Finite Group Databasebeta

← #13520976

Subgroups — #13520976

Order 1792.

2626 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90287C211yesmaximal, characteristic, complemented
2C2×#90291C211yesmaximal, characteristic, complemented
3C7×#2619C211yesmaximal, characteristic, complemented
4#11740626C211yesmaximal, characteristic, complemented
5Dic7×#127C211yesmaximal, characteristic, complemented
6#11740122C211yesmaximal, characteristic, complemented
7#11740121C211yesmaximal, characteristic, complemented
8#11739732C211yesmaximal, characteristic, complemented
9Dic7×#117C211yesmaximal, characteristic, complemented
10#11734441C214yesmaximal, complemented
11#11734335C214yesmaximal, complemented
12#11734152C214yesmaximal, complemented
13#11734110C214yesmaximal, complemented
14#11733819C211yesmaximal, characteristic, complemented
15#11733818C211yesmaximal, characteristic, complemented
16#11733738C211yesmaximal, characteristic, complemented
17#11733737C211yesmaximal, characteristic, complemented
18#11731641C211yesmaximal, characteristic, complemented
19#11731594C211yesmaximal, characteristic, complemented
20C22×#1159C2212yes—
21C2×C7×#127C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C7×#117C2211yescharacteristic
25C2×#6503C2211yescharacteristic
26C2×#6503C2211yescharacteristic
27C2×#6502C2212yes—
28C2×#6499C2211yescharacteristic
29C2×#6499C2211yescharacteristic
30C2×#6498C2212yes—
31C2×D4×Dic7C2212yes—
32C2×D4×Dic7C2211yescharacteristic
33C2×D4×Dic7C2211yescharacteristic
34C2×D4×Dic7C2214yes—
35C2×#6493C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39#90291—28no—
40#90287—28no—
41C2×#6456C2211yescharacteristic
42C2×#6453C2211yescharacteristic
43C2×#6451C2211yescharacteristic
44C2×#6450C2211yescharacteristic
45C2×#6448C2212yes—
46C2×(C22⋊D7)⋊C4C2212yes—
47C2×(C22⋊D7)⋊C4C2214yes—
48C2×#6442C2212yes—
49C2×#6440C2212yes—
50C2×#6438C2211yescharacteristic
51C7×#394C2214yes—
52C7×#392C2214yes—
53C7×#390C2211yescharacteristic
54C7×#390C2211yescharacteristic
55C7×#382C2211yescharacteristic
56#89995C2214yes—
57#89995C2214yes—
58#89995C2214yes—
59#89994C2214yes—
60#89993C2211yescharacteristic
61#89993C2211yescharacteristic
62#89993C2214yes—
63#89766C2214yes—
64#89760C2211yescharacteristic
65#89749C2211yescharacteristic
66#89748C2211yescharacteristic
67C4⋊C4×Dic7C2212yes—
68C4⋊C4×Dic7C2212yes—
69#89746C2211yescharacteristic
70#89733C2214yes—
71#89733C2214yes—
72#89733C2214yes—
73#89731C2214yes—
74#89729C2214yes—
75#89724C2214yes—
76#89720C2214yes—
77#89719C2214yes—
78#89716C2214yes—
79C22⋊C4×Dic7C2212yes—
80C22⋊C4×Dic7C2212yes—
81C22⋊C4×Dic7C2214yes—
82#89711C2211yescharacteristic
83#89707C2211yescharacteristic
84#89704C2211yescharacteristic
85#89704C2211yescharacteristic
86C42×Dic7C2211yescharacteristic
87C42×Dic7C2211yescharacteristic
88#89701C2211yescharacteristic
89#89441C2214yes—
90#89438C2214yes—
91#89429C2214yes—
92#89428C2214yes—
93#34624—71nomaximal, Sylow
94C22×C7×D4C2311yescharacteristic
95C22×C7×D4C2311yescharacteristic
96C22×C7×D4C2312yes—
97C22×C7×D4C2314yes—
98C22×C7×D4C2312yes—
99C23×C4×C7C2311yescharacteristic
100C22×C22⋊D7C2312yes—
101C22×C22⋊D7C2314yes—
102C22×C22⋊D7C2312yes—
103C22×C22⋊D7C2312yes—
104C23×Dic7C2312yes—
105C23×Dic7C2312yes—
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2311yescharacteristic
108C2×#1159—28no—
109C2×#1159—48no—
110C22×D28C2311yescharacteristic
111C22×C4×D7C2312yes—
112C22×Dic14C2311yescharacteristic
113C22×Dic14C2312yes—
114C7×#127—24no—
115C7×#121—24no—
116C7×#121—24no—
117C7×#117—24no—
118C2×C7×C4⋊C4C2311yescharacteristic
119C2×C7×C4⋊C4C2311yescharacteristic
120C2×C7×C4⋊C4C2312yes—
121C2×C7×C22⋊C4C2312yes—
122C2×C7×C22⋊C4C2312yes—
123C2×C7×C22⋊C4C2312yes—
124C2×C7×C22⋊C4C2314yes—
125C2×C7×C22⋊C4C2314yes—
126C2×C42×C7C2311yescharacteristic
127C2×C42×C7C2311yescharacteristic
128C2×C22⋊Dic7C2312yes—
129C2×C22⋊Dic7C2312yes—
130C2×C22⋊Dic7C2312yes—
131C2×C22⋊Dic7C2312yes—
132C2×C22⋊Dic7C2312yes—
133C2×C22⋊Dic7C2312yes—
134C2×C22⋊Dic7C2314yes—
135C2×C22⋊Dic7C2314yes—
136C2×C22⋊Dic7C2314yes—
137#6503—24no—
138#6503—24no—
139#6502—28no—
140#6499—24no—
141#6499—24no—
142#6498—28no—
143D4×Dic7—28no—
144D4×Dic7—24no—
145D4×Dic7—24no—
146D4×Dic7—48no—
147#6493—24no—
148C2×(C2×D7)⋊C4C2314yes—
149C2×(C2×D7)⋊C4C2312yes—
150C2×(C2×D7)⋊C4C2312yes—
151C2×(C2×D7)⋊C4C2314yes—
152C2×(C2×D7)⋊C4C2314yes—
153#6489—24no—
154C2×C4⋊Dic7C2312yes—
155C2×C4⋊Dic7C2311yescharacteristic
156C2×C4⋊Dic7C2311yescharacteristic
157C2×C4⋊Dic7C2312yes—
158C2×C4⋊Dic7C2314yes—
159#6487—24no—
160C2×Dic7⋊C4C2312yes—
161C2×Dic7⋊C4C2312yes—
162C2×Dic7⋊C4C2312yes—
163C2×Dic7⋊C4C2312yes—
164C2×Dic7⋊C4C2314yes—
165C2×C4×Dic7D418yescomplemented
166C2×C4×Dic7C2312yes—
167C2×C4×Dic7C2312yes—
168C2×C4×Dic7C2312yes—
169C2×C4×Dic7C2311yescharacteristic
170C2×C4×Dic7C2312yes—
171C2×C4×Dic7C2312yes—
172C2×C4×Dic7C2311yescharacteristic
173C2×C4×Dic7C2311yescharacteristic
174C2×C4×Dic7C2311yescharacteristic
175C2×C4×Dic7C2311yescharacteristic
176C2×C4×Dic7C2311yescharacteristic
177#6456—24no—
178#6453—24no—
179#6451—24no—
180#6450—24no—
181#6448—28no—
182(C22⋊D7)⋊C4—28no—
183(C22⋊D7)⋊C4—48no—
184#6442—28no—
185#6440—28no—
186#6438—24no—
187C7×#95C2314yes—
188C7⋊#95C2312yes—
189C7⋊#95C2314yes—
190C7⋊#95C2312yes—
191C7⋊#95C2314yes—
192C7⋊#95C2314yes—
193C7⋊#95C2312yes—
194C7⋊#95C2312yes—
195C2×#532—71no—
196C2×#529—71no—
197#2662—74no—
198#2661—74no—
199#2660—71no—
200#2657—71no—
201#2641—71no—
202#2640—71no—
203#2620—71no—
204#2620—71no—
205#2619—71no—
206#2619D711yescharacteristic, complemented
207#2392—74no—
208#2388—74no—
209C4×#127—71no—
210C4×#127—71no—
211C4×#124—71no—
212C4×#124—71no—
213C4×#117—71no—
214C24×C7C2412yes—
215C24×C7C2412yes—
216C24×C7C2411yescharacteristic
217C23×D7C2412yes—
218C2×C7×D4—24no—
219C2×C7×D4—24no—
220C2×C7×D4—22no—
221C2×C7×D4—22no—
222C2×C7×D4—22no—
223C2×C7×D4—22no—
224C2×C7×D4—28no—
225C2×C7×D4—22no—
226C2×C7×D4—22no—
227C2×C7×D4—44no—
228C2×C7×D4—44no—
229C2×C7×D4—44no—
230C2×C7×D4—44no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7C2×D414yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
236C22×C4×C7C2412yes—
237C22×C4×C7C2411yescharacteristic
238C22×C4×C7C2412yes—
239C22×C4×C7C2411yescharacteristic
240C2×C22⋊D7—24no—
241C2×C22⋊D7—24no—
242C2×C22⋊D7—24no—
243C2×C22⋊D7—28no—
244C2×C22⋊D7—44no—
245C2×C22⋊D7—44no—
246C2×C22⋊D7—44no—
247C2×C22⋊D7—44no—
248C2×C22⋊D7—44no—
249C22×Dic7—24no—
250C22×Dic7—24no—
251C22×Dic7—24no—
252C22×Dic7—28no—
253C22×Dic7—28no—
254C22×Dic7—42no—
255C22×Dic7C2×D414yes—
256C22×Dic7C2×D414yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2411yescharacteristic
262C22×Dic7C2411yescharacteristic
263C22×Dic7C2411yescharacteristic
264C22×Dic7C2412yes—
265C22×Dic7C2411yescharacteristic
266#1159—432no—
267C2×D28—22no—
268C2×D28—22no—
269C2×D28—22no—
270C2×C4×D7—24no—
271C2×C4×D7—28no—
272C2×Dic14—22no—
273C2×Dic14—22no—
274C2×Dic14—22no—
275C2×Dic14—24no—
276C2×Dic14—44no—
277C7×C4⋊C4—22no—
278C7×C4⋊C4—22no—
279C7×C4⋊C4—24no—
280C7×C22⋊C4—24no—
281C7×C22⋊C4—24no—
282C7×C22⋊C4—24no—
283C7×C22⋊C4—44no—
284C7×C22⋊C4—44no—
285C42×C7—22no—
286C42×C7#4114yescomplemented
287C22⋊Dic7—24no—
288C22⋊Dic7—24no—
289C22⋊Dic7—24no—
290C22⋊Dic7—24no—
291C22⋊Dic7—24no—
292C22⋊Dic7—24no—
293C22⋊Dic7—28no—
294C22⋊Dic7—44no—
295C22⋊Dic7—44no—
296(C2×D7)⋊C4—24no—
297(C2×D7)⋊C4—28no—
298(C2×D7)⋊C4—24no—
299(C2×D7)⋊C4—44no—
300(C2×D7)⋊C4—44no—
301C4⋊Dic7—22no—
302C4⋊Dic7—22no—
303C4⋊Dic7—24no—
304C4⋊Dic7—24no—
305C4⋊Dic7—44no—
306Dic7⋊C4—24no—
307Dic7⋊C4—24no—
308Dic7⋊C4—24no—
309Dic7⋊C4—24no—
310Dic7⋊C4—44no—
311C4×Dic7—22no—
312C4×Dic7—24no—
313C4×Dic7—24no—
314C4×Dic7—24no—
315C4×Dic7—42no—
316C4×Dic7—42no—
317C4×Dic7C2×D414yes—
318C4×Dic7C2×D414yes—
319C4×Dic7C2×D414yes—
320C4×Dic7C2×D414yes—
321C4×Dic7#4114yescomplemented
322C22×#41—72no—
323#532—148no—
324C2×C4⋊Q8—71no—
325C2×#127—71no—
326C2×#127—71no—
327C2×#127C2×D711yescharacteristic
328#529—148no—
329C2×#126—72no—
330C2×#125—71no—
331C2×#124—71no—
332C2×#124—71no—
333C2×#124—72no—
334C2×#124—71no—
335C2×#123—72no—
336C2×C22⋊Q8—71no—
337C2×#121—72no—
338C2×#121—71no—
339C2×#121C2×D711yescharacteristic
340C2×#121C2×D711yescharacteristic
341C2×C4×Q8—71no—
342C2×C4×D4—71no—
343C2×C4×D4—71no—
344C2×C4×D4—72no—
345C2×C4×D4—74no—
346C2×C4×D4—71no—
347C2×C4×D4—72no—
348C2×C4×D4—74no—
349C2×#117—71no—
350C2×#117—72no—
351C2×#117C2×D711yescharacteristic
352C22×C42—71no—
353#398—74no—
354#397—74no—
355#396—74no—
356#396—74no—
357#395—74no—
358#394—74no—
359#394—74no—
360#394—74no—
361#394—74no—
362#394—74no—
363#394C2×D714yes—
364#393—74no—
365#392—74no—
366#392—74no—
367#392—74no—
368#392C2×D714yes—
369#391—71no—
370#391—71no—
371#390—71no—
372#390—71no—
373#390—74no—
374#390—71no—
375#390—74no—
376#390—71no—
377#390C2×D711yescharacteristic
378#390C2×D711yescharacteristic
379#388—74no—
380#388—74no—
381#384—71no—
382#384—71no—
383#382—71no—
384#382C2×D711yescharacteristic
385C4×C4⋊C4—72no—
386C4×C4⋊C4—72no—
387C4×C22⋊C4—72no—
388C4×C22⋊C4—74no—
389C4×C22⋊C4—72no—
390C4×C22⋊C4—74no—
391#376—71no—
392#376—71no—
393C43—71no—
394C43—71no—
395C23×C7—21no—
396C23×C7—21no—
397C23×C7—22no—
398C23×C7—22no—
399C23×C7—22no—
400C23×C7—22no—
401C23×C7—22no—
402C23×C7—22no—
403C23×C7—22no—
404C23×C7—22no—
405C23×C7—24no—
406C23×C7—24no—
407C23×C7—24no—
408C23×C7—24no—
409C23×C7C22×D412yes—
410C23×C7C2511yescharacteristic
411C22×D7—22no—
412C22×D7—22no—
413C22×D7—22no—
414C22×D7—24no—
415C22×D7—24no—
416C7×D4—416no—
417C7×D4—48no—
418C7×D4—48no—
419C7×D4—44no—
420C7×D4—44no—
421C2×C4×C7—21no—
422C2×C4×C7—21no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—28no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—24no—
431C2×C4×C7—22no—
432C2×C4×C7—24no—
433C2×C4×C7C22×D412yes—
434C2×C4×C7C22×D412yes—
435C2×C4×C7C2×#4114yes—
436C2×C4×C7C2×#4112yes—
437C2×C4×C7C2×#4112yes—
438C22⋊D7—48no—
439C22⋊D7—48no—
440C22⋊D7—416no—
441C22⋊D7—48no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—28no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—24no—
456C2×Dic7—24no—
457C2×Dic7—22no—
458C2×Dic7—44no—
459C2×Dic7—48no—
460C2×Dic7—48no—
461C2×Dic7C22×D412yes—
462C2×Dic7C22×D412yes—
463C2×Dic7C22×D412yes—
464C2×Dic7C22×D412yes—
465C2×Dic7C2×#4114yes—
466C2×Dic7H(5,𝔽2)14yes—
467D28—44no—
468C4×D7—48no—
469Dic14—48no—
470Dic14—44no—
471C2×#41—148no—
472C2×#41—288no—
473C22×Q8—71no—
474C22×Q8—72no—
475C22×D4—72no—
476C22×D4—74no—
477C22×D4—72no—
478C22×D4—72no—
479C22×D4—71no—
480C22×D4C22×D711yescharacteristic
481C22×D4C22×D711yescharacteristic
482C22×D4C22×D712yes—
483C22×D4C22×D714yes—
484C22×D4C22×D712yes—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—72no—
488C23×C4—72no—
489C23×C4—72no—
490C23×C4C22×D711yescharacteristic
491C4⋊Q8—144no—
492#127—24no—
493#127—144no—
494#127—144no—
495#126—148no—
496#125—144no—
497#124—148no—
498#124—144no—
499#124—144no—
500#124—144no—
501#123—148no—
502C22⋊Q8—144no—
503#121—24no—
504#121—24no—
505#121—148no—
506#121—144no—
507C4×Q8—144no—
508C4×D4—148no—
509C4×D4—144no—
510C4×D4—144no—
511C4×D4—144no—
512C4×D4—148no—
513C4×D4—288no—
514C4×D4—288no—
515#117—24no—
516#117—148no—
517#117—144no—
518C2×C4⋊C4—72no—
519C2×C4⋊C4—72no—
520C2×C4⋊C4—72no—
521C2×C4⋊C4—72no—
522C2×C4⋊C4—71no—
523C2×C4⋊C4—71no—
524C2×C4⋊C4—72no—
525C2×C4⋊C4—72no—
526C2×C4⋊C4—74no—
527C2×C4⋊C4—74no—
528C2×C4⋊C4C22×D712yes—
529C2×C4⋊C4C22×D711yescharacteristic
530C2×C4⋊C4C22×D711yescharacteristic
531C2×C22⋊C4—72no—
532C2×C22⋊C4—72no—
533C2×C22⋊C4—72no—
534C2×C22⋊C4—72no—
535C2×C22⋊C4—72no—
536C2×C22⋊C4—72no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—72no—
539C2×C22⋊C4—72no—
540C2×C22⋊C4—74no—
541C2×C22⋊C4—74no—
542C2×C22⋊C4—74no—
543C2×C22⋊C4—74no—
544C2×C22⋊C4—74no—
545C2×C22⋊C4C22×D712yes—
546C2×C22⋊C4C22×D712yes—
547C2×C22⋊C4C22×D712yes—
548C2×C22⋊C4C22×D714yes—
549C2×C22⋊C4C22×D714yes—
550C2×C42—78no—
551C2×C42—71no—
552C2×C42—71no—
553C2×C42—71no—
554C2×C42—71no—
555C2×C42—71no—
556C2×C42—72no—
557C2×C42—71no—
558C2×C42—72no—
559C2×C42—72no—
560C2×C42—72no—
561C2×C42—72no—
562C2×C42C22×D711yescharacteristic
563C2×C42C22×D711yescharacteristic
564#95—72no—
565#95—72no—
566#95—72no—
567#95—72no—
568#95—74no—
569#95—74no—
570#95—74no—
571#95C22×D714yes—
572C22×C7—22no—
573C22×C7—22no—
574C22×C7—22no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7—42no—
582C22×C7—42no—
583C22×C7—44no—
584C22×C7—44no—
585C22×C7—44no—
586C22×C7—44no—
587C22×C7C23×D411yescharacteristic
588C22×C7C22×#4111yescharacteristic
589C22×C7C22×#4111yescharacteristic
590C22×C7C2×H(5,𝔽2)12yes—
591C22×C7#58512yes—
592C2×D7—42no—
593C2×D7—42no—
594C2×D7—42no—
595C2×D7—44no—
596C2×D7—44no—
597C4×C7—22no—
598C4×C7—24no—
599C4×C7—42no—
600C4×C7—42no—
601C4×C7—42no—
602C4×C7#53214yes—
603Dic7—22no—
604Dic7—22no—
605Dic7—22no—
606Dic7—24no—
607Dic7—42no—
608Dic7—42no—
609Dic7—42no—
610Dic7—42no—
611Dic7#53514yes—
612C24—72no—
613C24C23×D712yes—
614C24C23×D712yes—
615C24C23×D711yescharacteristic
616#41—2832no—
617C2×Q8—144no—
618C2×Q8—142no—
619C2×Q8—142no—
620C2×Q8—142no—
621C2×Q8—284no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—28no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—144no—
636C2×D4—144no—
637C2×D4—148no—
638C2×D4—144no—
639C2×D4—142no—
640C2×D4—142no—
641C2×D4—142no—
642C2×D4—284no—
643C2×D4—284no—
644C2×D4—284no—
645C2×D4—284no—
646C2×D4—284no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—71no—
650C22×C4—74no—
651C22×C4—72no—
652C22×C4—71no—
653C22×C4—71no—
654C22×C4—71no—
655C22×C4—74no—
656C22×C4—72no—
657C22×C4—72no—
658C22×C4—72no—
659C22×C4—72no—
660C22×C4—144no—
661C22×C4—148no—
662C22×C4—144no—
663C22×C4—144no—
664C22×C4—144no—
665C22×C4—148no—
666C22×C4—148no—
667C22×C4—282no—
668C22×C4D4×D714yes—
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C22×C4C23×D712yes—
672C22×C4C23×D711yescharacteristic
673C22×C4C23×D712yes—
674C22×C4C23×D711yescharacteristic
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—24no—
678C4⋊C4—144no—
679C4⋊C4—144no—
680C4⋊C4—144no—
681C4⋊C4—144no—
682C4⋊C4—144no—
683C4⋊C4—144no—
684C4⋊C4—142no—
685C4⋊C4—142no—
686C4⋊C4—284no—
687C4⋊C4—284no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—144no—
694C22⋊C4—144no—
695C22⋊C4—144no—
696C22⋊C4—144no—
697C22⋊C4—144no—
698C22⋊C4—144no—
699C22⋊C4—148no—
700C22⋊C4—144no—
701C22⋊C4—144no—
702C22⋊C4—148no—
703C22⋊C4—284no—
704C22⋊C4—284no—
705C22⋊C4—284no—
706C22⋊C4—284no—
707C42—22no—
708C42—74no—
709C42—74no—
710C42—74no—
711C42—74no—
712C42—74no—
713C42—144no—
714C42—144no—
715C42—144no—
716C42—142no—
717C42—282no—
718C42—282no—
719C42#115914yescomplemented
720C2×C7—42no—
721C2×C7—82no—
722C2×C7—82no—
723C2×C7C2×#53211yescharacteristic
724C2×C7C2×#53511yescharacteristic
725C2×C7#344911yescharacteristic
726C2×C7#346012yes—
727C2×C7#346012yes—
728D7—82no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—144no—
747C23—144no—
748C23C2×D4×D712yes—
749C23C24×D711yescharacteristic
750Q8—288no—
751Q8—284no—
752D4—416no—
753D4—48no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—2816no—
758D4—288no—
759D4—288no—
760D4—288no—
761D4—284no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—72no—
775C2×C4—74no—
776C2×C4—72no—
777C2×C4—72no—
778C2×C4—72no—
779C2×C4—74no—
780C2×C4—148no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—144no—
794C2×C4—144no—
795C2×C4—142no—
796C2×C4—288no—
797C2×C4—288no—
798C2×C4—288no—
799C2×C4—284no—
800C2×C4C2×D4×D712yes—
801C2×C4C2×D4×D712yes—
802C2×C4C2×#115914yes—
803C2×C4C2×#115912yes—
804C2×C4D7×#4112yes—
805C7#3462411yescharacteristic, complemented, Sylow
806C22—22no—
807C22—22no—
808C22—22no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—44no—
814C22—44no—
815C22—42no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—282no—
822C22—284no—
823C22—282no—
824C22—284no—
825C22—282no—
826C22C22×D4×D711yescharacteristic
827C22C22×#115911yescharacteristic
828C22C2×D7×#4111yescharacteristic
829C22D7×H(5,𝔽2)12yes—
830C22#9061812yes—
831C4—22no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—74no—
837C4—144no—
838C4—142no—
839C4—142no—
840C4—142no—
841C4—282no—
842C4—282no—
843C4—282no—
844C4—282no—
845C4#9028714yes—
846C2—42no—
847C2—82no—
848C2—82no—
849C2—562no—
850C2C2×#9028711yescharacteristic
851C2#1174338111yescharacteristic
852C2#1174338212yes—
853C2D7×#53511yescharacteristic
854C2#1174353612yes—
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2619C2
hypercenter#2619D7
hypocenterC7#34624
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. C2×#90287C2semidirect
2. C2×#90291C2semidirect
3. C7×#2619C2semidirect
4. #11740626C2semidirect
5. Dic7×#127C2semidirect
6. #11740122C2semidirect
7. #11740121C2semidirect
8. #11739732C2semidirect
9. Dic7×#117C2semidirect
10. #11734441C2semidirect
11. #11734335C2semidirect
12. #11734152C2semidirect
13. #11734110C2semidirect
14. #11733819C2semidirect
15. #11733818C2semidirect
16. #11733738C2semidirect
17. #11733737C2semidirect
18. #11731641C2semidirect
19. #11731594C2semidirect
165. C2×C4×Dic7D4semidirect
206. #2619D7semidirect
286. C42×C7#41semidirect
321. C4×Dic7#41semidirect
719. C42#1159semidirect
805. C7#34624semidirect

Maximal subgroups

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

subgroupindex
C2×#902872
C2×#902912
C7×#26192
#117406262
Dic7×#1272
#117401222
#117401212
#117397322
Dic7×#1172
#117344412
#117343352
#117341522
#117341102
#117338192
#117338182
#117337382
#117337372
#117316412
#117315942
#346247