Finite Group Databasebeta

← C73×#24028 #32933432

Subgroups — C73×#24028 #32933432

Order 18688.

1250 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3489C211yesmaximal, characteristic
2C73×#3093C211yesmaximal, characteristic, complemented
3C73×#2896C211yesmaximal, characteristic, complemented
4C73×#2499C211yesmaximal, characteristic, complemented
5C73×#2040C211yesmaximal, characteristic, complemented
6C73×#2039C211yesmaximal, characteristic, complemented
7C73×#2038C211yesmaximal, characteristic, complemented
8C73×#2038C211yesmaximal, characteristic, complemented
9C73×#1901C211yesmaximal, characteristic, complemented
10C73×#1871C211yesmaximal, characteristic, complemented
11C73×#1860C211yesmaximal, characteristic, complemented
12C73×#1859C211yesmaximal, characteristic, complemented
13C73×#1793C211yesmaximal, characteristic, complemented
14C73×#1793C211yesmaximal, characteristic, complemented
15C73×#1789C211yesmaximal, characteristic, complemented
16C2×2−1+4×C73C2211yescharacteristic
17C22×#41×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19D4×Q8×C73—21no—
20#548×C73—21no—
21#547×C73—21no—
22#547×C73—22no—
23#546×C73—21no—
24#546×C73—22no—
25#537×C73—21no—
26#537×C73C2211yescharacteristic
27#536×C73—21no—
28#536×C73C2211yescharacteristic
29#525×C73—21no—
30#525×C73C2211yescharacteristic
31C2×C22⋊Q8×C73—21no—
32C2×C22⋊Q8×C73C2211yescharacteristic
33#520×C73C2211yescharacteristic
34C2×#117×C73C2211yescharacteristic
35#485×C73—21no—
36#485×C73—21no—
37#482×C73—21no—
38#482×C73—21no—
39#428×C73C2211yescharacteristic, complemented
40#428×C73C2211yescharacteristic, complemented
41C2×#104×C73C2211yescharacteristic
42C2×#104×C73C2211yescharacteristic
43C2×#104×C73C2211yescharacteristic
44C2×#104×C73C2211yescharacteristic
45C2×#104×C73C2211yescharacteristic, complemented
46C2×#104×C73C2211yescharacteristic, complemented
47#419×C73—21no—
48#418×C73—21no—
49#417×C73C2211yescharacteristic
50#417×C73C2211yescharacteristic
51#417×C73C2211yescharacteristic
52#417×C73C2211yescharacteristic
53#417×C73C2211yescharacteristic, complemented
54#417×C73C2211yescharacteristic, complemented
55#416×C73—21no—
56#416×C73—21no—
57C2×#101×C73C2211yescharacteristic, complemented
58C2×#101×C73C2211yescharacteristic, complemented
59#407×C73C2211yescharacteristic
60#397×C73—22no—
61#391×C73C2211yescharacteristic, complemented
62#391×C73C2211yescharacteristic, complemented
63#387×C73—22no—
64#384×C73C2211yescharacteristic, complemented
65#382×C73C2211yescharacteristic, complemented
66C4×C22⋊C4×C73C2211yescharacteristic
67#343×C73C2211yescharacteristic, complemented
68#343×C73C2211yescharacteristic, complemented
69#339×C73C2211yescharacteristic, complemented
70#339×C73C2211yescharacteristic, complemented
712−1+4×C73—22no—
722−1+4×C73—22no—
732−1+4×C73—41no—
742−1+4×C73—41no—
75C2×#41×C73—21no—
76C2×#41×C73—21no—
77C2×#41×C73—21no—
78C2×#41×C73—22no—
79C2×#41×C73—21no—
80C2×#41×C73—22no—
81C2×#41×C73—22no—
82C2×#41×C73—41no—
83C2×#41×C73—41no—
84C2×#41×C73D411yescharacteristic
85C2×#41×C73D411yescharacteristic
86C2×#41×C73C2311yescharacteristic
87C2×#41×C73C2311yescharacteristic
88C2×#41×C73C2311yescharacteristic
89C22×Q8×C73—21no—
90C22×Q8×C73—21no—
91C22×Q8×C73D411yescharacteristic
92C22×Q8×C73C2311yescharacteristic
93C22×D4×C73—21no—
94C22×D4×C73D411yescharacteristic
95C23×C4×C73—21no—
96C23×C4×C73C2311yescharacteristic
97C2×M16×C73—21no—
98C2×M16×C73—41no—
99C2×M16×C73—41no—
100C2×M16×C73C2311yescharacteristic
101C2×M16×C73C2311yescharacteristic
102C2×M16×C73C2311yescharacteristic
103C2×M16×C73C2311yescharacteristic
104C22×C8×C73—21no—
105C4⋊Q8×C73—22no—
106C4⋊Q8×C73—21no—
107#124×C73—22no—
108#124×C73—21no—
109#123×C73—22no—
110#123×C73—22no—
111#123×C73—22no—
112#123×C73—21no—
113#123×C73—22no—
114C22⋊Q8×C73—22no—
115C22⋊Q8×C73—22no—
116C22⋊Q8×C73—22no—
117C22⋊Q8×C73—21no—
118C22⋊Q8×C73—21no—
119C22⋊Q8×C73—21no—
120C22⋊Q8×C73—21no—
121C22⋊Q8×C73—21no—
122C22⋊Q8×C73—21no—
123C22⋊Q8×C73—21no—
124C22⋊Q8×C73—21no—
125C22⋊Q8×C73D411yescharacteristic
126C22⋊Q8×C73D411yescharacteristic
127#121×C73—22no—
128#121×C73—22no—
129#121×C73—22no—
130#121×C73—21no—
131#121×C73—21no—
132#121×C73—22no—
133#121×C73D411yescharacteristic
134#121×C73D411yescharacteristic
135#120×C73—22no—
136#120×C73—21no—
137C4×Q8×C73—21no—
138C4×D4×C73—22no—
139C4×D4×C73—22no—
140C4×D4×C73—21no—
141C4×D4×C73—22no—
142C4×D4×C73—21no—
143C4×D4×C73—21no—
144#117×C73—21no—
145#117×C73—21no—
146#117×C73—21no—
147#117×C73—21no—
148#117×C73—21no—
149#117×C73C2311yescharacteristic
150C2×C4⋊C4×C73—22no—
151C2×C4⋊C4×C73—21no—
152C2×C4⋊C4×C73—22no—
153C2×C4⋊C4×C73D412yes—
154C2×C4⋊C4×C73C2311yescharacteristic
155C2×C4⋊C4×C73C2311yescharacteristic
156C2×C4⋊C4×C73C2311yescharacteristic
157C2×C22⋊C4×C73—22no—
158C2×C22⋊C4×C73—21no—
159C2×C22⋊C4×C73—21no—
160C2×C22⋊C4×C73D412yes—
161C2×C42×C73—21no—
162C2×C42×C73C2311yescharacteristic
163C2×C42×C73C2311yescharacteristic
164#107×C73—21no—
165#107×C73—21no—
166#106×C73—21no—
167#106×C73—21no—
168#104×C73—22no—
169#104×C73—22no—
170#104×C73—41no—
171#104×C73—41no—
172#104×C73—41no—
173#104×C73—41no—
174#103×C73—21no—
175#103×C73—21no—
176#103×C73—21no—
177#103×C73—21no—
178#103×C73—21no—
179#103×C73—21no—
180#102×C73—21no—
181#102×C73—21no—
182#102×C73—21no—
183#102×C73—21no—
184#102×C73—21no—
185#102×C73—21no—
186#101×C73—41no—
187#101×C73—41no—
188C22⋊C8×C73—21no—
189C22⋊C8×C73—21no—
190#95×C73—21no—
191#95×C73—22no—
192#95×C73—22no—
193#95×C73—22no—
194C24×C73—21no—
195C24×C73C2×D411yescharacteristic
196#41×C73—21no—
197#41×C73—21no—
198#41×C73—22no—
199#41×C73—22no—
200#41×C73—21no—
201#41×C73—21no—
202#41×C73—21no—
203#41×C73—21no—
204#41×C73—21no—
205#41×C73—21no—
206#41×C73—21no—
207#41×C73—21no—
208#41×C73—42no—
209#41×C73—42no—
210#41×C73—41no—
211#41×C73—41no—
212#41×C73—42no—
213#41×C73—42no—
214#41×C73—42no—
215#41×C73—42no—
216#41×C73—44no—
217#41×C73—44no—
218#41×C73—42no—
219#41×C73—42no—
220#41×C73#4112yes—
221#41×C73#4112yes—
222C2×Q8×C73—22no—
223C2×Q8×C73—21no—
224C2×Q8×C73—21no—
225C2×Q8×C73—21no—
226C2×Q8×C73—21no—
227C2×Q8×C73—21no—
228C2×Q8×C73—21no—
229C2×Q8×C73—21no—
230C2×Q8×C73—22no—
231C2×Q8×C73—41no—
232C2×Q8×C73—42no—
233C2×Q8×C73—42no—
234C2×Q8×C73—42no—
235C2×Q8×C73—42no—
236C2×Q8×C73C2×D411yescharacteristic
237C2×Q8×C73C2×D411yescharacteristic
238C2×Q8×C73C2×D411yescharacteristic
239C2×D4×C73—21no—
240C2×D4×C73—22no—
241C2×D4×C73—22no—
242C2×D4×C73—21no—
243C2×D4×C73—21no—
244C2×D4×C73—21no—
245C2×D4×C73—21no—
246C2×D4×C73—21no—
247C2×D4×C73—22no—
248C2×D4×C73—21no—
249C2×D4×C73—21no—
250C2×D4×C73—41no—
251C2×D4×C73—42no—
252C2×D4×C73—42no—
253C2×D4×C73C2×D411yescharacteristic
254C2×D4×C73C2×D411yescharacteristic
255C2×D4×C73C2×D411yescharacteristic
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—22no—
262C22×C4×C73—22no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—22no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—42no—
274C22×C4×C73—42no—
275C22×C4×C73C2×D412yes—
276C22×C4×C73C2×D411yescharacteristic
277C22×C4×C73C2×D411yescharacteristic
278C22×C4×C73C2×D411yescharacteristic
279C22×C4×C73C2×D411yescharacteristic
280C22×C4×C73C2×D411yescharacteristic
281C22×C4×C73C2×D412yes—
282C22×C4×C73C2411yescharacteristic
283M16×C73—21no—
284M16×C73—21no—
285M16×C73—21no—
286M16×C73—21no—
287M16×C73—21no—
288M16×C73—21no—
289M16×C73—21no—
290M16×C73—21no—
291M16×C73—42no—
292C2×C8×C73—21no—
293C2×C8×C73—21no—
294C2×C8×C73—21no—
295C2×C8×C73—21no—
296C2×C8×C73—42no—
297C4⋊C4×C73—22no—
298C4⋊C4×C73—22no—
299C4⋊C4×C73—22no—
300C4⋊C4×C73—22no—
301C4⋊C4×C73—21no—
302C4⋊C4×C73—22no—
303C4⋊C4×C73—22no—
304C4⋊C4×C73—21no—
305C4⋊C4×C73—21no—
306C4⋊C4×C73—21no—
307C4⋊C4×C73—21no—
308C4⋊C4×C73—21no—
309C4⋊C4×C73—21no—
310C4⋊C4×C73—21no—
311C4⋊C4×C73—44no—
312C4⋊C4×C73C2×D411yescharacteristic
313C4⋊C4×C73C2×D411yescharacteristic
314C22⋊C4×C73—22no—
315C22⋊C4×C73—22no—
316C22⋊C4×C73—22no—
317C22⋊C4×C73—22no—
318C22⋊C4×C73—22no—
319C22⋊C4×C73—21no—
320C22⋊C4×C73—22no—
321C22⋊C4×C73—22no—
322C22⋊C4×C73—21no—
323C22⋊C4×C73—21no—
324C22⋊C4×C73—21no—
325C22⋊C4×C73—21no—
326C22⋊C4×C73—42no—
327C22⋊C4×C73—41no—
328C22⋊C4×C73—41no—
329C42×C73—22no—
330C42×C73—21no—
331C42×C73—21no—
332C42×C73—21no—
333C42×C73—21no—
334C42×C73—21no—
335C42×C73—41no—
336C42×C73—41no—
337C23×C73—21no—
338C23×C73—21no—
339C23×C73—21no—
340C23×C73—21no—
341C23×C73—21no—
342C23×C73—41no—
343C23×C73—41no—
344C23×C73—42no—
345C23×C73—42no—
346C23×C73—81no—
347C23×C73#12011yescharacteristic
348C23×C73#12011yescharacteristic
349C23×C73C22×D411yescharacteristic
350Q8×C73—21no—
351Q8×C73—21no—
352Q8×C73—21no—
353Q8×C73—21no—
354Q8×C73—21no—
355Q8×C73—42no—
356Q8×C73—44no—
357Q8×C73—41no—
358Q8×C73—41no—
359Q8×C73—41no—
360Q8×C73—41no—
361Q8×C73#12312yes—
362D4×C73—22no—
363D4×C73—22no—
364D4×C73—21no—
365D4×C73—21no—
366D4×C73—21no—
367D4×C73—21no—
368D4×C73—21no—
369D4×C73—42no—
370D4×C73—42no—
371D4×C73—42no—
372D4×C73—42no—
373D4×C73—44no—
374D4×C73—41no—
375D4×C73—41no—
376D4×C73—41no—
377D4×C73—41no—
378D4×C73—81no—
379D4×C73—82no—
380D4×C73#12312yes—
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—21no—
389C2×C4×C73—21no—
390C2×C4×C73—21no—
391C2×C4×C73—21no—
392C2×C4×C73—22no—
393C2×C4×C73—22no—
394C2×C4×C73—22no—
395C2×C4×C73—21no—
396C2×C4×C73—22no—
397C2×C4×C73—21no—
398C2×C4×C73—21no—
399C2×C4×C73—22no—
400C2×C4×C73—21no—
401C2×C4×C73—22no—
402C2×C4×C73—22no—
403C2×C4×C73—42no—
404C2×C4×C73—42no—
405C2×C4×C73—42no—
406C2×C4×C73—44no—
407C2×C4×C73—41no—
408C2×C4×C73—44no—
409C2×C4×C73—41no—
410C2×C4×C73—41no—
411C2×C4×C73—41no—
412C2×C4×C73—41no—
413C2×C4×C73—41no—
414C2×C4×C73—42no—
415C2×C4×C73—41no—
416C2×C4×C73—42no—
417C2×C4×C73—41no—
418C2×C4×C73—42no—
419C2×C4×C73—41no—
420C2×C4×C73—41no—
421C2×C4×C73—41no—
422C2×C4×C73—82no—
423C2×C4×C73#12011yescharacteristic
424C2×C4×C73#12011yescharacteristic
425C2×C4×C73C22×D411yescharacteristic
426C2×C4×C73C22×D411yescharacteristic
427C2×C4×C73C2×#4111yescharacteristic
428C2×C4×C73C2×#4111yescharacteristic
429C2×C4×C73H(5,𝔽2)11yescharacteristic
430C2×C4×C73H(5,𝔽2)11yescharacteristic
431C8×C73—41no—
432C8×C73—41no—
433C8×C73—41no—
434C8×C73—41no—
435C22×C73—21no—
436C22×C73—21no—
437C22×C73—21no—
438C22×C73—21no—
439C22×C73—22no—
440C22×C73—21no—
441C22×C73—21no—
442C22×C73—21no—
443C22×C73—21no—
444C22×C73—41no—
445C22×C73—41no—
446C22×C73—41no—
447C22×C73—41no—
448C22×C73—41no—
449C22×C73—41no—
450C22×C73—41no—
451C22×C73—41no—
452C22×C73—81no—
453C22×C73—81no—
454C22×C73—84no—
455C22×C73C2×#12011yescharacteristic
456C22×C73#54611yescharacteristic
457C22×C73#54611yescharacteristic
458C4×C73—21no—
459C4×C73—21no—
460C4×C73—22no—
461C4×C73—42no—
462C4×C73—42no—
463C4×C73—41no—
464C4×C73—41no—
465C4×C73—42no—
466C4×C73—41no—
467C4×C73—41no—
468C4×C73—81no—
469C4×C73—81no—
470C4×C73—81no—
471C4×C73C2×#12311yescharacteristic
472C4×C73#53411yescharacteristic
473C4×C73#54611yescharacteristic
474C4×C73#54611yescharacteristic
475#24028C7311yesmaximal, characteristic, direct product factor, Sylow
476C2×C73—21no—
477C2×C73—21no—
478C2×C73—41no—
479C2×C73—41no—
480C2×C73—42no—
481C2×C73—81no—
482C2×C73—81no—
483C2×C73#240511yescharacteristic
484C2×C73#301811yescharacteristic
485C2×C73#302011yescharacteristic
486#3489C2×C7311yescharacteristic
487#3093C2×C7311yescharacteristic, complemented
488#2896C2×C7311yescharacteristic, complemented
489#2499C2×C7311yescharacteristic, complemented
490#2040C2×C7311yescharacteristic, complemented
491#2039C2×C7311yescharacteristic, complemented
492#2038C2×C7311yescharacteristic, complemented
493#2038C2×C7311yescharacteristic, complemented
494#1901C2×C7311yescharacteristic, complemented
495#1871C2×C7311yescharacteristic, complemented
496#1860C2×C7311yescharacteristic, complemented
497#1859C2×C7311yescharacteristic, complemented
498#1793C2×C7311yescharacteristic, complemented
499#1793C2×C7311yescharacteristic, complemented
500#1789C2×C7311yescharacteristic, complemented
501C73#2402811yescharacteristic, direct product factor, Sylow
502C2×2−1+4C22×C7311yescharacteristic
503C22×#41C22×C7311yescharacteristic
504C22×M16C22×C7311yescharacteristic
505D4×Q8—21no—
506#548—21no—
507#547—21no—
508#547—22no—
509#546—21no—
510#546—22no—
511#537—21no—
512#537C22×C7311yescharacteristic
513#536—21no—
514#536C22×C7311yescharacteristic
515#525—21no—
516#525C22×C7311yescharacteristic
517C2×C22⋊Q8—21no—
518C2×C22⋊Q8C22×C7311yescharacteristic
519#520C22×C7311yescharacteristic
520C2×#117C22×C7311yescharacteristic
521#485—21no—
522#485—21no—
523#482—21no—
524#482—21no—
525#428C22×C7311yescharacteristic, complemented
526#428C22×C7311yescharacteristic, complemented
527C2×#104C22×C7311yescharacteristic
528C2×#104C22×C7311yescharacteristic
529C2×#104C22×C7311yescharacteristic
530C2×#104C22×C7311yescharacteristic
531C2×#104C22×C7311yescharacteristic, complemented
532C2×#104C22×C7311yescharacteristic, complemented
533#419—21no—
534#418—21no—
535#417C22×C7311yescharacteristic
536#417C22×C7311yescharacteristic
537#417C22×C7311yescharacteristic
538#417C22×C7311yescharacteristic
539#417C22×C7311yescharacteristic, complemented
540#417C22×C7311yescharacteristic, complemented
541#416—21no—
542#416—21no—
543C2×#101C22×C7311yescharacteristic, complemented
544C2×#101C22×C7311yescharacteristic, complemented
545#407C22×C7311yescharacteristic
546#397—22no—
547#391C22×C7311yescharacteristic, complemented
548#391C22×C7311yescharacteristic, complemented
549#387—22no—
550#384C22×C7311yescharacteristic, complemented
551#382C22×C7311yescharacteristic, complemented
552C4×C22⋊C4C22×C7311yescharacteristic
553#343C22×C7311yescharacteristic, complemented
554#343C22×C7311yescharacteristic, complemented
555#339C22×C7311yescharacteristic, complemented
556#339C22×C7311yescharacteristic, complemented
5572−1+4—22no—
5582−1+4—22no—
5592−1+4—41no—
5602−1+4—41no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—22no—
565C2×#41—21no—
566C2×#41—22no—
567C2×#41—22no—
568C2×#41—41no—
569C2×#41—41no—
570C2×#41D4×C7311yescharacteristic
571C2×#41D4×C7311yescharacteristic
572C2×#41C23×C7311yescharacteristic
573C2×#41C23×C7311yescharacteristic
574C2×#41C23×C7311yescharacteristic
575C22×Q8—21no—
576C22×Q8—21no—
577C22×Q8D4×C7311yescharacteristic
578C22×Q8C23×C7311yescharacteristic
579C22×D4—21no—
580C22×D4D4×C7311yescharacteristic
581C23×C4—21no—
582C23×C4C23×C7311yescharacteristic
583C2×M16—21no—
584C2×M16—41no—
585C2×M16—41no—
586C2×M16C23×C7311yescharacteristic
587C2×M16C23×C7311yescharacteristic
588C2×M16C23×C7311yescharacteristic
589C2×M16C23×C7311yescharacteristic
590C22×C8—21no—
591C4⋊Q8—22no—
592C4⋊Q8—21no—
593#124—22no—
594#124—21no—
595#123—22no—
596#123—22no—
597#123—22no—
598#123—21no—
599#123—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8D4×C7311yescharacteristic
612C22⋊Q8D4×C7311yescharacteristic
613#121—22no—
614#121—22no—
615#121—22no—
616#121—21no—
617#121—21no—
618#121—22no—
619#121D4×C7311yescharacteristic
620#121D4×C7311yescharacteristic
621#120—22no—
622#120—21no—
623C4×Q8—21no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—21no—
627C4×D4—22no—
628C4×D4—21no—
629C4×D4—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117C23×C7311yescharacteristic
636C2×C4⋊C4—22no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4D4×C7312yes—
640C2×C4⋊C4C23×C7311yescharacteristic
641C2×C4⋊C4C23×C7311yescharacteristic
642C2×C4⋊C4C23×C7311yescharacteristic
643C2×C22⋊C4—22no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4D4×C7312yes—
647C2×C42—21no—
648C2×C42C23×C7311yescharacteristic
649C2×C42C23×C7311yescharacteristic
650#107—21no—
651#107—21no—
652#106—21no—
653#106—21no—
654#104—22no—
655#104—22no—
656#104—41no—
657#104—41no—
658#104—41no—
659#104—41no—
660#103—21no—
661#103—21no—
662#103—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—
671#102—21no—
672#101—41no—
673#101—41no—
674C22⋊C8—21no—
675C22⋊C8—21no—
676#95—21no—
677#95—22no—
678#95—22no—
679#95—22no—
680C24—21no—
681C24C2×D4×C7311yescharacteristic
682#41—21no—
683#41—21no—
684#41—22no—
685#41—22no—
686#41—21no—
687#41—21no—
688#41—21no—
689#41—21no—
690#41—21no—
691#41—21no—
692#41—21no—
693#41—21no—
694#41—42no—
695#41—42no—
696#41—41no—
697#41—41no—
698#41—42no—
699#41—42no—
700#41—42no—
701#41—42no—
702#41—44no—
703#41—44no—
704#41—42no—
705#41—42no—
706#41#41×C7312yes—
707#41#41×C7312yes—
708C2×Q8—22no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—22no—
717C2×Q8—41no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8C2×D4×C7311yescharacteristic
723C2×Q8C2×D4×C7311yescharacteristic
724C2×Q8C2×D4×C7311yescharacteristic
725C2×D4—21no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4C2×D4×C7311yescharacteristic
740C2×D4C2×D4×C7311yescharacteristic
741C2×D4C2×D4×C7311yescharacteristic
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4C2×D4×C7312yes—
762C22×C4C2×D4×C7311yescharacteristic
763C22×C4C2×D4×C7311yescharacteristic
764C22×C4C2×D4×C7311yescharacteristic
765C22×C4C2×D4×C7311yescharacteristic
766C22×C4C2×D4×C7311yescharacteristic
767C22×C4C2×D4×C7312yes—
768C22×C4C24×C7311yescharacteristic
769M16—21no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—42no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—42no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—21no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—44no—
798C4⋊C4C2×D4×C7311yescharacteristic
799C4⋊C4C2×D4×C7311yescharacteristic
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—21no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—42no—
813C22⋊C4—41no—
814C22⋊C4—41no—
815C42—22no—
816C42—21no—
817C42—21no—
818C42—21no—
819C42—21no—
820C42—21no—
821C42—41no—
822C42—41no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—41no—
829C23—41no—
830C23—42no—
831C23—42no—
832C23—81no—
833C23#120×C7311yescharacteristic
834C23#120×C7311yescharacteristic
835C23C22×D4×C7311yescharacteristic
836Q8—21no—
837Q8—21no—
838Q8—21no—
839Q8—21no—
840Q8—21no—
841Q8—42no—
842Q8—44no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8#123×C7312yes—
848D4—22no—
849D4—22no—
850D4—21no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—21no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—44no—
859D4—42no—
860D4—41no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—81no—
865D4—82no—
866D4#123×C7312yes—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—41no—
904C2×C4—42no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—82no—
909C2×C4#120×C7311yescharacteristic
910C2×C4#120×C7311yescharacteristic
911C2×C4C22×D4×C7311yescharacteristic
912C2×C4C22×D4×C7311yescharacteristic
913C2×C4C2×#41×C7311yescharacteristic
914C2×C4C2×#41×C7311yescharacteristic
915C2×C4H(5,𝔽2)×C7311yescharacteristic
916C2×C4H(5,𝔽2)×C7311yescharacteristic
917C8—41no—
918C8—41no—
919C8—41no—
920C8—41no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—22no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22C2×#120×C7311yescharacteristic
942C22#546×C7311yescharacteristic
943C22#546×C7311yescharacteristic
944C4—21no—
945C4—21no—
946C4—22no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—41no—
951C4—42no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4C2×#123×C7311yescharacteristic
958C4#534×C7311yescharacteristic
959C4#546×C7311yescharacteristic
960C4#546×C7311yescharacteristic
961C2—21no—
962C2—21no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—81no—
967C2—81no—
968C2C73×#240511yescharacteristic
969C2C73×#301811yescharacteristic
970C2C73×#302011yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3093C2semidirect
3. C73×#2896C2semidirect
4. C73×#2499C2semidirect
5. C73×#2040C2semidirect
6. C73×#2039C2semidirect
7. C73×#2038C2semidirect
8. C73×#2038C2semidirect
9. C73×#1901C2semidirect
10. C73×#1871C2semidirect
11. C73×#1860C2semidirect
12. C73×#1859C2semidirect
13. C73×#1793C2semidirect
14. C73×#1793C2semidirect
15. C73×#1789C2semidirect
39. #428×C73C22semidirect
40. #428×C73C22semidirect
45. C2×#104×C73C22semidirect
46. C2×#104×C73C22semidirect
53. #417×C73C22semidirect
54. #417×C73C22semidirect
57. C2×#101×C73C22semidirect
58. C2×#101×C73C22semidirect
61. #391×C73C22semidirect
62. #391×C73C22semidirect
64. #384×C73C22semidirect
65. #382×C73C22semidirect
67. #343×C73C22semidirect
68. #343×C73C22semidirect
69. #339×C73C22semidirect
70. #339×C73C22semidirect
475. #24028C73direct (N × H)
487. #3093C2×C73semidirect
488. #2896C2×C73semidirect
489. #2499C2×C73semidirect
490. #2040C2×C73semidirect
491. #2039C2×C73semidirect
492. #2038C2×C73semidirect
493. #2038C2×C73semidirect
494. #1901C2×C73semidirect
495. #1871C2×C73semidirect
496. #1860C2×C73semidirect
497. #1859C2×C73semidirect
498. #1793C2×C73semidirect
499. #1793C2×C73semidirect
500. #1789C2×C73semidirect
501. C73#24028direct (N × H)
525. #428C22×C73semidirect
526. #428C22×C73semidirect
531. C2×#104C22×C73semidirect
532. C2×#104C22×C73semidirect
539. #417C22×C73semidirect
540. #417C22×C73semidirect
543. C2×#101C22×C73semidirect
544. C2×#101C22×C73semidirect
547. #391C22×C73semidirect
548. #391C22×C73semidirect
550. #384C22×C73semidirect
551. #382C22×C73semidirect
553. #343C22×C73semidirect
554. #343C22×C73semidirect
555. #339C22×C73semidirect
556. #339C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34892
C73×#30932
C73×#28962
C73×#24992
C73×#20402
C73×#20392
C73×#20382
C73×#19012
C73×#18712
C73×#18602
C73×#18592
C73×#17932
C73×#17892
#2402873