Finite Group Databasebeta

← #33091124

Subgroups — #33091124

Order 18688.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989208C211yesmaximal, characteristic
2#22612287C211yesmaximal, characteristic, complemented
3#22610882C211yesmaximal, characteristic, complemented
4#22610878C211yesmaximal, characteristic, complemented
5#22610861C211yesmaximal, characteristic, complemented
6#22610861C211yesmaximal, characteristic, complemented
7#22610251C211yesmaximal, characteristic
8#22610246C211yesmaximal, characteristic
9#22610241C211yesmaximal, characteristic, complemented
10#22610236C211yesmaximal, characteristic, complemented
11#22609762C211yesmaximal, characteristic, complemented
12#22609757C211yesmaximal, characteristic, complemented
13C4×#14556516C211yesmaximal, characteristic, complemented
14C4×#14556513C211yesmaximal, characteristic, complemented
15C2×#433×C73C211yesmaximal, characteristic, complemented
16#17989208—24no—
17#17989208C418yescomplemented
18C2×#14556591C2211yescharacteristic
19C2×#14556586—21no—
20C2×#14556579C2211yescharacteristic
21C2×#14556577—21no—
22C2×#14556573—21no—
23C2×#14556570C2211yescharacteristic
24C2×#14556569—21no—
25C2×#14556565C2211yescharacteristic
26C2×C4×Dic146C2211yescharacteristic
27C2×C4×D292C2211yescharacteristic
28C2×#14556550C2211yescharacteristic
29C22×C4⋊Dic73C2211yescharacteristic
30C2×#14556516C2211yescharacteristic
31C2×#14556516C2211yescharacteristic
32C2×#14556516C2211yescharacteristic
33C2×#14556516C2211yescharacteristic
34C2×#14556513C2211yescharacteristic
35C2×#14556513C2211yescharacteristic
36C2×#14556513C2211yescharacteristic
37C2×#14556513C2211yescharacteristic
38C4⋊C4×Dic73—21no—
39C4⋊C4×Dic73—21no—
40C4×C4⋊Dic73C2211yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
42C4×C4⋊Dic73C2211yescharacteristic
43C4×C4⋊Dic73C2211yescharacteristic
44C22⋊C4×Dic73—21no—
45C22⋊C4×Dic73—21no—
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988350C2211yescharacteristic
54C2×#117×C73C2211yescharacteristic
55#433×C73—24no—
56C2×C4⋊C8×C73C2211yescharacteristic
57C2×C4⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×#97×C73C2211yescharacteristic
61C2×C4×C8×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×Dic146C2311yescharacteristic
64C22×D292C2311yescharacteristic
65C22×C22⋊D73—21no—
66C23×Dic73—21no—
67C22×C4×D73—21no—
68#14556591—22no—
69#14556591C2×C414yescomplemented
70#14556586—28no—
71#14556579—22no—
72#14556579C2×C414yescomplemented
73#14556577—28no—
74#14556573—28no—
75#14556570—22no—
76#14556570C2×C414yes—
77#14556569—28no—
78#14556565—22no—
79#14556565C2×C414yes—
80C4×Dic146—22no—
81C4×Dic146C2×C414yescomplemented
82C4×D292—22no—
83C4×D292C2×C414yescomplemented
84#14556550—22no—
85#14556550—22no—
86C2×C4⋊Dic73—22no—
87C2×C4⋊Dic73—22no—
88C2×C4⋊Dic73—21no—
89C2×C4⋊Dic73—21no—
90C2×C4⋊Dic73C2311yescharacteristic
91C2×C4⋊Dic73C2311yescharacteristic
92C2×C4⋊Dic73C2311yescharacteristic
93C2×C4⋊Dic73C2311yescharacteristic
94C2×C4⋊Dic73C2311yescharacteristic
95C2×C4⋊Dic73C2311yescharacteristic
96C2×#11924007—21no—
97C2×#11924007—21no—
98C2×C22⋊Dic73—21no—
99C2×C22⋊Dic73—21no—
100C2×#11924005—21no—
101C2×#11924005—21no—
102C2×#11924005—21no—
103C2×#11924005—21no—
104C2×C4×Dic73—21no—
105C2×C4×Dic73—21no—
106C2×C4×Dic73—21no—
107C2×C4×Dic73—21no—
108C2×C4×Dic73—21no—
109C2×C4×Dic73—21no—
110#14556516—22no—
111#14556516—22no—
112#14556516—22no—
113#14556516—22no—
114#14556513—22no—
115#14556513—22no—
116#14556513—22no—
117#14556513—22no—
118#14556498—21no—
119#14556498—21no—
120#14556498—21no—
121#14556498—21no—
122C23×C4×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C22×C8×C73C2311yescharacteristic
127#117×C73C2×C414yes—
128#117×C73D414yes—
129C2×C4⋊C4×C73D411yescharacteristic
130C2×C4⋊C4×C73D411yescharacteristic
131C2×C22⋊C4×C73D411yescharacteristic
132C2×C22⋊C4×C73D411yescharacteristic
133C2×C42×C73C2311yescharacteristic
134C2×C42×C73C2311yescharacteristic
135C4⋊C8×C73—22no—
136C4⋊C8×C73—22no—
137C22⋊C8×C73—22no—
138C22⋊C8×C73—22no—
139#97×C73—22no—
140C4×C8×C73—22no—
141C23×D73—21no—
142C2×Dic146—21no—
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—24no—
148C2×Dic146—81no—
149C2×Dic146—81no—
150C2×Dic146C22×C412yes—
151C2×D292—21no—
152C2×D292—21no—
153C2×D292—21no—
154C2×D292—21no—
155C2×D292—21no—
156C2×D292C22×C412yes—
157C2×C22⋊D73—24no—
158C2×C22⋊D73—81no—
159C2×C22⋊D73—81no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—24no—
168C22×Dic73—81no—
169C22×Dic73—81no—
170C2×C4×D73—24no—
171C2×C4×D73—81no—
172C2×C4×D73—81no—
173C4⋊Dic73—24no—
174C4⋊Dic73—24no—
175C4⋊Dic73—21no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73C22×C412yes—
182C4⋊Dic73C22×C412yes—
183C4⋊Dic73#4112yes—
184C4⋊Dic73#4112yes—
185C4⋊Dic73#4112yes—
186C4⋊Dic73#4112yes—
187#11924007—24no—
188#11924007—24no—
189C22⋊Dic73—24no—
190C22⋊Dic73—24no—
191#11924005—24no—
192#11924005—24no—
193#11924005—24no—
194#11924005—24no—
195C4×Dic73—24no—
196C4×Dic73—24no—
197C4×Dic73—81no—
198C4×Dic73—81no—
199C4×Dic73—81no—
200C4×Dic73—81no—
201C24×C73C2×D411yescharacteristic
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73C22×C412yes—
207C22×C4×C73C2×D412yes—
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2411yescharacteristic
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C4⋊C4×C73C22⋊C414yes—
227C4⋊C4×C73C22⋊C414yes—
228C22⋊C4×C73C22⋊C414yes—
229C22⋊C4×C73C22⋊C414yes—
230C42×C73C22×C412yes—
231C42×C73C22×C412yes—
232C42×C73C2×D412yes—
233C42×C73C2×D412yes—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73C2×C22⋊C412yes—
241C23×C73C22×D411yescharacteristic
242C22×D73—22no—
243C22×D73—41no—
244C22×D73—41no—
245C22×D73—41no—
246C22×D73—41no—
247C22×D73—41no—
248C22×D73—41no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73C2×C22⋊C412yes—
264C2×C4×C73C2×C22⋊C412yes—
265C2×C4×C73C2×C22⋊C412yes—
266C2×C4×C73C2×C22⋊C412yes—
267C2×C4×C73C2×C22⋊C412yes—
268C2×C4×C73C23×C411yescharacteristic
269C2×C4×C73C22×D411yescharacteristic
270C2×C4×C73C2×#4111yescharacteristic
271C2×C4×C73C2×#4111yescharacteristic
272C2×C4×C73C2×#4111yescharacteristic
273C2×C4×C73C2×#4111yescharacteristic
274C22⋊D73—84no—
275C2×Dic73—22no—
276C2×Dic73—22no—
277C2×Dic73—22no—
278C2×Dic73—22no—
279C2×Dic73—22no—
280C2×Dic73—22no—
281C2×Dic73—22no—
282C2×Dic73—41no—
283C2×Dic73—41no—
284C2×Dic73—41no—
285C2×Dic73—41no—
286C2×Dic73—41no—
287C2×Dic73—41no—
288C2×Dic73—41no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—84no—
297D292—22no—
298D292—22no—
299D292—41no—
300D292—41no—
301C4×D73—84no—
302Dic146—22no—
303Dic146—22no—
304Dic146—41no—
305Dic146—41no—
306Dic146—84no—
307C8×C73—41no—
308C8×C73—41no—
309C8×C73—41no—
310C8×C73—41no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73C22×C22⋊C411yescharacteristic
319C22×C73#52511yescharacteristic
320C22×C73#52511yescharacteristic
321C22×C73#57611yescharacteristic
322C22×C73#57711yescharacteristic
323C22×C73#57711yescharacteristic
324C22×C73#57811yescharacteristic
325C2×D73—42no—
326C2×D73—42no—
327C2×D73—42no—
328C2×D73—81no—
329C2×D73—81no—
330C2×D73—81no—
331C2×D73—81no—
332C4×C73—22no—
333C4×C73—22no—
334C4×C73—22no—
335C4×C73—22no—
336C4×C73—22no—
337C4×C73C4×#4111yescharacteristic
338C4×C73C4×#4111yescharacteristic
339C4×C73#53211yescharacteristic
340C4×C73#53211yescharacteristic
341Dic73—42no—
342Dic73—42no—
343Dic73—42no—
344Dic73—42no—
345Dic73—42no—
346Dic73—42no—
347Dic73—42no—
348#21397—731nomaximal, Sylow
349C2×C73—42no—
350C2×C73#229711yescharacteristic
351C2×C73#289711yescharacteristic
352C2×C73#289811yescharacteristic
353C2×C73#311811yescharacteristic
354C2×C73#312111yescharacteristic
355C2×C73#312411yescharacteristic
356C2×C73#312511yescharacteristic
357D73—82no—
358C2×#542—731no—
359C2×#433D7311yescharacteristic, complemented
360#2274—731no—
361#1988—731no—
362#1987—731no—
363#1983—731no—
364#1983—731no—
365#1875—731no—
366#1874—731no—
367#1873—731no—
368#1872—731no—
369#1763—731no—
370#1762—731no—
371C4×#103—731no—
372C4×#102—731no—
373C73#2139711yescharacteristic, complemented, Sylow
374#542—738no—
375#542—1464no—
376C2×C4⋊Q8—731no—
377C2×#126—1461no—
378C2×#124—731no—
379C2×#124—1461no—
380C2×#123—1461no—
381C2×C22⋊Q8—731no—
382C2×C22⋊Q8—1461no—
383C2×#121—731no—
384C2×C4×Q8—731no—
385C2×C4×D4—731no—
386C2×#117—731no—
387C2×#117C2×D7311yescharacteristic
388C22×C4⋊C4—731no—
389#433—24no—
390C2×C4⋊C8C2×D7311yescharacteristic
391C2×C4⋊C8C2×D7311yescharacteristic
392C2×#103—731no—
393C2×#103—731no—
394C2×#103—731no—
395C2×#103—731no—
396C2×#102—731no—
397C2×#102—731no—
398C2×#102—731no—
399C2×#102—731no—
400C2×C22⋊C8C2×D7311yescharacteristic
401C2×C22⋊C8C2×D7311yescharacteristic
402C2×#97C2×D7311yescharacteristic
403C2×C4×C8C2×D7311yescharacteristic
404C4×C4⋊C4—731no—
405C4×C4⋊C4—731no—
406C4×C4⋊C4—731no—
407C4×C4⋊C4—731no—
408C4×C4⋊C4—1461no—
409C4×C4⋊C4—1461no—
410C4×C22⋊C4—1461no—
411C4×C22⋊C4—1461no—
412#340—731no—
413#340—731no—
414#340—731no—
415#340—731no—
416#340—731no—
417#340—731no—
418#340—731no—
419#340—731no—
420C22×Q8—731no—
421C22×Q8—1461no—
422C22×D4—731no—
423C22×D4—1461no—
424C23×C4—1461no—
425C23×C4—1461no—
426C23×C4C22×D7311yescharacteristic
427C22×C8C22×D7311yescharacteristic
428C22×C8C22×D7311yescharacteristic
429C22×C8C22×D7311yescharacteristic
430C22×C8C22×D7311yescharacteristic
431C4⋊Q8—734no—
432C4⋊Q8—1462no—
433#126—1468no—
434#124—734no—
435#124—1468no—
436#124—1462no—
437#123—1468no—
438C22⋊Q8—734no—
439C22⋊Q8—1462no—
440C22⋊Q8—1468no—
441#121—734no—
442#121—1462no—
443C4×Q8—734no—
444C4×Q8—1462no—
445C4×D4—734no—
446C4×D4—1462no—
447#117—1462no—
448#117—1462no—
449#117C4×D7314yes—
450#117C22⋊D7314yes—
451C2×C4⋊C4—731no—
452C2×C4⋊C4—731no—
453C2×C4⋊C4—731no—
454C2×C4⋊C4—731no—
455C2×C4⋊C4—731no—
456C2×C4⋊C4—731no—
457C2×C4⋊C4—1462no—
458C2×C4⋊C4—1462no—
459C2×C4⋊C4—1461no—
460C2×C4⋊C4—1461no—
461C2×C4⋊C4—1461no—
462C2×C4⋊C4—1461no—
463C2×C4⋊C4D29211yescharacteristic
464C2×C4⋊C4D29211yescharacteristic
465C2×C22⋊C4—1461no—
466C2×C22⋊C4—1461no—
467C2×C22⋊C4—1461no—
468C2×C22⋊C4—1461no—
469C2×C22⋊C4—1461no—
470C2×C22⋊C4—1461no—
471C2×C22⋊C4D29211yescharacteristic
472C2×C22⋊C4D29211yescharacteristic
473C2×C42—1461no—
474C2×C42—1461no—
475C2×C42—1461no—
476C2×C42—1461no—
477C2×C42—1461no—
478C2×C42—1461no—
479C2×C42C22×D7311yescharacteristic
480C2×C42C22×D7311yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—22no—
483#103—1462no—
484#103—1462no—
485#103—1462no—
486#103—1462no—
487#102—1462no—
488#102—1462no—
489#102—1462no—
490#102—1462no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#97—22no—
494C4×C8—22no—
495#95—1461no—
496#95—1461no—
497#95—1461no—
498#95—1461no—
499C24—1461no—
500C24C2×D29211yescharacteristic
501C2×Q8—5841no—
502C2×Q8—5841no—
503C2×Q8—732no—
504C2×Q8—1461no—
505C2×Q8—1461no—
506C2×Q8—1461no—
507C2×Q8—1461no—
508C2×Q8—1464no—
509C2×Q8—1461no—
510C2×D4—5841no—
511C2×D4—5841no—
512C2×D4—732no—
513C2×D4—1464no—
514C2×D4—1461no—
515C2×D4—1461no—
516C2×D4—1461no—
517C2×D4—1461no—
518C2×D4—1461no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—5841no—
524C22×C4—5841no—
525C22×C4—5841no—
526C22×C4—5841no—
527C22×C4—1461no—
528C22×C4—1461no—
529C22×C4—1461no—
530C22×C4—1461no—
531C22×C4—1461no—
532C22×C4—1461no—
533C22×C4—1461no—
534C22×C4—1464no—
535C22×C4—1464no—
536C22×C4C2×C4×D7312yes—
537C22×C4C2×C22⋊D7312yes—
538C22×C4C2×D29211yescharacteristic
539C22×C4C2×D29211yescharacteristic
540C22×C4C2×D29211yescharacteristic
541C22×C4C2×D29211yescharacteristic
542C22×C4C2×D29211yescharacteristic
543C22×C4C23×D7311yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C4⋊C4—732no—
557C4⋊C4—732no—
558C4⋊C4—732no—
559C4⋊C4—732no—
560C4⋊C4—732no—
561C4⋊C4—732no—
562C4⋊C4—1464no—
563C4⋊C4—1464no—
564C4⋊C4—1464no—
565C4⋊C4—1464no—
566C4⋊C4—1461no—
567C4⋊C4—1461no—
568C4⋊C4—1461no—
569C4⋊C4—1461no—
570C4⋊C4—1461no—
571C4⋊C4—1461no—
572C4⋊C4#1192400514yes—
573C4⋊C4#1192400514yes—
574C22⋊C4—1464no—
575C22⋊C4—1464no—
576C22⋊C4—1464no—
577C22⋊C4—1464no—
578C22⋊C4—1464no—
579C22⋊C4—1464no—
580C22⋊C4#1192400514yes—
581C22⋊C4#1192400514yes—
582C42—5841no—
583C42—5841no—
584C42—5841no—
585C42—5841no—
586C42—1464no—
587C42—1464no—
588C42C2×C4×D7312yes—
589C42C2×C4×D7312yes—
590C42C2×C22⋊D7312yes—
591C42C2×C22⋊D7312yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—2921no—
599C23—2921no—
600C23—2921no—
601C23—2921no—
602C23—2921no—
603C23—2921no—
604C23—1462no—
605C23C2×#1192400512yes—
606C23C22×D29211yescharacteristic
607Q8—2921no—
608Q8—2921no—
609Q8—5844no—
610Q8—1462no—
611Q8—1462no—
612D4—2921no—
613D4—2921no—
614D4—5844no—
615D4—1462no—
616D4—1462no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—2921no—
632C2×C4—2921no—
633C2×C4—2921no—
634C2×C4—2921no—
635C2×C4—2921no—
636C2×C4—2921no—
637C2×C4—2921no—
638C2×C4—2921no—
639C2×C4—2921no—
640C2×C4—2921no—
641C2×C4—2921no—
642C2×C4—2921no—
643C2×C4—2921no—
644C2×C4—2921no—
645C2×C4—5844no—
646C2×C4—5844no—
647C2×C4—1462no—
648C2×C4—1462no—
649C2×C4—1462no—
650C2×C4—1462no—
651C2×C4—1462no—
652C2×C4—1462no—
653C2×C4—1462no—
654C2×C4C2×#1192400512yes—
655C2×C4C2×#1192400512yes—
656C2×C4C2×#1192400512yes—
657C2×C4C2×#1192400512yes—
658C2×C4C2×#1192400512yes—
659C2×C4C22×C4×D7311yescharacteristic
660C2×C4C22×C22⋊D7311yescharacteristic
661C2×C4#41×D7311yescharacteristic
662C2×C4#41×D7311yescharacteristic
663C2×C4#41×D7311yescharacteristic
664C2×C4#41×D7311yescharacteristic
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—2922no—
677C22—2922no—
678C22—2922no—
679C22—5841no—
680C22—5841no—
681C22—5841no—
682C22—5841no—
683C22C22×#1192400511yescharacteristic
684C22#1798909911yescharacteristic
685C22#1798909911yescharacteristic
686C22#1798939211yescharacteristic
687C22#1798939911yescharacteristic
688C22#1798939911yescharacteristic
689C22#1798940411yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—2922no—
696C4—2922no—
697C4—2922no—
698C4—2922no—
699C4—2922no—
700C4—2922no—
701C4—2922no—
702C4#1798905511yescharacteristic
703C4#1798905511yescharacteristic
704C4#1798913311yescharacteristic
705C4#1798913311yescharacteristic
706C2—42no—
707C2—5842no—
708C2#2261241911yescharacteristic
709C2#2261845811yescharacteristic
710C2#2261846511yescharacteristic
711C2#2262011711yescharacteristic
712C2#2262016211yescharacteristic
713C2#2262019511yescharacteristic
714C2#2262021011yescharacteristic
subgroupG/H
centerC23C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#433×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
cosocleC22×C4×C73C24
hypercenterC2×#433D73
hypocenterC73#21397
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #22612287C2semidirect
3. #22610882C2semidirect
4. #22610878C2semidirect
5. #22610861C2semidirect
6. #22610861C2semidirect
9. #22610241C2semidirect
10. #22610236C2semidirect
11. #22609762C2semidirect
12. #22609757C2semidirect
13. C4×#14556516C2semidirect
14. C4×#14556513C2semidirect
15. C2×#433×C73C2semidirect
17. #17989208C4semidirect
69. #14556591C2×C4semidirect
72. #14556579C2×C4semidirect
81. C4×Dic146C2×C4semidirect
83. C4×D292C2×C4semidirect
359. C2×#433D73semidirect
373. C73#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#179892082
#226122872
#226108822
#226108782
#226108612
#226102512
#226102462
#226102412
#226102362
#226097622
#226097572
C4×#145565162
C4×#145565132
C2×#433×C732
#2139773