Finite Group Databasebeta

← C73×#23115 #32932519

Subgroups — C73×#23115 #32932519

Order 18688.

762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3035C211yesmaximal, characteristic
2C73×#2935C211yesmaximal, characteristic, complemented
3C73×#2925C211yesmaximal, characteristic, complemented
4C73×#1975C211yesmaximal, characteristic, complemented
5C73×#1974C211yesmaximal, characteristic, complemented
6C73×#1963C211yesmaximal, characteristic, complemented
7C73×#1950C211yesmaximal, characteristic, complemented
8C73×#1929C211yesmaximal, characteristic, complemented
9C73×#1929C211yesmaximal, characteristic, complemented
10C73×#1876C211yesmaximal, characteristic, complemented
11C73×#1876C211yesmaximal, characteristic, complemented
12C73×#1768C211yesmaximal, characteristic, complemented
13C73×#1765C211yesmaximal, characteristic, complemented
14C73×#1764C211yesmaximal, characteristic, complemented
15C73×#1759C211yesmaximal, characteristic, complemented
16C2×#135×C73C2211yescharacteristic
17C2×#135×C73C2211yescharacteristic
18C2×#131×C73C2211yescharacteristic
19C2×#131×C73C2211yescharacteristic
20#532×C73C2211yescharacteristic
21C4×#41×C73C2211yescharacteristic
22#464×C73C411yescharacteristic, complemented
23#464×C73C411yescharacteristic, complemented
24#463×C73C411yescharacteristic, complemented
25#463×C73C411yescharacteristic, complemented
26#462×C73C411yescharacteristic, complemented
27#461×C73C411yescharacteristic, complemented
28#460×C73C411yescharacteristic, complemented
29#459×C73C411yescharacteristic, complemented
30#436×C73—21no—
31#435×C73—21no—
32#435×C73—21no—
33C8×D4×C73—21no—
34#433×C73—21no—
35#433×C73—21no—
36#432×C73—21no—
37#431×C73—21no—
38C2×#108×C73C2211yescharacteristic
39C2×#108×C73C2211yescharacteristic
40#423×C73C2211yescharacteristic
41C2×C4⋊C8×C73C2211yescharacteristic
42C2×C4⋊C8×C73C2211yescharacteristic
43C2×#104×C73C2211yescharacteristic
44C2×#104×C73C2211yescharacteristic
45C2×#104×C73C2211yescharacteristic
46C2×#104×C73C2211yescharacteristic
47C2×#104×C73C2211yescharacteristic
48C2×#104×C73C2211yescharacteristic
49#416×C73C2211yescharacteristic
50#416×C73C2211yescharacteristic
51#408×C73C2211yescharacteristic
52#408×C73C2211yescharacteristic
53#408×C73C2211yescharacteristic
54#408×C73C2211yescharacteristic
55#405×C73C2211yescharacteristic
56#405×C73C2211yescharacteristic
57C4×M16×C73C2211yescharacteristic
58C2×#97×C73C2211yescharacteristic
59C2×C4×C8×C73C2211yescharacteristic
60#376×C73C2211yescharacteristic
61#341×C73C2211yescharacteristic
62#341×C73C2211yescharacteristic
63#339×C73C2211yescharacteristic
64#339×C73C2211yescharacteristic
65#336×C73C2211yescharacteristic
66#336×C73C2211yescharacteristic
67C2×#41×C73C2311yescharacteristic
68C2×#41×C73C2311yescharacteristic
69C2×#41×C73C2311yescharacteristic
70#135×C73—41no—
71#135×C73—41no—
72#135×C73—41no—
73#135×C73—41no—
74C2×Q16×C73C2×C411yescharacteristic
75C2×Q16×C73C2×C411yescharacteristic
76C2×SD16×C73C2×C411yescharacteristic
77C2×SD16×C73C2×C411yescharacteristic
78C2×SD16×C73C2×C411yescharacteristic
79C2×SD16×C73C2×C411yescharacteristic
80C2×D8×C73C2×C411yescharacteristic
81C2×D8×C73C2×C411yescharacteristic
82#131×C73—22no—
83#131×C73—22no—
84#131×C73—41no—
85#131×C73—41no—
86C2×M16×C73—21no—
87C2×M16×C73—21no—
88C2×M16×C73C2311yescharacteristic
89C2×M16×C73C2311yescharacteristic
90C2×M16×C73C2311yescharacteristic
91C2×M16×C73C2311yescharacteristic
92C22×C8×C73—21no—
93C22×C8×C73—21no—
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2311yescharacteristic
96C22×C8×C73C2311yescharacteristic
97C22×C8×C73C2311yescharacteristic
98C4⋊Q8×C73C2×C411yescharacteristic
99#127×C73C2×C411yescharacteristic
100#124×C73C2×C411yescharacteristic
101#124×C73C2×C411yescharacteristic
102#121×C73—21no—
103#121×C73—21no—
104C4×Q8×C73C2×C411yescharacteristic
105C4×Q8×C73C2×C411yescharacteristic
106C4×D4×C73—21no—
107C4×D4×C73—21no—
108C4×D4×C73—21no—
109C4×D4×C73—21no—
110C4×D4×C73C2×C411yescharacteristic
111C4×D4×C73C2×C411yescharacteristic
112#117×C73—21no—
113#117×C73C2311yescharacteristic
114C2×C42×C73—21no—
115C2×C42×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118#108×C73—41no—
119#108×C73—41no—
120C4⋊C8×C73—21no—
121C4⋊C8×C73—21no—
122C4⋊C8×C73C2×C411yescharacteristic
123C4⋊C8×C73C2×C411yescharacteristic
124C4⋊C8×C73C2×C411yescharacteristic
125C4⋊C8×C73C2×C411yescharacteristic
126C4⋊C8×C73D411yescharacteristic
127C4⋊C8×C73D411yescharacteristic
128C4⋊C8×C73D411yescharacteristic
129C4⋊C8×C73D411yescharacteristic
130#104×C73—22no—
131#104×C73—22no—
132#104×C73—22no—
133#104×C73—22no—
134#104×C73—41no—
135#104×C73—41no—
136#103×C73C2×C411yescharacteristic
137#103×C73C2×C411yescharacteristic
138#103×C73C2×C411yescharacteristic
139#103×C73C2×C411yescharacteristic
140#102×C73C2×C411yescharacteristic
141#102×C73C2×C411yescharacteristic
142#102×C73C2×C411yescharacteristic
143#102×C73C2×C411yescharacteristic
144C22⋊C8×C73—21no—
145C22⋊C8×C73—21no—
146C22⋊C8×C73—21no—
147C22⋊C8×C73—21no—
148C22⋊C8×C73—21no—
149C22⋊C8×C73—21no—
150C22⋊C8×C73—21no—
151C22⋊C8×C73—21no—
152#97×C73—21no—
153#97×C73—21no—
154#97×C73—21no—
155#97×C73—41no—
156C4×C8×C73—21no—
157C4×C8×C73—21no—
158C4×C8×C73—21no—
159C4×C8×C73—41no—
160#95×C73—21no—
161#95×C73—21no—
162#41×C73—21no—
163#41×C73—21no—
164#41×C73—21no—
165#41×C73—21no—
166#41×C73—21no—
167#41×C73—21no—
168#41×C73—21no—
169#41×C73—21no—
170#41×C73—21no—
171#41×C73—21no—
172#41×C73—21no—
173#41×C73—21no—
174C2×Q8×C73C22×C411yescharacteristic
175C2×Q8×C73C22×C411yescharacteristic
176C2×Q8×C73C22×C411yescharacteristic
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73C22×C411yescharacteristic
183C2×D4×C73C22×C411yescharacteristic
184C2×D4×C73C22×C411yescharacteristic
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73#4111yescharacteristic
193C22×C4×C73#4111yescharacteristic
194C22×C4×C73C2411yescharacteristic
195Q16×C73—41no—
196Q16×C73—41no—
197SD16×C73—41no—
198SD16×C73—41no—
199SD16×C73—41no—
200SD16×C73—41no—
201D8×C73—41no—
202D8×C73—41no—
203M16×C73—21no—
204M16×C73—21no—
205M16×C73—21no—
206M16×C73—21no—
207M16×C73—21no—
208M16×C73—21no—
209M16×C73—21no—
210M16×C73—42no—
211M16×C73—42no—
212M16×C73#4112yes—
213C2×C8×C73—21no—
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—42no—
226C2×C8×C73—42no—
227C2×C8×C73C22×C411yescharacteristic
228C2×C8×C73C22×C411yescharacteristic
229C2×C8×C73C22×C411yescharacteristic
230C2×C8×C73C22×C411yescharacteristic
231C2×C8×C73C2×D411yescharacteristic
232C2×C8×C73C2×D411yescharacteristic
233C2×C8×C73C2×D411yescharacteristic
234C2×C8×C73C2×D411yescharacteristic
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73C22×C411yescharacteristic
240C4⋊C4×C73C22×C411yescharacteristic
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—21no—
248C42×C73—21no—
249C42×C73—21no—
250C42×C73—21no—
251C42×C73—21no—
252C42×C73—21no—
253C42×C73—21no—
254C42×C73C22×C411yescharacteristic
255C42×C73C22×C411yescharacteristic
256C42×C73C2×D411yescharacteristic
257C42×C73C2×D411yescharacteristic
258C42×C73#4112yes—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73C2×#4111yescharacteristic
263Q8×C73—21no—
264Q8×C73—21no—
265Q8×C73—21no—
266Q8×C73—21no—
267Q8×C73—21no—
268Q8×C73—21no—
269D4×C73—21no—
270D4×C73—21no—
271D4×C73—21no—
272D4×C73—21no—
273D4×C73—21no—
274D4×C73—21no—
275D4×C73—42no—
276D4×C73—41no—
277D4×C73—41no—
278D4×C73—41no—
279D4×C73—41no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—81no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—22no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—42no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—81no—
304C2×C4×C73C4×D411yescharacteristic
305C2×C4×C73C4×D411yescharacteristic
306C2×C4×C73C4×D411yescharacteristic
307C2×C4×C73C4×D411yescharacteristic
308C2×C4×C73C23×C411yescharacteristic
309C2×C4×C73C22×D411yescharacteristic
310C2×C4×C73C2×#4111yescharacteristic
311C2×C4×C73C2×#4111yescharacteristic
312C2×C4×C73H(5,𝔽2)11yescharacteristic
313C2×C4×C73H(5,𝔽2)11yescharacteristic
314C8×C73—21no—
315C8×C73—21no—
316C8×C73—21no—
317C8×C73—21no—
318C8×C73—21no—
319C8×C73—21no—
320C8×C73—21no—
321C8×C73—21no—
322C8×C73—22no—
323C8×C73—41no—
324C8×C73—41no—
325C8×C73—41no—
326C22×C73—21no—
327C22×C73—21no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73C2×C4×D411yescharacteristic
338C22×C73#55311yescharacteristic
339C22×C73#55511yescharacteristic
340C4×C73—21no—
341C4×C73—21no—
342C4×C73—21no—
343C4×C73—21no—
344C4×C73—42no—
345C4×C73—41no—
346C4×C73—41no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—81no—
351C4×C73C4×#4111yescharacteristic
352C4×C73#51811yescharacteristic
353C4×C73#54611yescharacteristic
354C4×C73#55011yescharacteristic
355#23115C7311yesmaximal, characteristic, direct product factor, Sylow
356C2×C73—21no—
357C2×C73—21no—
358C2×C73—81no—
359C2×C73—81no—
360C2×C73—81no—
361C2×C73#236311yescharacteristic
362C2×C73#295511yescharacteristic
363C2×C73#295711yescharacteristic
364#3035C2×C7311yescharacteristic
365#2935C2×C7311yescharacteristic, complemented
366#2925C2×C7311yescharacteristic, complemented
367#1975C2×C7311yescharacteristic, complemented
368#1974C2×C7311yescharacteristic, complemented
369#1963C2×C7311yescharacteristic, complemented
370#1950C2×C7311yescharacteristic, complemented
371#1929C2×C7311yescharacteristic, complemented
372#1929C2×C7311yescharacteristic, complemented
373#1876C2×C7311yescharacteristic, complemented
374#1876C2×C7311yescharacteristic, complemented
375#1768C2×C7311yescharacteristic, complemented
376#1765C2×C7311yescharacteristic, complemented
377#1764C2×C7311yescharacteristic, complemented
378#1759C2×C7311yescharacteristic, complemented
379C73#2311511yescharacteristic, direct product factor, Sylow
380C2×#135C22×C7311yescharacteristic
381C2×#135C22×C7311yescharacteristic
382C2×#131C22×C7311yescharacteristic
383C2×#131C22×C7311yescharacteristic
384#532C22×C7311yescharacteristic
385C4×#41C22×C7311yescharacteristic
386#464C4×C7311yescharacteristic, complemented
387#464C4×C7311yescharacteristic, complemented
388#463C4×C7311yescharacteristic, complemented
389#463C4×C7311yescharacteristic, complemented
390#462C4×C7311yescharacteristic, complemented
391#461C4×C7311yescharacteristic, complemented
392#460C4×C7311yescharacteristic, complemented
393#459C4×C7311yescharacteristic, complemented
394#436—21no—
395#435—21no—
396#435—21no—
397C8×D4—21no—
398#433—21no—
399#433—21no—
400#432—21no—
401#431—21no—
402C2×#108C22×C7311yescharacteristic
403C2×#108C22×C7311yescharacteristic
404#423C22×C7311yescharacteristic
405C2×C4⋊C8C22×C7311yescharacteristic
406C2×C4⋊C8C22×C7311yescharacteristic
407C2×#104C22×C7311yescharacteristic
408C2×#104C22×C7311yescharacteristic
409C2×#104C22×C7311yescharacteristic
410C2×#104C22×C7311yescharacteristic
411C2×#104C22×C7311yescharacteristic
412C2×#104C22×C7311yescharacteristic
413#416C22×C7311yescharacteristic
414#416C22×C7311yescharacteristic
415#408C22×C7311yescharacteristic
416#408C22×C7311yescharacteristic
417#408C22×C7311yescharacteristic
418#408C22×C7311yescharacteristic
419#405C22×C7311yescharacteristic
420#405C22×C7311yescharacteristic
421C4×M16C22×C7311yescharacteristic
422C2×#97C22×C7311yescharacteristic
423C2×C4×C8C22×C7311yescharacteristic
424#376C22×C7311yescharacteristic
425#341C22×C7311yescharacteristic
426#341C22×C7311yescharacteristic
427#339C22×C7311yescharacteristic
428#339C22×C7311yescharacteristic
429#336C22×C7311yescharacteristic
430#336C22×C7311yescharacteristic
431C2×#41C23×C7311yescharacteristic
432C2×#41C23×C7311yescharacteristic
433C2×#41C23×C7311yescharacteristic
434#135—41no—
435#135—41no—
436#135—41no—
437#135—41no—
438C2×Q16C2×C4×C7311yescharacteristic
439C2×Q16C2×C4×C7311yescharacteristic
440C2×SD16C2×C4×C7311yescharacteristic
441C2×SD16C2×C4×C7311yescharacteristic
442C2×SD16C2×C4×C7311yescharacteristic
443C2×SD16C2×C4×C7311yescharacteristic
444C2×D8C2×C4×C7311yescharacteristic
445C2×D8C2×C4×C7311yescharacteristic
446#131—22no—
447#131—22no—
448#131—41no—
449#131—41no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16C23×C7311yescharacteristic
453C2×M16C23×C7311yescharacteristic
454C2×M16C23×C7311yescharacteristic
455C2×M16C23×C7311yescharacteristic
456C22×C8—21no—
457C22×C8—21no—
458C22×C8C23×C7311yescharacteristic
459C22×C8C23×C7311yescharacteristic
460C22×C8C23×C7311yescharacteristic
461C22×C8C23×C7311yescharacteristic
462C4⋊Q8C2×C4×C7311yescharacteristic
463#127C2×C4×C7311yescharacteristic
464#124C2×C4×C7311yescharacteristic
465#124C2×C4×C7311yescharacteristic
466#121—21no—
467#121—21no—
468C4×Q8C2×C4×C7311yescharacteristic
469C4×Q8C2×C4×C7311yescharacteristic
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4C2×C4×C7311yescharacteristic
475C4×D4C2×C4×C7311yescharacteristic
476#117—21no—
477#117C23×C7311yescharacteristic
478C2×C42—21no—
479C2×C42C23×C7311yescharacteristic
480C2×C42C23×C7311yescharacteristic
481C2×C42C23×C7311yescharacteristic
482#108—41no—
483#108—41no—
484C4⋊C8—21no—
485C4⋊C8—21no—
486C4⋊C8C2×C4×C7311yescharacteristic
487C4⋊C8C2×C4×C7311yescharacteristic
488C4⋊C8C2×C4×C7311yescharacteristic
489C4⋊C8C2×C4×C7311yescharacteristic
490C4⋊C8D4×C7311yescharacteristic
491C4⋊C8D4×C7311yescharacteristic
492C4⋊C8D4×C7311yescharacteristic
493C4⋊C8D4×C7311yescharacteristic
494#104—22no—
495#104—22no—
496#104—22no—
497#104—22no—
498#104—41no—
499#104—41no—
500#103C2×C4×C7311yescharacteristic
501#103C2×C4×C7311yescharacteristic
502#103C2×C4×C7311yescharacteristic
503#103C2×C4×C7311yescharacteristic
504#102C2×C4×C7311yescharacteristic
505#102C2×C4×C7311yescharacteristic
506#102C2×C4×C7311yescharacteristic
507#102C2×C4×C7311yescharacteristic
508C22⋊C8—21no—
509C22⋊C8—21no—
510C22⋊C8—21no—
511C22⋊C8—21no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516#97—21no—
517#97—21no—
518#97—21no—
519#97—41no—
520C4×C8—21no—
521C4×C8—21no—
522C4×C8—21no—
523C4×C8—41no—
524#95—21no—
525#95—21no—
526#41—21no—
527#41—21no—
528#41—21no—
529#41—21no—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538C2×Q8C22×C4×C7311yescharacteristic
539C2×Q8C22×C4×C7311yescharacteristic
540C2×Q8C22×C4×C7311yescharacteristic
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4C22×C4×C7311yescharacteristic
547C2×D4C22×C4×C7311yescharacteristic
548C2×D4C22×C4×C7311yescharacteristic
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4#41×C7311yescharacteristic
557C22×C4#41×C7311yescharacteristic
558C22×C4C24×C7311yescharacteristic
559Q16—41no—
560Q16—41no—
561SD16—41no—
562SD16—41no—
563SD16—41no—
564SD16—41no—
565D8—41no—
566D8—41no—
567M16—21no—
568M16—21no—
569M16—21no—
570M16—21no—
571M16—21no—
572M16—21no—
573M16—21no—
574M16—42no—
575M16—42no—
576M16#41×C7312yes—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—42no—
590C2×C8—42no—
591C2×C8C22×C4×C7311yescharacteristic
592C2×C8C22×C4×C7311yescharacteristic
593C2×C8C22×C4×C7311yescharacteristic
594C2×C8C22×C4×C7311yescharacteristic
595C2×C8C2×D4×C7311yescharacteristic
596C2×C8C2×D4×C7311yescharacteristic
597C2×C8C2×D4×C7311yescharacteristic
598C2×C8C2×D4×C7311yescharacteristic
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4C22×C4×C7311yescharacteristic
604C4⋊C4C22×C4×C7311yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42C22×C4×C7311yescharacteristic
619C42C22×C4×C7311yescharacteristic
620C42C2×D4×C7311yescharacteristic
621C42C2×D4×C7311yescharacteristic
622C42#41×C7312yes—
623C23—21no—
624C23—21no—
625C23—21no—
626C23C2×#41×C7311yescharacteristic
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—21no—
632Q8—21no—
633D4—21no—
634D4—21no—
635D4—21no—
636D4—21no—
637D4—21no—
638D4—21no—
639D4—42no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—81no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—81no—
668C2×C4C4×D4×C7311yescharacteristic
669C2×C4C4×D4×C7311yescharacteristic
670C2×C4C4×D4×C7311yescharacteristic
671C2×C4C4×D4×C7311yescharacteristic
672C2×C4C23×C4×C7311yescharacteristic
673C2×C4C22×D4×C7311yescharacteristic
674C2×C4C2×#41×C7311yescharacteristic
675C2×C4C2×#41×C7311yescharacteristic
676C2×C4H(5,𝔽2)×C7311yescharacteristic
677C2×C4H(5,𝔽2)×C7311yescharacteristic
678C8—21no—
679C8—21no—
680C8—21no—
681C8—21no—
682C8—21no—
683C8—21no—
684C8—21no—
685C8—21no—
686C8—22no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—21no—
691C22—21no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22C2×C4×D4×C7311yescharacteristic
702C22#553×C7311yescharacteristic
703C22#555×C7311yescharacteristic
704C4—21no—
705C4—21no—
706C4—21no—
707C4—21no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—81no—
715C4C4×#41×C7311yescharacteristic
716C4#518×C7311yescharacteristic
717C4#546×C7311yescharacteristic
718C4#550×C7311yescharacteristic
719C2—21no—
720C2—21no—
721C2—81no—
722C2—81no—
723C2—81no—
724C2C73×#236311yescharacteristic
725C2C73×#295511yescharacteristic
726C2C73×#295711yescharacteristic
subgroupG/H
centerC2×C4×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
socleC22×C73C2×C4×D4
prime radicalC73×#3035C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C73 ◁ C2×C4⋊C8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2935C2semidirect
3. C73×#2925C2semidirect
4. C73×#1975C2semidirect
5. C73×#1974C2semidirect
6. C73×#1963C2semidirect
7. C73×#1950C2semidirect
8. C73×#1929C2semidirect
9. C73×#1929C2semidirect
10. C73×#1876C2semidirect
11. C73×#1876C2semidirect
12. C73×#1768C2semidirect
13. C73×#1765C2semidirect
14. C73×#1764C2semidirect
15. C73×#1759C2semidirect
22. #464×C73C4semidirect
23. #464×C73C4semidirect
24. #463×C73C4semidirect
25. #463×C73C4semidirect
26. #462×C73C4semidirect
27. #461×C73C4semidirect
28. #460×C73C4semidirect
29. #459×C73C4semidirect
355. #23115C73direct (N × H)
365. #2935C2×C73semidirect
366. #2925C2×C73semidirect
367. #1975C2×C73semidirect
368. #1974C2×C73semidirect
369. #1963C2×C73semidirect
370. #1950C2×C73semidirect
371. #1929C2×C73semidirect
372. #1929C2×C73semidirect
373. #1876C2×C73semidirect
374. #1876C2×C73semidirect
375. #1768C2×C73semidirect
376. #1765C2×C73semidirect
377. #1764C2×C73semidirect
378. #1759C2×C73semidirect
379. C73#23115direct (N × H)
386. #464C4×C73semidirect
387. #464C4×C73semidirect
388. #463C4×C73semidirect
389. #463C4×C73semidirect
390. #462C4×C73semidirect
391. #461C4×C73semidirect
392. #460C4×C73semidirect
393. #459C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30352
C73×#29352
C73×#29252
C73×#19752
C73×#19742
C73×#19632
C73×#19502
C73×#19292
C73×#18762
C73×#17682
C73×#17652
C73×#17642
C73×#17592
#2311573