Finite Group Databasebeta

← C73×#18416 #32927820

Subgroups — C73×#18416 #32927820

Order 18688.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3535C211yesmaximal, characteristic, complemented
2C73×#3194C211yesmaximal, characteristic, complemented
3C73×#3187C211yesmaximal, characteristic, complemented
4C73×#2661C211yesmaximal, characteristic, complemented
5C73×#1612C211yesmaximal, characteristic, complemented
6C73×#1611C211yesmaximal, characteristic, complemented
7C73×#1609C211yesmaximal, characteristic, complemented
8C73×#1608C211yesmaximal, characteristic, complemented
9C73×#1600C211yesmaximal, characteristic, complemented
10C73×#1599C211yesmaximal, characteristic, complemented
11C73×#1597C211yesmaximal, characteristic, complemented
12C73×#1596C211yesmaximal, characteristic, complemented
13C73×#1508C211yesmaximal, characteristic, complemented
14C73×#1501C211yesmaximal, characteristic, complemented
15C73×#1468C211yesmaximal, characteristic, complemented
16#563×C73—21no—
17#562×C73—21no—
18#554×C73—21no—
19#552×C73—21no—
20#551×C73—21no—
21#551×C73—21no—
22#547×C73—21no—
23#546×C73—21no—
24#544×C73C2211yescharacteristic
25#543×C73C2211yescharacteristic
26#542×C73—21no—
27#539×C73—21no—
28#539×C73—21no—
29#539×C73C2211yescharacteristic
30#538×C73C2211yescharacteristic
31#536×C73—21no—
32#525×C73C2211yescharacteristic
33C2×#123×C73C2211yescharacteristic
34C2×C22⋊Q8×C73C2211yescharacteristic
35C2×#121×C73C2211yescharacteristic
36#483×C73C2211yescharacteristic
37#483×C73C2211yescharacteristic
38#483×C73C2211yescharacteristic
39#482×C73—21no—
40#481×C73—21no—
41#480×C73C2211yescharacteristic
42#469×C73—21no—
43#468×C73—21no—
44#465×C73—21no—
45#465×C73—21no—
46#450×C73C2211yescharacteristic
47#450×C73C2211yescharacteristic
48#450×C73C2211yescharacteristic
49#449×C73—21no—
50#448×C73—21no—
51#447×C73C2211yescharacteristic
52#407×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54#398×C73C2211yescharacteristic
55#397×C73C2211yescharacteristic
56#394×C73—21no—
57#394×C73C2211yescharacteristic
58#392×C73—21no—
59#392×C73C2211yescharacteristic
60#390×C73—21no—
61#388×C73—21no—
62C4×C22⋊C4×C73C2211yescharacteristic
63#328×C73C2211yescharacteristic
64#328×C73C2211yescharacteristic
65#328×C73C2211yescharacteristic
66#328×C73C2211yescharacteristic
67#328×C73C2211yescharacteristic
68#328×C73C2211yescharacteristic
69#327×C73C2211yescharacteristic
70#327×C73C2211yescharacteristic
71#324×C73C2211yescharacteristic
72#324×C73C2211yescharacteristic
73#323×C73C2211yescharacteristic
74#323×C73C2211yescharacteristic
75C2×#41×C73—21no—
76C2×#41×C73D411yescharacteristic, complemented
77C22×Q8×C73D411yescharacteristic, complemented
78C22×D4×C73—21no—
79C22×D4×C73—21no—
80C22×D4×C73D411yescharacteristic
81C22×D4×C73C2311yescharacteristic
82C23×C4×C73C2311yescharacteristic
83C2×SD16×C73—21no—
84C2×SD16×C73—21no—
85C2×SD16×C73—21no—
86C2×D8×C73—21no—
87C2×M16×C73—21no—
88C22×C8×C73—21no—
89C4⋊Q8×C73—21no—
90C4⋊Q8×C73—21no—
91C4⋊Q8×C73—21no—
92#126×C73—21no—
93#126×C73—21no—
94#126×C73—21no—
95#126×C73—21no—
96#126×C73—21no—
97#126×C73—21no—
98#125×C73—21no—
99#125×C73—21no—
100#125×C73—21no—
101#125×C73—21no—
102#125×C73—21no—
103#124×C73—21no—
104#124×C73—21no—
105#124×C73—21no—
106#124×C73—21no—
107#123×C73—21no—
108#123×C73—21no—
109#123×C73—21no—
110#123×C73—21no—
111#123×C73—21no—
112#123×C73—21no—
113#123×C73—21no—
114#123×C73—21no—
115#123×C73—21no—
116#123×C73—21no—
117#123×C73—21no—
118#123×C73—21no—
119#123×C73—21no—
120#123×C73—21no—
121C22⋊Q8×C73—21no—
122C22⋊Q8×C73—21no—
123C22⋊Q8×C73—21no—
124C22⋊Q8×C73—21no—
125C22⋊Q8×C73—21no—
126C22⋊Q8×C73—21no—
127C22⋊Q8×C73—21no—
128C22⋊Q8×C73—21no—
129C22⋊Q8×C73—21no—
130C22⋊Q8×C73—21no—
131C22⋊Q8×C73—21no—
132C22⋊Q8×C73—21no—
133C22⋊Q8×C73—21no—
134C22⋊Q8×C73—21no—
135C22⋊Q8×C73D411yescharacteristic, complemented
136C22⋊Q8×C73D411yescharacteristic, complemented
137C22⋊Q8×C73D411yescharacteristic, complemented
138C22⋊Q8×C73C2311yescharacteristic
139C22⋊Q8×C73C2311yescharacteristic
140C22⋊Q8×C73C2311yescharacteristic
141#121×C73—21no—
142#121×C73—21no—
143#121×C73—21no—
144#121×C73—21no—
145#121×C73—21no—
146#121×C73—21no—
147#121×C73—21no—
148#121×C73—21no—
149#121×C73D411yescharacteristic, complemented
150#121×C73C2311yescharacteristic
151#120×C73—21no—
152#120×C73—21no—
153C4×Q8×C73—21no—
154C4×D4×C73—21no—
155C4×D4×C73—21no—
156C4×D4×C73—21no—
157C4×D4×C73—21no—
158C4×D4×C73—21no—
159C4×D4×C73—21no—
160C4×D4×C73—21no—
161#117×C73—21no—
162#117×C73—21no—
163#117×C73—21no—
164#117×C73D411yescharacteristic, complemented
165C2×C4⋊C4×C73—21no—
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73D411yescharacteristic
169C2×C4⋊C4×C73D411yescharacteristic, complemented
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73—21no—
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C22⋊C4×C73D411yescharacteristic
181C2×C22⋊C4×C73D411yescharacteristic
182C2×C22⋊C4×C73C2311yescharacteristic
183C2×C42×C73—21no—
184#107×C73—21no—
185#106×C73—21no—
186#106×C73—21no—
187#106×C73—21no—
188#103×C73—21no—
189#103×C73—21no—
190#103×C73—21no—
191#102×C73—21no—
192#102×C73—21no—
193#102×C73—21no—
194#102×C73—21no—
195#102×C73—21no—
196C22⋊C8×C73—21no—
197C22⋊C8×C73—21no—
198C22⋊C8×C73C2311yescharacteristic
199C22⋊C8×C73C2311yescharacteristic
200C22⋊C8×C73C2311yescharacteristic
201C22⋊C8×C73C2311yescharacteristic
202#95×C73—21no—
203#95×C73—21no—
204#95×C73C2311yescharacteristic
205#95×C73C2311yescharacteristic
206C24×C73—21no—
207C24×C73C2×D411yescharacteristic
208C24×C73C2×D411yescharacteristic
209#41×C73—82no—
210#41×C73—81no—
211C2×Q8×C73—21no—
212C2×Q8×C73—21no—
213C2×Q8×C73—21no—
214C2×Q8×C73—81no—
215C2×Q8×C73C2×D411yescharacteristic
216C2×Q8×C73C2×D411yescharacteristic
217C2×Q8×C73C2×D411yescharacteristic
218C2×D4×C73—21no—
219C2×D4×C73—21no—
220C2×D4×C73—21no—
221C2×D4×C73—21no—
222C2×D4×C73—21no—
223C2×D4×C73—21no—
224C2×D4×C73—21no—
225C2×D4×C73—21no—
226C2×D4×C73—21no—
227C2×D4×C73—42no—
228C2×D4×C73—41no—
229C2×D4×C73—41no—
230C2×D4×C73—81no—
231C2×D4×C73—81no—
232C2×D4×C73—81no—
233C2×D4×C73—81no—
234C2×D4×C73—81no—
235C2×D4×C73—81no—
236C2×D4×C73C2×D411yescharacteristic
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—81no—
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2411yescharacteristic
257SD16×C73—81no—
258SD16×C73—81no—
259SD16×C73—81no—
260D8×C73—81no—
261M16×C73—81no—
262C2×C8×C73—21no—
263C2×C8×C73—21no—
264C2×C8×C73—21no—
265C2×C8×C73—21no—
266C2×C8×C73—81no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73—21no—
282C4⋊C4×C73—21no—
283C4⋊C4×C73—21no—
284C4⋊C4×C73—21no—
285C4⋊C4×C73—21no—
286C4⋊C4×C73—21no—
287C4⋊C4×C73—21no—
288C4⋊C4×C73—21no—
289C4⋊C4×C73—21no—
290C4⋊C4×C73—21no—
291C4⋊C4×C73—21no—
292C4⋊C4×C73—81no—
293C4⋊C4×C73C2×D411yescharacteristic
294C4⋊C4×C73C2×D411yescharacteristic
295C4⋊C4×C73C2×D411yescharacteristic
296C4⋊C4×C73C2×D411yescharacteristic
297C22⋊C4×C73—21no—
298C22⋊C4×C73—21no—
299C22⋊C4×C73—21no—
300C22⋊C4×C73—21no—
301C22⋊C4×C73—21no—
302C22⋊C4×C73—21no—
303C22⋊C4×C73—21no—
304C22⋊C4×C73—21no—
305C22⋊C4×C73—21no—
306C22⋊C4×C73—21no—
307C22⋊C4×C73—21no—
308C22⋊C4×C73—21no—
309C22⋊C4×C73—21no—
310C22⋊C4×C73—21no—
311C22⋊C4×C73—21no—
312C22⋊C4×C73—21no—
313C22⋊C4×C73—21no—
314C22⋊C4×C73—21no—
315C22⋊C4×C73—21no—
316C22⋊C4×C73—21no—
317C22⋊C4×C73—21no—
318C22⋊C4×C73—21no—
319C22⋊C4×C73—21no—
320C22⋊C4×C73—42no—
321C22⋊C4×C73—42no—
322C22⋊C4×C73—41no—
323C22⋊C4×C73—41no—
324C22⋊C4×C73—81no—
325C22⋊C4×C73—81no—
326C22⋊C4×C73—81no—
327C42×C73—21no—
328C42×C73—21no—
329C42×C73—21no—
330C42×C73—21no—
331C42×C73—21no—
332C42×C73—81no—
333C23×C73—21no—
334C23×C73—21no—
335C23×C73—21no—
336C23×C73—21no—
337C23×C73—21no—
338C23×C73—21no—
339C23×C73—41no—
340C23×C73—41no—
341C23×C73—41no—
342C23×C73—41no—
343C23×C73—41no—
344C23×C73—41no—
345C23×C73—41no—
346C23×C73—41no—
347C23×C73—41no—
348C23×C73—41no—
349C23×C73—41no—
350C23×C73#12011yescharacteristic
351C23×C73#12011yescharacteristic
352C23×C73C22×D411yescharacteristic
353Q8×C73—41no—
354Q8×C73—41no—
355Q8×C73—41no—
356Q8×C73—81no—
357Q8×C73—81no—
358Q8×C73—81no—
359D4×C73—41no—
360D4×C73—41no—
361D4×C73—41no—
362D4×C73—41no—
363D4×C73—41no—
364D4×C73—42no—
365D4×C73—42no—
366D4×C73—41no—
367D4×C73—41no—
368D4×C73—81no—
369D4×C73—81no—
370D4×C73—81no—
371D4×C73—81no—
372D4×C73—84no—
373D4×C73—82no—
374D4×C73—82no—
375C2×C4×C73—22no—
376C2×C4×C73—21no—
377C2×C4×C73—21no—
378C2×C4×C73—21no—
379C2×C4×C73—21no—
380C2×C4×C73—21no—
381C2×C4×C73—21no—
382C2×C4×C73—21no—
383C2×C4×C73—21no—
384C2×C4×C73—21no—
385C2×C4×C73—21no—
386C2×C4×C73—21no—
387C2×C4×C73—21no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73—41no—
392C2×C4×C73—41no—
393C2×C4×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73—42no—
396C2×C4×C73—41no—
397C2×C4×C73—41no—
398C2×C4×C73—41no—
399C2×C4×C73—41no—
400C2×C4×C73—41no—
401C2×C4×C73—41no—
402C2×C4×C73—41no—
403C2×C4×C73—41no—
404C2×C4×C73—41no—
405C2×C4×C73—81no—
406C2×C4×C73—81no—
407C2×C4×C73—81no—
408C2×C4×C73—81no—
409C2×C4×C73—81no—
410C2×C4×C73—81no—
411C2×C4×C73#12011yescharacteristic
412C2×C4×C73#12011yescharacteristic
413C2×C4×C73C22×D411yescharacteristic
414C2×C4×C73C22×D411yescharacteristic
415C8×C73—41no—
416C8×C73—41no—
417C8×C73—41no—
418C8×C73—41no—
419C22×C73—21no—
420C22×C73—21no—
421C22×C73—21no—
422C22×C73—21no—
423C22×C73—21no—
424C22×C73—21no—
425C22×C73—21no—
426C22×C73—21no—
427C22×C73—41no—
428C22×C73—41no—
429C22×C73—41no—
430C22×C73—41no—
431C22×C73—41no—
432C22×C73—41no—
433C22×C73—81no—
434C22×C73—81no—
435C22×C73—81no—
436C22×C73—81no—
437C22×C73—81no—
438C22×C73—81no—
439C22×C73—81no—
440C22×C73—81no—
441C22×C73—81no—
442C22×C73—81no—
443C22×C73—81no—
444C22×C73C2×#12011yescharacteristic
445C22×C73#57711yescharacteristic
446C22×C73#57711yescharacteristic
447C4×C73—21no—
448C4×C73—21no—
449C4×C73—21no—
450C4×C73—21no—
451C4×C73—42no—
452C4×C73—41no—
453C4×C73—41no—
454C4×C73—41no—
455C4×C73—41no—
456C4×C73—41no—
457C4×C73—41no—
458C4×C73—41no—
459C4×C73—41no—
460C4×C73—41no—
461C4×C73—41no—
462C4×C73—81no—
463C4×C73—81no—
464#18416C7311yesmaximal, characteristic, direct product factor, Sylow
465C2×C73—21no—
466C2×C73—21no—
467C2×C73—41no—
468C2×C73—41no—
469C2×C73—81no—
470C2×C73—81no—
471C2×C73—161no—
472C2×C73#301011yescharacteristic
473C2×C73#301811yescharacteristic
474C2×C73#302611yescharacteristic
475#3535C2×C7311yescharacteristic, complemented
476#3194C2×C7311yescharacteristic, complemented
477#3187C2×C7311yescharacteristic, complemented
478#2661C2×C7311yescharacteristic, complemented
479#1612C2×C7311yescharacteristic, complemented
480#1611C2×C7311yescharacteristic, complemented
481#1609C2×C7311yescharacteristic, complemented
482#1608C2×C7311yescharacteristic, complemented
483#1600C2×C7311yescharacteristic, complemented
484#1599C2×C7311yescharacteristic, complemented
485#1597C2×C7311yescharacteristic, complemented
486#1596C2×C7311yescharacteristic, complemented
487#1508C2×C7311yescharacteristic, complemented
488#1501C2×C7311yescharacteristic, complemented
489#1468C2×C7311yescharacteristic, complemented
490C73#1841611yescharacteristic, direct product factor, Sylow
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C7311yescharacteristic
500#543C22×C7311yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C7311yescharacteristic
505#538C22×C7311yescharacteristic
506#536—21no—
507#525C22×C7311yescharacteristic
508C2×#123C22×C7311yescharacteristic
509C2×C22⋊Q8C22×C7311yescharacteristic
510C2×#121C22×C7311yescharacteristic
511#483C22×C7311yescharacteristic
512#483C22×C7311yescharacteristic
513#483C22×C7311yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C7311yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C7311yescharacteristic
522#450C22×C7311yescharacteristic
523#450C22×C7311yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C7311yescharacteristic
527#407C22×C7311yescharacteristic
528C2×C22⋊C8C22×C7311yescharacteristic
529#398C22×C7311yescharacteristic
530#397C22×C7311yescharacteristic
531#394—21no—
532#394C22×C7311yescharacteristic
533#392—21no—
534#392C22×C7311yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C7311yescharacteristic
538#328C22×C7311yescharacteristic
539#328C22×C7311yescharacteristic
540#328C22×C7311yescharacteristic
541#328C22×C7311yescharacteristic
542#328C22×C7311yescharacteristic
543#328C22×C7311yescharacteristic
544#327C22×C7311yescharacteristic
545#327C22×C7311yescharacteristic
546#324C22×C7311yescharacteristic
547#324C22×C7311yescharacteristic
548#323C22×C7311yescharacteristic
549#323C22×C7311yescharacteristic
550C2×#41—21no—
551C2×#41D4×C7311yescharacteristic, complemented
552C22×Q8D4×C7311yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C7311yescharacteristic
556C22×D4C23×C7311yescharacteristic
557C23×C4C23×C7311yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C7311yescharacteristic, complemented
611C22⋊Q8D4×C7311yescharacteristic, complemented
612C22⋊Q8D4×C7311yescharacteristic, complemented
613C22⋊Q8C23×C7311yescharacteristic
614C22⋊Q8C23×C7311yescharacteristic
615C22⋊Q8C23×C7311yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C7311yescharacteristic, complemented
625#121C23×C7311yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C7311yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C7311yescharacteristic
644C2×C4⋊C4D4×C7311yescharacteristic, complemented
645C2×C4⋊C4C23×C7311yescharacteristic
646C2×C4⋊C4C23×C7311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C7311yescharacteristic
656C2×C22⋊C4D4×C7311yescharacteristic
657C2×C22⋊C4C23×C7311yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C7311yescharacteristic
674C22⋊C8C23×C7311yescharacteristic
675C22⋊C8C23×C7311yescharacteristic
676C22⋊C8C23×C7311yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C7311yescharacteristic
680#95C23×C7311yescharacteristic
681C24—21no—
682C24C2×D4×C7311yescharacteristic
683C24C2×D4×C7311yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C7311yescharacteristic
691C2×Q8C2×D4×C7311yescharacteristic
692C2×Q8C2×D4×C7311yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C7311yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C7311yescharacteristic
724C22×C4C2×D4×C7311yescharacteristic
725C22×C4C2×D4×C7311yescharacteristic
726C22×C4C2×D4×C7311yescharacteristic
727C22×C4C2×D4×C7311yescharacteristic
728C22×C4C2×D4×C7311yescharacteristic
729C22×C4C2×D4×C7311yescharacteristic
730C22×C4C2×D4×C7311yescharacteristic
731C22×C4C24×C7311yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C7311yescharacteristic
769C4⋊C4C2×D4×C7311yescharacteristic
770C4⋊C4C2×D4×C7311yescharacteristic
771C4⋊C4C2×D4×C7311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C7311yescharacteristic
826C23#120×C7311yescharacteristic
827C23C22×D4×C7311yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C7311yescharacteristic
887C2×C4#120×C7311yescharacteristic
888C2×C4C22×D4×C7311yescharacteristic
889C2×C4C22×D4×C7311yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C7311yescharacteristic
920C22#577×C7311yescharacteristic
921C22#577×C7311yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C73×#301011yescharacteristic
947C2C73×#301811yescharacteristic
948C2C73×#302611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3535C2semidirect
2. C73×#3194C2semidirect
3. C73×#3187C2semidirect
4. C73×#2661C2semidirect
5. C73×#1612C2semidirect
6. C73×#1611C2semidirect
7. C73×#1609C2semidirect
8. C73×#1608C2semidirect
9. C73×#1600C2semidirect
10. C73×#1599C2semidirect
11. C73×#1597C2semidirect
12. C73×#1596C2semidirect
13. C73×#1508C2semidirect
14. C73×#1501C2semidirect
15. C73×#1468C2semidirect
76. C2×#41×C73D4semidirect
77. C22×Q8×C73D4semidirect
135. C22⋊Q8×C73D4semidirect
136. C22⋊Q8×C73D4semidirect
137. C22⋊Q8×C73D4semidirect
149. #121×C73D4semidirect
164. #117×C73D4semidirect
169. C2×C4⋊C4×C73D4semidirect
464. #18416C73direct (N × H)
475. #3535C2×C73semidirect
476. #3194C2×C73semidirect
477. #3187C2×C73semidirect
478. #2661C2×C73semidirect
479. #1612C2×C73semidirect
480. #1611C2×C73semidirect
481. #1609C2×C73semidirect
482. #1608C2×C73semidirect
483. #1600C2×C73semidirect
484. #1599C2×C73semidirect
485. #1597C2×C73semidirect
486. #1596C2×C73semidirect
487. #1508C2×C73semidirect
488. #1501C2×C73semidirect
489. #1468C2×C73semidirect
490. C73#18416direct (N × H)
551. C2×#41D4×C73semidirect
552. C22×Q8D4×C73semidirect
610. C22⋊Q8D4×C73semidirect
611. C22⋊Q8D4×C73semidirect
612. C22⋊Q8D4×C73semidirect
624. #121D4×C73semidirect
639. #117D4×C73semidirect
644. C2×C4⋊C4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35352
C73×#31942
C73×#31872
C73×#26612
C73×#16122
C73×#16112
C73×#16092
C73×#16082
C73×#16002
C73×#15992
C73×#15972
C73×#15962
C73×#15082
C73×#15012
C73×#14682
#1841673