17988936C2semidirect
9. C2×#17988826C2semidirect
11. C2×#17988691C2semidirect
12. C2×#17988690C2semidirect
13. C2×Q16×Dic73C2semidirect
14. C2×#17988674C2semidirect
15. C2×#17988545C2semidirect
16. C2×#470×C73C2semidirect
24. #17989197C22semidirect
44. #17988994C22semidirect
45. #17988980C22semidirect
46. #17988943C22semidirect
47. #17988936C22semidirect
49. #17988826C22semidirect
51. #17988691C22semidirect
52. #17988690C22semidirect
53. Q16×Dic73C22semidirect
54. #17988674C22semidirect
64. #17988545C22semidirect
73. #470×C73C22semidirect
362. C2×C73#3178semidirect
374. C2×#470D73semidirect
383. C73C2×#3178semidirect
419. #470C2×D73semidirect
729. C2#22620600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892102
C2×#179891972
#226206002
C2×#179889942
C2×#179889802
C2×#179889432
C2×#179889362
C2×#179888332
C2×#179888262
C2×#179888182
C2×#179886912
C2×#179886902
C2×Q16×Dic732
C2×#179886742
C2×#179885452
C2×#470×C732
C2×#317873