Finite Group Databasebeta

← C2×#11738921 #14232252

Subgroups — C2×#11738921 #14232252

Order 1792.

1942 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
1C2×#90326C211yesmaximal, characteristic
2C2×#90202C211yesmaximal, characteristic
3C2×C7×#484C211yesmaximal, characteristic, complemented
4C2×#89823C211yesmaximal, characteristic, complemented
5C22×#6381C211yesmaximal, characteristic, complemented
6#11738921C2116yesmaximal, direct product factor
7C2×#89647C211yesmaximal, characteristic, complemented
8C2×#89656C211yesmaximal, characteristic, complemented
9C2×D7×#107C211yesmaximal, characteristic, complemented
10C2×#89646C211yesmaximal, characteristic, complemented
11C2×#89581C211yesmaximal, characteristic, complemented
12C2×#89585C211yesmaximal, characteristic, complemented
13C2×#89566C211yesmaximal, characteristic, complemented
14C2×#89562C211yesmaximal, characteristic, complemented
15C2×(C22⋊D7)⋊C8C211yesmaximal, characteristic
16C2×#89494C211yesmaximal, characteristic, complemented
17C2×C7×C22⋊Q8C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C2×#6509C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C22×#1144C2211yescharacteristic
22C2×C4×C22⋊D7—21no—
23C2×C4×C22⋊D7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C2×#6487—21no—
26C2×#6487C2211yescharacteristic
27C23×C7⋊C8C2211yescharacteristic
28C22×C8×D7C2211yescharacteristic
29#90326—24no—
30#90326C2218yes—
31#90202—24no—
32#90202C2218yes—
33C2×#6460—21no—
34C2×#6460C2211yescharacteristic
35C2×#6459—21no—
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×#6452—21no—
39C2×#6452—21no—
40C2×#6451C2211yescharacteristic
41C2×#6451C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×(C22⋊D7)⋊C4—21no—
44C2×#6441—21no—
45C7×#484C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#107C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×(C2×D7)⋊C8C2211yescharacteristic
53C2×#6392C2211yescharacteristic
54C2×#6392C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89823C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6381C2211yescharacteristic
62C2×#6381C2211yescharacteristic
63C2×#6381C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2218yescomplemented
67#89656C2218yescomplemented
68D7×#107C2218yescomplemented
69#89647C2218yescomplemented
70#89646C2218yescomplemented
71#89585C2218yescomplemented
72#89581C2218yescomplemented
73#89566C2218yescomplemented
74#89562C2218yescomplemented
75(C22⋊D7)⋊C8C2218yes—
76#89494C2218yescomplemented
77C2×#3338—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7D411yescharacteristic
82C23×Dic7—21no—
83C22×C4×D7—21no—
84C22×C4×D7—21no—
85C22×C4×D7C2311yescharacteristic
86C22×Dic14—21no—
87C22×Dic14—21no—
88C22×Dic14C2311yescharacteristic
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8C2314yes—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4C2314yes—
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C22⋊C4—21no—
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7D411yescharacteristic
103#6509—22no—
104#6509C2314yes—
105Q8×Dic7—22no—
106Q8×Dic7C2314yes—
107C2×#1144—24no—
108C2×#1144C2314yes—
109C4×C22⋊D7—28no—
110C4×C22⋊D7D414yes—
111C4×C22⋊D7C2314yes—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4D411yescharacteristic
115C2×C4⋊Dic7—21no—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7—21no—
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7C2311yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4⋊Dic7C2314yes—
123#6487—22no—
124#6487—28no—
125#6487C2314yes—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4D411yescharacteristic
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7C2311yescharacteristic
137C22×C7⋊C8—24no—
138C22×C7⋊C8C2311yescharacteristic
139C22×C7⋊C8C2314yes—
140C22×C7⋊C8C2311yescharacteristic
141C2×C8×D7—24no—
142C2×C8×D7C2314yes—
143#6460—22no—
144#6460—28no—
145#6460C2314yes—
146#6459—28no—
147D7×C4⋊C4—22no—
148D7×C4⋊C4—22no—
149D7×C4⋊C4C2314yes—
150D7×C4⋊C4C2314yes—
151#6452—28no—
152#6452—28no—
153#6451—22no—
154#6451—22no—
155#6451C2314yes—
156#6451C2314yes—
157#6450—22no—
158#6450C2314yes—
159(C22⋊D7)⋊C4—28no—
160#6441—28no—
161C7×#107C2314yes—
162C7×#107C2314yes—
163C7×#103C2314yes—
164C7×#103C2314yes—
165C7×C22⋊C8C2314yes—
166#6409C2314yes—
167(C2×D7)⋊C8C2314yes—
168#6392C2314yes—
169#6392C2314yes—
170#6390C2314yes—
171#6390C2314yes—
172Dic7⋊C8C2314yes—
173C8×Dic7C2314yes—
174#6384C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#554—71no—
181C2×#554—71no—
182#3338—716no—
183C2×#500—71no—
184C2×#484—71no—
185C2×#484—71no—
186C2×#484—71no—
187C2×#484D711yescharacteristic, complemented
188C2×#477—71no—
189C2×#477—71no—
190C2×#467—71no—
191C2×#467—71no—
192C2×C4×Q16—71no—
193C2×C8×D4—71no—
194C22×#107—71no—
195C22×#107—71no—
196C24×C7C2×D411yescharacteristic
197C23×D7C2×D411yescharacteristic
198C2×C7×Q8—21no—
199C2×C7×Q8—22no—
200C2×C7×Q8—22no—
201C2×C7×Q8C2412yes—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—24no—
209C22×C4×C7—82no—
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2411yescharacteristic
214C2×C22⋊D7Q1618yescomplemented
215C2×C22⋊D7C2×D414yes—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—24no—
221C22×Dic7—82no—
222C22×Dic7C2×D411yescharacteristic
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C2×C4×D7—22no—
226C2×C4×D7—22no—
227C2×C4×D7—24no—
228C2×C4×D7—24no—
229C2×C4×D7—82no—
230C2×C4×D7—82no—
231C2×C4×D7C2×D412yes—
232C2×C4×D7C2412yes—
233C2×Dic14—22no—
234C2×Dic14—22no—
235C2×Dic14—21no—
236C2×Dic14—24no—
237C2×Dic14—24no—
238C2×Dic14—82no—
239C2×Dic14—82no—
240C2×Dic14C2412yes—
241C2×C7×C8—22no—
242C2×C7×C8—22no—
243C2×C7×C8C2412yes—
244C2×C7×C8C2412yes—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C7×C4⋊C4C2412yes—
253C7×C22⋊C4—24no—
254C22⋊Dic7—24no—
255C22⋊Dic7C2×D414yes—
256#1144—28no—
257(C2×D7)⋊C4—24no—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4C2×D414yes—
260C4⋊Dic7—21no—
261C4⋊Dic7—21no—
262C4⋊Dic7—24no—
263C4⋊Dic7—21no—
264C4⋊Dic7—24no—
265C4⋊Dic7—24no—
266C4⋊Dic7C2412yes—
267C4⋊Dic7C2412yes—
268C4⋊Dic7C2412yes—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4C2×D414yes—
277C4×Dic7—24no—
278C4×Dic7—24no—
279C4×Dic7C2×D412yes—
280C4×Dic7C2412yes—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—28no—
283C2×C7⋊C8#4114yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C8×D7—28no—
287C22×Q16—71no—
288C23×C8—71no—
289C23×C8—71no—
290#554—78no—
291#554—78no—
292#554—144no—
293#554—144no—
294C2×C4⋊Q8—71no—
295C2×C4⋊Q8—71no—
296C2×#125—141no—
297C2×#125—141no—
298C2×C22⋊Q8—71no—
299C2×C22⋊Q8—71no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—141no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×C22⋊Q8—141no—
305C2×C22⋊Q8C2×D711yescharacteristic
306C2×C4×Q8—71no—
307C2×C4×Q8—71no—
308C2×C4×D4—71no—
309C2×C4×D4—141no—
310C2×C4×D4—141no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4C2×D711yescharacteristic
315#500—78no—
316#484—78no—
317#484—78no—
318#484—78no—
319#484C2×D718yescomplemented
320#477—78no—
321#477—78no—
322#467—78no—
323#467—78no—
324C4×Q16—78no—
325C8×D4—78no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#107—78no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—78no—
335C2×#107C2×D711yescharacteristic
336C2×#107C2×D711yescharacteristic
337C2×C4⋊C8—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#103C2×D711yescharacteristic
343C2×#103C2×D711yescharacteristic
344C2×C22⋊C8—71no—
345C2×C22⋊C8C2×D711yescharacteristic
346C2×C4×C8—71no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7C2×Q1614yes—
350C23×C7C22×D412yes—
351C23×C7C22×D411yescharacteristic
352C22×D7—22no—
353C22×D7—22no—
354C22×D7C2×Q1614yes—
355C22×D7C22×D412yes—
356C7×Q8—22no—
357C7×Q8—22no—
358C7×Q8—42no—
359C2×C4×C7—22no—
360C2×C4×C7—24no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—84no—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C7C2×#4112yes—
375C2×C4×C72−1+412yes—
376C2×C4×C7C2511yescharacteristic
377C22⋊D7C2×Q16116yescomplemented
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—84no—
389C2×Dic7C2×Q1614yes—
390C2×Dic7C22×D412yes—
391C2×Dic7C22×D412yes—
392C2×Dic7C22×D412yes—
393C4×D7—24no—
394C4×D7—22no—
395C4×D7—22no—
396C4×D7—84no—
397C4×D7—84no—
398Dic14—22no—
399Dic14—22no—
400Dic14—42no—
401Dic14—84no—
402Dic14—84no—
403C7×C8—22no—
404C7×C8—22no—
405C7⋊C8—22no—
406C7⋊C8C2×#4114yes—
407C22×Q8—71no—
408C22×Q8—141no—
409C22×Q8—141no—
410C22×Q8C22×D711yescharacteristic
411C22×D4—71no—
412C23×C4—21no—
413C23×C4—71no—
414C23×C4—141no—
415C23×C4—141no—
416C23×C4—141no—
417C23×C4C22×D711yescharacteristic
418C2×Q16—74no—
419C2×Q16—144no—
420C22×C8—71no—
421C22×C8—71no—
422C22×C8—74no—
423C22×C8—74no—
424C22×C8—144no—
425C22×C8—144no—
426C22×C8C22×D711yescharacteristic
427C22×C8C22×D711yescharacteristic
428C4⋊Q8—74no—
429C4⋊Q8—74no—
430C4⋊Q8—142no—
431C4⋊Q8—142no—
432#125—148no—
433#125—148no—
434C22⋊Q8—22no—
435C22⋊Q8—74no—
436C22⋊Q8—74no—
437C22⋊Q8—74no—
438C22⋊Q8—148no—
439C22⋊Q8—148no—
440C22⋊Q8—148no—
441C22⋊Q8—148no—
442C22⋊Q8—142no—
443C22⋊Q8—142no—
444C22⋊Q8—142no—
445C22⋊Q8C22×D714yes—
446C4×Q8—74no—
447C4×Q8—74no—
448C4×Q8—142no—
449C4×Q8—142no—
450C4×D4—74no—
451C4×D4—74no—
452C4×D4—148no—
453C4×D4—148no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—142no—
465C2×C4⋊C4—142no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—142no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4C22×D711yescharacteristic
478C2×C4⋊C4C22×D711yescharacteristic
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C4⋊C4C22×D714yes—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—71no—
483C2×C22⋊C4—71no—
484C2×C22⋊C4—141no—
485C2×C22⋊C4—141no—
486C2×C22⋊C4—141no—
487C2×C42—71no—
488C2×C42—141no—
489C2×C42—141no—
490#107—74no—
491#107—74no—
492#107—74no—
493#107—74no—
494#107—74no—
495#107—74no—
496#107—74no—
497#107C22×D714yes—
498#107C22×D714yes—
499C4⋊C8—74no—
500#103—74no—
501#103—74no—
502#103—74no—
503#103—74no—
504#103C22×D714yes—
505#103C22×D714yes—
506C22⋊C8—74no—
507C22⋊C8C22×D714yes—
508C4×C8—74no—
509C22×C7—28no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7#54712yes—
513C22×C7C22×Q1614yes—
514C22×C7C22×Q1612yes—
515C22×C7#57612yes—
516C22×C7C23×D411yescharacteristic
517C2×D7—28no—
518C2×D7—22no—
519C2×D7—22no—
520C2×D7C22×Q1614yes—
521C4×C7—22no—
522C4×C7—42no—
523C4×C7—42no—
524C4×C7—42no—
525C4×C7—42no—
526C4×C7#54712yes—
527C4×C7C22×#4111yescharacteristic
528C4×C7C2×2−1+411yescharacteristic
529Dic7—22no—
530Dic7—22no—
531Dic7—42no—
532Dic7—42no—
533Dic7—42no—
534Dic7—42no—
535Dic7C22×Q1614yes—
536C24—71no—
537C24D4×D711yescharacteristic
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—72no—
542C2×Q8—144no—
543C2×Q8—144no—
544C2×Q8—141no—
545C2×Q8—142no—
546C2×Q8—142no—
547C2×Q8—562no—
548C2×Q8—562no—
549C2×Q8C23×D712yes—
550C2×D4—78no—
551C2×D4—74no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—71no—
560C22×C4—71no—
561C22×C4—71no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—82no—
565C22×C4—144no—
566C22×C4—144no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—141no—
573C22×C4—144no—
574C22×C4—562no—
575C22×C4—562no—
576C22×C4—562no—
577C22×C4D4×D712yes—
578C22×C4D4×D711yescharacteristic
579C22×C4C23×D712yes—
580C22×C4C23×D711yescharacteristic
581Q16—148no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—74no—
585C2×C8—72no—
586C2×C8—72no—
587C2×C8—148no—
588C2×C8—148no—
589C2×C8—142no—
590C2×C8C23×D712yes—
591C2×C8C23×D712yes—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—74no—
598C4⋊C4—72no—
599C4⋊C4—72no—
600C4⋊C4—72no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—144no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—144no—
608C4⋊C4—144no—
609C4⋊C4—144no—
610C4⋊C4—141no—
611C4⋊C4—144no—
612C4⋊C4—141no—
613C4⋊C4—141no—
614C4⋊C4C23×D712yes—
615C4⋊C4C23×D712yes—
616C4⋊C4C23×D712yes—
617C22⋊C4—24no—
618C22⋊C4—74no—
619C22⋊C4—74no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C42—72no—
624C42—72no—
625C42—144no—
626C42—144no—
627C2×C7—24no—
628C2×C7#333814yescomplemented
629C2×C7C2×#54711yescharacteristic
630C2×C7C23×Q1611yescharacteristic
631C2×C7C2×#57611yescharacteristic
632D7—24no—
633C23—22no—
634C23—22no—
635C23—74no—
636C23—72no—
637C23—142no—
638C23—142no—
639C23D7×Q1614yes—
640C23C2×D4×D712yes—
641C23C2×D4×D711yescharacteristic
642Q8—22no—
643Q8—22no—
644Q8—42no—
645Q8—142no—
646Q8—142no—
647Q8—282no—
648Q8—564no—
649Q8—564no—
650D4—716no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—74no—
664C2×C4—72no—
665C2×C4—72no—
666C2×C4—72no—
667C2×C4—84no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—144no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—282no—
678C2×C4—282no—
679C2×C4—282no—
680C2×C4—282no—
681C2×C4—564no—
682C2×C4—564no—
683C2×C4—564no—
684C2×C4C2×D4×D712yes—
685C2×C4C2×D4×D711yescharacteristic
686C2×C4D7×#4112yes—
687C2×C4#655412yes—
688C2×C4C24×D711yescharacteristic
689C8—22no—
690C8—22no—
691C8—74no—
692C8—142no—
693C7C2×#333811yescharacteristic, complemented, Sylow
694C22—22no—
695C22—28no—
696C22—22no—
697C22—74no—
698C22—142no—
699C22—148no—
700C22—142no—
701C22#9034612yes—
702C22C2×D7×Q1614yes—
703C22C2×D7×Q1612yes—
704C22#9046512yes—
705C22C22×D4×D711yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—74no—
712C4—142no—
713C4—142no—
714C4—282no—
715C4—282no—
716C4—282no—
717C4—282no—
718C4#9034612yes—
719C4C2×D7×#4111yescharacteristic
720C4C2×#655411yescharacteristic
721C2—24no—
722C2—144no—
723C2#1173892114yesdirect product factor
724C2C2×#9034611yescharacteristic
725C2C22×D7×Q1611yescharacteristic
726C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#484C2
socleC23×C7C22×D4
prime radicalC22×C22⋊D7D4
hypercenterC2×#484D7
hypocenterC7C2×#3338
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. C2×C7×#484C2semidirect
4. C2×#89823C2semidirect
5. C22×#6381C2semidirect
6. #11738921C2direct (N × H)
7. C2×#89647C2semidirect
8. C2×#89656C2semidirect
9. C2×D7×#107C2semidirect
10. C2×#89646C2semidirect
11. C2×#89581C2semidirect
12. C2×#89585C2semidirect
13. C2×#89566C2semidirect
14. C2×#89562C2semidirect
16. C2×#89494C2semidirect
45. C7×#484C22semidirect
59. #89823C22semidirect
66. C2×#6381C22semidirect
67. #89656C22semidirect
68. D7×#107C22semidirect
69. #89647C22semidirect
70. #89646C22semidirect
71. #89585C22semidirect
72. #89581C22semidirect
73. #89566C22semidirect
74. #89562C22semidirect
76. #89494C22semidirect
187. C2×#484D7semidirect
214. C2×C22⋊D7Q16semidirect
319. #484C2×D7semidirect
377. C22⋊D7C2×Q16semidirect
628. C2×C7#3338semidirect
693. C7C2×#3338semidirect
723. C2#11738921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903262
C2×#902022
C2×C7×#4842
C2×#898232
C22×#63812
#117389212
C2×#896472
C2×#896562
C2×D7×#1072
C2×#896462
C2×#895812
C2×#895852
C2×#895662
C2×#895622
C2×(C22⋊D7)⋊C82
C2×#894942
C2×#33387