Finite Group Databasebeta

← C4×#17988785 #33092178

Subgroups — C4×#17988785 #33092178

Order 18688.

1152 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988785C211yesmaximal, characteristic
2C2×C4×#11924015C211yesmaximal, characteristic, complemented
3C4×#14556587C211yesmaximal, characteristic
4C4×Q8×Dic73C211yesmaximal, characteristic, complemented
5#22610856C211yesmaximal, characteristic
6#22610691C211yesmaximal, characteristic, complemented
7#22610561C211yesmaximal, characteristic, complemented
8#22610557C211yesmaximal, characteristic, complemented
9#22610288C211yesmaximal, characteristic, complemented
10#22610284C211yesmaximal, characteristic, complemented
11#22609934C211yesmaximal, characteristic, complemented
12C4×#14556520C211yesmaximal, characteristic, complemented
13C4×#14556513C211yesmaximal, characteristic, complemented
14C4×#14556512C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
16C22×#11924015C2211yescharacteristic
17C2×#14556587C2211yescharacteristic
18C2×Q8×Dic73C2211yescharacteristic
19C2×Q8×Dic73C2211yescharacteristic
20C2×C4×D292C2211yescharacteristic
21C2×C4×C22⋊D73—21no—
22C2×C4×C22⋊D73—21no—
23#17988785C418yesdirect product factor
24C4×#11924015—24no—
25C2×#14556522C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556513C2211yescharacteristic
30C2×#14556513C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556511C2211yescharacteristic
34C2×C4×#10596831C2211yescharacteristic
35#17988490C2211yescharacteristic
36#17988488C2211yescharacteristic
37#17988487—21no—
38#17988487—21no—
39#17988456C2211yescharacteristic
40C4⋊C4×Dic73—21no—
41C4⋊C4×Dic73—21no—
42C4⋊C4×Dic73C2211yescharacteristic
43C4⋊C4×Dic73C2211yescharacteristic
44C4×C4⋊Dic73—21no—
45C4×C4⋊Dic73C2211yescharacteristic
46C42×Dic73—21no—
47C42×Dic73C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×SD16×C73C2211yescharacteristic
55C2×C4×Q8×C73C2211yescharacteristic
56C2×C4×D4×C73C2211yescharacteristic
57C4×SD16×C73—24no—
58C2×#106×C73C2211yescharacteristic
59C2×#103×C73C2211yescharacteristic
60C2×#102×C73C2211yescharacteristic
61C2×C4×C8×C73C2211yescharacteristic
62C22×D292C2311yescharacteristic
63C22×C22⋊D73—21no—
64C22×C22⋊D73—21no—
65C22×C4×D73—21no—
66C2×#11924015—22no—
67C2×#11924015—22no—
68C2×#11924015C2×C414yescomplemented
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556587—22no—
72#14556587C2×C414yes—
73Q8×Dic73—22no—
74Q8×Dic73—22no—
75Q8×Dic73—22no—
76Q8×Dic73C2×C414yescomplemented
77C4×D292—22no—
78C4×D292—22no—
79C4×C22⋊D73—44no—
80C4×C22⋊D73—44no—
81C2×C4⋊Dic73—21no—
82C2×C4⋊Dic73—21no—
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73—21no—
90C2×#11924005—21no—
91C2×#11924005—21no—
92C2×#11924005—21no—
93C2×C4×Dic73—21no—
94C2×C4×Dic73—21no—
95C2×C4×Dic73—21no—
96C2×C4×Dic73—21no—
97C2×C4×Dic73—21no—
98C2×C4×Dic73D411yescharacteristic
99C2×C4×Dic73D411yescharacteristic
100C2×C4×Dic73D411yescharacteristic
101C2×C4×Dic73D411yescharacteristic
102C2×C4×Dic73C2311yescharacteristic
103C2×C4×Dic73C2311yescharacteristic
104#14556522—22no—
105#14556520—22no—
106#14556520C2×C414yescomplemented
107#14556515—22no—
108#14556513—22no—
109#14556513C2×C414yescomplemented
110#14556512—22no—
111#14556512C2×C414yescomplemented
112#14556511—22no—
113C4×#10596831—22no—
114#14556498—21no—
115#14556498—21no—
116#14556498—21no—
117C22×Q8×C73C2311yescharacteristic
118C22×D4×C73C2311yescharacteristic
119C23×C4×C73—21no—
120C2×SD16×C73—22no—
121C2×SD16×C73—22no—
122C2×SD16×C73C2×C414yescomplemented
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C4×Q8×C73—22no—
126C4×Q8×C73D414yescomplemented
127C4×D4×C73—22no—
128C4×D4×C73—22no—
129C2×C4⋊C4×C73—21no—
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C4⋊C4×C73C2311yescharacteristic
132C2×C22⋊C4×C73—21no—
133C2×C42×C73—21no—
134C2×C42×C73C2311yescharacteristic
135#106×C73—22no—
136#103×C73—22no—
137#102×C73—22no—
138C4×C8×C73—22no—
139C23×D73—21no—
140C2×D292—21no—
141C2×D292—21no—
142C2×D292—21no—
143C2×D292—21no—
144C2×D292—21no—
145C2×D292C22×C412yes—
146C2×C22⋊D73—24no—
147C2×C22⋊D73—24no—
148C2×C22⋊D73—42no—
149C2×C22⋊D73—42no—
150C2×C22⋊D73—42no—
151C2×C22⋊D73—42no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73C2×D411yescharacteristic
156C22×Dic73C2×D411yescharacteristic
157C22×Dic73C2×D411yescharacteristic
158C22×Dic73C2×D411yescharacteristic
159C2×C4×D73—42no—
160C2×C4×D73—42no—
161C2×C4×D73—42no—
162#11924015—28no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831C22×C412yes—
169C4⋊Dic73—24no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—24no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73C22×C412yes—
176C4⋊Dic73#4112yes—
177#11924007—42no—
178#11924007—42no—
179C22⋊Dic73—42no—
180C22⋊Dic73—42no—
181#11924005—42no—
182#11924005—42no—
183#11924005—42no—
184C4×Dic73—24no—
185C4×Dic73—22no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—24no—
189C4×Dic73—22no—
190C4×Dic73—41no—
191C4×Dic73—42no—
192C4×Dic73—42no—
193C4×Dic73—42no—
194C4×Dic73SD1614yescomplemented
195C4×Dic73C22×C412yes—
196C4×Dic73#4112yes—
197C24×C73—21no—
198C2×Q8×C73—21no—
199C2×Q8×C73—21no—
200C2×Q8×C73—21no—
201C2×Q8×C73C22×C412yes—
202C2×Q8×C73C2×D412yes—
203C2×Q8×C73#4112yes—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—21no—
209C2×D4×C73C22×C412yes—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—42no—
214C22×C4×C73—42no—
215C22×C4×C73—42no—
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2411yescharacteristic
219SD16×C73—28no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73C22×C412yes—
226C4⋊C4×C73—24no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73C2×D412yes—
231C22⋊C4×C73—42no—
232C42×C73—24no—
233C42×C73C2×D412yes—
234C42×C73#4112yes—
235C23×C73—22no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73C22×D411yescharacteristic
243C22×D73—22no—
244C22×D73—41no—
245C22×D73—41no—
246C22×D73—41no—
247C22×D73—41no—
248C22×D73—41no—
249C22×D73—41no—
250Q8×C73—22no—
251Q8×C73—22no—
252Q8×C73—22no—
253Q8×C73C4×D414yescomplemented
254D4×C73—22no—
255D4×C73—22no—
256D4×C73—41no—
257D4×C73—41no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—22no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—84no—
270C2×C4×C73#12112yes—
271C2×C4×C73#12112yes—
272C2×C4×C73C2×SD1612yes—
273C2×C4×C73AGL(1,ℤ/8)12yes—
274C2×C4×C73C23×C411yescharacteristic
275C2×C4×C73C22×D411yescharacteristic
276C2×C4×C73C2×#4111yescharacteristic
277C2×C4×C73C2×#4111yescharacteristic
278C2×C4×C73C2×#4111yescharacteristic
279C2×C4×C73C2×#4111yescharacteristic
280C22⋊D73—48no—
281C22⋊D73—48no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—22no—
287C2×Dic73—21no—
288C2×Dic73—22no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73C4×D412yes—
299C2×Dic73C4×D412yes—
300C2×Dic73C2×SD1612yes—
301C2×Dic73C2×SD1612yes—
302C2×Dic73#13512yes—
303D292—22no—
304D292—22no—
305D292—41no—
306D292—41no—
307C4×D73—84no—
308C8×C73—22no—
309C8×C73—41no—
310#10596831—22no—
311#10596831—41no—
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73C2×C4×D411yescharacteristic
320C22×C73C2×#12111yescharacteristic
321C22×C73#52511yescharacteristic
322C22×C73C22×SD1611yescharacteristic
323C22×C73C2×#13511yescharacteristic
324C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C73#57511yescharacteristic
326C2×D73—42no—
327C2×D73—42no—
328C2×D73—42no—
329C2×D73—81no—
330C2×D73—81no—
331C2×D73—81no—
332C2×D73—81no—
333C4×C73—22no—
334C4×C73—24no—
335C4×C73—42no—
336C4×C73—81no—
337C4×C73#46014yescomplemented
338C4×C73C2×C4×D411yescharacteristic
339C4×C73C4×#4111yescharacteristic
340C4×C73#52911yescharacteristic
341C4×C73#53211yescharacteristic
342Dic73—22no—
343Dic73—22no—
344Dic73—41no—
345Dic73—42no—
346Dic73—42no—
347Dic73—81no—
348Dic73C4×SD1614yescomplemented
349C4×#460—731nomaximal, Sylow
350C2×C73—82no—
351C2×C73C4×#12111yescharacteristic
352C2×C73C2×C4×SD1611yescharacteristic
353C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
354C2×C73C2×#46011yescharacteristic
355C2×C73#303511yescharacteristic
356C2×C73#310311yescharacteristic
357C2×C73#310611yescharacteristic
358D73—82no—
359C2×#460—731no—
360C2×C4×SD16—731no—
361C2×C4×SD16D7311yescharacteristic, complemented
362C4×#127—731no—
363C42×Q8—731no—
364#1982—731no—
365#1948—731no—
366#1926—731no—
367#1926—731no—
368#1880—731no—
369#1880—731no—
370#1803—731no—
371C4×C4⋊C8—731no—
372C4×#102—731no—
373C4×#102—731no—
374C73C4×#46011yescharacteristic, complemented, Sylow
375C22×SD16—731no—
376C22×SD16C2×D7311yescharacteristic
377C2×#127—731no—
378C2×C4×Q8—731no—
379C2×C4×Q8—731no—
380C2×C4×Q8C2×D7311yescharacteristic
381C2×C4×D4—731no—
382C2×C4×D4—1461no—
383C2×C4×D4—1461no—
384C2×C4×D4C2×D7311yescharacteristic
385#460—738no—
386C4×SD16—24no—
387C4×SD16—1464no—
388C2×#106—731no—
389C2×#106C2×D7311yescharacteristic
390C2×C4⋊C8—731no—
391C2×C4⋊C8—731no—
392C2×#103—731no—
393C2×#103C2×D7311yescharacteristic
394C2×#102—731no—
395C2×#102—731no—
396C2×#102—731no—
397C2×#102—731no—
398C2×#102—731no—
399C2×#102C2×D7311yescharacteristic
400C2×C4×C8—731no—
401C2×C4×C8C2×D7311yescharacteristic
402#390—731no—
403#390—731no—
404#390—1461no—
405#390—1461no—
406#384—731no—
407C4×C4⋊C4—731no—
408C4×C4⋊C4—731no—
409C4×C4⋊C4—731no—
410C4×C4⋊C4—1461no—
411C4×C4⋊C4—1461no—
412C4×C4⋊C4—1461no—
413C43—731no—
414C43—1461no—
415#340—731no—
416#340—731no—
417#340—731no—
418#340—731no—
419#336—731no—
420#336—731no—
421C22×Q8C22×D7311yescharacteristic
422C22×D4—731no—
423C22×D4—1461no—
424C22×D4—1461no—
425C22×D4C22×D7311yescharacteristic
426C23×C4—21no—
427C23×C4—1461no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—734no—
431C2×SD16—1462no—
432C2×SD16—1462no—
433C2×SD16C4×D7314yescomplemented
434C22×C8—731no—
435C22×C8—731no—
436C22×C8C22×D7311yescharacteristic
437C22×C8C22×D7311yescharacteristic
438#127—734no—
439#127—1462no—
440C4×Q8—22no—
441C4×Q8—734no—
442C4×Q8—1462no—
443C4×Q8—1462no—
444C4×Q8—1462no—
445C4×Q8C22⋊D7314yescomplemented
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—2924no—
449C4×D4—2924no—
450C4×D4—1462no—
451C4×D4—1462no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—731no—
454C2×C4⋊C4—731no—
455C2×C4⋊C4—731no—
456C2×C4⋊C4—1461no—
457C2×C4⋊C4—1461no—
458C2×C4⋊C4—1461no—
459C2×C4⋊C4—1461no—
460C2×C4⋊C4C22×D7311yescharacteristic
461C2×C4⋊C4C22×D7311yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—1461no—
464C2×C22⋊C4—1461no—
465C2×C22⋊C4—1461no—
466C2×C22⋊C4—1461no—
467C2×C22⋊C4—1461no—
468C2×C42—21no—
469C2×C42—731no—
470C2×C42—731no—
471C2×C42—731no—
472C2×C42—731no—
473C2×C42—731no—
474C2×C42—731no—
475C2×C42—1461no—
476C2×C42—1461no—
477C2×C42—1461no—
478C2×C42—1461no—
479C2×C42—1461no—
480C2×C42C22×D7311yescharacteristic
481#106—22no—
482#106—1462no—
483C4⋊C8—734no—
484C4⋊C8—1462no—
485#103—22no—
486#103—1462no—
487#102—22no—
488#102—734no—
489#102—734no—
490#102—1462no—
491#102—1462no—
492#102—1462no—
493C4×C8—22no—
494C4×C8—1462no—
495#95—1461no—
496#95—1461no—
497#95—1461no—
498C24—21no—
499C24—1461no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×C4×D7312yes—
504C2×Q8C2×C22⋊D7312yes—
505C2×Q8#1192402812yes—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—2922no—
512C2×D4—2922no—
513C2×D4—2922no—
514C2×D4—2922no—
515C2×D4—732no—
516C2×D4—1464no—
517C2×D4—1464no—
518C2×D4—1461no—
519C2×D4—1461no—
520C2×D4—1461no—
521C2×D4—1461no—
522C2×D4—1461no—
523C2×D4C2×C4×D7312yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—2922no—
531C22×C4—2922no—
532C22×C4—2922no—
533C22×C4—731no—
534C22×C4—731no—
535C22×C4—731no—
536C22×C4—731no—
537C22×C4—1461no—
538C22×C4—1461no—
539C22×C4—1461no—
540C22×C4D4×D7311yescharacteristic
541C22×C4D4×D7311yescharacteristic
542C22×C4C23×D7311yescharacteristic
543SD16—28no—
544SD16—1468no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—732no—
551C2×C8—1461no—
552C2×C8—1461no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C2×C8C2×C4×D7312yes—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—2922no—
562C4⋊C4—2922no—
563C4⋊C4—732no—
564C4⋊C4—732no—
565C4⋊C4—1464no—
566C4⋊C4—1464no—
567C4⋊C4—1461no—
568C4⋊C4—1461no—
569C4⋊C4—1461no—
570C4⋊C4—1461no—
571C4⋊C4C2×C22⋊D7312yes—
572C22⋊C4—42no—
573C22⋊C4—2922no—
574C22⋊C4—2922no—
575C22⋊C4—2922no—
576C22⋊C4—2922no—
577C22⋊C4—2922no—
578C42—24no—
579C42—2921no—
580C42—2922no—
581C42—2922no—
582C42—2922no—
583C42—734no—
584C42—732no—
585C42—732no—
586C42—1462no—
587C42—1464no—
588C42—1464no—
589C42—1462no—
590C42—1461no—
591C42—1461no—
592C42C2×C22⋊D7312yes—
593C42#1192402712yes—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—2921no—
602C23—2921no—
603C23—2921no—
604C23—2921no—
605C23—2921no—
606C23—2921no—
607C23—1462no—
608C23C2×D4×D7311yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8C4×C22⋊D7314yescomplemented
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—2928no—
618D4—2928no—
619D4—2921no—
620D4—2921no—
621D4—1462no—
622D4—1462no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—2921no—
636C2×C4—2921no—
637C2×C4—2921no—
638C2×C4—2921no—
639C2×C4—2921no—
640C2×C4—2921no—
641C2×C4—2921no—
642C2×C4—5844no—
643C2×C4—732no—
644C2×C4—732no—
645C2×C4—732no—
646C2×C4—732no—
647C2×C4—732no—
648C2×C4—1462no—
649C2×C4—1462no—
650C2×C4—1461no—
651C2×C4—1461no—
652C2×C4—1461no—
653C2×C4—1461no—
654C2×C4—1461no—
655C2×C4—1461no—
656C2×C4—1461no—
657C2×C4#1455656312yes—
658C2×C4#1455656312yes—
659C2×C4SD16×D7312yes—
660C2×C4#1455661812yes—
661C2×C4C22×C4×D7311yescharacteristic
662C2×C4C22×C22⋊D7311yescharacteristic
663C2×C4#41×D7311yescharacteristic
664C2×C4#41×D7311yescharacteristic
665C2×C4C2×#1192402711yescharacteristic
666C2×C4C2×#1192402811yescharacteristic
667C8—22no—
668C8—41no—
669C8—2921no—
670C8—1462no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—2922no—
679C22—2922no—
680C22—2922no—
681C22—5841no—
682C22—5841no—
683C22—5841no—
684C22—5841no—
685C22C4×D4×D7311yescharacteristic
686C22C2×#1455656311yescharacteristic
687C22#1798909611yescharacteristic
688C22C2×SD16×D7311yescharacteristic
689C22#135×D7311yescharacteristic
690C22C2×#1455661811yescharacteristic
691C22#1798938411yescharacteristic
692C4—24no—
693C4—22no—
694C4—42no—
695C4—81no—
696C4—2922no—
697C4—2921no—
698C4—2922no—
699C4—5841no—
700C4—734no—
701C4—1462no—
702C4—1462no—
703C4#1798878514yesdirect product factor
704C4C2×C4×C22⋊D7311yescharacteristic
705C4C4×#1192402711yescharacteristic
706C4#1798911711yescharacteristic
707C4#1798913311yescharacteristic
708C2—82no—
709C2—5842no—
710C2C4×#1455656311yescharacteristic
711C2C4×SD16×D7311yescharacteristic
712C2C4×#1455661811yescharacteristic
713C2C2×#1798878511yescharacteristic
714C2#2261938211yescharacteristic
715C2#2261996011yescharacteristic
716C2#2261998911yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×C4×SD16×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556587C22
cosocleC22×C4×C73C24
hypercenterC2×C4×SD16D73
hypocenterC73C4×#460
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11924015C2semidirect
4. C4×Q8×Dic73C2semidirect
6. #22610691C2semidirect
7. #22610561C2semidirect
8. #22610557C2semidirect
9. #22610288C2semidirect
10. #22610284C2semidirect
11. #22609934C2semidirect
12. C4×#14556520C2semidirect
13. C4×#14556513C2semidirect
14. C4×#14556512C2semidirect
15. C2×C4×SD16×C73C2semidirect
23. #17988785C4direct (N × H)
68. C2×#11924015C2×C4semidirect
76. Q8×Dic73C2×C4semidirect
106. #14556520C2×C4semidirect
109. #14556513C2×C4semidirect
111. #14556512C2×C4semidirect
122. C2×SD16×C73C2×C4semidirect
126. C4×Q8×C73D4semidirect
194. C4×Dic73SD16semidirect
253. Q8×C73C4×D4semidirect
337. C4×C73#460semidirect
348. Dic73C4×SD16semidirect
361. C2×C4×SD16D73semidirect
374. C73C4×#460semidirect
433. C2×SD16C4×D73semidirect
445. C4×Q8C22⋊D73semidirect
612. Q8C4×C22⋊D73semidirect
703. C4#17988785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179887852
C2×C4×#119240152
C4×#145565872
C4×Q8×Dic732
#226108562
#226106912
#226105612
#226105572
#226102882
#226102842
#226099342
C4×#145565202
C4×#145565132
C4×#145565122
C2×C4×SD16×C732
C4×#46073